Effective slip over superhydrophobic surfaces in thin channels

TL;DR

This paper derives rigorous bounds on the effective slip length for various superhydrophobic surface textures in thin channels, guiding the design of surfaces to optimize drag reduction.

Contribution

It provides a theoretical framework with bounds on slip length for any two-component texture in thin channels, extending understanding beyond specific cases.

Findings

Parallel stripes maximize or minimize slip depending on orientation.

Hashin-Strikman bounds constrain slip for isotropic textures.

Results guide rational design of superhydrophobic surfaces.

Abstract

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. For isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.