Fluid flow through deformable porous media is a process of paramount importance in diverse applications ranging from the gravity-driven flow of water in soil to the interstitial flow of aqueous fluids in microbial biofilms, mammalian and plant tissues. Several different approaches have been used in the development of mathematical models for this process, including Biot's theory of poroelasticity, mixture theory, spatial homogenization and averaging methods, as well computational equation-free methods that bypass the explicit definition of constitutive equations for the macroscale stress tensors.

In this talk, a theoretical analysis will be presented for viscous-dominated flows in permeable poroelastic materials. The analysis is based on a continuum-based formulation of momentum transfer in a two-phase solid-fluid system at the pore scale, and the implementation of the spatial averaging method for the derivation of a set of differential equations that describe the dynamics of fluid flow and solid matrix deformation at the coarser (Darcian) scale. The conditions that delimit the domain of validity for a general biphasic model, as well as for two limiting monophasic descriptions, have been established through order-of-magnitude analysis. In the special case of a homogeneous medium and under certain other conditions, the derived equations become similar to those which are postulated in biphasic mixture theory and Biot's theory of poroelasticity. Results from the solution of the steady-state form of the established equations in two simple settings will also be presented. The first example involves the pressure-driven flow past and through a poroelastic layer and sheds light into the transmission of mechanical forces across the endothelial glycocalyx of blood vessels. The second example involves the shearing flow past a poroelastic protrusion and provides insight into the development of tensile stresses that lead to biofilm detachment from substrates.