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height="24"><span class="text">提交</年代pan></span><span class="sc-htoDjs kNoiZu sc-dqBHgY cQgXqt fileArrow icon-colored undefined icon-themeable" title="" font-size="16"></span></a> <div class="sc-krDsej ewCAZX hide__submenu journalSubmenuCheck" id="journalnav__submenu"> <button class="sc-itybZL kdvWPs journalSubmenuCheck"><span class="sc-htoDjs gvAGTV sc-fzsDOv hAFFGk journalSubmenuCheck icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="9"></span></button> </div> <div class="sc-dTdPqK lkWWFY hide__submenu journal__nav__desktop" id="journalnav__submenudesktop"> <div order="0" class="sc-kUaPvJ ehYbwJ"> <div class="sc-gPWkxV legory"></div> <div class="sc-gPWkxV legory"></div> </div> <div class="sc-jVODtj epgILe"></div> <span class="sc-fONwsr kCfRMJ"></span> </div> </nav> </div> <div class="sc-nrwXf byflLi breadcrumb__wrapper journal_article__BreadCrumbStyle-sc-12fk6zy-2 bjwAQR article"> <a class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jnt/" aria-label="Journal of Nanotechnology">纳米技术杂志》</一个>/<gydF4y2Ba一个class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/jnt/contents/year/2012/" aria-label="2012">2012年</一个>/<gydF4y2Ba年代pan class="sc-bhlBdH UVThf">文章</年代pan> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</gydF4y2Babutton> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</gydF4y2Bap> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt 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class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <p class="sc-kZmsYB bkiEfx article_type">评论文章|<gydF4y2Ba!-- -->开放获取</gydF4y2Bap> <div class="sc-RcBXQ ztvYg article_citation"> 体积<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</年代pan>文章的ID<gydF4y2Ba!-- --> 324380年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</年代pan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2012/324380" aria-label="Doi-link">https://doi.org/10.1155/2012/324380</一个></div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>贾斯汀·m·霍利,阿图尔Lutfurakhmanov,道格拉斯·l·舒尔茨伊斯坎德尔Akhatov<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<年代pan class="adjust-article-svg-size">回顾Aerosol-Based直写为微电子学及其应用</年代pan>”,<gydF4y2Ba!-- --><i>纳米技术杂志》</我>,<ggydF4y2BaydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2012年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->324380年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 22<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2012年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2012/324380</gydF4y2Bap> </div> <button class="sc-hSdWYo etauus sc-iBEsjs kPshFw" color="">显示引用</gydF4y2Babutton> </div> <h1 class="sc-iRbamj jZOxOO sc-iSDuPN cTnPQL article_title adjust-article-svg-size heading-title">回顾Aerosol-Based直写为微电子学及其应用</h1></gydF4y2Badiv> <div class="sc-jrIrqw eHMFfo article_authors"> <hr class="sc-cEvuZC XkrFe hr__author"> <span class=""><b>贾斯汀·m·霍利</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a>,<年代up>1</年代up></span> <span class="">阿图尔Lutfurakhmanov<gydF4y2Ba!-- -->,<年代up>1</年代up></span> <span class="">道格拉斯·l·舒尔茨<gydF4y2Ba!-- -->,<年代up>1</年代up> 和</年代pan> <span class="">伊斯坎德尔s Akhatov<年代up>1<gydF4y2Ba!-- -->,<gydF4y2Ba!-- -->2</年代up></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</年代up><span>机械工程系,纳米科学与工程中心,北达科塔州立大学法戈、ND 58105,美国</年代pan></p> <p><sup>2</年代up><span>中心微观和纳米级分散系统的动力学,巴什基尔语州立大学,乌法450076年,俄罗斯</年代pan></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</gydF4y2Bab>Kyoung月球</gydF4y2Badiv> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2011年12月25日</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">04年6月2012年</年代pan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代pan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">05年9月2012年</年代pan> </div> </div> </div> <article class="sc-jtRlXQ hDZsgu article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><gydF4y2Bap>Aerosol-based直写指印花CAD / CAM功能的添加剂过程从一个设备创建一个液体或固体气溶胶梁。直写技术将成为有用的工具在微电子行业快速原型的组件(如互联、传感器、薄膜晶体管(日前),被迅速构思新的气溶胶直写申请。本文旨在回顾直写技术,重点是aerosol-based系统。不同的目前最先进的系统,如气溶胶喷射CAB-DW, MCS,气动镜头。审查和分析背后的物理流体质点的相互作用包括斯托克斯和萨夫曼力,实验观测,以及理论与实验的完整理解如何导致新技术。最后,讨论了微电子气溶胶直写的应用。</gydF4y2Bap> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4><gydF4y2Bap>直写印刷是一种添加剂技术用于可控沉积特征在样本模式定义为计算机辅助设计/计算机辅助制造(CAD / CAM)软件允许快速成型各种几何图形,而无需使用光刻技术(<一个href="#B1">1</一个>,<gydF4y2Ba一个href="#B2">2</一个>]。2008年,鸿et al。<一个href="#B2">2</一个>回顾了这一领域,分类直写为四个主要类别。第一类是“流转直接写“技术,如nScript和MicroPen雇佣microdispensing系统用针或小至25孔不断沉积特性<年代vg height="9.6750002" id="M1" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>速度高达300毫米/秒。流速在nL /秒范围内典型,和流转直接写能够印刷材料的粘度在0.5到10<年代up>6</年代up>cP,允许各种油墨成分的沉积。</gydF4y2Bap> <p>第二类是基于“能量光束直接写”,包括一些技术,用高功率激光变换和/或推动材料衬底上。激光系统包括激光增强化学镀(之),matrix-assisted脉冲激光直写蒸发(MAPLE-DW) laser-engineered近净成形(透镜)<一个href="#B3">3</一个>),激光制导直写(LGDW) [<一个href="#B4">4</一个>),和Mesoscribe技术(<一个href="#B5">5</一个>]。而所有这些方法的细节超出了本文的范围,作为一个例子,我们简要描述MAPLE-DW这是一个过程,使用脉冲紫外激光正向传递一个薄膜材料的衬底透明的“丝带”。与溶剂激光组件的交互的“丝带”原因快速蒸发,辐照部分逐出丝带和运输<年代vg height="5.7874999" id="M2" style="vertical-align:-0.0pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 5.7874999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,5.7875)"> <g transform="translate(72,-67.37)"> <text transform="matrix(1,0,0,-1,-71.95,67.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</t年代pan> </text> </g> </g> </svg>100年<年代vg height="9.6750002" id="M3" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米的地方沉积到衬底(<一个href="#B1">1</一个>]。存款规模相似的区域维度与常见的直径约30激光领域<年代vg height="9.6750002" id="M4" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米(<一个href="#B6">6</一个>]。薄膜厚度从1到20<年代vg height="9.6750002" id="M5" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>通常观察到当丝带<年代vg height="5.7874999" id="M6" style="vertical-align:-0.0pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 5.7874999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,5.7875)"> <g transform="translate(72,-67.37)"> <text transform="matrix(1,0,0,-1,-71.95,67.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</t年代pan> </text> </g> </g> </svg>25<年代vg height="9.6750002" id="M7" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m是采用(<一个href="#B1">1</一个>]。这个过程需要专业油墨具有适当的粘度和紫外吸收。as-deposited线的最小分辨率是限制激光光斑大小但印刷特性线宽度为2<年代vg height="9.6750002" id="M8" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米可以实现激光微调模式(<一个href="#B6">6</一个>]。包括在这一类也非激光聚焦离子束(FIB)直写等方法。这种方法使用镓离子轰击前体气体沉积特性只有80海里0.05体积打印的<年代vg height="9.6750002" id="M9" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米<年代up>3</年代up>/秒(<一个href="#B2">2</一个>]。</gydF4y2Bap> <p>“基于探针直接写”是第三类,包括蘸水笔纳米(DPN) nanofountain笔临界多边形求解(),和要液体microdroplet沉积(<一个href="#B7">7</一个>]。DPN利用原子力显微镜(AFM)存款电影到衬底。AFM探针后蘸上液体,顶端被带入与底物接触的液体流到衬底的AFM纳米级分辨率的理想模式。NFP DPN的一种变体,液体通过空心分发小费与底物接触。这种方法已经扩展到多个技巧(12),而静维护子- 100纳米的分辨率。要液体microdroplet沉积是最近开发的应用到毛细管压力使液体半月板形式在出口<一个href="#B7">7</一个>]。与液体接触衬底半月板(不是毛细管)和随后的毛细管收缩给液体的衬底上沉积矿床的规模可以小到10%的毛细管内径尺寸小至32<年代vg height="9.6750002" id="M10" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>观察了300<年代vg height="9.6750002" id="M11" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m毛细管。替换的nanocapillary微细管在这种方法应该允许nanodroplet特性保持类似的决议已经证明了临界多边形求解由DPN。</gydF4y2Bap> <p>第四类是称为“droplet-based直接写。“也许最广泛调查droplet-based DW方法是热喷墨,压电、水动力,静电,和声学能量产生小水滴从喷嘴喷射的液体。连续喷墨(CIJ)和drop-on-demand (DOD)版本是可用的。分辨率< 20<年代vg height="9.6750002" id="M12" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>与喷墨m已经意识到,非接触的方法是可伸缩(到成千上万的喷嘴在一头)为高通量操作。喷墨油墨的特点是非常敏感,因为只有atomizable粘度范围有限,和喷嘴可以变得容易堵塞如果油墨太不稳定,但某些波动需要正确的干燥油墨沉积。nozzle-to-substrate距离必须精确控制复杂的印刷在空间的基板(<一个href="#B2">2</一个>]。</gydF4y2Bap> <p>Aerosol-based直写(dw)的一个子集droplet-based直写。两个这样的方法,采用液体饲料气溶胶喷射和CAB-DW(平行束气溶胶直接写)和由Optomec和北达科他州州立大学(NDSU),分别为(<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B9">9</一个>]。气溶胶喷射和CAB-DW使用集中与sub-10气溶胶喷雾沉积材料<年代vg height="9.6750002" id="M13" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m分辨率。气溶胶可以定义为一个悬浮的液体或固体颗粒的气体。采用固体饲料的一个方法是microcold喷雾(MCS)材料韧性金属粒子的加速到接近或高于声波速度通过聚焦喷嘴和沉积到衬底(<一个href="#B10">10</一个>,<gydF4y2Ba一个href="#B11">11</一个>]。MCS类似于气溶胶喷射沉积和CAB-DW但行展览导率附近的大部分价值没有postdeposition热处理。前面的技术很好但不用于纳米粒子介观粒子。聚焦技术由明尼苏达大学的研究人员使用一套气动镜头在真空条件下将纳米晶体聚集和沉积在衬底(<一个href="#B12">12</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B15">15</一个>]。这对直写技术应用的例子比如微机电系统(MEMS)是最小的,但是口供的痕迹,小如35<年代vg height="9.6750002" id="M14" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽的报道。</gydF4y2Bap> <p>本文的目的是提供一个全面的综述dw的方法包括讨论不同系统以及气溶胶物理流动。本文安排分为以下部分:<年代vg height="13.45" id="M15" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>讨论不同的dw系统;<年代vg height="13.45" id="M16" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>回顾有关气溶胶物理气溶胶聚焦和实验验证;<年代vg height="13.45" id="M17" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>回顾dw的应用程序正在使用电子设备的打印组件。</gydF4y2Bap> <h4 id="aerosol-direct-write-systems">2。气溶胶直写系统</h4><h5gydF4y2Baid="sec2.1">2.1。气溶胶Jet-Single喷嘴与液体气溶胶</h5><gydF4y2Bap>气溶胶直写是一个过程,一个气溶胶光束集中,针对生产所需的基质表面特征(例如,点或线)没有使用口罩或postpatterning(即。、激光微调)。气溶胶喷雾涂料行业已经使用了几十年的薄和厚的涂层。的能力重点小(< 100的气溶胶喷雾<年代vg height="9.6750002" id="M18" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)维度给梁的材料,并具体化直写这个词。第一个dw方法引入到社区是气溶胶喷射。气溶胶喷射曾被称为M<年代up>3</年代up>D(无掩模的中尺度材料沉积),是由Optomec [<一个href="#B16">16</一个>)下的国防高级研究计划局(DARPA)介观综合保形电子(老鼠)计划。商用系统打印从10痕迹<年代vg height="9.6750002" id="M19" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m以翻译速度5毫米宽200毫米/秒。液体油墨粘度0.5至2500 cP通常使用。使用气溶胶喷射沉积材料如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig1/" target="_blank">1</一个>。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.001" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.001.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 气溶胶喷射系统的图。</t一个ble> </div> </div> </div> <p>前体的沉积过程始于雾化液体油墨为1到5<年代vg height="9.6750002" id="M20" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径液滴与超声波(通常1.6 - -2.4 MHz)或气动雾化器。这些液滴夹带在载气和运输沉积的头,鞘的环状流气体补充道。鞘气体间接充当集中机制通过占据外层部分的流管。这导致气溶胶是有限的中心流的方式与鞘气体的体积成正比。如果使用气动雾化器,一个虚拟的撞击器放置立即沉积前的头。这个设备集中的气溶胶去除多余的气体流量和减少的多分散性气溶胶通过删除很小(< 1<年代vg height="9.6750002" id="M21" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米粒子。沉积的头后,气溶胶进一步集中在一个融合与退出喷嘴长约2厘米直径在50到300之间<年代vg height="9.6750002" id="M22" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m。交付过程是连续的气溶胶和气体流量不是骑开/关当沉积需要终止结束时(例如,一条线)。相反,快门手臂块气溶胶流在衬底转换到下一个位置/ CAD / CAM程序规定。气溶胶退出喷嘴10到100 m / s的速度和影响样本的同时保持一个nozzle-to-substrate(僵局)1 - 5毫米的距离。这个大范围的对峙距离简化印刷在不规则的基质层间电介质等或其他设备组件。40-nozzle气溶胶喷射系统现在可以并行处理,金属化层顶部15×15厘米<年代up>2</年代up>太阳能电池可以印刷在不到三秒钟的时间<一个href="#B2">2</一个>]。气溶胶喷射能产生高质量的特性,但是需要一些努力去除多余超范围和排除喷嘴堵塞。</gydF4y2Bap> <h5 id="sec2.2">2.2。CAB-DW:多个喷嘴与液体气溶胶</h5><gydF4y2Bap>CAB-DW在NDSU[是一个科技发达的<一个href="#B9">9</一个>,<gydF4y2Ba一个href="#B17">17</一个>由一个三分量converging-diverging-converging喷嘴(图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig2/" target="_blank">2</一个>从气溶胶喷射系统)能够减少口供5<年代vg height="9.6750002" id="M23" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>通过进一步的准直和聚焦气溶胶梁。其他特征的CAB-DW气溶胶喷射的几乎是一样的。开发一种改进的喷嘴设计的能力之后才意识到一个广泛的experimental-analytical分析气溶胶喷射系统。气溶胶粒子混合喷嘴在泊肃叶流建模使用拉格朗日追踪方案通过一个线性收敛喷嘴利用斯托克斯和萨夫曼部队流体质点的互动。单个粒子的轨迹计算,气溶胶波束宽度确定退出喷嘴后总结几个粒子的轨迹退出喷嘴。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.002" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 说明三分量converging-diverging-converging CAB-DW喷嘴和气溶胶波束宽度的测量。</t一个ble> </div> </div> </div> <p>气溶胶波束宽度是通过实验确定通过测量气溶胶的散射强度激光光束来自喷嘴使用CCD相机和显微镜。理论的波束宽度(以宽屏half-max,应用实验相比,理论和实验相似的预测粒子大小的调整和修正后的力量的相互作用。分析模型的开发后,新喷嘴的几何图形的输入模型,与相应的波束宽度计算。三分量喷嘴似乎更好的准直和焦点理论和被选为实验验证。CAB-DW喷嘴的波束宽度测量相比,单喷嘴(气溶胶喷射,传统气溶胶喷雾)如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig3/" target="_blank">3</一个>。在这种情况下,CAB-DW喷嘴提供了一个更加平行和聚焦束与最小波束宽度为1.9<年代vg height="9.6750002" id="M24" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m在2毫米相比过去的喷嘴出口至5.0<年代vg height="9.6750002" id="M25" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米在1.8毫米过去传统的喷嘴出口气溶胶喷雾(气溶胶喷射)<一个href="#B18">18</一个>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.003" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.003.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.45" id="M26" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg> <svg height="13.45" id="M27" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg> <a href="#B18">18</一个><t一个ble> 图实验气溶胶波束宽度与喷嘴出口的距离gydF4y2Ba气溶胶喷射(传统的气溶胶喷雾)和CAB-DW,gydF4y2Ba从舒尔茨et al。),gydF4y2BaIEEE 2010年版权所有。</t一个ble> </div> </div> </div> <p>不仅是气溶胶梁更集中与CAB-DW气溶胶喷射,但印刷线也薄当比较两个在相同的条件下(25 sccm载气,15 sccm鞘气体,2毫米对峙高度,30 mm / s翻译),气溶胶喷射提供31<年代vg height="9.6750002" id="M28" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽的线条和CAB-DW产生11<年代vg height="9.6750002" id="M29" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽线如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig4/" target="_blank">4</一个>。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.004" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.004.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B18">18</一个><t一个ble> 比较dw印刷线由气溶胶喷射(左)和CAB-DW(右)在相同的打印参数(25 sccm载气,15 sccm鞘气体,2毫米对峙高度,30 mm / s翻译),从舒尔茨等。),gydF4y2BaIEEE 2010年版权所有。</t一个ble> </div> </div> </div> <h5 id="sec2.3">2.3。气动镜头与液体气溶胶</h5><gydF4y2Bap>一个新的dw系统专为印刷纳米粒子使用气动透镜聚焦是由Qi et al。<一个href="#B15">15</一个>]。这个系统的沉积过程,示意图如图表示<一个href="//www.newsama.com/journals/jnt/2012/324380/fig5/" target="_blank">5</一个>,开始的气动雾化暂停CdSe /硫化锌核/壳纳米晶体在己烷。气溶胶主要是通过气动镜头和定向到一个真空容器和衬底上翻译的<年代vg height="9.875" id="M30" style="vertical-align:-2.29482pt;width:21.674999px;" version="1.1" viewbox="0 0 21.674999 9.875" width="21.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> - - - - - -</t年代pan> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> </t年代pan> </text> </g> </g> </svg>阶段。Microtowers microlines 158<年代vg height="9.6750002" id="M31" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>由27米<年代vg height="9.6750002" id="M32" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>2.9米宽,<年代vg height="9.6750002" id="M33" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米7<年代vg height="9.6750002" id="M34" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽沉积到蓝宝石、玻璃和硅基板与例子如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig6/" target="_blank">6</一个>。microlines印在翻译的速度10<年代vg height="9.6750002" id="M35" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m / s,远低于气溶胶喷射和CAB-DW,但这个系统可能仍然是有价值的因为不同气溶胶的喷气和CAB-DW,纳米颗粒可以成功地专注。此外,该系统是可靠和便宜的使用标准的气溶胶镜头不需要鞘气体。系统在商业化然而将挑战由于沉积速率较低,印刷需要一个疏散系统中执行。然而常用这种疏散系统是在微电子制造(<一个href="#B15">15</一个>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.005" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.005.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B15">15</一个><t一个ble> dw聚焦粒子束沉积系统的示意图,从气等。)gydF4y2Ba、气溶胶科学技术、版权2010年,山月桂,新泽西。允许转载。</t一个ble> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”324380。fig.006a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.006a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”324380。fig.006b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.006b.jpg"> <br> <strong>(b)</年代trong></div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig6"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”324380。fig.006a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.006a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”324380。fig.006b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.006b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig6"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B15">15</一个><t一个ble> SEM图像CdSe /硫化锌核/壳nanocrystal-based功能打印使用气动镜头;(一)microtower, (b) microline,从Qi et al。)gydF4y2Ba、气溶胶科学技术、版权2010年,山月桂,新泽西。允许转载。</t一个ble> </div> </div> </div> <h5 id="sec2.4">2.4。Microcold Spray-Solid气溶胶通过喷嘴</h5><gydF4y2Bap>冷喷涂是在1980年代初开发Papyrin et al。<一个href="#B19">19</一个>)和两阶段超音速流试验,发现在某些关键速度颗粒会附着。这种坚持是当气溶胶粒子引起的影响速度的衬底的足够引起塑性变形粒子和/或基质导致局部加热和高压地区创建粒子和基体之间的亲密接触。临界速度是依赖于粒子的组合材料,衬底材料,粒子温度在嵌入之前,和粒子的大小。临界速度为铜、铁、镍和铝据报道<年代vg height="5.7874999" id="M36" style="vertical-align:-0.0pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 5.7874999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,5.7875)"> <g transform="translate(72,-67.37)"> <text transform="matrix(1,0,0,-1,-71.95,67.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</t年代pan> </text> </g> </g> </svg>570,630,630,和690 m / s,分别<一个href="#B20">20.</一个>]。冷喷涂技术发展成为一个商业系统设计用于薄膜沉积2001年(<一个href="#B19">19</一个>,<gydF4y2Ba一个href="#B21">21</一个>]。</gydF4y2Bap> <p>的能力重点小(< 100的喷雾<年代vg height="9.6750002" id="M37" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)维度给梁的材料,并具体化术语microcold喷雾(MCS)直写。一个电路金属化利用MCS /互联是沉积材料不需要后处理。从我们之前的experimental-analytical比较液体气溶胶的建筑<一个href="#B11">11</一个>],米CS包含喷嘴系统存款行表现出的韧性金属导率达到90%的大部分价值。图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig7/" target="_blank">7</一个>的原理图NDSU MCS系统氦气首先通过两种质量流量控制器(mfc电池)。出口的MFC通过粉机固体颗粒雾化到他的地方,创建一个运载气体流(图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig7/" target="_blank">7</一个>(一))。第二MFC控制加速器气流2升分钟左右(与100 sccm承运人)。每一个流然后进入沉积(图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig7/" target="_blank">7</一个>(b))都是加热到抵消天然气的冷却效果加速度。两个流的怜锥部分交互沉积的头,最后通过融合喷嘴。喷嘴直径100到200<年代vg height="9.6750002" id="M38" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m通常雇佣,也可以采用多喷管系统。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.007" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.007.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B11">11</一个><t一个ble> 原理图(一)固体气溶胶,MCS系统(b) MCS沉积,从巴塔查里亚等。20.12年ASME)、版权。允许转载。</t一个ble> </div> </div> </div> <h5 id="sec2.5">2.5。雾化方法</h5><gydF4y2Bap>任何气溶胶打印系统的一个主要挑战是雾化过程。许多材料,尽管它可能容易分裂的过程集中气溶胶粒子对dw需要单分散气溶胶与统一的属性长期良好的打印质量。超声波技术前面提到的dw应用程序产生一个相对mono-disperse气溶胶但能力有限分裂粘性材料和遭受长期变化雾化油墨干燥和热等因素造成的。其他制造商如Sono-Tek [<一个href="#B22">22</一个>),年代on一个超声学(<一个href="#B23">23</一个>)开发了超声波角气溶胶发生器,能够创建气溶胶粒子平均液滴直径只有13岁<年代vg height="9.6750002" id="M39" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m和11.8<年代vg height="9.6750002" id="M40" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m,分别,但有一个高斯液滴大小分布。Sono-Tek雾化系统甚至发展成一个dw系统利用雾化器称为MicroMist就是能瘦400喷雾特性<年代vg height="9.6750002" id="M41" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米当耦合到一个精确的翻译系统(<一个href="#B22">22</一个>]。蔡et al。<一个href="#B24">24</一个>)开发了一种傅里叶角喷雾器由硅能够生产单分散颗粒的液滴直径7.0附近<年代vg height="9.6750002" id="M42" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m。Ju et al。<一个href="#B25">25</一个>)和Qi et al。<一个href="#B26">26</一个>]描述了声表面波(看到)雾化器能产生微米大小的液滴类似直写应用程序是必需的。更多细节在这些气泡雾化背后的物理学超出了本文的范围,但了各自的朋友和杨<一个href="#B27">27</一个>]。克服挑战任何雾化过程仍在进行中,相关与未来发展更多的单分散气溶胶生成技术将极大地影响所有dw的过程。</gydF4y2Bap> <h5 id="sec2.6">2.6。材料雾化</h5><gydF4y2Bap>对于任何dw技术,印刷材料是非常重要的。对MCS微米大小的粉就足够了。气溶胶喷射和CAB-DW沉积材料是稍微复杂。油墨必须atomizable,提供必要的打印特性如最小超范围和衬底附着力好,和传输所需的最后(即特征。、低电阻率、连续、稳定)使用方法与衬底兼容。金和汉<一个href="#B28">28</一个>)简述dw油墨所需的属性和一些商业供应商。许多油墨要求较高的烧结温度(400°C)为了实现批量导附近。这对柔性聚合物基质温度过高损坏的温度高达150°C。一些制造商生产油墨烧结温度较低(< 100°C)为灵活的应用程序,同时保持合理的电导率。导电油墨可通过几个制造商包括Cima商业纳米技术(美国圣保罗,明尼苏达州)NanoMas(恩迪科特,纽约美国),但点Inc .(香槟,美国),应用纳米技术(美国奥斯汀,得克萨斯州)Novacentrix(美国奥斯汀,得克萨斯州),卡博特公司(美国波士顿),Harima化学品(日本大阪),先进的纳米产品(韩国),光电转换纳米细胞(Migdal公顷'Emek,以色列)。许多油墨生产银或铜的基础和设计为喷墨或丝网印刷应用程序但可以减少溶剂为dw合适的粘度。必须选择正确的墨水为每个应用程序基于上述品质。在很多情况下,特定的油墨配方决定在试错的过程来建立最好的整体印刷特性平衡打印质量和物理和电气性能。</gydF4y2Bap> <h5 id="sec2.7">2.7。dw系统总结</h5><gydF4y2Bap>能够理解和气溶胶模型流动物理和比较实验设计在改善气溶胶直写技术是至关重要的。所有dw技术仍然遭受轻微超范围和nonoptimum线宽度。液体气溶胶技术面临的一个挑战是没有印刷本身,而是墨水配方。例如,金属痕迹可以使用纳米颗粒或metalorganic-based印刷油墨,但沉积后,油墨必须位。这种后处理增加了一个额外的成本对整个过程,可以限制一些热敏印刷基板的能力。此外,subbulk导电性由于孔隙度的存款和不完整的烧结是常见的。如果这些困难是克服用改进的气溶胶聚焦和墨水技术,dw的应用将大大受益于特征尺寸的减少和增加电导率提供。表<一个href="//www.newsama.com/journals/jnt/2012/324380/tab1/" target="_blank">1</一个>总结了dw技术的主要特征包括线宽、沉积速度,特殊要求,是否需要后处理。</gydF4y2Bap> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr class="thead"> <td align="left">方法</tgydF4y2Bad> <td align="center">最小线宽(<年代vg height="9.6750002" id="M43" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)</tgydF4y2Bad> <td align="center">沉积速度(毫米/秒)</tgydF4y2Bad> <td align="center">真空的要求</tgydF4y2Bad> <td align="center">超范围的洗涤器需要</tgydF4y2Bad> <td align="center">VOC的担忧</tgydF4y2Bad> <td align="center">后加工要求</tgydF4y2Bad> </tr> <tr> <td class="thead-hr" colspan="7"> <hr></td> </tr> <tr> <td align="left">气溶胶喷射</tgydF4y2Bad> <td align="center">< 10</tgydF4y2Bad> <td align="center">200年</tgydF4y2Bad> <td align="center">没有</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> </tr> <tr> <td align="left">CAB-DW</tgydF4y2Bad> <td align="center">< 5</tgydF4y2Bad> <td align="center">200年</tgydF4y2Bad> <td align="center">没有</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> </tr> <tr> <td align="left">空气动力学的镜头</tgydF4y2Bad> <td align="center">~ 10</tgydF4y2Bad> <td align="center">0.01</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">没有</tgydF4y2Bad> </tr> <tr> <td align="left">MCS</tgydF4y2Bad> <td align="center">50</tgydF4y2Bad> <td align="center">> 10<年代up>*</年代up></td> <td align="center">没有</tgydF4y2Bad> <td align="center">是的</tgydF4y2Bad> <td align="center">没有</tgydF4y2Bad> <td align="center">没有</tgydF4y2Bad> </tr> <tr class="table-tr"> <td colspan="7"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> <tr class="table-fn"> <td><sup>*</年代up>沉积速度大于10 mm / s是可能的但没有被实验验证。<gydF4y2Babr></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 总结dw技术打印系统特征。</gydF4y2Badiv> </div> </div> <p></p> <h4 id="physics-of-aerosols">3所示。气溶胶的物理</h4><h5gydF4y2Baid="sec3.1">3.1。部队气溶胶的总和</h5><gydF4y2Bap>基本了解气溶胶的物理流体相互作用的基础(即改进的沉积特征。、专注、准直、线宽、超范围的减少)为所有dw的方法。事实上,这种洞察力可能会导致新技术了CAB-DW和MCS。aerosol-fluid交互并不是新的建模,模型可以追溯到斯托克斯在1851年的工作。气溶胶粒子的运动可以由这些提到的部队应用牛顿第二定律,力等于质量乘以加速度,如下所示:<年代pan class="equation" id="EEq1"> <svg height="35.150002" id="M44" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.150002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.15)"> <g transform="translate(72,-43.88)"> <text transform="matrix(1,0,0,-1,159.1,60.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> </text> <g> <path d="m 159.1,55.98 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,159.1,44.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.041824" y="-8.7600002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.42,57.86)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,185.29,52.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.57,49.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,197.54,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.45,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 197.54,55.98 17.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,201.1,44.1)"> <tspan style="font-size: 12.50px; " x="18.790001" y="-8.7600002"> =</t年代pan> <tspan style="font-size: 12.50px; " x="30.83" y="-2.21"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.07" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="56.709332" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="273.01999" y="-10.71"> (</t年代pan> <tspan style="font-size: 12.50px; " x="277.1835" y="-10.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="283.435" y="-10.71"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="7.1750002" id="M45" style="vertical-align:-0.1254pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是粒子半径,<年代vg height="12.925" id="M46" style="vertical-align:-4.74141pt;width:13.9375px;" version="1.1" viewbox="0 0 13.9375 12.925" width="13.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是粒子密度,<年代vg height="13.2375" id="M47" style="vertical-align:-4.74141pt;width:13.9125px;" version="1.1" viewbox="0 0 13.9125 13.2375" width="13.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.2375)"> <g transform="translate(72,-61.41)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.7,63.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>粒子的速度矢量,<年代vg height="16.1" id="M48" style="vertical-align:-3.2729pt;width:26.5625px;" version="1.1" viewbox="0 0 26.5625 16.1" width="26.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代pan> <tspan style="font-size: 12.50px; " x="13.51" y="-0.029999999"> </t年代pan> </text> </g> </g> </svg>是所有力量的总和作用于气溶胶粒子。许多力量作用于粒子在流体被开发出来,但总的来说七部队通常用于气溶胶的流体质点交互建模:<年代pan class="equation" id="EEq2"> <svg height="22.7875" id="M49" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 22.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.7875)"> <g transform="translate(72,-53.77)"> <text transform="matrix(1,0,0,-1,82.32,53.