Electroosmotic flow of a viscoplastic material through a slit channel with walls of arbitrary zeta potential

Abstract

Electroosmotic (EO) flow is known to have a nearly uniform velocity profile, but such a plug-flow velocity can be considerably diminished if the fluid is a viscoplastic material having a yield stress. This paper aims to investigate the reduction of EO velocity (also known as Smoluchowski slip velocity) due to a yield stress as a function of the material rheological parameters and the zeta potential. Three rheological models are considered: Casson, Herschel–Bulkley, and Bingham fluids. In the absence of pressure forcing and without the Debye–Hückel approximation, the problems of EO flow of these materials in a slit channel with walls uniformly charged with an arbitrary zeta potential are analytically solved. Analytical expressions are deduced for the reduced Smoluchowski velocity under the limiting conditions of very small and very large zeta potentials. It is shown that qualitatively different asymptotic behaviors will be exhibited by materials of different models.