A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments

TL;DR

This paper develops a detailed pore-scale model for permeable biofilm formation, combining numerical simulations with laboratory experiments to analyze flow, nutrient transport, and biofilm dynamics in a two-dimensional pore.

Contribution

It introduces a comprehensive pore-scale model incorporating multiple biofilm components and validates it with experimental data, including sensitivity analysis of key parameters.

Findings

The model accurately predicts biofilm behavior under various conditions.

Sensitivity analysis highlights the importance of all parameters in biofilm formation.

Numerical results align well with laboratory experiments.

Abstract

In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substances (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation whereas a diffusion-convection equation is involved for the transport of nutrients. At the water/biofilm interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/dead of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by $\pm 10 \%$ of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected.