Occurrence of vortices in electro-osmotic microchannel flows

We study the electro-osmotic flow through a T-junction of micro-channels whose dielectric walls are weakly polarizable. The velocity field is obtained via superposition of an irrotational part associated with the equilibrium zeta potential and the induced-charge electroosmotic flow originating from the interaction of the externally-applied electric field and the charge cloud it induces owing to field leakage through the polarizable dielectric channel walls. Along the channel walls the latter component gives rise to fluid velocities converging toward the corner which dominate the flow in its immediate vicinity. Recent experimental observations in the literature regarding the appearance and subsequent expansion of flow reversal and vortices are rationalized in terms of the growing relative importance of this contribution to the global velocity field with increasing intensity of the externally applied electric field.