A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development. Issue 3 (2001) - Eberl Eberl, Herman J. Herman J.; Parker Parker, David F. David F.; Van Loosdrecht Van Loosdrecht, Mark C. M. Mark C. M.
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.