Electroosmotic flow of a two-layer fluid in a slit channel with gradually varying wall shape and zeta potential

This study aims to investigate electroosmotic (EO) flow of a two-layer fluid through a slit microchannel where the wall shape as well as zeta potential may vary slowly and periodically with axial position. The two-layer EO flow is a model for the flow of two immiscible fluids: a non-conducting working fluid being dragged into motion by a conducting sheath fluid. Electric double layers may develop in the conducting fluid near the interface between the two fluids, and near a wall that is assumed to be non-uniform in both shape and zeta potential distribution. Because of these geometrical and electrical non-uniformities, pressure is internally induced. The two-fluid flow is therefore driven by electrokinetic and hydrodynamic forcings, while subjected to the combined effects of the axial variations of the wall shape and potential distribution. The present problem is formulated by invoking the lubrication approximation, for a nearly parallel flow of low Reynolds number, and the governing equations are solved as analytically as possible. The induced pressure gradient and the deformed shape of the interface, which are functions of axial position, as well as the flow rates of the two fluids, are determined by an iterative trial-and-error numerical scheme. Results are generated to show the effects due to various factors, including the applied pressure difference, interfacial potential, viscosity ratio, wall undulation, and phase shift between the wall shape and potential distribution. Some of the effects on flow in a non-uniform channel can be qualitatively different from that in a uniform channel.