Effective slip in pressure-driven flow past super-hydrophobic stripes

TL;DR

This paper derives analytical formulas for effective slip lengths on super-hydrophobic striped surfaces with arbitrary local slip, providing insights into flow control and surface design in microfluidic applications.

Contribution

It introduces a comprehensive analytical framework for calculating effective slip lengths on striped super-hydrophobic surfaces with arbitrary local slip conditions, validated by numerical methods.

Findings

Effective slip depends on the ratio of local slip length to texture size.

Surface anisotropy leads to tensorial effective slip for large local slip.

Small local slip results in isotropic, surface-averaged flow.

Abstract

Super-hydrophobic array of grooves containing trapped gas (stripes), have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes, with limited guidance. Here, we analyze the experimentally relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive analytical formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that can be used for any surface slip fraction (validated by numerical calculations). By representing eigenvalues of the slip length-tensor, they allow us to obtain the effective slip for any orientation of stripes with respect to the mean flow. Our results imply that flow past stripes is controlled by the ratio of the local slip length to texture size. In case of a large (compared to the texture period) slip at the gas areas, surface anisotropy leads to a tensorial effective slip, by attaining the values predicted earlier for a perfect local slip. Both effective slip lengths and anisotropy of the flow decrease when local slip becomes of the order of texture period. In the case of small slip, we predict simple surface-averaged, isotropic flows (independent of orientation). These results provide a framework for the rational design of super-hydrophobic surfaces and devices.