Onset of Soret-induced convection in a horizontal layer of ternary fluid with fixed vertical heat flux at the boundaries

Abstract.

The paper deals with the investigation of the onset and weakly nonlinear regimes of the Soret-driven convection of ternary liquid mixture in a horizontal layer with rigid impermeable boundaries subjected to the prescribed constant vertical heat flux. It is found that there are monotonous and oscillatory longwave instability modes. The boundary of the monotonous longwave instability in the parameter plane Rayleigh number Ra - net separation ratio $\Psi$ at fixed separation ratio of one of solutes consists of two branches of hyperbolic type. One of the branches is located at ${\rm Ra} >0$, the other one at ${\rm Ra} <0$. The oscillatory longwave instability exists at $\Psi >0$ only for the heating from below and at $\Psi <0$ there exist two oscillatory longwave instability modes: one at ${\rm Ra} >0$ and the other at ${\rm Ra} <0$. Corrections to the Rayleigh number obtained in the higher order of the expansion show that the longwave perturbations can be most dangerous at any values of $\Psi$. The numerical solution of the linear stability problem for small perturbations with finite wave numbers confirms this conclusion. The weakly nonlinear analysis shows that all steady solutions are unstable to the modes of larger wavelength and stable to the modes of smaller wavelength, i.e. the solution with maximal possible wavelength is realized.

Graphical abstract