Flow past superhydrophobic surfaces with cosine variation in local slip length

TL;DR

This paper investigates how cosine variation in local slip length on superhydrophobic surfaces affects flow, deriving formulas for effective slip and comparing their efficiency to striped textures in microfluidic applications.

Contribution

It introduces approximate formulas for effective slip lengths on cosine-patterned superhydrophobic surfaces, validated against numerical simulations.

Findings

Cosine textures can produce large forward slip.

They are less effective than stripes in generating transverse flow.

Formulas agree well with simulations.

Abstract

Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of super-hydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length. We derive approximate formulae for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Bolzmann simulations for any surface slip fraction. The cosine texture can provide a very large effective (forward) slip, but it was found to be less efficient in generating a transverse flow as compared to super-hydrophobic stripes.