Interfacial nonequilibrium and Bénard-Marangoni instability of a liquid-vapor system

We study Bénard-Marangoni instability in a system formed by a horizontal liquid layer and its overlying vapor. The liquid is lying on a hot rigid plate and the vapor is bounded by a cold parallel plate. A pump maintains a reduced pressure in the vapor layer and evacuates the vapor. This investigation is undertaken within the classical quasisteady approximation for both the vapor and the liquid phases. The two layers are separated by a deformable interface. Temporarily frozen temperature and velocity distributions are employed at each instant for the stability analysis, limited to infinitesimal disturbances (linear regime). We use irreversible thermodynamics to model the phase change under interfacial nonequilibrium. Within this description, the interface appears as a barrier for transport of both heat and mass. Hence, in contrast with previous studies, we consider the possibility of a temperature jump across the interface, as recently measured experimentally. The stability analysis shows that the interfacial resistances to heat and mass transfer have a destabilizing influence compared to an interface that is in thermodynamic equilibrium. The role of the fluctuations in the vapor phase on the onset of instability is discussed. The conditions to reduce the system to a one phase model are also established. Finally, the influence of the evaporation parameters and of the presence of an inert gas on the marginal stability curves is discussed.