Onset of convection in a two–phase binary mixture with the Soret effect in weightlessness

Abstract

The linear stability of mechanical equilibrium in a two–layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane–methanol binary mixture, which has a liquid–liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long–wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers.