Modeling Heavy Metal Sorption and Interaction in a Multispecies Biofilm

Abstract

A mathematical model able to simulate the physical, chemical and biological interactions prevailing in multispecies biofilms in the presence of a toxic heavy metal is presented. The free boundary value problem related to biofilm growth and evolution is governed by a nonlinear ordinary differential equation. The problem requires the integration of a system of nonlinear hyperbolic partial differential equations describing the biofilm components evolution, and a systems of semilinear parabolic partial differential equations accounting for substrates diffusion and reaction within the biofilm. In addition, a semilinear parabolic partial differential equation is introduced to describe heavy metal diffusion and sorption. The biosoption process modeling is completed by the definition and integration of other two systems of nonlinear hyperbolic partial differential equations describing the free and occupied binding sites evolution, respectively. Numerical simulations of the heterotrophic-autotrophic interaction occurring in biofilm reactors devoted to wastewater treatment are presented. The high biosorption ability of bacteria living in a mature biofilm is highlighted, as well as the toxicity effect of heavy metals on autotrophic bacteria, whose growth directly affects the nitrification performance of bioreactors.

A general framework to model the fate of trace elements in anaerobic digestion environments

“…8 ). In the sorption/desorption reactions, a pivoting role is played by the concentration of binding sites 51 , 52 . The latter can be found in two states: free, when the sorption reaction has not occurred yet, and occupied when the bound between the adsorbent and adsorbing components is established.…”