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.24" y="-6.5500002"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.342665" y="-6.5500002"> =</t年代pan> <tspan style="font-size: 12.50px; " x="41.383053" y="-6.5500002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,131.35,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,141.83,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,160.81,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> B</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,173.81,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.79,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> V</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> 米</t年代pan> </text> <text transform="matrix(1,0,0,-1,209.2,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,228.18,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P</t年代pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> 年代</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.74,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,258.72,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> G</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> r</t年代pan> </text> <text transform="matrix(1,0,0,-1,271.23,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,290.21,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,305.16,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,324.14,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,333.39,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="140.73" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="144.89349" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="151.145" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="14.75" id="M50" style="vertical-align:-3.25792pt;width:19.299999px;" version="1.1" viewbox="0 0 19.299999 14.75" width="19.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> </g> </g> </svg>斯托克斯力(稳定的粘滞阻力),<年代vg height="14.7125" id="M51" style="vertical-align:-3.22281pt;width:22.450001px;" version="1.1" viewbox="0 0 22.450001 14.7125" width="22.450001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> B</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> 一个</t年代pan> </text> </g> </g> </svg>巴塞特力(非稳定粘滞阻力),<年代vg height="14.7125" id="M52" style="vertical-align:-3.23158pt;width:26.7125px;" version="1.1" viewbox="0 0 26.7125 14.7125" width="26.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> V</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> 米</t年代pan> </text> </g> </g> </svg>虚拟质量力(周围流体粒子添加到粒子的惯性),<年代vg height="14.7125" id="M53" style="vertical-align:-3.22281pt;width:20.65px;" version="1.1" viewbox="0 0 20.65 14.7125" width="20.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P</t年代pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> 年代</t年代pan> </text> </g> </g> </svg>是压强梯度力,<年代vg height="14.75" id="M54" style="vertical-align:-3.25792pt;width:21.8375px;" version="1.1" viewbox="0 0 21.8375 14.75" width="21.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> G</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> r</t年代pan> </text> </g> </g> </svg>由重力引起的浮力,<年代vg height="14.7125" id="M55" style="vertical-align:-3.22281pt;width:24.875px;" version="1.1" viewbox="0 0 24.875 14.7125" width="24.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> </g> </g> </svg>马格努斯升力是由于粒子旋转,然后呢<年代vg height="14.75" id="M56" style="vertical-align:-3.25792pt;width:21.237499px;" version="1.1" viewbox="0 0 21.237499 14.75" width="21.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> </g> </g> </svg>是一个粒子的萨夫曼升力与当地剪切流(<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B29">29日</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B37">37</一个>]。据悉,还有其他几个势力可能作用于气溶胶粒子在某些情况下包括布朗扩散、热迁移,扩散电泳,光致漂移,电磁辐射压力,声压,静电,范德瓦耳斯<一个href="#B38">38</一个>]。这里讨论的应用程序,气溶胶粒子上的力的影响很小,因为他们不是由于流体质点的相互作用,因此本文的范围。</gydF4y2Bap> <p>乔治·加布里埃尔·斯托克斯爵士(<一个href="#B39">39</一个>)开发的第一个理论模型的力量作用于球形气溶胶粒子在粘性流体在层流条件下。斯托克斯解决了运动方程(n - s)层流围绕一个圆柱体和球体和综合的力量应用于身体的表面。斯托克斯发现粒子上的力,<年代vg height="14.75" id="M57" style="vertical-align:-3.25792pt;width:19.299999px;" version="1.1" viewbox="0 0 19.299999 14.75" width="19.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> </g> </g> </svg>:<年代pan class="equation" id="EEq3"> <svg height="19.6" id="M58" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.6" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6)"> <g transform="translate(72,-56.32)"> <text transform="matrix(1,0,0,-1,151.9,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,159.54,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7785921" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,170.72,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.88121" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,210.13,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.62,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.864663" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="26.217386" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.09,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,255.87,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="218.25" y="-2.4200001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="222.4135" y="-2.4200001"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="228.66499" y="-2.4200001"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="12.7625" id="M59" style="vertical-align:-4.77652pt;width:17.174999px;" version="1.1" viewbox="0 0 17.174999 12.7625" width="17.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.7625)"> <g transform="translate(72,-61.79)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.71,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>流体粘度和吗<年代vg height="16.6" id="M60" style="vertical-align:-4.74141pt;width:49.787498px;" version="1.1" viewbox="0 0 49.787498 16.6" width="49.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-41.16,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.38,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg>流体速度相对于移动粒子(<一个href="#B40">40</一个>- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -- - - - - -<gydF4y2Ba一个href="#B42">42</一个>]。</gydF4y2Bap> <p>巴塞特力被定义为(<一个href="#B31">31日</一个>,<gydF4y2Ba一个href="#B32">32</一个>,<gydF4y2Ba一个href="#B34">34</一个>]<gydF4y2Ba年代pan class="equation" id="EEq4"> <svg height="48.1875" id="M61" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,97.04,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,104.68,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> B</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,118.38,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,142.94,54.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,147.82,47.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代pan> </text> <g> <path d="m 159.42,58.84 33.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,159.42,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.6018238" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.26,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.67,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.94,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.43,41.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,202.44,63.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="-1.25" y="25.530001"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,208.14,39.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.3" y="-20.469999"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.951595" y="-20.469999"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.203096" y="-20.469999"> /</t年代pan> <tspan style="font-size: 12.50px; " x="27.67893" y="-20.469999"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.330524" y="-20.469999"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.01963" y="-20.469999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="52.359852" y="-20.469999"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.011448" y="-20.469999"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,273.41,57.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,278.19,60.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.12743" y="0"> </t年代pan> </text> <g> <path d="m 219.44,52.73 72.79,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,237.82,36.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代pan> </text> <g> <path d="m 249.42,48.6 24.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,249.42,36.9)"> <tspan style="font-size: 12.50px; " x="44.009998" y="-2.97"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.689105" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="18.029325" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="56.189999" y="-12.7"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.841595" y="-12.7"> </t年代pan> <tspan style="font-size: 12.50px; " x="69.243134" y="-12.7"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="224.7" y="-12.7"> (</t年代pan> <tspan style="font-size: 12.50px; " x="228.86349" y="-12.7"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="235.11501" y="-12.7"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="12.975" id="M62" style="vertical-align:-4.77652pt;width:15.975px;" version="1.1" viewbox="0 0 15.975 12.975" width="15.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是流体的密度。</gydF4y2Bap> <p>假设一个简单的模型和恒定加速度,曹国伟朱镕基和Liang-Shih风扇CRC手册的流体动力学(<一个href="#B43">43</一个>]提到巴塞特力的比值斯托克斯力看起来如下:<年代pan class="equation" id="EEq5"> <svg height="49.212502" id="M63" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.212502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.2125)"> <g transform="translate(72,-32.63)"> <text transform="matrix(1,0,0,-1,143,48.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,149.05,45.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> B</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,162.74,48.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-11.39"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-8.2299995"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.74" y="-9.8000002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,186.12,55.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> B</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,196.34,60.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> </text> <g> <path d="m 175.98,52.05 22.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,177.24,40.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,187.38,35.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.08,40.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="8.4300003" y="-8.21"> =</t年代pan> <tspan style="font-size: 12.50px; " x="20.469999" y="1.66"> </t年代pan> </text> <g> <path d="m 229,70.71 43.71,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,230.19,56.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 8</t年代pan> </text> <g> <path d="m 230.19,52.05 12.51,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,232.65,40.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.44" y="-19.530001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,251.37,56.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 245.09,52.05 12.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,245.9,40.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.18,37.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.16,59.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,265.69,56.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 260.16,52.05 11.36,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,263.88,40.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.8299999" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="210.24001" y="-9.0200005"> (</t年代pan> <tspan style="font-size: 12.50px; " x="214.4035" y="-9.0200005"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="220.655" y="-9.0200005"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="12.725" id="M64" style="vertical-align:-4.74141pt;width:14.3125px;" version="1.1" viewbox="0 0 14.3125 12.725" width="14.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.725)"> <g transform="translate(72,-61.82)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.42,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>斯托克斯弛豫时间:<年代vg height="19.725" id="M65" style="vertical-align:-4.77652pt;width:102.4px;" version="1.1" viewbox="0 0 102.4 19.725" width="102.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.725)"> <g transform="translate(72,-56.22)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.42,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-57.12,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,-27.68,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.41,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-16.63,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,0.34,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,6.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> </text> </g> </g> </svg></p> <p>马歇尔(<一个href="#B33">33</一个>)发现,巴塞特力的比值阻力可以表示为<年代pan class="equation" id="EEq6"> <svg height="41.912498" id="M66" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.912498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.9125)"> <g transform="translate(72,-38.47)"> <text transform="matrix(1,0,0,-1,163.45,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,173.59,58.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> B</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,183.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> </text> <g> <path d="m 163.45,55.23 22.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,164.71,43.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.85,39.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,182.55,43.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="8.4300003" y="-8.2200003"> ≅</t年代pan> <tspan style="font-size: 12.50px; " x="20.457886" y="-8.2200003"> R</t年代pan> <tspan style="font-size: 12.50px; " x="28.797386" y="-8.2200003"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,216.91,57.11)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,232.07,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≪</t年代pan> <tspan style="font-size: 12.50px; " x="15.12863" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="21.380131" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="242.05" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="246.2135" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="252.465" y="0"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="16.375" id="M67" style="vertical-align:-4.74141pt;width:23.4625px;" version="1.1" viewbox="0 0 23.4625 16.375" width="23.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.375)"> <g transform="translate(72,-58.9)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是粒子的雷诺数对流体:<年代pan class="equation" id="EEq7"> <svg height="43.237499" id="M68" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.237499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.2375)"> <g transform="translate(72,-37.41)"> <text transform="matrix(1,0,0,-1,157.72,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,171.61,47.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.86,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≡</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.78"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="19.491501" y="-10.78"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.768005" y="-10.78"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.9,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,220.39,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.527166" y="1.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.867388" y="1.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.52,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254.29,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> </text> <g> <path d="m 193.1,54.1 63.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,218.12,42.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.36,39.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,257.99,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="216.13" y="-0.61000001"> (</t年代pan> <tspan style="font-size: 12.50px; " x="220.2935" y="-0.61000001"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="226.545" y="-0.61000001"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>虚拟质量力,<年代vg height="14.7125" id="M69" style="vertical-align:-3.23158pt;width:26.7125px;" version="1.1" viewbox="0 0 26.7125 14.7125" width="26.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> V</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> 米</t年代pan> </text> </g> </g> </svg>,是由<一个href="#B29">29日</一个>,<gydF4y2Ba一个href="#B33">33</一个>]<gydF4y2Ba年代pan class="equation" id="EEq8"> <svg height="40.837502" id="M70" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.8375)"> <g transform="translate(72,-39.33)"> <text transform="matrix(1,0,0,-1,129.37,52.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,137.01,49.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> V</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> 米</t年代pan> </text> <text transform="matrix(1,0,0,-1,154.11,52.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="20.592442" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.9,49.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.18,63.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,197.45,60.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 191.18,55.98 12.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,191.99,44.1)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.27,40.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,205.05,52.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.96" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="21.540001" y="-7.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.191595" y="-7.25"> </t年代pan> </text> <g> <path d="m 226.59,55.98 12.9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,227.76,44.1)"> <tspan style="font-size: 12.50px; " x="15.7" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.24" y="-19.5"> </t年代pan> <tspan style="font-size: 12.50px; " x="34.891598" y="-19.5"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,268.91,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 256,55.98 17.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,259.56,44.1)"> <tspan style="font-size: 12.50px; " x="15.32" y="-1.4299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.780001" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="214.56" y="-8.4399996"> (</t年代pan> <tspan style="font-size: 12.50px; " x="218.7235" y="-8.4399996"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="224.97501" y="-8.4399996"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="7.1374998" id="M71" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>粒子的质量和吗<年代vg height="10.925" id="M72" style="vertical-align:-3.13504pt;width:19.2125px;" version="1.1" viewbox="0 0 19.2125 10.925" width="19.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>附加质量系数,也就是0.5一个球体。</gydF4y2Bap> <p>压强梯度力,<年代vg height="14.7125" id="M73" style="vertical-align:-3.22281pt;width:20.65px;" version="1.1" viewbox="0 0 20.65 14.7125" width="20.65" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P</t年代pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> 年代</t年代pan> </text> </g> </g> </svg>由于外部的加速度,流过去的粒子,由以下方程计算(<一个href="#B29">29日</一个>,<gydF4y2Ba一个href="#B33">33</一个>]:<gydF4y2Ba年代pan class="equation" id="EEq9"> <svg height="37.337502" id="M74" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.337502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.3375)"> <g transform="translate(72,-42.13)"> <text transform="matrix(1,0,0,-1,170.66,55.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,178.29,52.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> P</t年代pan> <tspan style="font-size: 8.75px; " x="4.8748641" y="0"> 年代</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.55,55.66)"> <tspan style="font-size: 12.50px; " x="22.110001" y="-10.78"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.93,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 212.66,58.79 12.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,213.47,46.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.75,43.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.73,62.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> </t年代pan> </text> <g> <path d="m 227.73,58.79 16.13,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,228.9,46.91)"> <tspan style="font-size: 12.50px; " x="16.15" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="245.22" y="-7.0300002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="249.3835" y="-7.0300002"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="255.63499" y="-7.0300002"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.9125" id="M75" style="vertical-align:-0.17555pt;width:34.049999px;" version="1.1" viewbox="0 0 34.049999 10.9125" width="34.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="13.353204" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="23.230574" y="0"> </t年代pan> </text> </g> </g> </svg>表示的速率随时间变化后流体粒子,这样<年代pan class="equation" id="EEq10"> <svg height="30.762501" id="M76" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.762501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7625)"> <g transform="translate(72,-47.39)"> <text transform="matrix(1,0,0,-1,137.68,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> </t年代pan> </text> <g> <path d="m 137.68,59.47 16.13,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,138.85,47.59)"> <tspan style="font-size: 12.50px; " x="19.629999" y="-8.7600002"> =</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.8773699" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.860001" y="-16.01"> </t年代pan> <tspan style="font-size: 12.50px; " x="39.511597" y="-16.01"> </t年代pan> </text> <g> <path d="m 171.71,59.47 12.91,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,172.88,47.59)"> <tspan style="font-size: 12.50px; " x="15.71" y="-8.7600002"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.689999" y="-8.7600002"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.6515961" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="27.049999" y="-6.2399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="31.83865" y="-6.2399998"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,216.82,53.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,224.38,56.35)"> <tspan style="font-size: 12.50px; " x="17.6" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="41.720001" y="2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.23" y="0"> ⋅</t年代pan> <tspan style="font-size: 12.50px; " x="32.569019" y="0"> ∇</t年代pan> <tspan style="font-size: 12.50px; " x="48.59" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.841499" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="243.49001" y="-0.22"> (</t年代pan> <tspan style="font-size: 12.50px; " x="247.6535" y="-0.22"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="253.905" y="-0.22"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="260.15649" y="-0.22"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>浮力,<年代vg height="14.75" id="M77" style="vertical-align:-3.25792pt;width:21.8375px;" version="1.1" viewbox="0 0 21.8375 14.75" width="21.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> G</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> r</t年代pan> </text> </g> </g> </svg>,由于重力=<年代pan class="equation" id="EEq11"> <svg height="40.099998" id="M78" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.099998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.1)"> <g transform="translate(72,-39.92)"> <text transform="matrix(1,0,0,-1,154.66,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,162.3,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> G</t年代pan> <tspan style="font-size: 8.75px; " x="6.318944" y="0"> r</t年代pan> </text> <text transform="matrix(1,0,0,-1,175.51,53.45)"> <tspan style="font-size: 12.50px; " x="23" y="7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.939999" y="-10.77"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.380001" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="41.394665" y="0"> −</t年代pan> </text> <text transform="matrix(1,0,0,-1,235.73,61.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 229.45,56.57 12.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,230.27,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.54,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,243.33,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.46" y="-7.3299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.7115" y="-7.3299999"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="224.53999" y="-6.71"> (</t年代pan> <tspan style="font-size: 12.50px; " x="228.70351" y="-6.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="234.955" y="-6.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="241.2065" y="-6.71"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.725" id="M79" style="vertical-align:-2.58324pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 10.725" width="7.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,66.