Modeling sorption of emerging contaminants in biofilms

TL;DR

This paper presents a comprehensive mathematical model for the sorption of emerging contaminants in multispecies biofilms, integrating diffusion, reaction, and biofilm growth dynamics to better understand contaminant fate.

Contribution

It introduces a novel continuum-based model combining hyperbolic PDEs and ODEs to simulate contaminant sorption and biofilm growth, including two specific case studies.

Findings

Model successfully describes contaminant diffusion and binding in biofilms.

Case studies demonstrate the model's ability to simulate different contaminant behaviors.

Provides a framework for predicting contaminant fate in biofilm systems.

Abstract

A mathematical model for emerging contaminants sorption in multispecies biofilms, based on a continuum approach and mass conservation principles is presented. Diffusion of contaminants within the biofilm is described using a diffusion-reaction equation. Binding sites formation and occupation are modeled by two systems of hyperbolic partial differential equations are 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. Two real special cases are modelled. The first one 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 contaminants has been modelled.