Theoretical Analysis of the Influence of a Diffuse Double-Layer On Darcy’s Law

Abstract

It is known that when the concentration of background electrolyte in a charged porous medium increases, the permeability of the porous medium also increases. In this paper, a set of coupled governing equations is derived that describe Navier-Stokes flow of a pore fluid through a charged porous medium (i.e. flow in the presence of a diffuse double-layer). The set of coupled partial differential equations describe the transport of the individual ions along their electrochemical potential gradient, the transport of the pore fluid together with the ions in solution, and the voltage distribution through the porous medium, while simultaneously maintaining electro-neutrality of the system. The governing equations are solved for an example problem. By using this approach, new insight is gained into the origin of permeability changes arising from changes in the background electrolyte concentration.