Effect of surface tension on the stability of a binary fluid layer under reduced gravity

Abstract

A temperature gradient imposed across a binary fluid layer with a nonzero Soret coefficient will induce a solute concentration gradient. The ratio of these two gradients is proportional to the separation ratio χ, a property of the fluid. Similarly, the ratio of the thermal and solutal Marangoni numbers, which are nondimensional increments in surface tension due to changes in temperature and concentration, is also proportional to the separation ratio. As a consequence, the stability of a given binary fluid layer with a free surface under zero gravity depends only on the temperature difference, ΔT, imposed across the layer or, equivalently, on the thermal Marangoni number, M, albeit the dependence, is rather complicated. When the gravity is nonzero but of small magnitude, such that the buoyancy effects are not dominant, the stability characteristics of the layer are functions of two parameters, M and R, the thermal Rayleigh number. In this paper, the stability of such a binary layer under zero and reduced gravity by means of linear stability analysis is studied. Results show that the nature of the instability depends on the product χK, where K is a material constant=(α/αS)(γS/γ), with α and αS denoting the volumetric expansion coefficient due to temperature and solute concentration, respectively, and γ and γS the rate of change of surface tension with respect to temperature and solute concentration, respectively. Both χ and K can assume positive and negative values. Under zero gravity, instability at the critical value of M onsets in steady convection if χK<0 and in oscillating convection if χK≳0. For a layer that is being heated from below and K≳0, the steady instability in the case of χK<0 can be rendered stable by subjecting the layer to a gravity of small magnitude. But for χK≳0, the effect of gravity is always destabilizing.