Combined Pressure-Driven and Electroosmotic Flow of Casson Fluid through a Slit Channel

Abstract

Analytical solutions are developed for steady electroosmotic (EO) flow of a Casson fluid through a parallel-plate microchannel. The flow is driven by electric as well as pressure forcings. A very thin electric double layer is assumed, and the Debye-Hückel approximation is used. A first step of the analysis is to locate the yield surface, which divides the flow section into sheared and unsheared regions. Different combinations of the electric and pressure forcings can lead to different types of distribution of stress relative to the yield stress. In this study, integrals of the nonlinear coupling terms of the two forcings are analytically expressed by uniformly valid approximations derived using the boundary-layer theory. It is shown that even a small value of the Casson yield stress can considerably reduce the rate of flow of the fluid through a microchannel by electroosmosis. The decreasing effect of the yield stress on the flow is intensified by the presence of a pressure gradient, whether favorable or adverse.