Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect

Abstract

Abstract. We have explored the combined long-wave Marangoni and Rayleigh instability of the quiescent state of a binary-liquid layer heated from below or from above in the presence of the Soret effect. We found that in the case of small Biot numbers there are two longwave regions of interest k ∼ Bi 1/2 and k ∼ Bi 1/4 . The dependence of both monotonic and oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond numbers has been investigated. The complete linear stability analysis reveals the diversity of instability types in the long-wave region, and a need in the development of the nonlinear theory of the discovered phenomena becomes obvious.

Longwave oscillatory patterns in liquids: outside the world of the complex Ginzburg–Landau equation

“…That circumstance creates a rather complex picture of neutral curves for monotonic and oscillatory instabilities. A generalization of the theory for combined Marangoni and Rayleigh instabilities, that was carried out in [127], revealed a diversity of instability types in the longwave region.…”

Surface deformation on thermocapillary convection in a binary fluid with internal heat generation and temperature dependent viscosity

“…[4] analysed the effect of evaporation on Bénard-Marangoni convection in a binary fluid layer, where the liquid-gas interface was assumed undeformable. Few researchers also study the binary fluid layer instability by applying other physical influences such as the Soret number [5], [6], nonlinear Soret effect [7] and with throughflow and Soret effect [8]. It is crucial to control the Bénard-Marangoni convection in a binary fluid since thermosolutal problem (behaviour of convection with both temperature and salinity (salt) gradients) is very important in oceanography.…”