Non-steady electro-osmotic flow of a micropolar fluid in a microchannel

Abstract

We formulated the initial-boundary-value problem of non-steady electro-osmotic flow of a micropolar fluid in a rectangular microchannel of height much larger than the Debye length and length much larger the height. Solving the governing differential equations numerically when a spatially uniform electric field is applied as an impulse of finite magnitude, we found that the effect is instantaneous on the flow, just as for simple Newtonian fluids. The decay times of the fluid velocity and the microrotation, however, are smaller in micropolar fluids than in simple Newtonian fluids. The maximum magnitude of microrotation decreases as the micropolarity increases. The effect of microrotation on the stress tensor is more dominant than that of the fluid speed, and a threshold effect with respect to the magnitude of the zeta potential is evident in the spatial profile of the couple stress tensor. We expect similar trends even when the applied electric field varies over some finite interval of time.