Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas

A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid-gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.