Pore-Scale Coupling of Flow, Biofilm Growth, and Nutrient Transport: A Microcontinuum Approach

Biofilms are microbial communities that influence the chemical and physical properties of porous media. Understanding their formation is essential for different topics, such as water management, bioremediation, and oil recovery. In this work, we present a pore-scale model for biofilm dynamics that is fully coupled with fluid flow and transport of growth-limiting nutrients. Built upon micro-continuum theory, the model considers biofilm as a fluid-filled micro-porous medium and simulates flow based on a coupled Darcy-Brinkman-Stokes model. We outline the key assumptions of the model and present the governing equations of biofilm dynamics, along with details of their numerical implementation. Through numerical simulations of biofilm development at the scale of a single pore, we analyze the influence of flow dynamics upon biofilm spatial distribution, as well as the way effective permeability is altered and evolves under different growth conditions. Our emphasis is on the critical hydrodynamic point, that is, the transition between bulky and dispersive biofilm shapes as a function of the driving parameters. We introduce a dimensionless number, termed Dt D-t, defined as the ratio between hydrodynamic and biomass cohesion forces, which provides a bulk characterization of the biomass-flow system, and allows to assess biofilm morphology and growth patterns. We then discuss results in relation to available experimental data, where estimated Dt values are in line with specific biofilm growth patterns, ranging from boundary-layer appearance Dt> 1 to bulky shapes Dt<1