Modelling sorption of trace-elements in multispecies biofilms
The presentation will concern a mathematical model for micro-elements sorption in multispecies biofilms, based on a continuum approach and mass conservation principles. Diffusion of contaminants within the biofilm is described using a diffusion-reaction equation. Binding sites formation and occupation are modelled by two systems of hyperbolic partial differential equations mutually connected through the two growth rate terms. The model is completed with a system of hyperbolic equations governing the microbial species growth within the biofilm, a system of parabolic equations for substrates diffusion and reaction and a nonlinear ordinary differential equation describing the free boundary evolution. The Mathematical Modelling of three real special cases will be presented. The first describes the dynamics of a free sorbent component diffusing and reacting in a multispecies biofilm. In the second illustrative case, the fate of two different trace-elements is modelled. In the third case the microbial growth is directly related to the contaminant concentration.