Electrokinetics of a charged permeable porous aggregate in an aqueous medium

Abstract

The combined effects of hydrodynamical flow and electric field on the transport of permeable aggregate with fixed charged density are analyzed. Electrophoretic separation is often combined with a hydrodynamically driven flow to speed-up the transport of colloidal particles. The electrophoresis of the aggregate is governed by the interaction of electroosmotic flow in and around the particle, its hydrodynamical friction and the electric force experienced by the particle. The imposed convection of the aggregate further modifies the double layer polarization (DLP) and counterion penetration compared to the electrophoresis case. We have analyzed the effects of convection on DLP and diffusion dominated counterions penetration for a wide range of key parameters such as, permeability, fixed charge density and Debye layer thickness. Our numerical model is based on the non-linear Nernst–Planck equations for ion transport coupled with the Darcy–Brinckman extended Navier–Stokes equations and the Poisson equation for electric field. The electroosmotic flow within and around the aggregate produces a retardation effect which results in the drag experienced by the aggregate being higher than the corresponding Stokes drag of an uncharged aggregate. The induced electric field, which is opposite to the direction of an applied electric field, grows with the rise of the translation speed of the aggregate. At large convection speed, the strong momentum of the aggregate nullifies the retarding effect due to electroosmosis. The electroosmosis of the electrolyte has a significant impact on the dynamics of the aggregate when the Debye layer thickness is high. The impact of electroosmosis enhances for a higher charge density as well as a higher permeability of the particle when the Debye layer is thick.