  Rough surfaces immersed under water remain practically dry if the
liquid-solid contact is on roughness peaks, while the roughness valleys are
filled with gas. Mechanisms that prevent water from invading the valleys are
well studied. However, to remain practically dry under water, additional
mechanisms need consideration. This is because trapped gas (e.g. air) in the
roughness valleys can dissolve into the water pool, leading to invasion.
Additionally, water vapor can also occupy the roughness valleys of immersed
surfaces. If water vapor condenses, that too leads to invasion. These effects
have not been investigated, and are critically important to maintain surfaces
dry under water. In this work, we identify the critical roughness scale below
which it is possible to sustain the vapor phase of water and/or trapped gases
in roughness valleys - thus keeping the immersed surface dry. Theoretical
predictions are consistent with molecular dynamics simulations and experiments.
