Hydrodynamic interaction with super-hydrophobic surfaces

TL;DR

This paper analytically investigates how super-hydrophobic surfaces with trapped gas bubbles can reduce hydrodynamic drag, emphasizing the roles of slip length, gas fraction, and gap thickness.

Contribution

It introduces a harmonic mean correction function for drag prediction, linking effective slip lengths and pattern geometry in hydrodynamic interactions.

Findings

Drag reduction is significant for thin gaps.

Reduction depends on gas fraction and local slip length.

Pattern geometry has limited impact on drag reduction.

Abstract

Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a correction function to the Reynolds equation, which is shown to be the harmonic mean of corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (compared to texture period) gap. It is not really sensitive to the pattern geometry, but depends strongly on the fraction of the gas phase and local slip length at the gas area.