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Herman J. Eberl, David F. Parker, Mark C. M. Van Loosdrecht, "A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development",Computational and Mathematical Methods in Medicine, vol.3, Article ID429794, 15 pages, 2001. https://doi.org/10.1080/10273660108833072
A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development
Abstract
A new mathematical model for the development of spatially heterogeneous biofilm structures is presented. Unlike previous hybrid discrete/continuum models it is a continuum model throughout, describing the interaction of nutrient availability and biomass production. Spatial biomass spreading is described by a nonlinear density-dependent diffusion mechanism. The diffusion operator degenerates for small biomass densities and is singular at the biomass density bound. The model can be interpreted as a predator-prey model for biomass and nutrients. First numerical simulations show that the model is able to predict experimentally observed cluster-and-channel biofilm structures. The results are reliable and in qualitatively good agreement with experimental expectations.
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Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under theCreative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
