Cross-diffusional effects on the onset of convection of a ternary liquid layer heated from below

We develop the linear stability analysis of the rest state of a ternary liquid layer heated from below, with Soret effects and submitted to free, permeable and conductive boundary conditions. We include in our study the influence of the cross-diffusional effects. In binary mixtures the critical Rayleigh number and Hopf frequency are mainly determined by Psi, the separation ratio. We show that the approximate formulas of binary systems for the overstability branch are still good approximations for ternary mixtures, provided we define a new Psi taking into account the cross-diffusion. It represents the contribution of the two independent rest mass fraction gradients, to the rest density gradient, relative to the rest temperature gradient.