Soret Effect and Mixed Convection in Porous Media

Abstract

We study the pattern formation of a binary mixture in a porous medium heated from below in the presence of an horizontal flow. The asymptotic response of the system to a localized perturbation in the both directions of the horizontal plane is evaluated in two different situations. When the system exhibits a supercritical bifurcation, a linear stability analysis is performed. Presence of through flow breaks the rotational symmetry and the system at the absolute instability threshold, selects transversal rolls among an infinity of unstable modes. We show that in binary mixtures with negative separation ratio ψ, contrary to the case of positive ψ, the through flow shrinks the region of convective instabilities, and even may suppress the convective/absolute transition. In the case of subcritical bifurcation, a quintic Ginzburg-Landau equation is derived. A threshold of nonlinear absolute instability is found below the linear one when nonlinear front propagation dominates the dynamics. The velocity and wavenumber of these fronts are determined. An exists in nonlinear absolute instability region and its extent is ruled by the through flow rate. Moreover, special emphasis on the determination of ψ is given.