The onset of Soret-driven convection in a binary mixture heated from above

The onset of buoyancy-driven convection in an initially quiescent, horizontal fluid layer heated from above is analyzed theoretically. The present system of binary mixtures is a thermally stable one but the Soret diffusion can induce buoyancy-driven motion. With highly unstable density gradients the convective motion sets in during the transient diffusion stage. Here the onset time of convective motion is analyzed by employing the propagation theory. The dimensionless critical time tau(c) and the critical wavenumber a(c) to mark the onset of convective motion is presented as a function of the Rayleigh number Ra, the Lewis number Le, and the separation ratio psi. The results show that the onset time decreases with increasing buoyancy force Ra(Le/psi)(-1) and the predicted a(c)-values agree well with available experimental data. For the ethanol-water system the predicted critical reduced Rayleigh number r(c)(=Ra-c/1708)=-0.0464 agrees reasonably with existing experimental results of r=-0.1. It is found that the visible motion can be detected from a certain time tau congruent to 4(3/4)tau(c).