Generalizing Darcy’s law for filtration radial flows through porous media

Abstract

We study the filtration process in porous media and compare the filtration coefficients for two possible geometries of flows: cylindrical and radial ones. Solving balance equations for impurity concentration in the simplest axially-symmetric stationary case, one finds the radial filtration process more effective. Therefore, we restrict our attention to the radial filters with non-homogeneous grain filling. First, we describe the transverse diffusion effect and then suggest the generalization of the Darcy’s filtration law, its dynamical origin being stressed. Using the perturbation method, we find the structure of the Stokes stream function for some particular choices of the porosity.