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>重力加速度矢量。</gydF4y2Bap> <p>马格努斯力,<年代vg height="14.7125" id="M80" style="vertical-align:-3.22281pt;width:24.875px;" version="1.1" viewbox="0 0 24.875 14.7125" width="24.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> </g> </g> </svg>存在,如果粒子在旋转对周围的流体,是由<一个href="#B31">31日</一个>,<gydF4y2Ba一个href="#B33">33</一个>]<gydF4y2Ba年代pan class="equation" id="EEq12"> <svg height="37.337502" id="M81" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.337502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.3375)"> <g transform="translate(72,-42.13)"> <text transform="matrix(1,0,0,-1,110.39,55.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,118.03,52.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,133.66,55.66)"> <tspan style="font-size: 12.50px; " x="21.799999" y="-7.25"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代pan> </text> <g> <path d="m 155.46,58.79 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,155.46,46.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.52" y="-19.530001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,179.26,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 172.98,58.79 12.68,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,173.8,46.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,180.07,43.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,188.94,50.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.5600004" y="-12.17"> 1</t年代pan> </text> <g> <path d="m 197.5,58.79 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,197.5,46.91)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="39.389999" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="49.77" y="-8.75"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="62.630001" y="-6.2399998"> </t年代pan> <tspan style="font-size: 12.50px; " x="68.480003" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.74021" y="-8.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="30.080429" y="-8.75"> Ω</t年代pan> </text> <text transform="matrix(1,0,0,-1,272.24,52.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,279.79,55.66)"> <tspan style="font-size: 12.50px; " x="17.6" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.530001" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="188.08" y="1.72"> (</t年代pan> <tspan style="font-size: 12.50px; " x="192.2435" y="1.72"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="198.495" y="1.72"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="204.74651" y="1.72"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="7.1875" id="M82" style="vertical-align:-0.13794pt;width:10.7625px;" version="1.1" viewbox="0 0 10.7625 7.1875" width="10.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是周围的流体粒子和涡度<年代vg height="10.6875" id="M83" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>是粒子的旋转角速率。基于所作的分析(<一个href="#B43">43</一个>),它可以指出,马格努斯效应比斯托克斯力等于<年代pan class="equation" id="EEq13"> <svg height="44.224998" id="M84" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.224998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,44.225)"> <g transform="translate(72,-36.62)"> <text transform="matrix(1,0,0,-1,123.82,50.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,129.87,47.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.51,50.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-11.39"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-8.2200003"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.73" y="-9.8000002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.88,56.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.05,61.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> </text> <g> <path d="m 158.74,53.38 24.81,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,160.97,42.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,171.11,37.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7785921" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,178.81,42.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="9.4099998" y="-8.2200003"> =</t年代pan> <tspan style="font-size: 12.50px; " x="22.639999" y="-18.99"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,207.73,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,212.6,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.88,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.37,62.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="60.82" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="60.82" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.6634989" y="1.58"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="12.914999" y="1.58"> /</t年代pan> <tspan style="font-size: 12.50px; " x="16.390833" y="1.58"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="22.642332" y="1.58"> )</t年代pan> <tspan style="font-size: 12.50px; " x="28.88133" y="1.58"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.171539" y="1.58"> −</t年代pan> <tspan style="font-size: 12.50px; " x="51.511761" y="1.58"> Ω</t年代pan> </text> <g> <path d="m 201.45,53.38 89.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.12,41.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,249.61,38.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,291.89,50.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="175.98" y="-0.92000002"> (</t年代pan> <tspan style="font-size: 12.50px; " x="180.14349" y="-0.92000002"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="186.395" y="-0.92000002"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="192.6465" y="-0.92000002"> )</t年代pan> </text> </g> </g> </svg></span>假设流体无旋,气溶胶粒子旋转由于承运人的地方剪切流,<年代vg height="13.55" id="M85" style="vertical-align:-2.29482pt;width:184.1125px;" version="1.1" viewbox="0 0 184.1125 13.55" width="184.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5006001" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="6.6640992" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="12.915599" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="16.391434" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="22.642933" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="26.806433" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="38.096642" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="49.436863" y="0"> Ω</t年代pan> <tspan style="font-size: 12.50px; " x="58.739094" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="64.71553" y="0"> ≈</t年代pan> <tspan style="font-size: 12.50px; " x="76.743416" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="79.244011" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="85.633049" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="91.559471" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="95.035301" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="101.43684" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="107.63833" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="113.60226" y="0"> ≈</t年代pan> <tspan style="font-size: 12.50px; " x="125.64265" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="134.45726" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="137.93309" y="0"> </t年代pan> </text> </g> </g> </svg>,这一比率的马格努斯力斯托克斯力可以进一步简化<年代pan class="equation" id="EEq14"> <svg height="44.137501" id="M86" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.137501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,44.1375)"> <g transform="translate(72,-36.69)"> <text transform="matrix(1,0,0,-1,172.78,50.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,178.84,47.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,194.47,50.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≅</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.77"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.98,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.86,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.13,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.54,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 207.71,53.38 34.02,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,210.14,41.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.63,38.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.04,41.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.89" y="-8.7600002"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="237.83" y="-9.7200003"> (</t年代pan> <tspan style="font-size: 12.50px; " x="241.9935" y="-9.7200003"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="248.245" y="-9.7200003"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="254.49651" y="-9.7200003"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="7.1624999" id="M87" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是气体轴向速度分量,<年代vg height="10.5375" id="M88" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>的平均速度是流体通过毛细管,然后呢<年代vg height="10.325" id="M89" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>毛细管的半径。因此,比率<年代vg height="11.0375" id="M90" style="vertical-align:-3.22281pt;width:22.9px;" version="1.1" viewbox="0 0 22.9 11.0375" width="22.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代pan> <tspan style="font-size: 8.75px; " x="7.7805281" y="0"> 一个</t年代pan> </text> </g> </g> </svg>是关于<年代vg height="14.2" id="M91" style="vertical-align:-0.17555pt;width:29.3375px;" version="1.1" viewbox="0 0 29.3375 14.2" width="29.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代pan> </text> </g> </g> </svg>假设1的气溶胶粒子<年代vg height="9.6750002" id="M92" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径朝着氮在标准条件下的平均速度50 m / s通过毛细管的100<年代vg height="9.6750002" id="M93" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米半径。</gydF4y2Bap> <p>萨夫曼力,<年代vg height="14.75" id="M94" style="vertical-align:-3.25792pt;width:21.237499px;" version="1.1" viewbox="0 0 21.237499 14.75" width="21.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.31,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> </g> </g> </svg>是升力用于气溶胶粒子在一个简单的层流剪切流(泊肃叶流动),并于1965年由p·g .萨夫曼[<一个href="#B36">36</一个>]。电梯正比于剪切和粒子的相对速度的大小对流体:<年代pan class="equation" id="EEq15"> <svg height="49.212502" id="M95" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 49.212502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,49.2125)"> <g transform="translate(72,-32.63)"> <text transform="matrix(1,0,0,-1,83.21,47.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,90.85,44.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,103.57,47.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,143.77,52.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,150.72,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.549585" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="25.902309" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,182.55,44.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,187.33,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="5.6399999"> </t年代pan> </text> <g> <path d="m 208.72,70.71 48.39,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,208.72,47.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.99,44.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.4,47.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,228.64,44.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,237.13,59.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="24.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="3.8299999" y="5"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.219033" y="5"> </t年代pan> </text> <g> <path d="m 240.82,50.33 12.6,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,240.82,38.45)"> <tspan style="font-size: 12.50px; " x="13.79" y="-21"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.79" y="-10.34"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.79" y="0.33000001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.79" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="45.470001" y="-1.42"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.379999" y="-8.75"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="23.243668" y="-8.75"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="26.719501" y="-8.75"> g</t年代pan> <tspan style="font-size: 12.50px; " x="32.971001" y="-8.75"> n</t年代pan> <tspan style="font-size: 12.50px; " x="56.18" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="62.55653" y="-16"> </t年代pan> </text> <g> <path d="m 296.86,50.33 12.59,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,296.86,38.45)"> <tspan style="font-size: 12.50px; " x="13.79" y="-1.42"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.25" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,327.66,44.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,332.5,47.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="135.37" y="-1.99"> (</t年代pan> <tspan style="font-size: 12.50px; " x="139.53349" y="-1.99"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="145.785" y="-1.99"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="152.0365" y="-1.99"> )</t年代pan> </text> </g> </g> </svg></span>值6.46是一个常数的数值积分决定萨夫曼[附录的<一个href="#B36">36</一个>),<gydF4y2Ba年代vg height="7.1624999" id="M96" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是气体轴向速度分量,<年代vg height="12.925" id="M97" style="vertical-align:-4.74141pt;width:13.5px;" version="1.1" viewbox="0 0 13.5 12.925" width="13.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.02,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是颗粒轴向速度分量。</gydF4y2Bap> <p>详细评估萨夫曼力之间的比例和斯托克斯力在气溶胶主要是(<一个href="#B8">8</一个>]Akhatov等人计算出的地方<年代pan class="equation" id="EEq16"> <svg height="41.912498" id="M98" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.912498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.9125)"> <g transform="translate(72,-38.47)"> <text transform="matrix(1,0,0,-1,94.64,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,100.69,48.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,113.41,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-11.39"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-8.2200003"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.74" y="-9.8000002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,136.78,58.78)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,146.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> </text> <g> <path d="m 126.64,55.23 21.9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,127.42,43.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,137.56,39.18)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,145.26,43.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="38.290001" y="-15.47"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-8.2200003"> ≈</t年代pan> <tspan style="font-size: 12.50px; " x="19.980389" y="-8.2200003"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.23189" y="-8.2200003"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.357639" y="-8.2200003"> 3</t年代pan> </text> <g> <path d="m 182.07,55.23 9.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,182.07,43.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.44" y="-8.3900003"> √</t年代pan> </text> <g> <path d="m 204.12,63.5 18.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,204.12,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.01,48.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.58,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.118526" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="33.458027" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,261.6,48.98)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.64,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.77"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="19.491501" y="-10.77"> </t年代pan> <tspan style="font-size: 12.50px; " x="28.743719" y="-10.77"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.558334" y="-10.77"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,313.47,59.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 282.88,55.23 37,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,294.55,43.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,301.79,40.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,321.07,52.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="146.8" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="150.9635" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="157.215" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="163.46649" y="0"> )</t年代pan> </text> </g> </g> </svg></span>根据他们的分析,发现<年代vg height="11.075" id="M99" style="vertical-align:-3.25792pt;width:19.25px;" version="1.1" viewbox="0 0 19.25 11.075" width="19.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.9,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> </g> </g> </svg>大约是0.05。</gydF4y2Bap> <p>类似的结果对斯托克斯萨夫曼力的比值阻力是由朱曹国伟和Liang-Shih风扇手册的流体动力学(<一个href="#B43">43</一个>]:<gydF4y2Ba年代pan class="equation" id="EEq17"> <svg height="50.112499" id="M100" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.112499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.1125)"> <g transform="translate(72,-31.91)"> <text transform="matrix(1,0,0,-1,111.66,46.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,117.71,43.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.43,46.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-11.39"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-8.2200003"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.73" y="-9.8000002"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.8,53.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,163.05,57.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1700001"> |</t年代pan> </text> <g> <path d="m 143.66,49.54 21.89,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,144.44,38.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.58"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,154.58,33.49)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,162.28,38.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="7.9400001" y="-8.2200003"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.18" y="-15.47"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="27.431499" y="-15.47"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="30.557249" y="-15.47"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="36.80875" y="-15.47"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="43.060249" y="-15.47"> </t年代pan> </text> <g> <path d="m 183.46,49.54 28.15,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,190.61,37.67)"> <tspan style="font-size: 12.50px; " x="22.200001" y="-25.629999"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.200001" y="-20.27"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.200001" y="-14.91"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.200001" y="5.71"> ⎷</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <g> <path d="m 227.61,70.71 76.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,229.29,57.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,235.57,54.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 228.81,49.54 13.64,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,228.81,37.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.05,34.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,245.73,58.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="24.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="3.7" y="1.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.17" y="4.02"> </t年代pan> <tspan style="font-size: 12.50px; " x="18.02" y="1.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.722088" y="1.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="38.062309" y="1.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.73,54.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,294.51,54.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 249.43,49.54 50.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,268.6,37.67)"> <tspan style="font-size: 12.50px; " x="32.950001" y="-21"> |</t年代pan> <tspan style="font-size: 12.50px; " x="32.950001" y="-10.34"> |</t年代pan> <tspan style="font-size: 12.50px; " x="32.950001" y="0.33000001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="32.950001" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="35.450001" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="199.27" y="-11.16"> (</t年代pan> <tspan style="font-size: 12.50px; " x="203.4335" y="-11.16"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="209.685" y="-11.16"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="215.93649" y="-11.16"> )</t年代pan> </text> </g> </g> </svg></span>的简化形式萨夫曼斯托克斯力比可以由以下方程假设简单的剪切流:<年代pan class="equation" id="EEq18"> <svg height="43.337502" id="M101" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.337502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.3375)"> <g transform="translate(72,-37.33)"> <text transform="matrix(1,0,0,-1,79.69,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,85.74,47.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,98.46,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-11.39"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-8.2299995"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.74" y="-9.8100004"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,121.84,57.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,131.09,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> </text> <g> <path d="m 111.7,54.1 21.89,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,112.47,42.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,122.61,38.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7785921" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,130.31,42.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="7.9499998" y="-8.21"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.18" y="-15.47"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="27.431499" y="-15.47"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="30.557249" y="-15.47"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="36.80875" y="-15.47"> 6</t年代pan> </text> <g> <path d="m 151.49,54.1 21.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,152.38,42.22)"> <tspan style="font-size: 12.50px; " x="22.190001" y="-4.25"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="12.503" y="0"> </t年代pan> </text> <g> <path d="m 187.78,65.46 18.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,187.78,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,201.67,47.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.45,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="33.470531" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,245.48,47.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.73,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.78"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="19.481501" y="-10.78"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.921505" y="-10.78"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,289.93,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,298.42,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="2.5" y="1.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.527166" y="1.75"> −</t年代pan> <tspan style="font-size: 12.50px; " x="22.867388" y="1.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,327.55,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,332.33,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> </text> <g> <path d="m 266.96,54.1 67.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,294.07,42.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,301.31,39.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,336.02,50.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="131.85001" y="-0.56999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="136.0135" y="-0.56999999"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="142.265" y="-0.56999999"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="148.51649" y="-0.56999999"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>气溶胶粒子上的力是重要的如果他们明显的比斯托克斯力。0.5 - 5的气溶胶粒子的分析<年代vg height="9.6750002" id="M102" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米,重力是不明显的。马歇尔发现巴塞特力可能被忽略<一个href="#B33">33</一个>]。Crowe et al。<一个href="#B31">31日</一个>)发现,压力梯度力,虚拟质量力和巴塞特力也可能被忽视。Akhatov等人同意这消除部队和总结,这两个最有价值的力量斯托克斯和萨夫曼<一个href="#B8">8</一个>]。</gydF4y2Bap> <h5 id="sec3.2">3.2。斯托克斯稀薄气体的校正因子</h5><gydF4y2Bap>斯托克斯力的阻力假设一个线性依赖于粒子的相对速度的流体(滞后)。线性依赖实验偏差适用于许多颗粒流体组合,但在某些情况下,如在稀薄的流动需要解决如果粒径很小(< 0.5<年代vg height="9.6750002" id="M103" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)。一些滞后模型,包括那些由坎宁安(<一个href="#B44">44</一个>)和更修正模型由卡尔森和霍格伦德(<一个href="#B45">45</一个>),考虑到气体粒子表面滑由于气体rarefication(基于克努森数)和粒子的相对速度的大小对液体,已经设计了。