Effective electrokinetic parameters of porous media with ellipsoidal inclusions. The differential effective medium approximation

Abstract

Many porous media such as natural rocks have mesoscale inhomogeneities. The characteristic sizes of such inhomogeneities are much larger than the pore sizes but much less than the characteristic scale of the problem, such as the length of the sample on which the measurements taken. In this paper, we have solved the one-particle problem for depolarization of an ellipsoidal particle located in a porous medium with electrokinetic effect. To calculate the effective physical properties of a porous medium with many interacted ellipsoidal inclusions we have applied the homogenization scheme named differential effective medium method. This method leads to some system of differential equations for the effective constant determination. General theory is illustrated by calculations of these constants for media containing spherical and ellipsoidal inclusions.