Onset of morphological instability in two binary liquid layers

Abstract

We consider the linear stability of a horizontal liquid bilayer subject to vertical heating. The two layers consist of a binary liquid that has undergone a phase transition, resulting in a horizontal interphase boundary between two phases with different compositions. We perform linear stability calculations to determine the critical values for the applied temperature difference across the system that is necessary to produce instability using both numerical computations and small-wavenumber approximations. We focus on an instability primarily due to the phase change, which can occur in the absence of buoyancy and surface-tension-driven convection. We find both direct and oscillatory modes of instability, either of which can persist to small wavenumbers that allow approximate analytical descriptions. The interaction of flow with a deforming phase boundary plays a critical role in the instability, and the results are compared to morphological stability results that can be obtained in the absence of flow.