Analysis of onset of Soret-driven convection by the energy method

The Soret-driven instability in binary mixture heated from above is analyzed by using the energy method and its modification. The horizontal fluid layer placed between two plates is in initially quiescent state but the Soret diffusion can induce buoyancy-driven convection in the case of the negative Soret coefficient. For the case of highly unstable density stratification the buoyancy-driven motion sets in during the transient diffusion stage. Here the stability limits which are related to the onset time of instabilities are presented as a function of the Rayleigh number Ra, the Lewis number Le, and the separation ratio psi. The present stability analysis predicts that the onset time of convective instability decreases with increasing buoyancy parameter Ra(Le/psi)(-1). The relaxed energy method shows that the first visible motion can be detected from a certain time five times larger than the predicted onset time and the critical wave number is not zero but a finite value.