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Soret separation in a quasi-vertical cylinder

Published online by Cambridge University Press:  21 April 2006

D. Henry  and
B. Roux
D. Henry
Affiliation:
Laboratoire de Mécanique des Fluides, Ecole Centrale de Lyon, BP163, F-69131 Ecully cedex, France
B. Roux
Affiliation:
Institut de Mécanique des Fluides, UM 34 du CNRS, F-13003 Marseille, France
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Abstract

This paper deals with the Soret separation of a binary mixture in a cylinder subjected to an axial temperature gradient. The study is connected to an experiment designed to measure the Soret coefficient of an AgI-KI mixture corresponding to a moderate Prandtl number (Pr = 0.6) and a high Schmidt number (Sc = 60). In such an experiment the species separation is often hidden by a mixing effect due to the buoyancy-driven convection generated by a horizontal temperature gradient induced by some defect of the heating system. Here, such a defect is simulated by a slight misorientation of the cell with respect to the vertical; a small inclination (γ = 1°) of the cell has been considered, but the results can be generalized for any other small γ. For situations corresponding to a top heating and a positive Soret parameter, S, two quite different regimes have been exhibited depending on the value of S. For moderate S, the induced solutal buoyancy balances the imposed thermal buoyancy, slowing down the flow and giving a good separation rate. For small S this balance does not exist (except in the centre), leading to a remixing of the species and thus to poor separation (the separation would be still worse for negative S). The smaller the (positive) Soret parameter is, the smaller the cell misorientation γ has to be to allow a good separation rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 175 - 200
Copyright
© 1988 Cambridge University Press