</gydF4y2Bap> <p>坎宁安(<一个href="#B44">44</一个>斯托克斯力变化]相关的克努森数<年代pan class="equation" id="EEq19"> <svg height="33.487499" id="M104" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.487499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.4875)"> <g transform="translate(72,-45.21)"> <text transform="matrix(1,0,0,-1,153.92,54.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.64,51.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7785921" y="0"> t</t年代pan> <tspan style="font-size: 8.75px; " x="7.1941438" y="0"> o</t年代pan> <tspan style="font-size: 8.75px; " x="11.570144" y="0"> k</t年代pan> <tspan style="font-size: 8.75px; " x="15.832368" y="0"> e</t年代pan> <tspan style="font-size: 8.75px; " x="19.718256" y="0"> 年代</t年代pan> </text> <text transform="matrix(1,0,0,-1,184.76,51.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,198.67,54.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="21.91" y="-9.2700005"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,228.31,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> <tspan style="font-size: 8.75px; " x="7.1853919" y="0"> o</t年代pan> <tspan style="font-size: 8.75px; " x="11.561392" y="0"> k</t年代pan> <tspan style="font-size: 8.75px; " x="15.823616" y="0"> e</t年代pan> <tspan style="font-size: 8.75px; " x="19.709503" y="0"> 年代</t年代pan> </text> <g> <path d="m 211.9,57.65 48.7,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,211.9,45.77)"> <tspan style="font-size: 12.50px; " x="49.889999" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.332039" y="0"> ′</t年代pan> <tspan style="font-size: 12.50px; " x="32.945404" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="42.472691" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="255.97" y="-9.71"> (</t年代pan> <tspan style="font-size: 12.50px; " x="260.13348" y="-9.71"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="266.38501" y="-9.71"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="272.63651" y="-9.71"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.45" id="M105" style="vertical-align:-0.10033pt;width:19.799999px;" version="1.1" viewbox="0 0 19.799999 10.45" width="19.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.45)"> <g transform="translate(72,-63.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5272856" y="0"> </t年代pan> </text> </g> </g> </svg>是粒子克努森数(平均自由程/直径)和<年代vg height="10.725" id="M106" style="vertical-align:-0.0pt;width:15.85px;" version="1.1" viewbox="0 0 15.85 10.725" width="15.85" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.9646511" y="0"> ′</t年代pan> </text> </g> </g> </svg>是一个无因次系数。在这个模型中,斯托克斯力的影响不大<年代vg height="10.45" id="M107" style="vertical-align:-0.10033pt;width:19.799999px;" version="1.1" viewbox="0 0 19.799999 10.45" width="19.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.45)"> <g transform="translate(72,-63.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5272856" y="0"> </t年代pan> </text> </g> </g> </svg>增加由于粒子表面上滑的液体。</gydF4y2Bap> <p>克努森和韦伯(<一个href="#B46">46</一个>]发现(<一个href="#EEq19">19</一个>)只适用于很小<年代vg height="10.45" id="M108" style="vertical-align:-0.10033pt;width:19.799999px;" version="1.1" viewbox="0 0 19.799999 10.45" width="19.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.45)"> <g transform="translate(72,-63.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5272856" y="0"> </t年代pan> </text> </g> </g> </svg>。将大的差异<年代vg height="10.45" id="M109" style="vertical-align:-0.10033pt;width:19.799999px;" version="1.1" viewbox="0 0 19.799999 10.45" width="19.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.45)"> <g transform="translate(72,-63.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5272856" y="0"> </t年代pan> </text> </g> </g> </svg><i>,</我>三个额外的参数包括生成Stokes-Cunningham方程:<年代pan class="equation" id="EEq20"> <svg height="41.037498" id="M110" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.037498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.0375)"> <g transform="translate(72,-39.17)"> <text transform="matrix(1,0,0,-1,117.37,54.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,125.1,51.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> <tspan style="font-size: 8.75px; " x="7.1853919" y="0"> o</t年代pan> <tspan style="font-size: 8.75px; " x="11.561392" y="0"> k</t年代pan> <tspan style="font-size: 8.75px; " x="15.823616" y="0"> e</t年代pan> <tspan style="font-size: 8.75px; " x="19.709503" y="0"> 年代</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.21,51.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="5.872592" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,162.13,54.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="58.450001" y="-9.2700005"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,228.31,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> <tspan style="font-size: 8.75px; " x="7.1853919" y="0"> o</t年代pan> <tspan style="font-size: 8.75px; " x="11.561392" y="0"> k</t年代pan> <tspan style="font-size: 8.75px; " x="15.823616" y="0"> e</t年代pan> <tspan style="font-size: 8.75px; " x="19.709503" y="0"> 年代</t年代pan> </text> <g> <path d="m 175.36,57.65 121.78,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,175.36,43.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.894672" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,211.48,40.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.34,41.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.590317" y="-2.52"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.930538" y="-2.52"> </t年代pan> <tspan style="font-size: 12.50px; " x="37.632626" y="-2.52"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.54,48.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="12.244048" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="14.677104" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="21.346128" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,287.24,46.5)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,291.29,41.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.0500002" y="-13.09"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="176.58" y="-11.03"> (</t年代pan> <tspan style="font-size: 12.50px; " x="180.7435" y="-11.03"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="186.995" y="-11.03"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="193.24651" y="-11.03"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.55" id="M111" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="10.325" id="M112" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,<年代vg height="10.325" id="M113" style="vertical-align:-0.0pt;width:12.225px;" version="1.1" viewbox="0 0 12.225 10.325" width="12.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是常数测定实验(<一个href="#B41">41</一个>,<gydF4y2Ba一个href="#B47">47</一个>]。</gydF4y2Bap> <p>表<一个href="//www.newsama.com/journals/jnt/2012/324380/tab2/" target="_blank">2</一个>给出了一个抽样的实验值参数坎宁安滑校正因子。许多修正因素根据米利根(油滴实验<一个href="#B42">42</一个>滑动的0.3)<年代vg height="9.6750002" id="M114" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米油滴在空气中被评估。粒子的漂移速度测量和用于确定滑移修正因素。</gydF4y2Bap> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr class="thead"> <td align="left">作者,年</tgydF4y2Bad> <td align="center">平均自由程(<年代vg height="9.6750002" id="M115" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)</tgydF4y2Bad> <td align="center"><span style="width: 11.325px;"> <svg height="10.55" id="M116" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 11.625px;"> <svg height="10.325" id="M117" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 12.225px;"> <svg height="10.325" id="M118" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.225 10.325" width="12.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 40.487499px;"> <svg height="11.1875" id="M119" style="vertical-align:-0.51414pt" version="1.1" viewbox="0 0 40.487499 11.1875" width="40.487499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1875)"> <g transform="translate(72,-63.05)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.740317" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.080538" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr> <td align="left">克努森和韦伯,1911<一个href="#B46">46</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.09417</tgydF4y2Bad> <td align="center">0.772</tgydF4y2Bad> <td align="center">0.40</tgydF4y2Bad> <td align="center">1.63</tgydF4y2Bad> <td align="center">1.172</tgydF4y2Bad> </tr> <tr> <td align="left">米利根,1923<一个href="#B42">42</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.09417</tgydF4y2Bad> <td align="center">0.864</tgydF4y2Bad> <td align="center">0.29</tgydF4y2Bad> <td align="center">1.25</tgydF4y2Bad> <td align="center">1.154</tgydF4y2Bad> </tr> <tr> <td align="left">朗缪尔,1942<一个href="#B48">49</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.133</tgydF4y2Bad> <td align="center">0.62</tgydF4y2Bad> <td align="center">0.22</tgydF4y2Bad> <td align="center">2.20</tgydF4y2Bad> <td align="center">0.84</tgydF4y2Bad> </tr> <tr> <td align="left">戴维斯,1945<一个href="#B49">50</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.066</tgydF4y2Bad> <td align="center">1.257</tgydF4y2Bad> <td align="center">0.40</tgydF4y2Bad> <td align="center">1.10</tgydF4y2Bad> <td align="center">1.657</tgydF4y2Bad> </tr> <tr> <td align="left">DeMarcus和托马斯,1952<一个href="#B50">51</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.0655</tgydF4y2Bad> <td align="center">1.25</tgydF4y2Bad> <td align="center">0.44</tgydF4y2Bad> <td align="center">1.09</tgydF4y2Bad> <td align="center">1.690</tgydF4y2Bad> </tr> <tr> <td align="left">赖夫,1958<一个href="#B51">52</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.0652</tgydF4y2Bad> <td align="center">1.26</tgydF4y2Bad> <td align="center">0.45</tgydF4y2Bad> <td align="center">1.08</tgydF4y2Bad> <td align="center">1.710</tgydF4y2Bad> </tr> <tr> <td align="left">福克斯,1964<一个href="#B52">53</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.0653</tgydF4y2Bad> <td align="center">1.246</tgydF4y2Bad> <td align="center">0.42</tgydF4y2Bad> <td align="center">0.87</tgydF4y2Bad> <td align="center">1.666</tgydF4y2Bad> </tr> <tr> <td align="left">Dahneke et al ., 1982<一个href="#B53">54</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.066</tgydF4y2Bad> <td align="center">1.234</tgydF4y2Bad> <td align="center">0.414</tgydF4y2Bad> <td align="center">0.87</tgydF4y2Bad> <td align="center">1.648</tgydF4y2Bad> </tr> <tr> <td align="left">艾伦和拉伯,1982<一个href="#B54">48</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">0.0673</tgydF4y2Bad> <td align="center">1.155</tgydF4y2Bad> <td align="center">0.471</tgydF4y2Bad> <td align="center">0.596</tgydF4y2Bad> <td align="center">1.626</tgydF4y2Bad> </tr> <tr> <td align="left">巴克利和Loyalka, 1989<一个href="#B55">55</一个>]</tggydF4y2BaydF4y2Bad> <td align="center">- - - - - -</tgydF4y2Bad> <td align="center">1.099</tgydF4y2Bad> <td align="center">0.518</tgydF4y2Bad> <td align="center">0.425</tgydF4y2Bad> <td align="center">1.617</tgydF4y2Bad> </tr> <tr class="table-tr"> <td colspan="6"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> Stokes-Cunningham滑移修正因素,从李,王(转载<一个href="#B41">41</一个>]<gydF4y2Ba一个href="http://link.aps.org/doi/10.1103/PhysRevE.68.061206" target="_blank">http://link.aps.org/doi/10.1103/PhysRevE.68.061206</一个>和艾伦·拉伯(<一个href="#B54">48</一个>),版权2003年和1982年,分别与美国物理学会的许可和爱思唯尔。</gydF4y2Badiv> </div> </div> <p></p> <p></p> <h5 id="sec3.3">3.3。斯托克斯修正雷诺和马赫数</h5><gydF4y2Bap>斯托克斯拖曳力作用在一个球形颗粒,(<一个href="#EEq3">3</一个>),推导了低雷诺数(<年代vg height="16.6" id="M120" style="vertical-align:-4.74141pt;width:54.537498px;" version="1.1" viewbox="0 0 54.537498 16.6" width="54.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≪</t年代pan> <tspan style="font-size: 12.50px; " x="15.12863" y="0"> 1</t年代pan> </text> </g> </g> </svg>);因此,如果考虑与广泛的球形粒子的流动雷诺数,斯托克斯方程应该修订;这些修正尤其MCS等建模应用程序的关键。克利夫特et al。<一个href="#B56">56</一个>总结经验和半经验的阻力修正<年代vg height="14.3375" id="M121" style="vertical-align:-3.13504pt;width:20.0375px;" version="1.1" viewbox="0 0 20.0375 14.3375" width="20.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>为不同的雷诺数范围表<一个href="//www.newsama.com/journals/jnt/2012/324380/tab3/" target="_blank">3</一个>斯托克斯力与哪里<年代vg height="14.3375" id="M122" style="vertical-align:-3.13504pt;width:20.0375px;" version="1.1" viewbox="0 0 20.0375 14.3375" width="20.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>根据(<一个href="#EEq21">21</一个>)如下:<年代pan class="equation" id="EEq21"> <svg height="27.875" id="M123" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 27.875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,27.875)"> <g transform="translate(72,-49.7)"> <text transform="matrix(1,0,0,-1,143.56,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,151.2,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7698398" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,162.37,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-7.25"> </t年代pan> </text> <g> <path d="m 175.61,61.63 7.6,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,176.28,49.75)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="8.1199999" y="-8.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,192.79,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,200.34,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,206.61,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.02,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.3,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,224.17,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.877166" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="26.217386" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,256.65,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,261.42,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,267.28,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,272.15,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="195.72" y="0.77999997"> (</t年代pan> <tspan style="font-size: 12.50px; " x="199.8835" y="0.77999997"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="206.13499" y="0.77999997"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="212.38651" y="0.77999997"> )</t年代pan> </text> </g> </g> </svg></span>断崖等人也调查了斯托克斯力的阻力系数修正的情况下任意形状的固体颗粒(球状体、磁盘、气瓶等)和椭圆形流体粒子(<一个href="#B56">56</一个>),但对颗粒形状阻力的依赖超出了本文的范围。一般来说,修正斯托克斯力不仅依赖于颗粒形状,方向流动,在马赫数和雷诺数也和流体的湍流程度。卡尔森和霍格伦德<一个href="#B45">45</一个>)设计了一种改进的基于颗粒雷诺数经验修正系数,<年代vg height="16.375" id="M124" style="vertical-align:-4.74141pt;width:23.4625px;" version="1.1" viewbox="0 0 23.4625 16.375" width="23.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.375)"> <g transform="translate(72,-58.9)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,马赫数,<年代vg height="16.237499" id="M125" style="vertical-align:-4.74141pt;width:21.799999px;" version="1.1" viewbox="0 0 21.799999 16.237499" width="21.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2375)"> <g transform="translate(72,-59.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-59.38,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>根据(<一个href="#EEq22">22</一个>)如下:<年代pan class="equation" id="EEq22"> <svg height="30.9125" id="M126" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.9125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.9125)"> <g transform="translate(72,-47.27)"> <text transform="matrix(1,0,0,-1,113.38,56.25)"> <tspan style="font-size: 12.50px; " x="24.68" y="4.9200001"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.619999" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.640533" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.049999" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="41.077168" y="0"> +</t年代pan> </text> <g> <path d="m 167,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,167,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="7.4400001" y="-8.7600002"> R</t年代pan> <tspan style="font-size: 12.50px; " x="15.779501" y="-8.7600002"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,188.34,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,200.02,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6773224" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.049999" y="-4.9200001"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.077166" y="-4.9200001"> +</t年代pan> <tspan style="font-size: 12.50px; " x="37.417385" y="-4.9200001"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,243.01,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 4</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="21.311119" y="0"> 7</t年代pan> <tspan style="font-size: 8.75px; " x="25.68712" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="28.120176" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,280.71,64.75)"> <tspan style="font-size: 6.25px; " x="-0.79000002" y="5.6900001"> </t年代pan> <tspan style="font-size: 6.25px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 6.25px; " x="3.1259999" y="0"> 。</t年代pan> <tspan style="font-size: 6.25px; " x="4.6890001" y="0"> 6</t年代pan> <tspan style="font-size: 6.25px; " x="7.8150001" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,292.65,51.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.6800003" y="-4.9200001"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="175.22" y="-5.1799998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="179.3835" y="-5.1799998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="185.63499" y="-5.1799998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="191.88651" y="-5.1799998"> )</t年代pan> </text> </g> </g> </svg></span>的相对马赫数粒子流体相比<年代pan class="equation" id="EEq23"> <svg height="43.200001" id="M127" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.200001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.2)"> <g transform="translate(72,-37.44)"> <text transform="matrix(1,0,0,-1,98.8,51.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,111.36,47.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,119.62,51.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-12.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-9"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.73" y="-10.74"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.757166" y="-10.74"> −</t年代pan> <tspan style="font-size: 12.50px; " x="36.097385" y="-10.74"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,161.97,58.62)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,166.75,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> </text> <g> <path d="m 132.85,54.13 36.4,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,144.28,42.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,152.67,39.13)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,170.45,51.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,203.22,47.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.7785921" y="0"> t</t年代pan> </text> <text transform="matrix(1,0,0,-1,214.4,51.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="25.88121" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="32.157715" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,253.8,47.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,260.21,51.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.51" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.360001" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="26.387165" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="37.727386" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,304.2,47.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,308.98,48.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="158.89" y="-3.0999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="163.0535" y="-3.0999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="169.30499" y="-3.0999999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="175.5565" y="-3.0999999"> )</t年代pan> </text> </g> </g> </svg></span>和<年代vg height="16.375" id="M128" style="vertical-align:-4.77652pt;width:17.049999px;" version="1.1" viewbox="0 0 17.049999 16.375" width="17.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.375)"> <g transform="translate(72,-58.9)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>气体的声速。</gydF4y2Bap> <div class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-content fig-content-tab3"> <table class="table-group" id="tab3"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr class="thead"> <td align="left">作者(年代)</tgydF4y2Bad> <td align="center">雷诺数范围</tgydF4y2Bad> <td align="center"><span style="width: 20.0375px;"> <svg height="14.3375" id="M129" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 20.0375 14.3375" width="20.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr> <td align="left">席勒和Nauman</tgydF4y2Bad> <td align="center"><span style="width: 66.287498px;"> <svg height="16.6" id="M130" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 66.287498 16.6" width="66.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 162.27499px;"> <svg height="19.762501" id="M131" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 162.27499 19.762501" width="162.27499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.7625)"> <g transform="translate(72,-56.19)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="28.481834" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.92,57.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.14,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="34.945885" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="38.071636" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="44.323135" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="52.662636" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="61.002136" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,33.42,65.96)"> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 6</t年代pan> <tspan style="font-size: 8.75px; " x="10.94" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="15.316" y="0"> 7</t年代pan> </text> <text transform="matrix(1,0,0,-1,53.61,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">Lapple</tgydF4y2Bad> <td align="center"><span style="width: 74.112503px;"> <svg height="16.6" id="M132" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 74.112503 16.6" width="74.112503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 164.625px;"> <svg height="19.674999" id="M133" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 164.625 19.674999" width="164.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="28.481834" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.92,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.14,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="34.945885" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="38.071636" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="44.323135" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="50.574635" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="58.914135" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="67.253639" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,39.67,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 7</t年代pan> <tspan style="font-size: 8.75px; " x="10.94" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,55.48,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">朗缪尔,Blodgett</tgydF4y2Bad> <td align="center"><span style="width: 93.5px;"> <svg height="16.6" id="M134" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 93.5 16.6" width="93.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="30.094721" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.3,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.05,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.543388" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 287.71249px;"> <svg height="19.887501" id="M135" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 287.71249 19.887501" width="287.71249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8875)"> <g transform="translate(72,-56.09)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="28.481834" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.92,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.14,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="34.945885" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="38.071636" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="44.323135" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="50.574635" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="58.914135" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="67.253639" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,39.67,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 6</t年代pan> <tspan style="font-size: 8.75px; " x="10.94" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,58.26,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="20.71747" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="29.744637" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="40.522224" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="46.773724" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,111.3,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,124.25,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,138.14,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 3</t年代pan> <tspan style="font-size: 8.75px; " x="10.94" y="0"> 8</t年代pan> </text> <text transform="matrix(1,0,0,-1,153.