Theoretical and numerical analysis of Soret-driven convection in a horizontal porous layer saturated by an n-component mixture: Application to ternary hydrocarbon mixture tetralin, isobutyl benzene, n-dodecane with mass fractions 0.8-0.1-0.1

Abstract

The purpose of this paper is to present an analytical model for the thermogravitational separation process in a porous rectangular cavity, saturated by a multi-component mixture. In the first part, an analytical and a numerical study of the onset of the Soret driven convection of an n-component mixture saturating a homogeneous porous horizontal layer are presented. This study is based on the classical Darcy-Boussinesq equations which admit a mechanical equilibrium solution associated with the pure double diffusive regime. This solution is linearly stable up to a critical value of the stability parameters. The dispersion relation is obtained for an n-component mixture and the associated critical parameters are calculated analytically and numerically using the Galerkin spectral method for the stationary transition. Concerning the oscillatory transition, only the Galerkin spectral method is used. The second part of the study presents an analytical model based on the parallel flow approximation. The analytical solution for the unicellular flow is obtained and the separation is expressed in terms of the Lewis numbers (Le), the separation ratio (ψ), the cross diffusion coefficients (Cr) and the thermal Rayleigh number (Ra). The analytical results are validated using direct numerical simulations. The numerical and the analytical results obtained are in good agreement.