  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.