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">艾伦</tgydF4y2Bad> <td align="center"><span style="width: 93.5px;"> <svg height="16.7875" id="M136" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 93.5 16.7875" width="93.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7875)"> <g transform="translate(72,-58.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="30.094721" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.3,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.05,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.543388" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 57.825001px;"> <svg height="19.674999" id="M137" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 57.825001 19.674999" width="57.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.47,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="12.804176" y="0"> 2</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">艾伦</tgydF4y2Bad> <td align="center"><span style="width: 101.3125px;"> <svg height="16.6" id="M138" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 101.3125 16.6" width="101.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="30.094721" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-36.3,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-28.05,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.543388" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="30.794889" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 68.449997px;"> <svg height="19.8125" id="M139" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 68.449997 19.8125" width="68.449997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="14.578498" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="22.917999" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-43.47,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 6</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="21.311119" y="0"> 5</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">吉尔伯特et al。</tgydF4y2Bad> <td align="center"><span style="width: 113.0375px;"> <svg height="16.6" id="M140" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 113.0375 16.6" width="113.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="19.092081" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="31.132469" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="39.47197" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.67,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 107.9875px;"> <svg height="19.8125" id="M141" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 107.9875 19.8125" width="107.9875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="15.62875" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="24.655916" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="42.247639" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="50.587139" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="58.92664" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-7.47,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> 5</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">Kurten et al。</tgydF4y2Bad> <td align="center"><span style="width: 113.0375px;"> <svg height="16.6" id="M142" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 113.0375 16.6" width="113.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="19.092081" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="31.132469" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="39.47197" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-26.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.67,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 149.91251px;"> <svg height="19.8125" id="M143" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 149.91251 19.8125" width="149.91251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="15.62875" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="24.655916" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="42.247639" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="45.723473" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="54.062973" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-12.33,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 5</t年代pan> </text> <text transform="matrix(1,0,0,-1,1.89,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="35.646053" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,43.1,57.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">亚伯拉罕</tgydF4y2Bad> <td align="center"><span style="width: 74.112503px;"> <svg height="16.725" id="M144" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 74.112503 16.725" width="74.112503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.725)"> <g transform="translate(72,-58.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="30.782387" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 154.1875px;"> <svg height="23.1" id="M145" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 154.1875 23.1" width="154.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.1)"> <g transform="translate(72,-53.52)"> <text transform="matrix(1,0,0,-1,-71.95,58.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="15.62875" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="21.880251" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="28.13175" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="34.383251" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="38.546749" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="47.573914" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="58.914135" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="65.165634" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="68.291389" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="74.542885" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="82.882385" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="91.221886" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,24.83,63.29)"> <tspan style="font-size: 8.75px; " x="0" y="8.1199999"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 5</t年代pan> </text> <text transform="matrix(1,0,0,-1,42.26,58.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,46.42,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">健康指标等。</tgydF4y2Bad> <td align="center"><span style="width: 64.574997px;"> <svg height="19.887501" id="M146" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 64.574997 19.887501" width="64.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8875)"> <g transform="translate(72,-56.09)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.27,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 180.3875px;"> <svg height="19.8125" id="M147" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 180.3875 19.8125" width="180.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="15.62875" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="24.655916" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="42.247639" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="45.373386" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="51.624886" y="0"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="57.876389" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="61.352222" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="69.691719" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,3.3,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 5</t年代pan> <tspan style="font-size: 8.75px; " x="10.94" y="0"> 7</t年代pan> <tspan style="font-size: 8.75px; " x="15.316" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,26.27,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="27.319056" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="35.658558" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,67.48,57.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">Rumpf</tgydF4y2Bad> <td align="center"><span style="width: 58.474998px;"> <svg height="16.6" id="M148" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 58.474998 16.6" width="58.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 68.900002px;"> <svg height="16.6" id="M149" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 68.900002 16.6" width="68.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="26.618887" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="32.870388" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="36.346222" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="44.685722" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">Rumpf</tgydF4y2Bad> <td align="center"><span style="width: 66.287498px;"> <svg height="16.6" id="M150" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 66.287498 16.6" width="66.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> 0</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 68.900002px;"> <svg height="16.6" id="M151" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 68.900002 16.6" width="68.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="26.618887" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="32.870388" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="36.346222" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="44.685722" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-21.71,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">Rumpf</tgydF4y2Bad> <td align="center"><span style="width: 64.574997px;"> <svg height="20.025" id="M152" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 64.574997 20.025" width="64.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.025)"> <g transform="translate(72,-55.98)"> <text transform="matrix(1,0,0,-1,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,57.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-25.27,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 80.625px;"> <svg height="16.7875" id="M153" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 80.625 16.7875" width="80.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7875)"> <g transform="translate(72,-58.57)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="18.404415" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.744637" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="42.247639" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="45.723473" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="54.062973" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-12.33,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">克利夫特和Gauvin</tgydF4y2Bad> <td align="center"><span style="width: 89.337502px;"> <svg height="20.025" id="M154" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 89.337502 20.025" width="89.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.025)"> <g transform="translate(72,-55.98)"> <text transform="matrix(1,0,0,-1,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,57.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="21.067554" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="31.84514" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="38.096642" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.46,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 371.16251px;"> <svg height="19.887501" id="M155" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 371.16251 19.887501" width="371.16251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8875)"> <g transform="translate(72,-56.09)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="28.481834" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-37.92,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-33.14,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="8.3269978" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="17.354164" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="34.945885" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="38.071636" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="44.323135" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="52.662636" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="61.002136" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,33.42,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 6</t年代pan> <tspan style="font-size: 8.75px; " x="10.94" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="15.316" y="0"> 7</t年代pan> </text> <text transform="matrix(1,0,0,-1,53.61,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="6.9391651" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="31.820135" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="38.071636" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="44.323135" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="47.798969" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="51.962467" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="60.989635" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="72.329857" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="78.581352" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="81.707108" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="87.958603" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="96.985771" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="107.77586" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="114.02736" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,173.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 4</t年代pan> </text> <text transform="matrix(1,0,0,-1,180.85,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,194.74,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> 6</t年代pan> </text> <text transform="matrix(1,0,0,-1,216.55,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">布劳尔</tgydF4y2Bad> <td align="center"><span style="width: 89.337502px;"> <svg height="20.025" id="M156" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 89.337502 20.025" width="89.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.025)"> <g transform="translate(72,-55.98)"> <text transform="matrix(1,0,0,-1,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,57.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="21.067554" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="31.84514" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="38.096642" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.46,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 142.10001px;"> <svg height="19.8125" id="M157" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 142.10001 19.8125" width="142.10001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.8125)"> <g transform="translate(72,-56.15)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="18.404415" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="29.744637" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="35.996136" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="39.47197" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="47.811474" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.58,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="6.5640001" y="0"> 5</t年代pan> </text> <text transform="matrix(1,0,0,-1,-4.36,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="17.579218" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="35.646053" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,36.85,57.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr> <td align="left">田中和Iinoya</tgydF4y2Bad> <td align="center"><span style="width: 89.337502px;"> <svg height="20.025" id="M158" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 89.337502 20.025" width="89.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.025)"> <g transform="translate(72,-55.98)"> <text transform="matrix(1,0,0,-1,-71.95,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,57.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-49.81,60.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="21.067554" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="31.84514" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="38.096642" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-5.46,65.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代pan> </text> </g> </g> </svg></span></td> <td align="center"><span style="width: 270.66251px;"> <svg height="19.674999" id="M159" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 270.66251 19.674999" width="270.66251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代pan> </text> <text transform="matrix(1,0,0,-1,-55.97,57.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,-44.64,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.653036" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="24.680922" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-13.67,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,-8.8,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,0.89,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,8.54,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,26.16,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,31.04,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.465491" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="23.805712" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,61.13,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,66,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="7.2892489" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="20.454908" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="32.482796" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="35.95863" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="42.210129" y="0"> g</t年代pan> </text> <text transform="matrix(1,0,0,-1,114.47,57.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,125.81,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,139.7,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg></span></td> </tr> <tr class="table-tr"> <td colspan="3"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 总结文献的阻力系数在不同雷诺数从断崖et al。(转载<一个href="#B56">56</一个>200年5年],版权许可多佛出版物,Inc .)</gydF4y2Badiv> </div> </div> <p>卡尔森的校正因子,霍格伦德(<一个href="#B45">45</一个>是类似于席勒和Nauman [<一个href="#B57">57</一个>),但与马赫数修正包括流压缩。常数也几乎与1/6取代0.15和0.687 2/3取代。更改进方程已经被王收集et al。<一个href="#B58">58</一个>)使用的工作(<一个href="#B36">36</一个>,<gydF4y2Ba一个href="#B45">45</一个>,<gydF4y2Ba一个href="#B52">53</一个>,<gydF4y2Ba一个href="#B59">59</一个>)占所有前面提到的修正因素:<年代pan class="equation" id="EEq24"> <svg height="55.612499" id="M160" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 55.612499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,55.6125)"> <g transform="translate(72,-27.51)"> <text transform="matrix(1,0,0,-1,86.08,42.87)"> <tspan style="font-size: 12.50px; " x="25.889999" y="-11.91"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="12.653036" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="31.74" y="-14.42"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="40.767166" y="-14.42"> +</t年代pan> <tspan style="font-size: 12.50px; " x="52.107388" y="-14.42"> (</t年代pan> <tspan style="font-size: 12.50px; " x="56.270885" y="-14.42"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="62.522385" y="-14.42"> /</t年代pan> <tspan style="font-size: 12.50px; " x="65.998222" y="-14.42"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="72.249718" y="-14.42"> )</t年代pan> <tspan style="font-size: 12.50px; " x="78.488716" y="-14.42"> R</t年代pan> <tspan style="font-size: 12.50px; " x="86.828217" y="-14.42"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,178.47,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="8.1300001"> </t年代pan> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,190.16,54.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="2.4100001"> </t年代pan> <tspan style="font-size: 12.50px; " x="15.3" y="-2.51"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="24.314663" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="35.667385" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.39,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 4</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> 2</t年代pan> <tspan style="font-size: 8.75px; " x="21.311119" y="0"> 7</t年代pan> <tspan style="font-size: 8.75px; " x="25.68712" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="28.120176" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,269.1,65.79)"> <tspan style="font-size: 6.25px; " x="-0.79000002" y="5.6900001"> </t年代pan> <tspan style="font-size: 6.25px; " x="0" y="0"> 4</t年代pan> <tspan style="font-size: 6.25px; " x="3.1259999" y="0"> 。</t年代pan> <tspan style="font-size: 6.25px; " x="4.6890001" y="0"> 6</t年代pan> <tspan style="font-size: 6.25px; " x="7.8150001" y="0"> 3</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.54,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> (</t年代pan> <tspan style="font-size: 8.75px; " x="8.9095364" y="0"> 3</t年代pan> <tspan style="font-size: 8.75px; " x="13.285536" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="15.718592" y="0"> R</t年代pan> <tspan style="font-size: 8.75px; " x="21.556175" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,305.98,65.79)"> <tspan style="font-size: 6.25px; " x="0" y="5.6900001"> </t年代pan> <tspan style="font-size: 6.25px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 6.25px; " x="3.1259999" y="0"> 。</t年代pan> <tspan style="font-size: 6.25px; " x="4.6890001" y="0"> 8</t年代pan> <tspan style="font-size: 6.25px; " x="7.8150001" y="0"> 8</t年代pan> </text> <text transform="matrix(1,0,0,-1,317.42,62.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,320.83,52.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 111.97,45.99 216.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,141.73,32.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.367388" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="29.894672" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,177.84,29.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,184.7,29.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8600001" y="-2.51"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="12.1115" y="-2.51"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="15.23725" y="-2.51"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="21.48875" y="-2.51"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="30.503412" y="-2.51"> +</t年代pan> <tspan style="font-size: 12.50px; " x="41.856136" y="-2.51"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="48.107635" y="-2.51"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="51.233387" y="-2.51"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="57.484886" y="-2.51"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="63.736385" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,254,37.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 8</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> 6</t年代pan> <tspan style="font-size: 8.75px; " x="21.311119" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="23.744177" y="0"> </t年代pan> <tspan style="font-size: 8.75px; " x="30.4132" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,288.77,34.84)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,292.82,29.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="36.810001" y="-13.09"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="175.05" y="-16.85"> (</t年代pan> <tspan style="font-size: 12.50px; " x="179.2135" y="-16.85"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="185.465" y="-16.85"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="191.71649" y="-16.85"> )</t年代pan> </text> </g> </g> </svg></span>席勒的校正和瑙曼(<一个href="#B57">57</一个>)已经被一些研究人员广泛使用,包括王et al。<一个href="#B60">60</一个>)矿和施瓦兹(<一个href="#B61">61年</一个>]它在垂直管道模型特点的相互作用。小王和Osiptsov<一个href="#B62">62年</一个>)使用校正卡尔森和霍格伦德(<一个href="#B45">45</一个>]在层流模型粒子的运动区域附近一堵墙在尘土飞扬的气体激波。</gydF4y2Bap> <h5 id="sec3.4">3.4。萨夫曼力</h5><gydF4y2Bap>首先指出了泊肃叶(<一个href="#B63">63年</一个>),血液细胞倾向于远离血管壁。塞格雷和Silberberg<一个href="#B64">64年</一个>)注意到球体在泊肃叶流动迁移到0.6从管的中心线半径。这种现象无法解释任何种类的斯托克斯力和/或粒子的惯性。旋转运动的粒子可能导致迁移中心线由于马格努斯效应,而不是远离中心线,因为流量剖面(<一个href="#B65">65年</一个>]。