Effect of Anisotropy on the Permeability of Electroosmotic Flow Through Porous Media: Multiscale Approach

Electroosmotic flow through porous media is a crucial contemporary research field that finds its application in the areas of various engineering, geological, and biological settings. Obeying Darcy's law for electroosmotic flow through porous media in similar lines to that of pressure-driven flow yields a very important physical property of electro-permeability. This work aims to examine the influence of wall zeta potential, Debye length, the solid particle shape, and preferential orientation on the electro-permeability tensor using multiscale homogenization methodology for a single-phase fluid flow. For determining the range of possible particle shapes from prolate-oblate ellipsoid to sphere, the parameter of aspect ratio is employed. Additionally, anisotropy ratio and tortuosity have been explored. The governing equations for this study comprise a mass continuity equation, an advection-diffusion equation, a Poisson-Boltzmann equation for electric double layer, and a Laplace equation for solving the electric field in a fully coupled manner. A two-scale computational homogenization technique is employed to model the fluid-saturated periodic media subjected to external electric effects. The finite element approach is adopted to solve the multiscale and multi-physics problem in a coupled manner. The results indicate that the electro-permeability is significantly affected by wall zeta potential, aspect ratio, and orientation of solid particles. Also, one of the major findings is that the EDL thickness has a vital effect on the electro-permeability, anisotropy ratio, and tortuosity of the porous media. Permeability of porous media is estimated for a Newtonian fluid when subjected to an external electric field.Electrical double layer (EDL) thickness impacts the tortuosity and anisotropy ratio of the porous media.Wall zeta potential, EDL thickness, solid phase aspect ratio, and orientation affect the permeability.