Stability of Stationary Plane-Parallel Flow of Binary Fluid with the Soret Effect in Vertical Layer with Differentially Heated Boundaries

Abstract

Stability of stationary plane-parallel flow of binary mixture with the Soret effect in vertical layer with differentially heated boundaries is studied. Main attention is paid to the thermal wave instability mode. The dependence of the threshold value of Prandtl number Pr∗, at which the growing thermal wave appear, on the separation ratio e is obtained. Complex scenario of stability change with respect to thermal waves is discovered for the case of positive Soret effect: it is shown that for e Pr∗, with the increase in separation ratio, additional range of growing thermal waves appears near Pr = 0, for e > 0.2634 the thermal wave instability exists at $$ 0\le \mathit{\Pr}\le {\mathit{\Pr}}_1^{\ast } $$ and at $$ \mathit{\Pr}>{\mathit{\Pr}}_2^{\ast } $$. For e > 0.278 the thermal wave instability is possible at any values of Prandtl number.