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 ${D}_{t}$ values are in line with specific biofilm growth patterns, ranging from boundary‐layer appearance Dt>1 $\left({D}_{t} > 1\right)$ to bulky shapes Dt<1 $\left({D}_{t}< 1\right)$. Plain Language Summary: We present a computational model to simulate biofilm formation in porous materials under varying flow and transport conditions. The framework is designed for small‐scale analysis (mm−cm) $(mm-cm)$ and is based on a micro‐continuum approach, where biofilm is treated as a micro‐porous material. This approach addresses the technical challenges of explicitly representing the biofilm‐liquid interface. Through numerical simulations, we analyze the effect of flow dynamics on biofilm formation at the scale of a single pore. The model predicts distinct growth patterns and biofilm shapes depending on the hydrodynamic conditions. Increasing the flow rate promotes biofilm growth up to a critical hydrodynamic point, after which biomass detachment becomes dominant. We discuss these results in relation to experimental observations and interpret the growth patterns using a dimensionless number, Dt ${D}_{t}$, which represents the ratio between drag forces and biomass cohesion forces. Furthermore, we conduct a numerical analysis to explore the relationship between biomass accumulation and permeability changes, which is a critical factor in many engineering and environmental applications including bioremediation and degradation of organic contaminants. Using a simple porous system, we demonstrate how the porosity‐permeability relationship is significantly influenced by biofilm growth conditions and how the biofilm is distributed within the pore space. Key Points: We develop a pore‐scale model for biofilm dynamics coupled with fluid flow and transport of nutrientsThe model considers biofilm as a fluid‐filled micro‐porous medium and simulates flow based on a coupled Darcy‐Brinkman‐Stokes modelBiofilm morphology and bioclogging can be characterized and predicted by a dimensionless ratio of hydrodynamic to biomass cohesion forces [ABSTRACT FROM AUTHOR]