Influence of combined electromagnetohydrodynamics on microchannel flow with electrokinetic effect and interfacial slip

Abstract

We investigate analytically the combined consequences of electromagnetohydrodynamic forces and interfacial slip on streaming potential mediated pressure-driven flow in a microchannel. Going beyond traditional Debye–Hückel limit, we first derive a closed-form analytical solution for velocity field by considering nonlinear electrical potential distribution, wall slip effects, externally imposed transverse magnetic field, and laterally applied electric field in the plane of flow. The effects of electrical double-layer (EDL) formation and the consequent interfacial phenomena are critically examined under such situations. An expression for induced streaming potential in the microchannel is deduced considering EDL formation and the consequences of finite conductance of the immobilized Stern layer. This simplified analytical expression is later on critically assessed against three-dimensional simulation paradigm of streaming potential mediated flows, which is a first effort of this kind. We demonstrate that flow rate increases progressively with increasing surface potential and eventually approaches to a limiting value. Combination of electromagnetohydrodynamic effect with liquid slip is shown to amplify the flow rate, even at lower values of surface potential. Our study brings out the possibility of achieving an optimum flow rate by judicious application of combined electromagnetohydrodynamics. The present analysis has significant consequence in the design of advanced microfluidic devices with improved efficiency and functionality.