Thermodynamics of sustaining gases in the roughness of submerged superhydrophobic surfaces

TL;DR

This paper investigates the thermodynamics of sustaining gases like air in the roughness of submerged superhydrophobic surfaces, providing a critical roughness scale estimate essential for maintaining gases and reducing drag.

Contribution

It introduces a thermodynamic framework and solution methodology to determine the critical roughness scale needed to sustain gases in submerged surfaces, extending prior vapor-focused work.

Findings

Roughness spacings less than a micron are necessary to sustain gases in water at atmospheric pressure.

The critical roughness scale depends on the degree of gas saturation in the liquid.

Results align with prior empirical data on superhydrophobic surfaces.

Abstract

Rough surfaces submerged in a liquid can remain almost dry if the liquid does not fully wet the roughness and gases are sustained in roughness grooves. Such partially dry surfaces can help reduce drag or enhance boiling. Gases sustained in roughness grooves would be composed of air and the vapor phase of the liquid itself. The thermodynamics of sustaining vapor was considered in a prior work [Patankar, Soft Matter, 2010, 6:1613]. Here, the thermodynamics of sustaining gases (e.g. air) is considered. Governing equations are presented along with a solution methodology to determine a critical condition to sustain gases. The critical roughness scale to sustain gases is estimated for different degrees of saturation of gases dissolved in the liquid. It is shown that roughness spacings of less than a micron are essential to sustain gases on surfaces submerged in water at atmospheric pressure. This is consistent with prior empirical data.