Stability analysis of an evaporating binary mixture*

Rayleigh-B\'{e}nard-Marangoni instabilities in an evaporating binary mixture, consisting of a solvent and a solute of weak concentration, are studied theoretically. Local thermodynamic equilibrium is assumed at the flat gas-liquid interface. Solvent evaporation and air absorption in the liquid are neglected. At a certain height above the interface, the temperature and the concentration are fixed. One of the goals of the study is to track down the effects of this artifact on the results. Non-linear quasi-stationary basic profiles (due to evaporation) of the temperature and the solute concentration in the gas phase are considered, while the temperature distribution in the liquid is assumed to be linear and quasi-stationary. For the solute concentration in the liquid phase, two variants of the reference solution are studied, one just linear and quasi-stationary, whereas the other involves a fully transient non-linear profile. The latter is a more realistic option, given the relatively slow diffusion time in the liquid. A linear stability analysis is then carried out numerically, and illustrated for an aqueous solution of ethyl alcohol.