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The columns commonly used for the species separation of a binary fluid are very thin vertical parallelepipedic columns, filled with a porous medium (i.e. TGC columns). This species separation is due to the mass flux induces by the thermal gradient applied on walls of the cavity, namely the Soret effect, in the gravity field. In this paper, a new configuration used to study the species separation in a binary fluid was presented. The evolution of species separation in a binary fluid saturating a porous media, in a cavity between two concentric spheres, was studied analytically and numerically. The thickness of the cavity is e = R o - R i , where R i and R o are the internal and external radii, respectively. First, an analytical solution was developed using the parallel flow approximation considering e ≪ R i . The analytical results obtained are in a good agreement with the numerical ones performed with a spectral method or Comsol Multiphysics software. Thus, the results in the spherical configuration were compared with those obtained in a porous TGC column of same thickness, e, height, H = π R i , and depth, L = 2 R o .The numerical and analytical studies showed that the differences in mass fractions, C max - C min , and the time needed to obtain the stationary separation starting from a homogeneous binary solution were almost equal in the two configurations. The amount of species separated is greater in the spherical configuration than in the vertical column used. [ABSTRACT FROM AUTHOR]

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid mixture and subjected to vertical high-frequency and small-amplitude vibrations. Two configurations have been considered and compared: an infinite horizontal layer and a bounded domain with a large aspect ratio. In both cases, the initial temperature gradient is produced by a constant uniform heat flux applied on the horizontal boundaries. A formulation using time-averaged equations is used. The linear stability of the equilibrium solution is carried out for various Soret separation ratios φ, vibrational Rayleigh numbers Rv, Lewis numbers Le and normalized porosity. For an infinite horizontal layer, the critical Rayleigh number Rac is determined analytically. For a steady bifurcation to a one-cell solution (the critical wavenumber is zero), we obtain Rac=12/(φ(Le+1)+1) for all Rv. When the bifurcation is a Hopf bifurcation or when the critical wavenumber is not zero, we use a Galerkin method to compute the critical values. Our study is completed by a nonlinear analysis of the bifurcation to one-cell solutions in an infinite horizontal layer that is compared to numerical simulations in bounded horizontal domains with large aspect ratio. [ABSTRACT FROM AUTHOR]