Comptes Rendus
Simple ideas about thermodiffusion in a binary liquid mixture
Comptes Rendus. Mécanique, Volume 341 (2013) no. 4-5, pp. 365-371.

The simplest system where the microscopic physical nature of thermodiffusion can be understood theoretically is a binary mixture. The case of a liquid mixture is considered here, starting from the equilibrium state such as described by thermodynamics. Under a uniform temperature, gradients of composition and/or pressure bring about a non-equilibrium state where local enthalpy is not minimum and/or local entropy is not maximum. The gradients of enthalpy and entropy define a thermodynamic force which is shown to drive composition and pressure diffusions. The thermodynamic force considered in this paper has the physical dimension of a force, it is defined per particle, it is invariant under gauge transformations of enthalpy and entropy and lastly it obeys Newtonʼs third law. Under a non-uniform temperature, it is shown that such a thermodynamic force does not account for thermodiffusion. The thermodiffusive force is of a non-thermodynamic essence. The kinetic-theory account of the transport coefficients is examined in mixtures of long macromolecules with small solvent molecules.

Published online:
DOI: 10.1016/j.crme.2013.01.010
Keywords: Binary liquid, Gauge invariance, Soret effect, Thermodiffusion, Thermodynamic force

Éric Bringuier 1

1 Matériaux et phénomènes quantiques, UMR 7162 du CNRS, université de Paris-7, 5, rue Thomas-Mann, 75205 Paris cedex 13, France
     author = {\'Eric Bringuier},
     title = {Simple ideas about thermodiffusion in a binary liquid mixture},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {365--371},
     publisher = {Elsevier},
     volume = {341},
     number = {4-5},
     year = {2013},
     doi = {10.1016/j.crme.2013.01.010},
     language = {en},
AU  - Éric Bringuier
TI  - Simple ideas about thermodiffusion in a binary liquid mixture
JO  - Comptes Rendus. Mécanique
PY  - 2013
SP  - 365
EP  - 371
VL  - 341
IS  - 4-5
PB  - Elsevier
DO  - 10.1016/j.crme.2013.01.010
LA  - en
ID  - CRMECA_2013__341_4-5_365_0
ER  - 
%0 Journal Article
%A Éric Bringuier
%T Simple ideas about thermodiffusion in a binary liquid mixture
%J Comptes Rendus. Mécanique
%D 2013
%P 365-371
%V 341
%N 4-5
%I Elsevier
%R 10.1016/j.crme.2013.01.010
%G en
%F CRMECA_2013__341_4-5_365_0
Éric Bringuier. Simple ideas about thermodiffusion in a binary liquid mixture. Comptes Rendus. Mécanique, Volume 341 (2013) no. 4-5, pp. 365-371. doi : 10.1016/j.crme.2013.01.010.

[1] C. Ludwig Diffusion zwischen ungleich erwärmten Orten gleich zusammengesetzter Lösungen, Sitzungsber. k. Akad. Wiss. Math.-Naturw. Kl., Volume XX (1856), p. 539

[2] S. Wiegand 150 Jahre Ludwig–Soret Effekt, Bunsen-Magazin, Volume 8 (2006) no. Heft 5, pp. 130-134

[3] S.G. Brush Kinetic Theory, vol. 3, Pergamon, Oxford, 1972

[4] E.A. Desloge Transport properties of a gas mixture, Am. J. Phys., Volume 32 (1964), pp. 742-748

[5] J.H. Ferziger; H.G. Kaper Mathematical Theory of Transport Processes in Gases, North-Holland, Amsterdam, 1972

[6] S. Hess In memoriam Ludwig Waldmann, Z. Naturforschung A, Volume 58 (2003), pp. 269-274

[7] D. Lhuillier; D. Lhuillier; D. Lhuillier Thermodiffusion of rigid particles in pure liquids, Physica A, Volume 47 (1986), pp. 1687-1696

[8] L.D. Landau; E.M. Lifshitz Fluid Mechanics, Pergamon, Oxford, 1959 (Chapter 6)

[9] J. Newman Thermoelectric effects in electrochemical systems, Ind. Eng. Chem. Res., Volume 34 (1995), pp. 3208-3216

[10] E. Bringuier Transport of volume in a binary liquid, Physica A, Volume 391 (2012), pp. 5064-5075

[11] E. Bringuier Anatomy of particle diffusion, Eur. J. Phys., Volume 50 (2009), pp. 1447-1470