解释粒子的横向迁移萨夫曼[<一个href="#B36">36</一个>首先从理论上分析了简单的剪切流。这是确定,四个条件必须满足有一个明显的粒子的迁移:<年代vg height="13.45" id="M161" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>雷诺数很小的粒子,<年代vg height="13.45" id="M162" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>非常小的剪切颗粒雷诺数,<年代vg height="13.45" id="M163" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>之比的平方根的雷诺数粒子流体的雷诺数大于1,<年代vg height="13.45" id="M164" style="vertical-align:-2.21957pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代pan> </text> </g> </g> </svg>粒子的转动速度必须小(<一个href="#B36">36</一个>]。下面描述的四个条件:<年代pan class="equation" id="EEq25"> <svg height="101.4375" id="M165" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 101.4375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,101.4375)"> <g transform="translate(72,9.15)"> <text transform="matrix(1,0,0,-1,71.28,50.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,85.17,46.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,93.42,50.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-12.53"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-9.04"> |</t年代pan> <tspan style="font-size: 12.50px; " x="15.73" y="-10.78"> </t年代pan> <tspan style="font-size: 12.50px; " x="24.432089" y="-10.78"> −</t年代pan> <tspan style="font-size: 12.50px; " x="35.772308" y="-10.78"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,135.13,57.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,139.9,62.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="4.5900002" y="1.75"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.8415" y="1.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.118006" y="1.75"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,163.29,57.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 106.65,53.21 63.05,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,131.35,41.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,138.59,38.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,174.37,50.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≪</t年代pan> <tspan style="font-size: 12.50px; " x="15.12863" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="21.380131" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="46.511162" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="54.850662" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,234.78,46.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,244.66,50.08)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.24" y="-10.78"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,264.17,57.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,270.58,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.691505" y="0"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,291.43,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 257.9,53.21 38.41,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,270.28,41.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.52,38.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,299.59,62.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.66"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="21.33"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="24.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="3.8299999" y="5"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.219033" y="5"> </t年代pan> </text> <g> <path d="m 303.28,53.21 12.59,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,303.28,41.33)"> <tspan style="font-size: 12.50px; " x="13.79" y="-21"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.79" y="-10.34"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.79" y="0.33000001"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.79" y="3.49"> |</t年代pan> <tspan style="font-size: 12.50px; " x="-180.47" y="27.66"> √</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3890328" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.76" y="-8.75"> ≪</t年代pan> <tspan style="font-size: 12.50px; " x="34.901134" y="-8.75"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="41.152634" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="-203.23" y="36.91"> </t年代pan> <tspan style="font-size: 12.50px; " x="-193.70271" y="36.91"> =</t年代pan> </text> <g> <path d="m 134.41,25.42 20.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,134.41,15.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,148.3,12.33)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 122.81,7.54 31.9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,129.43,-4.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,143.32,-7.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,159.38,4.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≫</t年代pan> <tspan style="font-size: 12.50px; " x="15.12863" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="21.380131" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="46.523663" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="54.863163" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,219.8,1.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Ω</t年代pan> </text> <text transform="matrix(1,0,0,-1,230.28,4.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.74"> Ω</t年代pan> <tspan style="font-size: 12.50px; " x="22.532232" y="-10.74"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,259.09,12.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.87,15.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="10.4115" y="0.0099999998"> </t年代pan> <tspan style="font-size: 12.50px; " x="16.688005" y="0.0099999998"> )</t年代pan> </text> <text transform="matrix(1,0,0,-1,284.72,20.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <g> <path d="m 243.51,7.54 46.09,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,259.73,-4.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,266.97,-7.46)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,294.27,4.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≪</t年代pan> <tspan style="font-size: 12.50px; " x="15.12863" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="21.380131" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="173.60001" y="-23.879999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="177.7635" y="-23.879999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="184.015" y="-23.879999"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="190.26649" y="-23.879999"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.6875" id="M166" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>粒子的转动速度和吗<年代vg height="14.375" id="M167" style="vertical-align:-3.13504pt;width:26.25px;" version="1.1" viewbox="0 0 26.25 14.375" width="26.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>是粒子的旋转雷诺数。萨夫曼派生粒子上的力作用在一个简单的剪切流(层流)和进一步发展力的方程在泊肃叶流管。</gydF4y2Bap> <p>图萨夫曼力的方向作用于粒子的速度小于流体图中可以看到<一个href="//www.newsama.com/journals/jnt/2012/324380/fig8/" target="_blank">8</一个>。注意,粒子是被迫向增加速度。萨夫曼[<一个href="#B36">36</一个>)指定的力的方向增加滞后粒子速度和减少速度为主要的粒子。同时,粒子上的力作用增加增加流体速度梯度和流体速度相对于粒子。萨夫曼力的方向是验证的结果相比,奥利弗(<一个href="#B66">66年</一个>]。奥利弗发现沉降粒子向下流动的液体会迁移管的墙壁。相反,浮动粒子迁移对轴向下流动的液体。这种现象可以解释为萨夫曼力的影响。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.008" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.008.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 示意图说明萨夫曼力在剪切流的方向。</t一个ble> </div> </div> </div> <h5 id="sec3.5">3.5。萨夫曼力修正</h5><gydF4y2Bap>与斯托克斯力,萨夫曼力需要修正适用在许多情况下,如大雷诺数。一个方程模拟高雷诺数下的萨夫曼力是由美<一个href="#B59">59</一个>]。模型是基于工作由花花公子和德怀尔<一个href="#B67">67年</一个>)用一个三维的数值模拟模型线性剪切流过去一个小球体。指出剪力系数(萨夫曼力)雷诺数接近常数中间气体或气体的平方根成正比雷诺数颗粒雷诺数小于40所示:<年代pan class="equation" id="EEq26"> <svg height="84.787498" id="M168" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 84.787498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,84.7875)"> <g transform="translate(72,-4.17)"> <text transform="matrix(1,0,0,-1,66.11,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,74.5,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 61.73,57.7 23.84,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,61.73,45.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,70.12,42.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,76.32,42.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,90.24,54.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.04" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.889999" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="26.917166" y="0"> −</t年代pan> <tspan style="font-size: 12.50px; " x="38.257385" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="44.508888" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="47.634636" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="53.886135" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="60.137638" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="66.389137" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="72.64064" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,169.94,59.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,181.62,52.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,195.12,59.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> R</t年代pan> <tspan style="font-size: 8.75px; " x="11.832704" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,210.84,57.38)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,214.39,59.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="2.4330561" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,228.85,54.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="20.71747" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="26.968971" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="33.22047" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="39.47197" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="45.723473" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,281.63,59.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,293.32,54.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="15.166139" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="23.50564" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,322.38,51.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,330.63,54.57)"> <tspan style="font-size: 12.50px; " x="-210.75" y="29.209999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> ,</t年代pan> </text> <text transform="matrix(1,0,0,-1,128.27,22.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 115.51,19.35 23.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,115.51,7.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,123.9,4.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,130.09,4.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,144.01,16.22)"> <tspan style="font-size: 12.50px; " x="46.419998" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.417639" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="33.920639" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="40.172138" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="52.279999" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.319187" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="67.658691" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,217.23,13.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.01,13.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.86,23.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> /</t年代pan> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,239.54,16.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="15.166139" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="23.50564" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,268.6,13.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,276.86,16.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="191.00999" y="-18.74"> (</t年代pan> <tspan style="font-size: 12.50px; " x="195.17349" y="-18.74"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="201.425" y="-18.74"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="207.6765" y="-18.74"> )</t年代pan> </text> </g> </g> </svg></span>用于萨夫曼力的修正因素是升力系数,<年代vg height="14.3375" id="M169" style="vertical-align:-3.13504pt;width:18.975px;" version="1.1" viewbox="0 0 18.975 14.3375" width="18.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-63.56,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg><span class="equation" id="EEq27"> <svg height="39.099998" id="M170" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.099998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.1)"> <g transform="translate(72,-40.72)"> <text transform="matrix(1,0,0,-1,157.05,54.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,165.44,51.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,175.61,54.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="40.330002" y="-9.1400003"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,223.67,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 188.84,57.77 68.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,188.84,45.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代pan> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="13.890833" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="20.142332" y="0"> )</t年代pan> <tspan style="font-size: 12.50px; " x="26.38133" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,221.51,42.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.91,45.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.6018238" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,241.79,48.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,246.66,45.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,252.59,48.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,258.66,54.65)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="209.21001" y="1.42"> (</t年代pan> <tspan style="font-size: 12.50px; " x="213.3735" y="1.42"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="219.625" y="1.42"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="225.8765" y="1.42"> )</t年代pan> </text> </g> </g> </svg></span>和<年代vg height="7.1750002" id="M171" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>:<年代pan class="equation" id="EEq28"> <svg height="30.700001" id="M172" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.7)"> <g transform="translate(72,-47.44)"> <text transform="matrix(1,0,0,-1,177.45,56.25)"> <tspan style="font-size: 12.50px; " x="23.76" y="-7.25"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.527526" y="0"> =</t年代pan> </text> <g> <path d="m 201.21,59.37 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,201.21,47.49)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="7.4499998" y="-8.7600002"> R</t年代pan> <tspan style="font-size: 12.50px; " x="15.789501" y="-8.7600002"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,222.55,53.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,227.33,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,233.38,61.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,238.25,56.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="229.62" y="-0.34999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="233.78349" y="-0.34999999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="240.035" y="-0.34999999"> 8</t年代pan> <tspan style="font-size: 12.50px; " x="246.2865" y="-0.34999999"> )</t年代pan> </text> </g> </g> </svg></span>的校正(<一个href="#B59">59</一个>]在[<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B58">58</一个>,<gydF4y2Ba一个href="#B62">62年</一个>,<gydF4y2Ba一个href="#B68">68年</一个>可以进一步表示:<年代pan class="equation" id="EEq29"> <svg height="80.474998" id="M173" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 80.474998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,80.475)"> <g transform="translate(72,-7.62)"> <text transform="matrix(1,0,0,-1,55.77,36.69)"> <tspan style="font-size: 12.50px; " x="26.43" y="-20.200001"> ⎧</t年代pan> <tspan style="font-size: 12.50px; " x="26.43" y="-8.6800003"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="26.43" y="3.1900001"> ⎨</t年代pan> <tspan style="font-size: 12.50px; " x="26.43" y="15.07"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="26.43" y="26.530001"> ⎩</t年代pan> <tspan style="font-size: 12.50px; " x="81.32" y="-8.9899998"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.390953" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="34.43" y="-11.5"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="40.681499" y="-11.5"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="43.807251" y="-11.5"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="50.05875" y="-11.5"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="56.310249" y="-11.5"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="62.561749" y="-11.5"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="68.813248" y="-11.5"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="87.169998" y="-11.5"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="96.197166" y="-11.5"> −</t年代pan> <tspan style="font-size: 12.50px; " x="107.53738" y="-11.5"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,168.88,53.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="16.93512" y="0"> R</t年代pan> <tspan style="font-size: 8.75px; " x="22.772703" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,195.54,51)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,199.59,45.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="6.6300001"> </t年代pan> </text> <g> <path d="m 220.98,70.71 22.69,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,222.17,58.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,236.06,55.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 222.17,51.32 20.3,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,222.99,39.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,236.88,36.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,246.44,48.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,263.35,53.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代pan> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 0</t年代pan> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 。</t年代pan> <tspan style="font-size: 8.75px; " x="12.55912" y="0"> 1</t年代pan> </text> <text transform="matrix(1,0,0,-1,280.29,53.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 8.75px; " x="5.837584" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,290.01,51)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,294.06,48.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="9.1021843" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="17.441685" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,317.06,45.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,325.31,48.19)"> <tspan style="font-size: 12.50px; " x="-131.94" y="34.799999"> √</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-166.32001" y="33.02"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-160.0685" y="33.02"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="-156.94275" y="33.02"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-150.69125" y="33.02"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="-144.43974" y="33.02"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="-138.18825" y="33.02"> 1</t年代pan> </text> <g> <path d="m 204.98,25.15 20.29,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,204.98,15.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,218.87,12.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.27,15.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="77.900002" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="86.239502" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,317.06,12.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,325.31,15.17)"> <tspan style="font-size: 12.50px; " x="24.540001" y="-41.720001"> ⎫</t年代pan> <tspan style="font-size: 12.50px; " x="24.540001" y="-30.200001"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="24.540001" y="-18.33"> ⎬</t年代pan> <tspan style="font-size: 12.50px; " x="24.540001" y="-6.4499998"> ⎪</t年代pan> <tspan style="font-size: 12.50px; " x="24.540001" y="5.0700002"> ⎭</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="34.630001" y="-21.52"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="142.56" y="-21.52"> (</t年代pan> <tspan style="font-size: 12.50px; " x="146.7235" y="-21.52"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="152.97501" y="-21.52"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="159.2265" y="-21.52"> )</t年代pan> </text> </g> </g> </svg></span>萨夫曼力在哪里呢<年代pan class="equation" id="EEq30"> <svg height="39.599998" id="M174" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.599998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.6)"> <g transform="translate(72,-40.32)"> <text transform="matrix(1,0,0,-1,77.54,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,85.18,47.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,97.9,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="38.084137" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="48.999256" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.18,55.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,160.14,48.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.539585" y="-2.51"> −</t年代pan> <tspan style="font-size: 12.50px; " x="25.892309" y="-2.51"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,191.96,47.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,196.74,48.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.9299998" y="3"> </t年代pan> </text> <g> <path d="m 218.73,70.71 48.12,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,218.73,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225,47.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,231.41,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,238.65,47.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,247.14,57.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="10.67"> |</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="13.83"> |</t年代pan> <tspan style="font-size: 12.50px; " x="3.7" y="-0.33000001"> </t年代pan> <tspan style="font-size: 12.50px; " x="10.07653" y="-0.33000001"> </t年代pan> </text> <g> <path d="m 250.84,54.06 12.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,251.25,42.18)"> <tspan style="font-size: 12.50px; " x="13.1" y="-15.67"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.1" y="-5"> |</t年代pan> <tspan style="font-size: 12.50px; " x="13.1" y="-1.84"> |</t年代pan> <tspan style="font-size: 12.50px; " x="44.779999" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="17.68" y="-8.75"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="22.543667" y="-8.75"> 我</t年代pan> <tspan style="font-size: 12.50px; " x="26.019501" y="-8.75"> g</t年代pan> <tspan style="font-size: 12.50px; " x="32.271" y="-8.75"> n</t年代pan> <tspan style="font-size: 12.50px; " x="53.34" y="-16"> </t年代pan> <tspan style="font-size: 12.50px; " x="59.71653" y="-16"> </t年代pan> </text> <g> <path d="m 304.59,54.06 12.31,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,305,42.18)"> <tspan style="font-size: 12.50px; " x="13.1" y="-3.8299999"> </t年代pan> <tspan style="font-size: 12.50px; " x="22.780001" y="-8.75"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,333.33,47.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,338.17,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="129.7" y="-2.0999999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="133.86349" y="-2.0999999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="140.11501" y="-2.0999999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="146.3665" y="-2.0999999"> )</t年代pan> </text> </g> </g> </svg></span>麦克劳林调查萨夫曼力更高的雷诺数(校正<年代vg height="16.424999" id="M175" style="vertical-align:-4.77652pt;width:55.337502px;" version="1.1" viewbox="0 0 55.337502 16.424999" width="55.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.425)"> <g transform="translate(72,-58.86)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-58.06,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-51.65,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="13.540749" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-32.55,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>)(<一个href="#B69">69年</一个>)和报告的修正数据表时的情况<年代vg height="12.4875" id="M176" style="vertical-align:-1.29163pt;width:96.099998px;" version="1.1" viewbox="0 0 96.099998 12.4875" width="96.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4875)"> <g transform="translate(72,-62.