  We give a general theoretical description of electro-osmotic flow at striped
super-hydrophobic surfaces in a thin double layer limit, and derive a relation
between the electro-osmotic mobility and hydrodynamic slip-length tensors. Our
analysis demonstrates that electro-osmotic flow shows a very rich behavior
controlled by slip length and charge at the gas sectors. In case of uncharged
liquid-gas interface, the flow is the same or inhibited relative to flow in
homogeneous channel with zero interfacial slip. By contrast, it can be
amplified by several orders of magnitude provided slip regions are uniformly
charged. When gas and solid regions are oppositely charged, we predict a flow
reversal, which suggests a possibility of huge electro-osmotic slip even for
electro-neutral surfaces. On the basis of these observations we suggest
strategies for practical microfluidic mixing devices. These results provide a
framework for the rational design of super-hydrophobic surfaces.
