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Anisotropic super-hydrophobic surfaces have the potential to greatly reducedrag and enhance mixing phenomena in microfluidic devices. Recent work hasfocused mostly on cases of super-hydrophobic stripes. Here, we analyze arelevant situation of cosine variation of the local slip length. We deriveapproximate formulae for maximal (longitudinal) and minimal (transverse)directional effective slip lengths that are in good agreement with the exactnumerical solution and lattice-Bolzmann simulations for any surface slipfraction. The cosine texture can provide a very large effective (forward) slip,but it was found to be less efficient in generating a transverse flow ascompared to super-hydrophobic stripes.

Flow past superhydrophobic surfaces with cosine variation in local slip length