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="15.62875" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="21.880251" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="31.595081" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="43.635471" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="53.162758" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="65.203148" y="0"> ∞</t年代pan> </text> </g> </g> </svg>(<年代vg height="20.4125" id="M177" style="vertical-align:-5.0342pt;width:94.637497px;" version="1.1" viewbox="0 0 94.637497 20.4125" width="94.637497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4125)"> <g transform="translate(72,-55.67)"> <text transform="matrix(1,0,0,-1,-71.95,60.74)"> <tspan style="font-size: 12.50px; " x="21.559999" y="1.78"> √</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5147829" y="0"> =</t年代pan> </text> <g> <path d="m -38.78,70.71 20.29,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-38.78,60.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-24.89,57.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-18.49,60.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代pan> <tspan style="font-size: 12.50px; " x="3.4758339" y="0"> R</t年代pan> <tspan style="font-size: 12.50px; " x="11.815335" y="0"> e</t年代pan> </text> <text transform="matrix(1,0,0,-1,-1.12,57.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>)。梅(<一个href="#B59">59</一个>)进一步分析了麦克劳克林表格数据的范围<年代vg height="12.3" id="M178" style="vertical-align:-1.29163pt;width:81.625px;" version="1.1" viewbox="0 0 81.625 12.3" width="81.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="19.092081" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="31.132469" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="40.659756" y="0"> ≤</t年代pan> <tspan style="font-size: 12.50px; " x="52.700146" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="58.951645" y="0"> 0</t年代pan> </text> </g> </g> </svg>建议使用以下功能以适应修正数据:<年代pan class="equation" id="EEq31"> <svg height="63.6875" id="M179" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 63.6875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,63.6875)"> <g transform="translate(72,-21.05)"> <text transform="matrix(1,0,0,-1,74.35,63.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,82.74,60.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 69.98,57.7 23.83,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,69.98,45.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,78.37,42.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,84.56,42.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 8.75px; " x="4.8661122" y="0"> 一个</t年代pan> </text> <text transform="matrix(1,0,0,-1,98.48,54.57)"> <tspan style="font-size: 12.50px; " x="90.889999" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="139.67" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="12.728054" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="18.979553" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="22.105305" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="28.356804" y="0"> 4</t年代pan> <tspan style="font-size: 12.50px; " x="34.608303" y="0"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="43.635471" y="0"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="54.413055" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="60.664555" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="63.790306" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="70.041809" y="0"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="76.293304" y="0"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="82.544807" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="95.68" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="104.70717" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="116.04739" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="119.52322" y="0"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="125.07455" y="0"> n</t年代pan> <tspan style="font-size: 12.50px; " x="131.32605" y="0"> h</t年代pan> <tspan style="font-size: 12.50px; " x="145.52" y="0"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="151.7715" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="154.89725" y="0"> 5</t年代pan> <tspan style="font-size: 12.50px; " x="161.14874" y="0"> l</t年代pan> <tspan style="font-size: 12.50px; " x="164.62459" y="0"> o</t年代pan> <tspan style="font-size: 12.50px; " x="170.87608" y="0"> g</t年代pan> </text> <text transform="matrix(1,0,0,-1,279.78,51.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代pan> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代pan> </text> <text transform="matrix(1,0,0,-1,289.03,54.57)"> <tspan style="font-size: 12.50px; " x="-90.300003" y="29.76"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-27.42" y="29.76"> ]</t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="8.8146152" y="0"> +</t年代pan> <tspan style="font-size: 12.50px; " x="20.167339" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="26.418839" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="29.544588" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="35.796089" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="42.047588" y="0"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="48.299999" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="54.151405" y="2.51"> </t年代pan> <tspan style="font-size: 12.50px; " x="-175.03999" y="29.719999"> ×</t年代pan> <tspan style="font-size: 12.50px; " x="-162.17441" y="29.719999"> {</t年代pan> <tspan style="font-size: 12.50px; " x="-156.17297" y="29.719999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-149.92148" y="29.719999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="-146.79573" y="29.719999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="-140.54422" y="29.719999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="-134.29272" y="29.719999"> 7</t年代pan> <tspan style="font-size: 12.50px; " x="-125.26556" y="29.719999"> +</t年代pan> <tspan style="font-size: 12.50px; " x="-113.92534" y="29.719999"> t</t年代pan> <tspan style="font-size: 12.50px; " x="-110.4495" y="29.719999"> 一个</t年代pan> <tspan style="font-size: 12.50px; " x="-104.89817" y="29.719999"> n</t年代pan> <tspan style="font-size: 12.50px; " x="-98.646667" y="29.719999"> h</t年代pan> <tspan style="font-size: 12.50px; " x="-86.139999" y="29.719999"> 6</t年代pan> <tspan style="font-size: 12.50px; " x="-77.813004" y="29.719999"> (</t年代pan> <tspan style="font-size: 12.50px; " x="-73.649506" y="29.719999"> </t年代pan> <tspan style="font-size: 12.50px; " x="-64.822388" y="29.719999"> −</t年代pan> <tspan style="font-size: 12.50px; " x="-53.469662" y="29.719999"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="-47.218163" y="29.719999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="-44.092411" y="29.719999"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="-37.840912" y="29.719999"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="-31.589411" y="29.719999"> )</t年代pan> <tspan style="font-size: 12.50px; " x="-23.26" y="29.709999"> }</t年代pan> <tspan style="font-size: 12.50px; " x="-15.183062" y="29.709999"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="178.84" y="11.17"> (</t年代pan> <tspan style="font-size: 12.50px; " x="183.00349" y="11.17"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="189.255" y="11.17"> 1</t年代pan> <tspan style="font-size: 12.50px; " x="195.5065" y="11.17"> )</t年代pan> </text> </g> </g> </svg></span></p> <p>比较萨夫曼力和梅提出的修正因素<一个href="#B59">59</一个>),连同工作麦克劳克林(<一个href="#B69">69年</一个>),可以看到在图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig9/" target="_blank">9</一个>。注意,整个重对数坐标图萨夫曼力是线性的。梅的校正因子接近萨夫曼小雷诺数。雷诺数大于约5后,离开萨夫曼力的相关性。使用美相关的能力允许更大的雷诺数萨夫曼力。事实上,雷诺兹数高达1000 - 1100已使用(<一个href="#B70">70年</一个>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig9"> <div class="floats-partial-content fig-content-fig9"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.009" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.009.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B59">59</一个><一个href="#B69">69年</一个><一个href="#B36">36</一个><一个href="#B59">59</一个><t一个ble> 图剪切系数与雷诺数的分析的基础上,梅(),gydF4y2Ba麦克劳克林(),gydF4y2Ba萨夫曼[gydF4y2Ba从梅),转载gydF4y2Ba从爱思唯尔),1992年版权许可。</t一个ble> </div> </div> </div> <h4 id="theoretical-application-of-forces">4所示。力的理论应用</h4><h5gydF4y2Baid="sec4.1">4.1。斯托克斯力</h5><gydF4y2Bap>气溶胶聚焦一直得到广泛的研究与雷诺数很大的超音速飞机。程提供的研究和Dahneke [<一个href="#B71">71年</一个>),Dahneke et al。<一个href="#B53">54</一个>],和Fernandez de la Mora Riesco-Chueca [<一个href="#B40">40</一个>]。正是由这些实验者认为粒子集中发生严格由于惯性效应和斯托克斯力,其中一个会推断萨夫曼力不适用。</gydF4y2Bap> <p>Fernandez De La Mora和Riesco-Chueca<一个href="#B40">40</一个>,<gydF4y2Ba一个href="#B72">72年</一个>]发现粒子的主要依赖的斯托克斯数与粒子与流体的耦合量的特点,<年代vg height="12.725" id="M180" style="vertical-align:-4.74141pt;width:14.3125px;" version="1.1" viewbox="0 0 14.3125 12.725" width="14.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.725)"> <g transform="translate(72,-61.82)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.42,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,除以一个特征长度,<年代vg height="10.725" id="M181" style="vertical-align:-3.13504pt;width:15.4px;" version="1.1" viewbox="0 0 15.4 10.725" width="15.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.42,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>:<年代pan class="equation" id="EEq32"> <svg height="44.087502" id="M182" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.087502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,44.0875)"> <g transform="translate(72,-36.73)"> <text transform="matrix(1,0,0,-1,113.5,50.29)"> <tspan style="font-size: 12.50px; " x="27.43" y="-10.74"> </t年代pan> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="6.8266382" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="13.7533" y="0"> =</t年代pan> </text> <text transform="matrix(1,0,0,-1,146.46,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 140.5,53.42 12.22,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,140.5,41.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,146.02,38.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,153.91,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,184.57,47.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,193.88,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.23" y="-10.74"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="19.481501" y="-10.74"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.64,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,224.51,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,230.79,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 207.11,53.42 28.46,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,209.31,41.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,222.8,38.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,236.76,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="25.131029" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,267.42,47.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,277.59,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="13.9" y="-7.25"> </t年代pan> </text> <g> <path d="m 290.82,53.42 10.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,290.82,41.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="11.39" y="-8.75"> ,</t年代pan> <tspan style="font-size: 12.50px; " x="177.05" y="-9.6999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="181.2135" y="-9.6999998"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="187.465" y="-9.6999998"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="193.71649" y="-9.6999998"> )</t年代pan> </text> </g> </g> </svg></span>在哪里<年代vg height="10.325" id="M183" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>是流体特征长度尺度,斯托克斯数计算如下:<年代pan class="equation" id="EEq33"> <svg height="44.087502" id="M184" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.087502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,44.0875)"> <g transform="translate(72,-36.73)"> <text transform="matrix(1,0,0,-1,174.44,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代pan> <tspan style="font-size: 12.50px; " x="6.8141351" y="0"> t</t年代pan> <tspan style="font-size: 12.50px; " x="13.7533" y="0"> =</t年代pan> <tspan style="font-size: 12.50px; " x="26.99" y="-10.74"> 2</t年代pan> <tspan style="font-size: 12.50px; " x="33.241501" y="-10.74"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,213.96,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,218.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,225.01,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代pan> </text> <text transform="matrix(1,0,0,-1,229.89,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <g> <path d="m 201.43,53.42 38.65,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,206.38,41.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 9</t年代pan> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,219.87,38.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,226.28,41.54)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="14.99" y="-8.75"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="241.59" y="-9.6999998"> (</t年代pan> <tspan style="font-size: 12.50px; " x="245.75349" y="-9.6999998"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="252.005" y="-9.6999998"> 3</t年代pan> <tspan style="font-size: 12.50px; " x="258.2565" y="-9.6999998"> )</t年代pan> </text> </g> </g> </svg></span>应该注意的是,较大的斯托克斯数与粒子具有更少的倾向于遵循流。它被发现(以色列和弗里德兰德(<一个href="#B73">73年</一个>)、以色列和重击(<一个href="#B74">74年</一个>],年代toffels [<一个href="#B75">75年</一个>),年代我nh一个et一个l。<一个href="#B76">76年</一个>),埃斯蒂斯et al。<一个href="#B77">77年</一个>),Kievit et al。<一个href="#B78">78年</一个>),Reent年代et一个l。<一个href="#B79">79年</一个>),米一个ll我n一个et一个l。<一个href="#B47">47</一个>),和李,王<一个href="#B41">41</一个>]),聚焦粒子的喷嘴主要由斯托克斯数与Fernandez De La Mora在协议和Riesco-Chueca<一个href="#B40">40</一个>,<gydF4y2Ba一个href="#B72">72年</一个>]。焦点距离喷嘴的出口,<年代vg height="12.975" id="M185" style="vertical-align:-4.77652pt;width:16.725px;" version="1.1" viewbox="0 0 16.725 12.975" width="16.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,见图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig10/" target="_blank">10</一个>取决于斯托克斯数和初始的径向位置,<年代vg height="11.05" id="M186" style="vertical-align:-3.2316pt;width:12.1375px;" version="1.1" viewbox="0 0 12.1375 11.05" width="12.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>(<一个href="#B80">80年</一个>]。焦点走向无穷斯托克斯数达到临界斯托克斯数<年代vg height="11.775" id="M187" style="vertical-align:-0.1254pt;width:17.725px;" version="1.1" viewbox="0 0 17.725 11.775" width="17.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.775)"> <g transform="translate(72,-62.58)"> <text transform="matrix(1,0,0,-1,-71.95,62.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.95,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代pan> </text> </g> </g> </svg>(大约1)。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig10"> <div class="floats-partial-content fig-content-fig10"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0010" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0010.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图10</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="11.05" id="M188" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 12.1375 11.05" width="12.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <svg height="12.975" id="M189" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 16.725 12.975" width="16.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <a href="#B40">40</一个><t一个ble> 图初始种子颗粒的半径,,gydF4y2Ba退出喷嘴和集中在远处,gydF4y2Ba后,从喷嘴((])gydF4y2Ba。</t一个ble> </div> </div> </div> <p>Rao et al。<一个href="#B80">80年</一个>]他的实验进行中等雷诺数(3 - 1000)和注意到聚焦效应在粘性流动下政权实际上可能比那些潜在的流动。这种理解是只有斯托克斯力作用在粒子上。Mallina et al。<一个href="#B47">47</一个>)描述的集中机制适用于喷嘴和毛细血管聚焦可以预测的斯托克斯数,坎宁安校正系数。气溶胶主要通过一个喷嘴的图500<年代vg height="9.6750002" id="M190" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径的图中可以看到<一个href="//www.newsama.com/journals/jnt/2012/324380/fig11/" target="_blank">11</一个>。注意,大粒子集中在喷嘴距离增加,直到一个临界直径,聚焦不再发生。在这种情况下,所有粒子被播种在0.1<年代vg height="14.3625" id="M191" style="vertical-align:-3.2316pt;width:17.325001px;" version="1.1" viewbox="0 0 17.325001 14.3625" width="17.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>,在那里<年代vg height="14.3625" id="M192" style="vertical-align:-3.2316pt;width:17.325001px;" version="1.1" viewbox="0 0 17.325001 14.3625" width="17.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>毛细管的初始半径。一个类似的实验做了500年的毛细管<年代vg height="9.6750002" id="M193" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径,由程和Dahneke[32厘米长<一个href="#B71">71年</一个>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig11"> <div class="floats-partial-content fig-content-fig11"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0011" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0011.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图11</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="9.6750002" id="M194" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <svg height="9.6750002" id="M195" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <a href="#B47">47</一个><t一个ble> -40年7.5轨迹图gydF4y2Ba退出500米直径粒子gydF4y2Bam喷嘴,转载来自Mallina et al。gydF4y2Ba从爱思唯尔),1999年版权许可。</t一个ble> </div> </div> </div> <p>刘等人。<一个href="#B81">81年</一个>,<gydF4y2Ba一个href="#B82">82年</一个>),Di Fonzo et al。<一个href="#B83">83年</一个>),小王和McMurry [<一个href="#B84">84年</一个>),和其他几个设计气动透镜系统校准气溶胶梁使用一系列的薄板。许多系统被设计用于低压和粒子在纳米范围内。建模的气溶胶粒子是只使用斯托克斯力,发现连续近似只适用于<年代vg height="11.0625" id="M196" style="vertical-align:-0.30096pt;width:58.724998px;" version="1.1" viewbox="0 0 58.724998 11.0625" width="58.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="9.5272856" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="19.204609" y="0"> <</t年代pan> <tspan style="font-size: 12.50px; " x="31.244997" y="0"> 0</t年代pan> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> 。</t年代pan> <tspan style="font-size: 12.50px; " x="40.622246" y="0"> 1</t年代pan> </text> </g> </g> </svg>。小王和McMurry<一个href="#B84">84年</一个>)后设计了一个计算机程序决定正确的参数一个气动透镜系统。参数,如流量、压力、直径的镜头,镜头之间的间距优化提供一个平行气溶胶的多分散的粒子。程序使用价值流动的数值模拟得到的气溶胶粒子通过透镜系统。图的一个例子如图透镜系统<一个href="//www.newsama.com/journals/jnt/2012/324380/fig12/" target="_blank">12</一个>。典型值的流量、压力、喷嘴之间的长度,和喷嘴直径是100 sccm, 93 - 600 Pa, 10 - 20毫米,1.26 - -3.2毫米,分别。通常有3 - 5镜头,但多达10常用。粒子大小范围从3到250海里,但是粒子一样大3<年代vg height="9.6750002" id="M197" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米已经被其他人(用于透镜系统<一个href="#B84">84年</一个>,<gydF4y2Ba一个href="#B85">85年</一个>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig12"> <div class="floats-partial-content fig-content-fig12"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0012" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0012.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图12</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig12/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B85">85年</一个><t一个ble> 气动透镜聚焦气溶胶粒子系统的示意图(尺寸在毫米),从王et al。)gydF4y2Ba、气溶胶科学技术、版权2005年,山月桂,新泽西。允许转载。</t一个ble> </div> </div> </div> <p>Rao et al。<一个href="#B80">80年</一个>)注意到,聚焦粒子的减少是由于“几何畸变效应。”的效果是由粒子被播种到喷嘴在不同的半径。沿着轴粒子集中在不同的位置,导致沉闷的焦点。主要是提高了播种的气溶胶粒子接近轴清洁空气鞘气体。饶的实验中,50%的鞘气体被用来帮助实现不到2%的喷嘴直径的焦点。这些结果来完成一个薄板喷嘴直径1毫米的。Renn et al。<一个href="#B86">88年</一个>)建模的聚焦气溶胶粒子通过一个100<年代vg height="9.6750002" id="M198" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m喷嘴与变量鞘气体只使用斯托克斯力和粒子的惯性。他们建议气溶胶粒子的主要是依赖于粒子的斯托克斯数。粒子斯托克斯数高,在这种情况下,粒子在1<年代vg height="9.6750002" id="M199" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径较大,收敛和衬底上沉积。颗粒小于1<年代vg height="9.6750002" id="M200" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径按照流流线和不会沉积在衬底。充分的证据表明集中机制缺少来自Renn et al。<一个href="#B16">16</一个>),气溶胶粒子退出100年的波束宽度<年代vg height="9.6750002" id="M201" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>喷嘴与模拟。在这种情况下,实际聚焦比预计更好的聚焦粒子束聚焦于渲染小于喷嘴直径(<一个href="#B4">4</一个>]。</gydF4y2Bap> <h5 id="sec4.2">4.2。萨夫曼力</h5><gydF4y2Bap>大多数研究使用萨夫曼力是应用程序的粒子在平板或长毛细管流动。然而我们有包括萨夫曼力建模的气溶胶主要为直写应用程序(<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B68">68年</一个>]。Lipatov et al。<一个href="#B70">70年</一个>,<gydF4y2Ba一个href="#B87">89年</一个>]描述了奥利弗的情况相似<一个href="#B66">66年</一个>),发现重粒子在降液管将迁移到墙上。在上升气流条件相反的发生,对管轴粒子迁移。Lipatov et al。<一个href="#B87">89年</一个>)实验验证萨夫曼力的影响在风洞中使用管道。管道直径范围从3 - 10毫米,10 - 25厘米长。单分散的<我>石松属植物</我>孢子的半径16<年代vg height="9.6750002" id="M202" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m是用作气溶胶粒子。流速度范围从0.4到1.5 m / s。粒子沉积系数向下流和上升气流<年代vg height="14.375" id="M203" style="vertical-align:-3.24037pt;width:16.512501px;" version="1.1" viewbox="0 0 16.512501 14.375" width="16.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="14.3375" id="M204" style="vertical-align:-3.21404pt;width:15.2125px;" version="1.1" viewbox="0 0 15.2125 14.3375" width="15.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>分别计算实验和分析使用萨夫曼力。结果发现,<年代vg height="14.375" id="M205" style="vertical-align:-3.24037pt;width:16.512501px;" version="1.1" viewbox="0 0 16.512501 14.375" width="16.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>从15 - 30%,而不等<年代vg height="14.3375" id="M206" style="vertical-align:-3.21404pt;width:15.2125px;" version="1.1" viewbox="0 0 15.2125 14.3375" width="15.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>小于3。大的异常<年代vg height="14.375" id="M207" style="vertical-align:-3.24037pt;width:16.512501px;" version="1.1" viewbox="0 0 16.512501 14.375" width="16.512501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>和<年代vg height="14.3375" id="M208" style="vertical-align:-3.21404pt;width:15.2125px;" version="1.1" viewbox="0 0 15.2125 14.3375" width="15.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>与萨夫曼力解释道。</gydF4y2Bap> <p>尘埃颗粒在层流区域模型在煤矿激波后,小王和Osiptsov [<一个href="#B62">62年</一个>和王et al。<一个href="#B58">58</一个>)包括斯托克斯和萨夫曼部队。结果表明,马格努斯效应并不相关的在这种情况下,因为附近的粒子的角速度相同的数量级的速度方向垂直于墙上。萨夫曼力计算与梅等使用的校正因子。<一个href="#B59">59</一个>在方程(<一个href="#EEq26">26</一个>)。斯托克斯力计算使用(<一个href="#EEq22">22</一个>)。注意到,一个粒子的横向迁移从一堵墙离墙局部累积造成的。用拉格朗日方法确定速度(<一个href="#B58">58</一个>,<gydF4y2Ba一个href="#B62">62年</一个>)和双向耦合粒子的流体在高颗粒浓度在<一个href="#B58">58</一个>]。黄(<一个href="#B88">90年</一个>)使用萨夫曼力在类似的情况下与一个弱激波灰尘沉积。决定,在激波后,速度梯度和随后的力量作用于尘埃粒子垂直于速度梯度。</gydF4y2Bap> <p>使用计算流体动力学(CFD)数值计算程序,考虑萨夫曼力,研究了矿和施瓦兹(<一个href="#B61">61年</一个>]和El-Batsh [<一个href="#B89">91年</一个>]。矿和施瓦兹<一个href="#B61">61年</一个>]研究了煤尘的40 - 80<年代vg height="9.6750002" id="M209" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米平均直径在垂直管道用于燃煤电厂。使用拉格朗日粒子跟踪完成的方法。El-Batsh [<一个href="#B89">91年</一个>)使用萨夫曼力墙附近的交互模型的气溶胶粒子湍流的涡轮级联。巴顿(<一个href="#B90">92年</一个>)使用萨夫曼力模型,开发了一种四阶龙格-库塔方法求解运动方程的颗粒流在一个“面向后方的一步。“模型包括斯托克斯阻力、重力、虚拟质量,压力,和巴塞特力(历史积分)。这是确定粒子沿着流线低斯托克斯数和打捞筒的流线更高的斯托克斯数萨夫曼力增加的影响随着粒子斯托克斯数的增加由于越来越相对速度(滞后)的粒子。</gydF4y2Bap> <p>有文献描述了建模的气溶胶粒子喷嘴(微细管)使用变化的斯托克斯力和粒子惯性没有萨夫曼de la Mora等(<一个href="#B40">40</一个>,<gydF4y2Ba一个href="#B41">41</一个>,<gydF4y2Ba一个href="#B47">47</一个>,<gydF4y2Ba一个href="#B84">84年</一个>,<gydF4y2Ba一个href="#B86">88年</一个>]。萨夫曼力主要使用在无界的墙壁和王长管或毛细血管和梅<一个href="#B58">58</一个>,<gydF4y2Ba一个href="#B59">59</一个>,<gydF4y2Ba一个href="#B62">62年</一个>例如,]。包含萨夫曼力集中的气溶胶粒子通过一个喷嘴可能需要更完整的模型我们已经描述了在<一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B68">68年</一个>];斯托克斯力、萨夫曼力和粒子的惯性被要求描述气溶胶粒子的聚焦来自微细管。</gydF4y2Bap> <h4 id="experimental-validation-of-aerosol-physics">5。气溶胶物理实验验证</h4><gydF4y2Bap>悬浮颗粒的流体质点的相互作用的理论建模是一个宝贵的工具在预测气溶胶粒子的聚焦。模型的准确性和随后的预测必须由实验观察验证之前的完整理解气溶胶的物理,和随后的改进在dw技术实现。很多工作是发表在量化的方法间接气溶胶主要通过测量衬底上沉积的宽度。Rao et al。<一个href="#B80">80年</一个>)和Mallina et al。<一个href="#B47">47</一个>),例如使用一个醉的衬底来捕获气溶胶粒子和波束宽度近似。Fuerstenau et al。<一个href="#B72">72年</一个>)和Akhatov et al。<一个href="#B68">68年</一个>)直接测量气溶胶的散射光成像波束宽度的气溶胶粒子退出一个孔和喷嘴,分别。就像把线放在抹油的盘子,从分散梁获得图像创建一个直方图,鉴于气溶胶粒子的位置,单个粒子轨迹信息,如何对这些粒子集中发生不直接。粒子图像测速仪(PIV)使用播种气溶胶粒子的散射激光表通常用于确定流体流场的轨迹在宏观尺度的维度,但此外不是为个人气溶胶粒子的跟踪和微尺度极难实现。</gydF4y2Bap> <p>最近,我们实现了一个皮影戏的方法来确定单个粒子的轨迹集中由一个喷嘴(<一个href="#B91">86年</一个>]。皮影戏的PIV系统选项可以从洛杉矶愿景inc .)被用来测量气溶胶粒子退出一个线性收敛喷管。系统的示意图如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig13/" target="_blank">13</一个>。照明是由一对Nd: YAG脉冲激光器,送入染料激光器,液体纤维指南,和菲涅耳透镜。气溶胶流放置相机和光源之间产生一个阴影在相机上。对校准和以前的结果与散射光相比,连续波激光器也纳入该系统。这个系统是有利的,它可以测量粒子的位置,速度,同时和大小。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig13"> <div class="floats-partial-content fig-content-fig13"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0013" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0013.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图13</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig13/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B91">86年</一个><t一个ble> 皮影戏气溶胶粒子的测量系统的示意图,从Mahmud et al。20。10gydF4y2BaASME)、版权。允许转载。</t一个ble> </div> </div> </div> <p>这些测量数据所示的结果<一个href="//www.newsama.com/journals/jnt/2012/324380/fig14/" target="_blank">(14日)</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jnt/2012/324380/fig14/" target="_blank">14 (b)</一个>,<gydF4y2Ba一个href="//www.newsama.com/journals/jnt/2012/324380/fig14/" target="_blank">14 (c)</一个>(一)粒度分布,(b)平均水平,至少和最大粒子从喷嘴出口速度和距离,和(c)波束宽度从光散射和粒子数从皮影戏和径向位置显示(焦点)。在这种情况下,粒度分布从一个超声雾化器大约是2.5<我>μ</gydF4y2Ba我>米直径,在假设范围内0.5到5的建模<我>μ</gydF4y2Ba我>米。粒子速度增加到约1毫米显示远离喷嘴。这些结果与理论建模,在协议之外的地方集中粒子速度增加喷嘴,后来降低了。最后,气溶胶粒子的波束宽度测量连续波激光器和皮影戏是非常相似的。