Anisotropic electro-osmotic flow over super-hydrophobic surfaces

TL;DR

This paper investigates how anisotropic super-hydrophobic surfaces with patterned slip affect electro-osmotic flows, revealing tensorial mobility and conditions for flow enhancement.

Contribution

It introduces a theory for electro-osmotic flow over anisotropic patterned surfaces with arbitrary double-layer thickness, highlighting the tensorial nature of electro-osmotic mobility.

Findings

Electro-osmotic mobility becomes tensorial due to surface anisotropy.

Flow enhancement occurs only with charged liquid-gas interfaces.

Mobility tensor is generally not directly related to slip tensor.

Abstract

Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to greatly enhance electrokinetic phenomena. Existing theories assume either homogeneous flat surfaces or patterned surfaces with thin double layers (compared to the texture correlation length) and thus predict simple surface-averaged, isotropic flows (independent of orientation). By analyzing electro-osmotic flows over striped slip-stick surfaces with arbitrary double-layer thickness, we show that surface anisotropy generally leads to a tensorial electro-osmotic mobility and subtle, nonlinear averaging of surface properties. Interestingly, the electro-osmotic mobility tensor is not simply related to the hydrodynamic slip tensor, except in special cases. Our results imply that significantly enhanced electro-osmotic flows over super-hydrophobic surfaces are possible, but only with charged liquid-gas interfaces.