Homogenization of the Ionic Transport Equations in Periodic Porous Media

The transport of an N-component electrolyte in a dilute Newtonian solvent through a rigid, porous body subjected to a static (d.c.) electric field is studied. The microscopic description is given by the linearized ionic transport (electrokinetic) equations, including the effects of ion diffusion, electromigration and convection. Periodic homogenization is used to derive effective governing equations for the fluid velocity, ionic flux and current density that capture the macroscopic behavior. Explicit expressions for the transport coefficient tensors are given in terms of solutions to cell problems. Without any additional assumptions, we rigorously prove that these transport coefficient tensors obey certain fundamental thermodynamic requirements, namely, Onsager’s reciprocal relations and the positive definiteness of the diagonal coefficient tensors.