Boussinesq approximations, and beyond, in a tall thermo-gravitational column

Gérard Labrosse

doi:10.1016/j.crme.2007.08.012

Boussinesq approximation, convection

Boussinesq approximations, and beyond, in a tall thermo-gravitational column
[Approximations de Boussinesq et au delà, en très haute colonne thermo-gravitationnelle]

Gérard Labrosse ^1,^2,³

¹ Université Paris-sud, Limsi-CNRS, bâtiment 508, 91405 Orsay cedex, France
² Mathematics Department, Federal University of Santa Catarina, Florianópolis, Brazil
³ Department of Chemical Engineering, University of Florida 237 ChE, P.O. Box 116005, Gainesville, FL 32611, USA

Comptes Rendus. Mécanique, Volume 335 (2007) no. 9-10, pp. 628-637.

Résumé
Abstract

Cet article présente les points essentiels d'un traitement non-Boussinesq nécessaire pour une analyse théorique des écoulements de base dans une colonne thermo-gravitationnelle, où le coefficient de Soret $S_{T}$ dépend de la température et de la composition, $S_{T} (T, C)$ . Le résultat principal est que la structure horizontale est contrôlée par la dépendance thermique de $S_{T}$ , alors que la dépendance compositionnelle de $S_{T}$ fixe la structure de la stratification compositionnelle verticale.

This article focuses on the main aspects of the non-Boussinesq treatment that is required for analyzing the simplest flow regimes occurring in a tall thermo-gravitational column, when the Soret coefficient $S_{T}$ is considered as depending upon temperature and composition, $S_{T} (T, C)$ . As a main result, the horizontal dynamics is mainly governed by the Soret thermal sensitivity, and the species vertical separation by its compositional one.

Reçu le : 2006-12-06
Accepté le : 2007-05-25
Publié le : 2007-09-01

DOI : 10.1016/j.crme.2007.08.012

Keywords: Fluid mechanics, Boussinesq approximations, Thermo-gravitational column
Mot clés : Mécanique des fluides, Approximations de Boussinesq, Colonne thermo-gravitationnelle

Affiliations des auteurs :

Gérard Labrosse ^{1, 2, 3}

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     title = {Boussinesq approximations, and beyond, in a tall thermo-gravitational column},
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Gérard Labrosse. Boussinesq approximations, and beyond, in a tall thermo-gravitational column. Comptes Rendus. Mécanique, Volume 335 (2007) no. 9-10, pp. 628-637. doi : 10.1016/j.crme.2007.08.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.012/

Bibliographie
Cité par

[1] J.K. Platten; J.C. Legros Convection in Liquids, Springer-Verlag, 1984

[2] W. Kohler; S. Wiegand Thermal Nonequilibrium Phenomena in Fluid Mixtures, Lecture Notes in Physics, vol. 584, Springer-Verlag, Berlin, Heidelberg, 2002

[3] W.H. Furry; R.C. Jones; L. Onsager On the theory of isotope separation by thermal diffusion, Phys. Rev., Volume 55 (1939), pp. 1083-1095

[4] R.C. Jones; W.H. Furry The separation of isotopes by thermal diffusion, Rev. Mod. Phys., Volume 18 (1946) no. 2, pp. 151-224

[5] M.M. Bou-Ali; O. Ecenarro; J.A. Madariaga; C.M. Santamaría; J.J. Valencia Thermogravitational measurement of the Soret coefficient of liquid mixtures, J. Phys.: Condens. Matter, Volume 10 (1998), pp. 3321-3331

[6] E. Blums; S. Odenbach Thermophoretic separation of ultrafine particles in ferrofluids in thermal diffusion column under the effect of an MHD convection, Int. J. Heat Mass Transfer, Volume 43 (2000), pp. 1637-1649

[7] J.F. Dutrieux; J.K. Platten; G. Chavepeyer; M.M. Bou-Ali On the measurement of positive Soret coefficients, J. Phys. Chem. B, Volume 106 (2002), pp. 6104-6114

[8] G. Labrosse Free convection of binary liquid with variable Soret coefficient in thermogravitational column: The steady parallel base states, Phys. Fluids, Volume 15 (2003) no. 9, pp. 2694-2727

[9] G. Farsang; H.J.V. Tyrrell Thermal diffusion factors and heats of transfer in Benzene-Methanol and Benzene-Ethanol mixtures at 25°, J. Chem. Soc. (A) (1969), pp. 1839-1843

[10] D.R. Caldwell Measurement of negative thermal diffusion coefficients by observing the onset of thermohaline convection, J. Phys. Chem., Volume 77 (1973) no. 16, pp. 2004-2008

[11] P. Poty; J.C. Legros; G. Thomaes Thermal diffusion in some binary liquid mixtures by the flowing cell method, Z. Naturforsh., Volume 29a (1974), pp. 1915-1916

[12] H. Korshing Thermodiffusionsfaktor von n-Heptan-Benzol mit einer Autokollimationsmethode, Z. Naturforsh., Volume 29a (1974), p. 1914

[13] V. Sanchez; J. Mahenc Détermination du coefficient de Soret de systèmes binaires liquides par interférométrie holographique, J. de Chimie Physique, Volume 73 (1976) no. 5, pp. 485-490

[14] P. Kolodner; H. Williams; C. Moe Optical measurement of the Soret coefficient of ethanol/water solutions, J. Chem. Phys., Volume 88 (1988) no. 10, pp. 6512-6524

[15] G.K. Batchelor Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Quart. Appl. Math., Volume XII (1954) no. 3, pp. 209-233

[16] R.C. Reid; J.M. Prausnitz; T.K. Sherwood The Properties of Gases and Liquids, McGraw–Hill Book Company, 1977

[17] B. Hafskjold Computer simulations of thermal diffusion in binary fluid mixtures (W. Kohler; S. Wiegand, eds.), Thermal Nonequilibrium Phenomena in Fluid Mixtures, Lecture Notes in Physics, vol. 584, Springer-Verlag, Berlin, Heidelberg, 2002, pp. 3-23

[18] P. Lallemand, Private communication

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