Abstract
We present a class of deterministic continuum models for spatially heterogeneous biofilm communities. The prototype is a single-species biofilm growth model, which is formulated as a highly non-linear system of reaction-diffusion equations for the biomass density and the concentration of the growth controlling substrate. While the substrate concentration satisfies a standard semi-linear reaction-diffusion equation the equation for the biomass density comprises two non-linear diffusion effects: a porous medium-type degeneracy and super diffusion. When further biofilm processes are taken into account equations for several substrates and multiple biomass components have to be included in the model. The structure of these multi-component extensions is essentially different from the mono-species case, since the diffusion operator forthe biomass componentsdepends on the total biomass in the system and the equations are strongly coupled. We present the prototype biofilm growth model and give an overview of its multi-component extensions. Moreover, we summarize analytical results that were obtained for these models.
Highlights
The dominant mode of microbial life in aquatic ecosystems are biofilm communities rather than planktonic cultures ([1])
Whenever environmental conditions allow for bacterial growth, microbial cells can attach to a substratum and switch to a sessile life form
While the nutrient is dissolved in the domain and the substrate concentration satisfies a standard semilinear reaction-diffusion equation, the spatial spreading of biomass is determined by the density-dependent diffusion coefficient
Summary
The dominant mode of microbial life in aquatic ecosystems are biofilm communities rather than planktonic cultures ([1]). The structure of these multi-species models differs essentially from the mono-species model, and the analytical results for the prototype model could not all be carried over to the more involved multi-species case In both articles, existence proofs for the solutions were given, and numerical studies presented, but the question of uniqueness of solutions remained unanswered in [4] and [13]. Existence proofs for the solutions were given, and numerical studies presented, but the question of uniqueness of solutions remained unanswered in [4] and [13] Another multi-component biofilm model was proposed in [11], which describes quorum-sensing in growing biofilm communities. In [8] extensions in other directions of the prototype biofilm growth model are discussed, e.g., models that take the effect of hydrodynamics into account
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