[12] J.O. Hirschfelder; C.F. Curtiss; R.B. Bird Molecular Theory of Gases and Liquids, Wiley, New York, 1954 (p. 454)

[13] E. Bringuier From mechanical motion to Brownian motion, thermodynamics and particle transport theory, Eur. J. Phys., Volume 29 (2008), pp. 1243-1262 (Corrigendum)

[14] I. Müller A History of Thermodynamics: The Doctrine of Energy and Entropy, Springer, Berlin, 2007

[15] S.R. de Groot On the development of nonequilibrium thermodynamics, J. Math. Phys., Volume 4 (1963), pp. 147-153

[16] E. Bringuier Gauge-invariant approach to thermodiffusion in a liquid binary mixture, Physica A, Volume 390 (2011), pp. 1861-1875

[17] S.R. de Groot; P. Mazur Non-Equilibrium Thermodynamics, North-Holland, Amsterdam, 1962 (pp. 25–27, 273–284)

[18] R.J. Bearman; J.G. Kirkwood Statistical mechanics of transport processes. XI. Equations of transport in multicomponent systems, J. Chem. Phys., Volume 28 (1958), pp. 136-145

[19] G.H. Wannier Statistical Physics, Wiley, New York, 1966 (p. 486)

[20] R. Krishna; J.A. Wesselingh; J.A. Wesselingh; R. Krishna, Chem. Eng. Sci. (Mass Transfer in Multicomponent Mixtures), Volume 52, VSSD-Delft University Press, Delft, 1997, pp. 861-911

[21] K.I. Morozov Soret effect in molecular mixtures, Phys. Rev. E, Volume 79 (2009), p. 031204

[22] J.G. Kirkwood; I. Oppenheim Chemical Thermodynamics, McGraw–Hill, New York, 1961 (pp. 92–95)

[23] M.T. Tyn; W.F. Calus Temperature and concentration dependence of some binary liquid systems, J. Chem. Eng. Data, Volume 20 (1975), pp. 310-316

[24] I. Goldhirsch; D. Ronis; I. Goldhirsch; D. Ronis Theory of thermophoresis. II. Low-density behavior, Phys. Rev. A, Volume 27 (1983), pp. 1616-1634

[25] S. Wiegand Thermal diffusion in liquid mixtures and polymer solutions, J. Phys.: Condens. Matter, Volume 16 (2004), p. R357-R379

[26] D. Stadelmaier; W. Köhler; D. Stadelmaier; W. Köhler Thermal diffusion of dilute polymer solutions: The role of chain flexibility and the effective segment size, Macromol., Volume 41 (2008), pp. 6205-6208

[27] E. Bringuier Scaling theory of polymer thermodiffusion, Physica A, Volume 389 (2010), pp. 4545-4551

[28] F. Brochard-Wyart How to separate polydisperse polyelectrolytes by thermal field flow fractionation techniques, Macromol., Volume 16 (1983), pp. 149-150

[29] M. Yang; M. Ripoll Driving forces and polymer hydrodynamics in the Soret effect, J. Phys.: Condens. Matter, Volume 24 (2012), p. 195101

[30] F. Brochard; P.-G. de Gennes Effet Soret des macromolécules flexibles, C. R. Acad. Sci. Paris, Ser. II, Volume 293 (1981), pp. 1025-1027

[31] E. Bringuier; E. Bringuier Connection between thermophoresis and thermodiffusion in a liquid binary mixture, Phil. Mag., Volume 87 (2007), pp. 873-883

[32] J.S. Vrentas; J.L. Duda Molecular diffusion in polymer solutions, AIChE J., Volume 25 (1979), pp. 1-24

[33] M. Doi; S.F. Edwards The Theory of Polymer Dynamics, Oxford University Press, Oxford, 1986 (pp. 91–100)

[34] J. Rauch, Diffusion und Thermodiffusion in Polymerlösungen, PhD thesis, University of Bayreuth, 2006, p. 128.

[35] D. Enskog; D. Enskog Bermerkungen zu einer Fundamentalgleichung in der kinetischen Gastheorie, Physik. Zeitschrift, Volume XII (1911), pp. 56-60

[36] E.M. Lifshitz; L.P. Pitaevskii Physical Kinetics, Pergamon, Oxford, 1981 (Section 11)

Cited by Sources:

Comments - Policy