On the stability of an evaporating liquid surface

Abstract

The stability of the interface between a volatile liquid and a gaseous phase has been studied in this paper. We consider the case when the liquid volume is not a film and thus the thin-film approximation might not be valid. A linear stability analysis leads to the Orr-Sommerfeld equation for the stream function and a second-order differential equation for the temperature. This system is solved semi-analytically. A parameter study shows that surface tension is stabilizing, while viscosity is destabilizing the liquid surface. The capillary number is identified as the most significant factor. The analytical results were compared with the growth of an initial perturbation for the full system by direct numerical simulations, and excellent agreement was observed.