Onset of convection in two layers of a binary liquid

Abstract

We perform linear stability calculations for horizontal bilayers of a two-component fluid that can undergo a phase transformation, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. Critical values for the applied temperature difference across the system that is necessary to produce instability are obtained by a linear stability analysis, using both numerical computations and small wavenumber approximations. Thermophysical properties are taken from the aluminum–indium monotectic system, which includes a liquid–liquid miscibility gap. In addition to buoyant and thermocapillary modes of instability, we find an oscillatory phase-change instability due to the combined effects of solute diffusion and fluid flow that persists at small wavenumbers. This mode is sensitive to the ratio of the layer depths, and for certain layer depths can occur for heating from either above or below.