Onset of convection in two liquid layers with phase change

Abstract

We perform linear stability calculations for horizontal fluid bilayers that can undergo a phase transformation, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. We find that the entropy difference between the phases plays a crucial role in determining the stability of the system. For small values of the entropy difference between the phases, the system can be linearly unstable to heating from either above or below. The instability is due to the Marangoni effect in combination with the effects of buoyancy (for heating from below). For larger values of the entropy difference, the system is unstable only to heating from below, and the driving force for the instability is thermodynamic in nature, dominating the Marangoni effect. This long-wavelength instability can be understood qualitatively in terms of a variation of the classical morphological stability analysis of a phase boundary. The interface is unstable if either of the adjacent bulk phases is thermodynamically unstable. To help elucidate the mechanisms driving the instability on heating from below, we have performed both long-wavelength and short-wavelength analyses of the two-phase system, and have performed numerical calculations using materials parameters for a water-steam system. The two-phase system also allows a conventional Rayleigh-Taylor instability if the heavier fluid overlies the lighter fluid; applying a temperature gradient allows a stabilization of the interface.