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References

Abernathey, J. R. & Rosenberger F. 1981 Soret diffusion and convective stability in a closed vertical cylinder. Phys. Fluids 24, 377–381.Google Scholar
Agar, J. N. & Turner J. C. R. 1960 Thermal diffusion in solutions of electrolytes Proc. R. Soc. Lond. A 255, 307–330.Google Scholar
Bert J., Henry D., Layani P., Chuzeville G., Dupuy, J. & Roux B. 1984 Space experiment on thermal diffusion-preparation and theoretical analysis. Proc. Fifth European Symposium on Material Sciences under Microgravity (ESA SP-222), pp. 347–351. ESA Publ. Division c/o ESTEC. Noordwijk. The Netherlands.
Bert J. Moussa, I. & Dupuy, J. 1987 Space thermal diffusion experiment in a molten AgI-KI mixture. Proc. Sixth European Symposium on Material Sciences under Microgravity (ESA SP-256), pp. 471–475. ESA Publ. Division c/o ESTEC, Noordwijk, The Netherlands.
Caldwell D. R. 1973 Measurement of negative thermal diffusion coefficients by observing the onset of thermohaline convection. J. Phys. Chem. 77, 2004–2008.Google Scholar
Chien, C. P. & Mattes B. L. 1983 Thermal Soret diffusion in the liquid phase epitaxial growth of binary III–V compounds. J. Vac. Sci. Technol. B Microelec. Proc. and Phen. 1, 648–655.Google Scholar
Chock, D. P. & Li C. H. 1975 Direct integration method applied to Soret-driven instability. Phys. Fluids 18, 1401–1406.Google Scholar
Crespo, E. & Velarde M. G. 1982 Two component-Bénard convection in cylinders. Intl J. Heat Mass Transfer 25, 1451–1456.Google Scholar
De Groot S. R. 1947 L'effet Soret. North-Holland.
Dulieu B., Chanu, J. & Walch J. P. 1981 A propos de l'influence de la convection sur la mesure de l'effet Soret: le cas d'un défaut d'horizontalité J. Chim. Phys. 78, 193–201.Google Scholar
Gutkowicz-Krusin D., Collins, M. A. & Ross J. 1979 Rayleigh-Bénard instability in nonreactive binary fluids. II. Results. Phys. Fluids 22, 1451–1460.Google Scholar
Hardin G. R., Sani R. L., Henry, D. & Roux B. 1988 Buoyancy driven instability in a vertical cylinder: Binary fluid with Soret effect. Part 1. General theory and stationary stability results. Intl J. Num. Math Fluids. (submitted).Google Scholar
Harp, E. J. & Hurle D. J. T. 1968 Phil. Mag. 17, 1033.
Hart J. E. 1971 On sideways diffusive instability. J. Fluid Mech. 49, 279–288.Google Scholar
Hart J. E. 1973 Finite amplitude sideways diffusive instability. J. Fluid Mech. 59, 47–64.Google Scholar
Henry D. 1986 Simulation numérique 3D des mouvements de convection thermosolutale d'un mélange binaire - étude paramétrique de l'influence de la convection sur la séparation des espèces du mélange, par effet Soret, dans un cylindre incliné. Thèse de Doctorat d'Etat, Université Claude Bernard Lyon I.
Henry, D. & Roux B. 1983 Stationary and oscillatory instabilities for mixture subjected to Soret effect in vertical cylinder with axial temperature gradient. Proc. Fourth European Symposium on Material Sciences under Microgravity (ESA SP-191), pp. 145–152. ESA Publ. Division c/o ESTEC, Noordwijk, The Netherlands.
Henry, D. & Roux B. 1986 Three-dimensional numerical study of convection in a cylindrical thermal diffusion cell: its influence on the separation of constituents. Phys. Fluids 29, 3562–3572.Google Scholar
Henry, D. & Roux B. 1987a Three-dimensional numerical study of convection in a cylindrical thermal diffusion cell: inclination effect. Phys. Fluids 30, 1656–1666.Google Scholar
Henry, D. & Roux B. 1987b Numerical study of the perturbation of Soret experiments by 3D buoyancy driven flows. Proc. Sixth European Symposium on Material Sciences under Microgravity (ESA SP-256), pp. 487–491. ESA Publ. Division c/o ESTEC, Noordwijk, The Netherlands.
Huppert, H. E. & Turner J. S. 1981 Double-diffusive convection. J. Fluid Mech. 106, 299–329.Google Scholar
Hurle, D. T. J. & Jakeman E. 1969 Significance of the Soret effect in the Rayleigh-Jeffreys' problem. Phys. Fluids 12, 2704–2705.Google Scholar
Hurle, D. T. J. & Jakeman E. 1971 Soret-driven thermosolutal convection. J. Fluid Mech. 47, 667–688.Google Scholar
Hurle, D. T. J. & Jakeman E. 1973 Thermal oscillations in convecting fluids. Phys. Fluids 16, 2056–2059.Google Scholar
Legros J. C., Van Hook, W. A. & Thomaes, G. 1968 Convection and thermal diffusion in a solution heated from below. Chem. Phys. Lett. 2, 249–250.Google Scholar
Legros J. C., Rasse, D. & Thomaes G. 1970 Convection and thermal diffusion in a solution heated from below. Chem. Phys. Lett. 4, 1383–1385.Google Scholar
Leong, S. S. & de Vahl Davis G. 1979 Natural convection in a horizontal cylinder. In Proc. First Intl Conf. on Numerical Methods in Thermal Problems, University College, Swansea, pp. 287–296. Pineridge.
Longree D., Legros, J. C. & Thomaes G. 1980 Measured Soret coefficients for simple liquified gas mixture at low temperatures. J. Phys. Chem. 84, 3480–3483.Google Scholar
Malmejac, Y. & Praizey J. P. 1984 Thermomigration of cobalt in liquid tin. Proc. Fifth European Symposium on Material Sciences under Microgravity (ESA SP-222), pp. 147–152. ESA Publ. Division c/o ESTEC, Noordwijk, The Netherlands.
Olson, J. M. & Rosenberger F. 1979 Convective instabilities in a closed vertical cylinder heated from below. Part 2. Binary gas mixtures. J. Fluid Mech. 92, 631–642.Google Scholar
Paliwal, R. C. & Chen C. F. 1980a Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation. J. Fluid Mech. 98, 755–768.Google Scholar
Paliwal, R. C. & Chen C. F. 1980b Double-diffusive instability in an inclined fluid layer. Part 2. Stability analysis. J. Fluid Mech. 98, 769–785.Google Scholar
Platten, J. K. & Chavepeyer G. 1972 Soret driven instability. Phys. Fluids 15, 1555–1557.Google Scholar
Platten, J. K. & Chavepeyer G. 1976 Instabilité et flux de chaleur dans le problème de Bénard à deux constituants aux coefficients de Soret positifs. Intl J. Heat Mass Transfer 19, 27–32.Google Scholar
Platten, J. K. & Chavepeyer G. 1977 Nonlinear two dimensional Bénard convection with Soret effect: free boundaries. Intl J. Heat Mass Transfer 20, 113–122.Google Scholar
Platten, J. K. & Legros J. C. 1984 Convection in Liquids, pp. 650–652. Springer.
Praizey J. P. 1987 Results of the D1-WL-GHF-07 thermomigration in metallic alloys. In Sixth European Symposium on Material Sciences under Microgravity (ESA SP-256), pp. 501–508. ESA Publ. Division c/o ESTEC, Noordwijk, The Netherlands.
Schechter R. S., Prigogine, I. & Hamm J. R. 1972 Thermal diffusion and convective stability. Phys. Fluids 15, 379–386.Google Scholar
Schechter R. S., Velarde, M. G. & Platten J. K. 1974 The two-component Bénard problem. Adv. Chem. Phys. 26, 265–301.Google Scholar
Shirtcliffe T. G. L. 1969 An experimental investigation of thermosolutal convection at marginal stability. J. Fluid Mech. 35, 677–688.Google Scholar
Smutek C., Roux B., Bontoux, P. & de Vahl Davis G. 1984 3D finite difference for natural convection in cylinders. In Proc. Fifth Gesellschaft für Angewandte Mathematik und Mechanik-Conference. Notes on Numerical Fluid Mechanics, vol. 7, pp. 338–345. Vieweg.
Sundheim, B. R. & Kellner J. D. 1965 Thermoelectric properties of the molten silver nitrate-sodium nitrate system. J. Phys. Chem. 69, 1204–1208.Google Scholar
Thomaes G. 1975 The Bénard instability in liquid mixtures. Adv. Chem. Phys. 32, 269–279Google Scholar
Thorpe S. A., Hutt, P. K. & Soulsby R. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375–400.Google Scholar
Turner, J. S. & Chen C. F. 1974 Two-dimensional effects in double-diffusive convection. J. Fluid Mech. 63, 577–592.Google Scholar
Velarde, M. G. & Schechter R. S. 1971 Thermal diffusion and convective stability: a critical survey of Soret coefficient measurements. Chem. Phys. Lett. 12, 312–315.Google Scholar
Verhoeven J. D. 1969 Experimental study of thermal convection in a vertical cylinder of mercury heated from below. Phys. Fluids 12, 1733–1740.Google Scholar