Fundamental aspects of concentration polarization arising from nonuniform electrokinetic transport

Abstract

Recent experiments have demonstrated that large-scale ion concentration gradients, or “concentration polarization,” can be generated from perm-selective transport through nanochannels or nonuniform surface conduction around polarizable electrodes. The theoretical modeling of concentration polarization phenomena is, however, a daunting task: for example, an analysis of the above mentioned systems requires the treatment of a set of highly coupled, nonlinear partial differential equations for the ion concentrations, electric field, and fluid flow. In this paper, we present and analyze a model system that simply and clearly highlights a variety of fundamental aspects of concentration polarization. Specifically, we consider a binary symmetric electrolyte overlying a flat wall, whose surface charge varies periodically. An electric field applied parallel to the wall causes nonuniform ionic transport within the thin diffuse layer adjacent to the wall. In turn, this nonuniform transport drives gradients in the bulk ion, or salt, concentration and electric field. Notably, the bulk variations persist over the macroscopic length scale L of the surface charge variation rather than the microscopic (Debye length λD) thickness of the diffuse layer. We formalize these ideas by deriving effective boundary conditions coupling the diffuse-layer transport to the bulk electrolyte dynamics. In the limit of a weak applied field and small surface charge density (the Debye–Huckel limit), the electrolyte response is investigated for three prototypical cases: (i) a steady (dc) field, (ii) a suddenly applied field, and (iii) an oscillatory (ac) field. In particular, for a steady field we examine the interplay of diffusion and advection in shaping the bulk concentration polarization zones.