Anisotropic Electro-Osmotic Flow Over Super-Hydrophobic Surfaces

Textured super-hydrophobic (SH) surfaces with trapped gas bubbles are promising for use in microfluidic devices, due to their low viscous resistance, or large effective slip length, in pressure-driven flow. Recently, the possibility of using SH surfaces to amplify electro-osmotic flow has also attracted attention, e.g. in the context of nanofluidic energy conversion (by harvesting streaming current). For textured surfaces, both of these properties of SH surfaces are generally anisotropic, and the slip length and electro-osmotic mobility must be replaced by appropriate tensorial generalizations. Here, we discuss tensorial hydrodynamic slip and calculate the electro-osmotic mobility tensor for a model SH surface consisting of flat stripes of alternating charge and slip length, for arbitrary Debye length in the linear regime. Large enhancements of electro-osmotic flow are predicted only if charge can be maintained on the gas-liquid interfaces.