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Abstract We present a new computational fluid dynamics approach for simulating two‐phase flow in hybrid systems containing solid‐free regions and deformable porous matrices. Our approach is based on the derivation of a unique set of volume‐averaged partial differential equations that asymptotically approach the Navier‐Stokes Volume‐of‐Fluid equations in solid‐free regions and multiphase Biot Theory in porous regions. The resulting equations extend our recently developed Darcy‐Brinkman‐Biot framework to multiphase flow. Through careful consideration of interfacial dynamics (relative permeability and capillary effects) and extensive benchmarking, we show that the resulting model accurately captures the strong two‐way coupling that is often exhibited between multiple fluids and deformable porous media. Thus, it can be used to represent flow‐induced material deformation (swelling, compression) and failure (cracking, fracturing). The model's open‐source numerical implementation,hybridBiotInterFoam, effectively marks the extension of computational fluid mechanics into modeling multiscale multiphase flow in deformable porous systems. The versatility of the solver is illustrated through applications related to material failure in poroelastic coastal barriers and surface deformation due to fluid injection in poro‐visco‐plastic systems. 

Abstract The coupled hydrology and mechanics of soft porous materials (such as clays, hydrogels, membranes, and biofilms) is an important research area in several fields, including water and energy technologies as well as biomedical engineering. Well‐established models based on poromechanics theory exist for describing these coupled properties, but these models are not adapted to describe systems with more than one characteristic length scale, that is, systems that contain both macropores and micropores. In this paper, we expand upon the well‐known Darcy‐Brinkman formulation of fluid flow in two‐scale porous media to develop a “Darcy‐Brinkman‐Biot” formulation: a general coupled system of equations that approximates the Navier‐Stokes equations in fluid‐filled macropores and resembles the equations for poroelasticity in microporous regions. We parameterized and validated our model for systems that contain either plastic (swelling clay) or elastic microporous regions. In particular, we used our model to predict the permeability of an idealized siliciclastic sedimentary rock as a function of pore water salinity and clay content. Predicted permeability values are well described by a single parametric relation between permeability and clay volume fraction that agrees with existing experimental data sets. Our novel formulation captures the coupled hydro‐chemo‐mechanical properties of sedimentary rocks and other deformable porous media in a manner that can be readily implemented within the framework of Digital Rock Physics. 

Bacteria in porous media, such as soils, aquifers, and filters, often form surface-attached communities known as biofilms. Biofilms are affected by fluid flow through the porous medium, for example, for nutrient supply, and they, in turn, affect the flow. A striking example of this interplay is the strong intermittency in flow that can occur when biofilms nearly clog the porous medium. Intermittency manifests itself as the rapid opening and slow closing of individual preferential flow paths (PFPs) through the biofilm–porous medium structure, leading to continual spatiotemporal rearrangement. The drastic changes to the flow and mass transport induced by intermittency can affect the functioning and efficiency of natural and industrial systems. Yet, the mechanistic origin of intermittency remains unexplained. Here, we show that the mechanism driving PFP intermittency is the competition between microbial growth and shear stress. We combined microfluidic experiments quantifying Bacillus subtilis biofilm formation and behavior in synthetic porous media for different pore sizes and flow rates with a mathematical model accounting for flow through the biofilm and biofilm poroelasticity to reveal the underlying mechanisms. We show that the closing of PFPs is driven by microbial growth, controlled by nutrient mass flow. Opposing this, we find that the opening of PFPs is driven by flow-induced shear stress, which increases as a PFP becomes narrower due to microbial growth, causing biofilm compression and rupture. Our results demonstrate that microbial growth and its competition with shear stresses can lead to strong temporal variability in flow and transport conditions in bioclogged porous media.