Jp. Larre et Jk. Platten, Cross-diffusional effects on the onset of convection of a ternary liquid layer heated from below, J NON-EQU T, 23(4), 1998, pp. 391-403
We develop the linear stability analysis of the rest state of a ternary liq
uid layer heated from below, with Soret effects and submitted to free, perm
eable and conductive boundary conditions. We include in our study the influ
ence of the cross-diffusional effects. In binary mixtures the critical Rayl
eigh number and Hopf frequency are mainly determined by Psi, the separation
ratio. We show that the approximate formulas of binary systems for the ove
rstability branch are still good approximations for ternary mixtures, provi
ded we define a new Psi taking into account the cross-diffusion. It represe
nts the contribution of the two independent rest mass fraction gradients, t
o the rest density gradient, relative to the rest temperature gradient.