Convective instability in multicomponent mixtures with Soret effect

Abstract

We study the two-dimensional modes of gravity-dependent convective instability arising in a ternary mixture in a plane horizontal layer. The gravity force is oriented perpendicular to the layer heated from below. It is assumed that the system is in the state of mechanical equilibrium of a mixture considered as the base state of the system, which can become unstable under certain conditions. The mathematical model uses two-dimensional Navier-Stokes equations, transfer equations for describing mixture components with the Soret effect, and a heat transfer equation. Under the influence of a concentration gradient, the heat transfer symmetric to the Soret effect is neglected because it is usually small in water-based mixtures. The possible concentration-dependent diffusion and cross-diffusion of dissolved components are also neglected. We investigate a convective stability using linear approximation and under finite-amplitude convection regimes. The stability analysis of the base state after linearization of the governing equations with respect to the state of mechanical equilibrium predicts various convection modes. For each case, a neutral curve and the dependences of the disturbance growth decrements on both the Rayleigh number and the wave number are plotted. We show that in the case of the layer being heated from below, there are ranges of governing parameters where both long-wave and short-wave modes of oscillatory instability occur. The numerical analysis of a nonlinear coupling between these modes has revealed that such instabilities develop in the ternary mixtures whose components are arranged (due to the Soret effect) in different directions with respect to the temperature gradient. The effect of the Rayleigh number on the flow structure and heat mass transfer is demonstrated.