Electro-osmotic flow along superhydrophobic surfaces with embedded electrodes

The effect of the secondary fluid enclosed in the indentations of a superhydrophobic surface on electro-osmotic flow is investigated. We derive analytical expressions for the net electro-osmotic flow over periodically structured surfaces, accounting for the influence of dissipation within the secondary fluid as well as for the role of charges at the fluid-fluid interfaces that are generated by auxiliary electrodes. Specifically, for a surface with rectangular grooves, the electro-osmotic flow velocity is related to the geometric parameters of the surface and the viscosity of an arbitrary secondary fluid filling the grooves. The results suggest that on specific superhydrophobic surfaces a flow enhancement by more than two orders of magnitude compared to unstructured surfaces can be expected.