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In this paper, an analytical and numerical analysis of the species separation in a binary mixture is performed. The main objective is to study the influence of the thickness and the nature of the bounding plates of the thermogravitational column (TGC) on species separation. The theory of Furry, Jones and Onsager is extended to the cases where bounding conducting walls enclose the TGC. The governing 2-dimensional equations are solved numerically using COMSOL Multiphysics software. A good agreement is found between the analytical and the numerical results. It is shown that the determination of the thermal diffusion coefficient, DT, from the measurement of the vertical mass fraction gradient of binary solutions, does not depend on the temperature difference imposed on the vertical column either on the outer walls of the cavity or on the inner walls in contact with the binary solutions. However, it is found that this result is no longer valid in the case of a binary gas. To our knowledge, in all earlier studies, dealing with the measurement of Soret coefficients in binary fluids, the nature and the thickness of the bounding walls were not considered.

In this paper, an analytical and numerical analysis of the species separation in a binary mixture is performed. The main objective is to study the influence of the thickness and the nature of the bounding plates of the thermogravitational column (TGC) on species separation. The theory of Furry, Jones and Onsager is extended to the cases where bounding conducting walls enclose the TGC. The governing 2-dimensional equations are solved numerically using COMSOL Multiphysics software. A good agreement is found between the analytical and the numerical results. It is shown that the determination of the thermal diffusion coefficient, DT, from the measurement of the vertical mass fraction gradient of binary solutions, does not depend on the temperature difference imposed on the vertical column either on the outer walls of the cavity or on the inner walls in contact with the binary solutions. However, it is found that this result is no longer valid in the case of a binary gas. To our knowledge, in all earlier studies, dealing with the measurement of Soret coefficients in binary fluids, the nature and the thickness of the bounding walls were not considered. [ABSTRACT FROM AUTHOR]

In this paper, an analytical and numerical study of species separation in binary mixtures taking account of the presence of bounding plates for the cell is presented. A rectangular horizontal porous cavity saturated by a binary mixture and heated from below is considered. This cavity is bounded by thin plates of uniform thickness, the outer surfaces of which are subjected to a constant heat flux. The transition from the equilibrium solution to the convective one, either stationary or oscillatory, was previously studied by Ouattara et al. (2012). Thus in the first part of this paper, the critical parameters associated with the onset of long wavelength disturbances, obtained analytically, are recalled. Then the hypothesis of parallel flow is used to determine an analytical solution which describes the unicellular flow which may appear in the case of a large aspect ratio cell for a given range of separation ratio, ψ , Rayleigh number, Ra , Lewis number, Le, the ratio of the plate to the porous layer thickness, δ, and their thermal conductivity ratio, d . The analytical results are corroborated by direct numerical simulations. We verify that if d goes to infinity, the walls become infinitely conductive and we find the results obtained by Charrier-Mojtabi et al. (2007). When d tends to 0, the walls become infinitely thin the results obtained by Yacine et al. (2016) are recovered. A linear stability analysis of the unicellular flow is also presented. The eigenvalue problem resulting from the temporal stability analysis is solved by a Tau spectral method. The optimal Rayleigh number leading to an optimal value of the separation horizontal gradient is determined for different values of physical parameters. We show that the species separation depends sensitively on the ratio of the plate to the porous layer thickness, and the ratio of their thermal conductivities. Furthermore, we have shown that in the stationary state and for a given value of the thermal conductivity ratio ( d  = 29), the maximum separation is almost equal for walls of the same thickness than the one of porous cavity or for the case of porous cell delimited by the infinitely thin walls. [ABSTRACT FROM AUTHOR]

An analytical and numerical study of Soret-driven convection in a horizontal porous layer saturated by a binary fluid and subjected to uniform cross heat fluxes is presented. The flow is driven by the combined buoyancy effect due to temperature and induced mass fraction variations through a binary water ethanol mixture. In the first part of the study, a closed-form analytical solution in the limit of a large aspect ratio of the cell ( A >> 1) is developed. We are mainly concerned with the determination of the mass fraction gradient of the component of interest along the horizontal direction, which determines the species separation. In the second part, numerous numerical simulations are carried out in order to validate the analytical results and extend heat and mass transfer to an area not covered by the analytical study. Good agreement is found between analytical and numerical results concerning the species separation obtained for a unicellular flow. In this configuration, the Soret separation process is improved by two control parameters: the heat flux density imposed on the horizontal walls of the cell and the ratio, a , of heat flux density imposed on vertical walls to that on horizontal walls. The influence of the heat flux density ratio, a , on the transient regime (relaxation time) is also investigated numerically. We observe that an increase in the parameter a leads to a decrease in the relaxation time. Thus, for a cell heated from below without lateral heating, the onset of convection from the mechanical equilibrium state is analyzed. The linear stability analysis shows that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The linear stability results are widely corroborated by direct 2D numerical simulations. The thresholds of various multicellular solutions are determined in terms of the governing parameters of the problem using nonlinear direct numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: The onset of Soret-driven convection in a shallow porous horizontal layer filled with a binary mixture and submitted to a vertical heat flux on the two horizontal walls is investigated. We study the species separation between the two vertical ends of the cell, which appears for low values of the Rayleigh number and for positive separation ratio. An analytical solution is performed and the separation is expressed in terms of thermal Rayleigh number, Lewis number, separation ratio and aspect ratio of the cell. These analytical results are corroborated by direct non-linear numerical simulations. Then, the results are compared with those obtained in a differentially heated vertical cavity. [Copyright &y& Elsevier]

Abstract: The aim of this article is to present briefly a summary of the state of art in theoretical, experimental and numerical approaches in thermodiffusion. The concepts and equations giving the mass flux of constituents in binary, ternary and multicomponent mixtures are presented. [Copyright &y& Elsevier]