这些测量结果显示皮影戏的有效性方法描述气溶胶流退出粒度的喷嘴,速度,和分布。未来的结果将允许更多的流体质点细化部队给予更准确的模型预测气溶胶聚焦(<一个href="#B91">86年</一个>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig14"> <div class="floats-partial-content fig-content-fig14"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”324380。fig.0014a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0014a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”324380。fig.0014b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0014b.jpg"> <br> <strong>(b)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(c)”n一个米e=”324380。fig.0014c" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0014c.jpg"> <br> <strong>(c)</年代trong></div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig14"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”324380。fig.0014a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0014a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”324380。fig.0014b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0014b.jpg"><br><strong>(b)</年代trong></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)”n一个米e=”324380。fig.0014c" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0014c.jpg"><br><strong>(c)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig14"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图14</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig14/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B91">86年</一个><t一个ble> 皮影戏结果显示(a)直方图的粒子大小、粒子(b)从喷嘴出口速度和距离,以及(c)从shadowgraphy连续波激光波束宽度和粒子数和径向位置(重点),从Mahmud et al。20。10gydF4y2BaASME)、版权。允许转载。</t一个ble> </div> </div> </div> <h4 id="aerosol-direct-write-applications">6。气溶胶直写应用程序</h4><gydF4y2Bap>仍然dw技术成熟,这些电子产品的应用尚未完全建立。然而,有丰富的设备与一个例子在文学dw打印所有组件。打印使用无触点的能力,快速原型工具尤其有利于科技的发展阶段,与面具相关的时间和成本的限制因素。此外,非接触高宽高比特征可能会对一些印有dw证明有用的在特定的利基市场,如太阳能电池。所有dw技术能够连续印刷痕迹可能是顺从的互联和通过简单的电路。示例应用程序的dw相当普遍,使用dw的优点(气溶胶喷射专门)所描述的国王和Renn [<一个href="#B92">87年</一个>)如下:首先,减少产品开发时间由于无掩模的方法;其次,降低成本与掩码设置初始小生产运行;第三,提高材料利用率,降低了成本,更环保。他们还描述一个特定的应用程序3 d互联的大型对峙距离可以打印痕迹在对象(如氧化铝立方体如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig15/" target="_blank">15</一个>。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig15"> <div class="floats-partial-content fig-content-fig15"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0015" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0015.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图15</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig15/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="9.6750002" id="M210" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <a href="#B92">87年</一个><t一个ble> 气溶胶喷射印花Ag)的痕迹,150年gydF4y2Ba米宽,氧化铝的多维数据集,从国王和Renn [),2009gydF4y2BaOptomec版权。允许转载。</t一个ble> </div> </div> </div> <p>MCS可以印刷的痕迹从固体气溶胶的锡、铝和铜在各种困难和灵活的基质。形成连续的线条既取决于衬底材料以及固体颗粒沉积。表<一个href="//www.newsama.com/journals/jnt/2012/324380/tab4/" target="_blank">4</一个>显示一个列表的基质(+)或(−)指定是否一个特定的固体金属气溶胶连续线。电特性测量对铜准备使用100痕迹<年代vg height="9.6750002" id="M211" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>400聚焦喷嘴,ccm载气(气溶胶)流,<年代vg height="5.7874999" id="M212" style="vertical-align:-0.0pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 5.7874999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,5.7875)"> <g transform="translate(72,-67.37)"> <text transform="matrix(1,0,0,-1,-71.95,67.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</t年代pan> </text> </g> </g> </svg>0.75 MPa加速器(鞘)气体压力,距离0.5毫米对峙,1毫米/秒翻译速度(更大的速度可能)。这些痕迹<年代vg height="5.7874999" id="M213" style="vertical-align:-0.0pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 5.7874999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,5.7875)"> <g transform="translate(72,-67.37)"> <text transform="matrix(1,0,0,-1,-71.95,67.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</t年代pan> </text> </g> </g> </svg>50<年代vg height="9.6750002" id="M214" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽(图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig16/" target="_blank">16</一个>)和电阻率是1.9<年代vg height="13.55" id="M215" style="vertical-align:-2.29482pt;width:21.275px;" version="1.1" viewbox="0 0 21.275 13.55" width="21.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.6018238" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米。除了金属痕迹,填补从75年通过的能力<年代vg height="9.6750002" id="M216" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m - 150<年代vg height="9.6750002" id="M217" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米直径与金属展示,创造的可能性,包括跟踪沉积和通过填充到一个过程。</gydF4y2Bap> <div class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-content fig-content-tab4"> <table class="table-group" id="tab4"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr class="thead"> <td align="left">底物</tgydF4y2Bad> <td align="center">锡</tgydF4y2Bad> <td align="center">铝</tgydF4y2Bad> <td align="center">铜</tgydF4y2Bad> </tr> <tr> <td class="thead-hr" colspan="4"> <hr></td> </tr> <tr> <td align="left">玻璃</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">硅</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">英国电信<年代up>1</年代up></td> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> </tr> <tr> <td align="left">偷看<年代up>2</年代up></td> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">聚酰亚胺薄膜</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> </tr> <tr> <td align="left">聚四氟乙烯</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">PES<年代up>3</年代up></td> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">连结控制协定<年代up>4</年代up></td> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">Teslin</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr> <td align="left">FR4<年代up>5</年代up></td> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> </tr> <tr> <td align="left">聚酯薄膜</tgydF4y2Bad> <td align="center">−</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> <td align="center">+</tgydF4y2Bad> </tr> <tr class="table-tr"> <td colspan="4"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> <tr class="table-fn"> <td><sup>1</年代up>玻璃纤维加强了bt树脂环氧树脂。<gydF4y2Babr><sup>2</年代up>聚醚醚酮。<gydF4y2Babr><sup>3</年代up>Polyethersulfone。<gydF4y2Babr><sup>4</年代up>液晶聚合物。<gydF4y2Babr><sup>5</年代up>玻璃增强环氧层压板。<gydF4y2Babr></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> MCS material-substrate兼容性,从巴塔查里亚等。<一个href="#B11">11</一个>2012年ASME)、版权。允许转载。</gydF4y2Badiv> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig16"> <div class="floats-partial-content fig-content-fig16"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0016" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0016.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图16</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig16/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="9.6750002" id="M218" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <a href="#B11">11</一个><t一个ble> MCS打印50的形象gydF4y2Ba米宽铜在玻璃,从巴塔查里亚et al。20.12年ASME)、版权。允许转载。</t一个ble> </div> </div> </div> <p></p> <p>气溶胶喷射被用来打印进行银痕迹塑料和印刷电路板(pcb)用于一个所有直接签单chemisensor神经毒气的检测(<一个href="#B93">93年</一个>]。在这个设计中,聚合物/炭黑复合喷雾涂层在集PCB板上的互相交叉的痕迹。银痕迹是20 ~ 50岁不等<年代vg height="9.6750002" id="M219" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽8 - 10<年代vg height="9.6750002" id="M220" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米厚,4 - 12的电导率<年代vg height="13.55" id="M221" style="vertical-align:-2.29482pt;width:21.275px;" version="1.1" viewbox="0 0 21.275 13.55" width="21.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.6018238" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米后烧结在200°C。肿胀等共聚物的组合包括乙烯/醋酸乙烯酯和苯乙烯/丁二烯嵌段共聚物与炭黑添加导电性增加5 - 20%。聚合物膨胀会导致电阻率的变化。可以看到chemisensors图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig17/" target="_blank">17</一个>。神经毒气的传感器进行模拟的dimethylethyl膦酸酯(DMMP)。测试的结果得出结论,传感器确实预想的工作,是可靠的,并证明直接签单的可行性为气体chemisensors痕迹。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig17"> <div class="floats-partial-content fig-content-fig17"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0017" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0017.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图17</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig17/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B93">93年</一个><t一个ble> 光学显微照片all-direct-written chemisensors检测神经毒气,转载来自Marinov et al。),gydF4y2BaIEEE 2007年版权所有。</t一个ble> </div> </div> </div> <p>气溶胶喷射的其他应用程序包括技术开发的Marinov et al。<一个href="#B93">93年</一个>增强M]他们开发出了术语<年代up>3</年代up>d .这个过程有两个步骤;第一个海沟是激光加工到衬底;第二,一个金属墨水直接签单到海沟。这种技术可能有利于应用程序尤其敏感超范围的固有的气溶胶喷射比如无线电频率识别(RFID)标签,因为沟定义的形状跟踪从而减少边缘效应和超范围的高频传输的是有害的。银共面波导有或没有激光加工槽准备测试的改善提高的方法。测试的结果是有前途的直流电阻率从9.2下降到4.3<年代vg height="13.55" id="M222" style="vertical-align:-2.29482pt;width:21.275px;" version="1.1" viewbox="0 0 21.275 13.55" width="21.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> <tspan style="font-size: 12.50px; " x="7.6018238" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米和AC损失6 GHz减少从0.33 dB /毫米到0.02 dB /毫米没有和激光加工槽波导。这些结果表明,这两步技术产生结果典型的商业设备损失在0.005到0.03 dB /毫米的范围是常见的。增强的米<年代up>3</年代up>D是更加昂贵由于两步的过程,但是考虑到多个十年改善损失,它可能仍然是可行的。</gydF4y2Bap> <p>Maiwald et al。<一个href="#B94">94年</一个>]报道的应变仪使用气溶胶喷射进行无损检测。设备是一个多层结构利用印刷聚合物隔离层,2<年代vg height="9.6750002" id="M223" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米厚,下面一个银气溶胶喷射印刷应变仪,1 - 3<年代vg height="9.6750002" id="M224" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米厚的痕迹,和打印封装。该设备在一个铝表面如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig18/" target="_blank">18</一个>的总大小,传感器只有大约7毫米×3毫米。从先进的纳米银纳米墨水使用采购产品公司和高达70%的金属痕迹体积电导率在烧结温度为350°C。实验结果表明,该应变仪的工作正如预期的那样,有一个可靠的传感器信号经过反复循环。气溶胶喷射是有益的,因为它提供了能够快速打印应变仪在任意的位置在一个小的形式因素。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig18"> <div class="floats-partial-content fig-content-fig18"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0018" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0018.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图18</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig18/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B94">94年</一个><t一个ble> 所有气溶胶喷射印花应变仪与聚合物隔离和铝基板封装、转载来自Maiwald et al。gydF4y2Ba从爱思唯尔),2010年版权许可。</t一个ble> </div> </div> </div> <p>dw系统气溶胶喷射和CAB-DW MAPLE-DW被用来打印银nanoparticle-based RFID天线在聚酰亚胺薄膜膜NDSU [<一个href="#B95">95年</一个>]。研究的目的是确定直写方法是否适合射频识别应用程序。天线设计是基于“蠕动”模式所使用的外星科技的超高频915 MHz频带标签。每个天线都有不同的表面形态很大程度上取决于dw工具的类型。图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig19/" target="_blank">19</一个>显示每个天线,以及详细的表面图像,边缘,(一)是铜蚀刻天线,(b)是CAB-DW印刷天线,(c)是气溶胶喷射印刷天线,和(d)是MAPLE-DW印刷天线。印刷痕迹被热位之后,RFID芯片连接,最大印刷天线射频识别标签的读取距离测量和商用copper-etched标签。发现即使直接签单天线的厚度远小于1<年代vg height="9.6750002" id="M225" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米,比4<年代vg height="9.6750002" id="M226" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米铜蚀刻的标签,也获得了类似的阅读距离。本次测试的结果是令人信服的证据的可行性使用dw RFID天线的快速原型。这些技术的使用可能协助RFID工程师开发新产品和改进天线的设计能够增加阅读范围。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig19"> <div class="floats-partial-content fig-content-fig19"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”324380。fig.0019a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”324380。fig.0019b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019b.jpg"> <br> <strong>(b)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(c)”n一个米e=”324380。fig.0019c" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019c.jpg"> <br> <strong>(c)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(d)”n一个米e=”324380。fig.0019d" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019d.jpg"> <br> <strong>(d)</年代trong></div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig19"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”324380。fig.0019a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”324380。fig.0019b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019b.jpg"><br><strong>(b)</年代trong></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)”n一个米e=”324380。fig.0019c" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019c.jpg"><br><strong>(c)</年代trong></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)”n一个米e=”324380。fig.0019d" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0019d.jpg"><br><strong>(d)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig19"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图19</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig19/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B95">95年</一个><t一个ble> 照片和显微图外星花体天线用的(a)铜蚀刻,(b) CAB-DW, (c)气溶胶喷射,和(d) MAPLE-DW,转载来自霍利et al。),gydF4y2BaIEEE 2009年版权所有。</t一个ble> </div> </div> </div> <p>Folgar et al。<一个href="#B96">101年</一个>)利用基于陶瓷生产多层结构与气溶胶喷射墨水印刷形成电容器。3 d结构形成通过使用气溶胶喷射和选择性激光烧结(SLS)。他们的工作是额外的证据使用dw系统多层组件的能力。更复杂的多层设备由Ha et al。<一个href="#B97">96年</一个>和赵等。<一个href="#B98">102年</一个>]使用气溶胶喷射与印刷问日前主动层。通过光刻源和漏了,而其他的印刷设备。活跃层印刷用水性分散碳纳米管的介电是印刷离子凝胶,并门印刷PEDOT: PSS。图表和图像设备的数据所示<一个href="//www.newsama.com/journals/jnt/2012/324380/fig20/" target="_blank">20.</一个>(一)和<一个href="//www.newsama.com/journals/jnt/2012/324380/fig20/" target="_blank">20.</一个>(b)。这个设备的性能(即令人印象深刻。,从200年流动性,提高开关速度)<年代vg height="9.6750002" id="M227" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>50年代<年代vg height="9.6750002" id="M228" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>年代相比其他印刷设备在文学即使在电源电压低于3 v (<一个href="#B97">96年</一个>,<gydF4y2Ba一个href="#B99">103年</一个>,<gydF4y2Ba一个href="#B100">104年</一个>]。在哈的工作,TFT 50<年代vg height="9.6750002" id="M229" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m×400<年代vg height="9.6750002" id="M230" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米的长度和宽度。琼斯等人。<一个href="#B101">97年</一个>),瓦兰蔻et al。<一个href="#B102">105年</一个>,国王和Renn [<一个href="#B92">87年</一个>)每个印刷类似CNT-based TFT使用气溶胶喷射在特性10一样好<年代vg height="9.6750002" id="M231" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>100 m通道长度<年代vg height="9.6750002" id="M232" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m是提供(<一个href="#B103">106年</一个>]。TFT的影像图所示<一个href="//www.newsama.com/journals/jnt/2012/324380/fig20/" target="_blank">20.</一个>(c)。这个TFT银nanoparticle-based来源,排水,和门联系问活跃层、离子凝胶介质,PEDOT门由气溶胶喷射。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig20"> <div class="floats-partial-content fig-content-fig20"> <div class="partial-carousel--single-image"> <img alt="" name="324380.fig.0020" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0020.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图20</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig20/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B97">96年</一个><一个href="#B92">87年</一个><一个href="#B101">97年</一个><t一个ble> (一)气溶胶喷射印花CNT-based TFT的示意图表示。源和漏光刻而活跃的(问),介质(离子凝胶),和门(PEDOT: PSS)气溶胶喷射。(b)的形象图案TFT (]gydF4y2Ba。版权2010年美国化学学会。(c)问基于TFT的形象用银接触产生的气溶胶喷射,spin-coated问电影,离子凝胶介质,和PEDOT: PSS大门,从国王和Renn转载,琼斯et al。,]gggydF4y2BaydF4y2BaydF4y2Ba。2010年版权许可Optomec爱思唯尔,分别。</t一个ble> </div> </div> </div> <p>硅基日前使用CAB-DW印刷source-drain接触者产生NDSU [<一个href="#B104">107年</一个>活性物质(Si)<年代ub>6</年代ub>H<年代ub>12</年代ub>的液体硅烷墨水)旋转到氮化硅涂层硅晶片(<一个href="#B105">98年</一个>]。TFT显示的初始特征场效应,但没有性能特征(即。开/关比率,流动)报道。保利3-hexylthiophene (P3HT)日前,使用CAB-DW印刷source-drain电极产生的罗宾逊et al。<一个href="#B105">98年</一个>]。这个TFT,如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig21/" target="_blank">21</一个>,由一个n<年代up>+ +</年代up>掺杂硅晶片,300纳米氮化硅闸极介电层、15<年代vg height="9.6750002" id="M233" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m通道长度银nanoparticle-based source-drain电极,50 nm spin-coated P3HT电影使用三氯苯(TCB)和spin-coated聚(甲基丙烯酸甲酯)(甲基)苯甲醚(茴香醚)。TFT本身的流动性约10<年代up>−2</年代up>厘米<年代up>2</年代up>/ v。这个TFT演示了使用CAB-DW的高分辨率(5<年代vg height="9.6750002" id="M234" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)印刷很容易能够产生15<年代vg height="9.6750002" id="M235" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m通道长度。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig21"> <div class="floats-partial-content fig-content-fig21"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”324380。fig.0021a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0021a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”324380。fig.0021b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0021b.jpg"> <br> <strong>(b)</年代trong></div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig21"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”324380。fig.0021a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0021a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”324380。fig.0021b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0021b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig21"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图21</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig21/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <sub><i>x</我></年代ub> <svg height="9.6750002" id="M236" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg> <a href="#B105">98年</一个><t一个ble> (一)光学显微照片CAB-DW Ag)源极和栅极形成的罪gydF4y2Ba涂硅晶片的通道长度15gydF4y2Ba米,(b)处理的所有解决方案示意图底导坑P3HT活跃TFT (]gydF4y2Ba。</t一个ble> </div> </div> </div> <p>气溶胶喷雾对太阳能电池的应用金属化层已经被几组调查印刷的金属化层顶部。好处与dw相关联的结果打印线一样薄的能力5<年代vg height="9.6750002" id="M237" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米,这样可以减少阴影,串联电阻和生产成本。由于非接触方法利用气溶胶喷雾,细晶片(即。,100年<年代vg height="9.6750002" id="M238" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米)可以使用没有破损与接触印刷丝网印刷等方法给予更多的太阳能电池/ Si单晶议会(<一个href="#B17">17</一个>,<gydF4y2Ba一个href="#B106">108年</一个>]。我们印刷基痕迹7一样薄<年代vg height="9.6750002" id="M239" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m与内在薄层异质结(打击)与NREL合作生产的太阳能电池。影响细胞利用一个氧化铟锡ITO透明导电氧化物(TCO)横向传输层,所以不需要焊穿是<一个href="#B17">17</一个>,<gydF4y2Ba一个href="#B107">109年</一个>]。这项工作的结果得出结论,改善太阳能电池效率约5时实现<年代vg height="9.6750002" id="M240" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>在90年的地方使用m的痕迹<年代vg height="9.6750002" id="M241" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m痕迹具有类似几何阴影。高(9.8米<年代vg height="10.6875" id="M242" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米<年代up>2</年代up>)在ITO-Ag界面接触电阻,从而导致电池串联电阻增加,可能倾斜的比较结果。最近的结果使用Ag纳米油墨显示0.015的接触电阻<年代vg height="10.6875" id="M243" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米<年代up>2</年代up>和体积电阻率的3.5到4×大部分银(<一个href="#B108">110年</一个>]。范训谕et al。<一个href="#B106">108年</一个>,<gydF4y2Ba一个href="#B109">111年</一个>]利用金属种油墨为Si设计<年代ub>3</年代ub>N<年代ub>4</年代ub>增透膜(电弧)太阳能电池。他们印刷金属油墨,基于结合银,镍,铜,在环境和惰性氛围与跟踪宽度约50<年代vg height="9.6750002" id="M244" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m。除了金属油墨,他们正在调查硅掺杂剂含有导电油墨,激光烧结的气溶胶喷射印刷痕迹,并打印互相交叉接触(IBC)细胞。如果需要更多的信息关于太阳能电池导电油墨,审查的无机太阳能电池和可用的油墨印刷导电包含摘要的痕迹,纳米粒子,例如玻璃熔块是由同一组写的国家可再生能源实验室(傻瓜等。)<一个href="#B110">112年</一个>]。</gydF4y2Bap> <p>弗劳恩霍夫研究员伊势(<一个href="#B113">99年</一个>,<gydF4y2Ba一个href="#B112">One hundred.</一个>,<gydF4y2Ba一个href="#B111">113年</一个>)设计了一个前金属化方案的正面与气溶胶喷射沉积金属化层,治愈,跟着光致镀银(嘴唇)。唇过程优先电镀银在气溶胶喷射印刷痕迹当照明下的太阳能电池是由于潜在的金属。最后一行的宽度50<年代vg height="9.6750002" id="M245" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m和10的高度<年代vg height="9.6750002" id="M246" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>25 - 30 m可以实现<年代vg height="9.6750002" id="M247" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米宽1<年代vg height="9.6750002" id="M248" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>米高的气溶胶喷射印刷种子层。这种方法减少了串联电阻通常造成的损失大于印刷银色痕迹的体电阻率镀银在接触从而减少有效的体电阻率(<一个href="#B112">One hundred.</一个>]。种子层痕迹14一样薄<年代vg height="9.6750002" id="M249" style="vertical-align:-2.29482pt;width:9.6374998px;" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.675)"> <g transform="translate(72,-64.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代pan> </text> </g> </g> </svg>m是一个摘要墨水,但差的边缘定义如图<一个href="//www.newsama.com/journals/jnt/2012/324380/fig22/" target="_blank">(22日)</一个>(<gydF4y2Ba一个href="#B113">99年</一个>]。SEM图像完成跟踪的太阳能电池与种子层橙色可以看到在图所示<一个href="//www.newsama.com/journals/jnt/2012/324380/fig22/" target="_blank">22 (b)</一个>(<gydF4y2Ba一个href="#B112">One hundred.</一个>];注意到大部分的体积跟踪是镀银。弗劳恩霍夫所使用的过程大大降低了太阳能电池制造的复杂性相比photolithographically定义金属化层,可以看到商业应用。气溶胶喷射与嘴唇的改进方法被报道了et al。<一个href="#B111">113年</一个>),激光化学处理(LCP)被用来同时形成选择性重掺杂发射器,通过SiO燃烧<年代ub>2</年代ub>气溶胶喷射印花前弧层。最小接触电阻通过气溶胶喷射是0.99米<年代vg height="10.6875" id="M250" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米<年代up>2</年代up>,远远大于通过蒸发Ti / Pd / Ag)联系人(<年代vg height="5.7874999" id="M251" style="vertical-align:-0.0pt;width:10.825px;" version="1.1" viewbox="0 0 10.825 5.7874999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,5.7875)"> <g transform="translate(72,-67.37)"> <text transform="matrix(1,0,0,-1,-71.95,67.42)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∼</t年代pan> </text> </g> </g> </svg>0.15米<年代vg height="10.6875" id="M252" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米<年代up>2</年代up>),但足够低的用于1-sun照明(<一个href="#B111">113年</一个>]。没有LCP治疗,接触电阻最低是2米<年代vg height="10.6875" id="M253" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ω</t年代pan> </text> </g> </g> </svg>厘米<年代up>2</年代up>(<一个href="#B112">One hundred.</一个>]。该方法的另一个例子与dw技术创新可能与其他技术相结合。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig22"> <div class="floats-partial-content fig-content-fig22"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”324380。fig.0022a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0022a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”324380。fig.0022b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0022b.jpg"> <br> <strong>(b)</年代trong></div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig22"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”324380。fig.0022a" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0022a.jpg"><br><strong>(一)</年代trong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”324380。fig.0022b" src="https://static-01.hindawi.com/articles/jnt/volume-2012/324380/figures/324380.fig.0022b.jpg"><br><strong>(b)</年代trong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig22"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图22</年代pan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/jnt/2012/324380/fig22/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <a href="#B113">99年</一个><一个href="#B112">One hundred.</一个><t一个ble> 气溶胶喷射印花Ag)太阳能电池的痕迹;转载(a)光学图像在唇前,从Mette et al。),2007gydF4y2Ba年版权许可约翰威利& Sons有限公司(b)的横截面扫描电镜图像气溶胶喷射打印跟踪与嘴唇。气溶胶喷射印花种子层是用橙色突出,从Horteis转载,Glunz [),2008gydF4y2Ba年版权许可约翰威利& Sons有限公司。</t一个ble> </div> </div> </div> <h4 id="conclusions">7所示。结论</h4><gydF4y2Bap>气溶胶直写技术是一个相对较新的类迅速成为用于商业使用无触点电子应用中,高分辨率,和3 d工具是必需的。气溶胶喷射是最主要的商业技术用于dw, CAB-DW, MCS和气溶胶透镜聚焦仍在开发阶段。这些设备都依靠空气动力集中创建可控好存款。的理解物理学dw的流体质点的相互作用使开发人员技术进一步提高这些设备减少超范围,提高分辨率,减少停机时间的工具。最近的进步在气溶胶可视化和测量使用shadowgraphy和其他技术已经导致了一种改进的理解有关dw的气溶胶聚焦技术。</gydF4y2Bap> <p>dw的耦合技术,电子产品会导致几个优势传统技术包括降低成本,减少启动时间,决议和改进的功能。dw已被证明能够印刷特性日前和太阳能电池等电子设备。新技术如MCS不习惯在许多应用程序中,但是已经被证明能够印刷没有后处理,这一特性可以减少生产成本。dw技术的整体发展可能导致更广泛用于微电子应用尤其是在快速原型。</gydF4y2Bap> <h4 id="acknowledgments">确认</h4><gydF4y2Bap>作者要感谢Orven斯文森博士,扎卡里亚马哈茂德博士,博士格雷格•麦卡锡博士拉里Pederson Aaron Reinholz Sourin Bhattacharya迈克·罗宾逊,雅各布·芬克罗伯帆船,Jason Daugs Drew Thompson和协作,有益的讨论,和支持。这项工作是基于研究由国防微电子活动处()协议。h94003 - 11 - 2 - 1102。本文所包含的观点和结论是作者和不应被解释为一定代表官方政策或支持,表示或暗示,国防微电子的活动。</gydF4y2Bap> </div> <div class="xml-content"> <h4 class="references" id="references">引用</h4><ol><l我我d="B1">公元Halvorsen, p . 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Granek&publication_year=2011" target="_blank">谷歌学术搜索</一个></年代pan></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4><gydF4y2Bap>版权©2012贾斯汀·m·霍利et al。这是一个开放的分布式下文章<一个rel=”l我cense" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</gydF4y2Bap> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 kgAKHb hrTitleRef">更多相关文章</h4><gydF4y2Badiv id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 kVscyQ"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-cBdUnI hRnXob article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW 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height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</年代pan><span class="sc-gkFcWv gWTCXQ">更多的</年代pan></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/jnt/2012/324380.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</gydF4y2Badiv><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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height="24"><span class="sc-dRFtgE jrsDZP">订单打印副本</年代pan><span class="sc-gkFcWv gWTCXQ">订单</年代pan></span><span class="sc-htoDjs kNoiZu sc-gbOuXE jGPvPL right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-hBbWxd kdRRST"> <div class="sc-dyGzUR cHatnS"> <div> 的观点<年代pan>6094年</年代pan> </div> <div> 下载<年代pan>3794年</年代pan> </div> </div> <div> <div class="sc-drKuOJ kxdGAZ"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2012/324380" data-style="small_circle"></span>引用</gydF4y2Badiv> </div> </div> <nav class="sc-bRBYWo fXBKFa sc-hUfwpO jHPgUP" id="toolbar__iconNav"> <h3 class="sc-Rmtcm hNPrIr">分享文章</h3><gydF4y2Baul class="sc-hzDkRC bnbfTS"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2012/324380&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" 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