Instability of the equilibrium of a liquid below its vapour between horizontal heated plates

Abstract

We study the stability of a motionless liquid below its vapour between heated horizontal plates. The temperature of the bottom plate is held below the vaporization temperature and the top plate is hotter than the vaporization temperature. A water film is on the cold plate and a vapour film on the hot plate. We find a basic solution depending only on the variable y normal to the plates, with steady distributions of temperature, a null velocity and no phase change. The linear stability of this basic state is studied in the frame of incompressible fluid dynamics, without convection, but allowing for phase change. An ambiguity in the choice of the conditions to be required of the temperature at the phase-change boundary is identified and discussed. It is shown that the basic state of equilibrium is overstable under conditions of large temperature gradient, when the other parameters have suitable values. An analysis of the energy of the most dangerous disturbance shows that the source of the instability is associated with change of phase.