The Electrokinetic Cross-Coupling Coefficient: Two-Scale Homogenization Approach

By the two-scale homogenization approach we justify a two-scale model of ion transport through a layered membrane, with flows being driven by a pressure gradient and an external electrical field. By up-scaling, the electroosmotic flow equations in horizontal thin slits separated by thin solid layers are approximated by a homogenized system of macroscale equations in the form of the Poisson equation for induced vertical electrical field and Onsager's reciprocity relations between global fluxes (hydrodynamic and electric) and forces (horizontal pressure gradient and external electrical field). In addition, the two-scale approach provides macroscopic mobility coefficients in the Onsager relations. On this way, the cross-coupling kinetic coefficient is obtained in a form which does involves the ζ -potential among the data provided the surface current is negligible.