Thermodynamics of Trapping Gases for Underwater Superhydrophobicity

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, enhance boiling, and reduce biofouling. Gases sustained in roughness grooves would be composed of air and the vapor phase of the liquid itself. In this work, 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.