Electroviscous effects in purely pressure driven flow and stationary plane analysis in electroosmotic flow of power-law fluids in a slit microchannel

Abstract

This paper is a comprehensive work on flow of power-law fluids in a slit microchannel. The first part of the paper deals with study of electrokinetic effects in steady, fully developed, laminar pressure driven flow of power-law fluids. The second part of the work provides analysis of stationary plane that is formed during electroosmotic flow (EOF) of power-law fluids inside a closed slit microchannel. In the entire analysis, the flow of power-law fluid is characterized by the modified Navier–Stokes equation incorporating the electric body force term. The electric double layer (EDL) potential is described by the Poisson–Boltzmann distribution under Debye Hückel approximation. In pressure driven flow, analytical expressions for velocity profiles of various power-law fluids are obtained for n = 1, 1/2, 1/3. Numerical simulation is carried out for all values of n to find induced streaming potential without any approximations for entire range of flow behavior indices. The analytical solutions are compared with numerical results. The effects of flow behavior index, zeta potential and channel dimension on velocity distribution, streaming potential, apparent viscosity, volumetric flow rate and friction coefficient are discussed. In the analysis of EOF in closed slit microchannel, the positions of stationary planes for various flow behavior indices at different EDL thicknesses are found both analytically and numerically. It is found that the electroosmotic counter pressure developed inside the cell is strongly dependent on zeta potential and weakly dependent on EDL thickness.