Electro-osmotic flow in a rotating rectangular microchannel

An analytical model is presented for low-Rossby-number electro-osmotic flow in a rectangular channel rotating about an axis perpendicular to its own. The flow is driven under the combined action of Coriolis, pressure, viscous and electric forces. Analytical solutions in the form of eigenfunction expansions are developed for the problem, which is controlled by the rotation parameter (or the inverse Ekman number), the Debye parameter, the aspect ratio of the channel and the distribution of zeta potentials on the channel walls. Under the conditions of fast rotation and a thin electric double layer (EDL), an Ekman-EDL develops on the horizontal walls. This is essentially an Ekman layer subjected to electrokinetic effects. The flow structure of this boundary layer as a function of the Ekman layer thickness normalized by the Debye length is investigated in detail in this study. It is also shown that the channel rotation may have qualitatively different effects on the flow rate, depending on the channel width and the zeta potential distributions. Axial and secondary flows are examined in detail to reveal how the development of a geostrophic core may lead to a rise or fall of the mean flow.