Description
In soft matter and biology, liquids permeating porous media are often found due to the occurrence of (polymeric) fibers, membranes, and colloidal particles. It is a key challenge to describe the flow through such systems —typically at a low Reynolds number— while also accounting for the precise porous microstructure of the medium. Therefore, understanding the macroscale flow properties often requires a coarse-grained approach. In the Brinkman-Debye-Bueche (BDB) method, the porous features of the system are represented by an effective mesoscopic medium that exerts an additional force density on the permeating fluid that is linear in the fluid velocity.
In this talk, we will consider the case when the effective porous medium exhibits (nematic) anisotropy. In particular, we study the hydrodynamic drag force exerted on a sphere in such a medium. This problem is analyzed using the Brinkman-Debye-Bueche equations with an axisymmetric shielding (or permeability) tensor. Using the exact Green’s functions for this model fluid within a single-layer boundary element formulation, we numerically compute the friction tensor for a translating sphere subjected to stick boundary conditions. Furthermore, we derive approximate analytical expressions for small anisotropy using the Lorentz reciprocal theorem. By benchmarking this result against the numerical solutions, we find that a linear approximation is valid in a broad parameter regime. Our results are important for studying self diffusion in general anisotropic porous media, but can also be applied to small tracers in nematic fluids composed of disk- or rodlike crowders.
References
A. Vilfan, B. Cichocki, and J. C. Everts, Stokes drag on a sphere in a three-dimensional anisotropic porous medium, Phys. Rev. E 112, 015107 (2025).