Mathematical Modeling of Heavy Metal Biosorption in Multispecies Biofilms

The biofilm matrix is a complex of secreted polymers, absorbed nutrients and metabolites, cell lysis products, and even particulate material. Being polyanionic in nature, this matrix plays a crucial role in the biosorption of metal cations. In this work, the adsorption process of heavy metals in biofilms is modeled in one space dimension. The mathematical model is a free-boundary value problem for nonlinear hyperbolic and parabolic partial differential equations. Biomass and extracellular polymeric substances (EPS) growth is governed by hyperbolic equations, and substrate evolution by parabolic equations. All equations are mutually connected. The model is general and can work for any number of microbial species, EPS, and substrates. In numerical analysis, heterotrophic-autotrophic competition for space with oxygen as common substrate is considered. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, EPS formation, and, in particular, is able to simulate heavy metal diffusion and adsorption into biofilm. Numerical simulations for representative examples are obtained by the method of characteristics. Results indicate that model is able to capture the main features of heavy metal adsorption process on EPS.