Combined pressure-driven and electroosmotic flow of Casson fluid through a slit microchannel

•Analytical solutions for electroosmotic flow of Casson fluid in a microchannel.•Various combinations of pressure and electrokinetic forcings.•Asymptotic approximations for integrals of nonlinear coupling terms.•Flow-rate shown to be sensitively affected by the yield stress. This study aims to develop analytical solutions for steady electroosmotic (EO) flow of a viscoplastic material, namely 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. The Casson yield stress makes the present problem distinct from existing studies on EO flow of other kinds of non-Newtonian such as power-law fluids. A first step of the analysis is to locate the yield surface, which divides the flow section into sheared and unsheared regions, where the stress is larger and smaller in magnitude than the yield stress, respectively. 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, characteristic of that of blood, 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.