Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures

  • José M. Ortiz de ZárateEmail author
Regular Article
Part of the following topical collections:
  1. Thermal Non-Equilibrium Phenomena in Soft Matter


The definitions of thermodiffusion and Soret coefficients for a binary mixture include a concentration prefactor x(1 - x), when mole fraction x is used, or w(1 - w), when mass fraction w is used. In this paper the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the thermodiffusion and the Soret coefficients invariant upon changing in the concentration representation, using either mole fraction or mass faction. Then, it is shown how this invariance property can be extended to ternary mixtures by using appropriate concentration prefactors in matrix form. The paper is completed with some considerations about alternative definitions of thermodiffusion coefficients, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, use of molar concentrations and, finally, extension to multi-component mixtures.

Graphical abstract


Topical issue: Thermal Non-Equilibrium Phenomena in Soft Matter 


  1. 1.
    W. Köhler, K.I. Morozov, J. Non-Equilib. Thermodyn. 41, 151 (2016)ADSCrossRefGoogle Scholar
  2. 2.
    S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962Google Scholar
  3. 3.
    Y. Demirel, Nonequilibrium Thermodynamics (Elsevier, Amsterdam, 2002)Google Scholar
  4. 4.
    G. Lebon, D. Jou, J. Casas-Vázquez, Understanding Nonequilibrium Thermodynamics (Springer, 2008)Google Scholar
  5. 5.
    S. Kjelstrup, D. Bedeaux, E. Johannessen, J. Gross, Non-Equilibrium Thermodynamics for Engineers (World Scientific, Singapore, 2010)Google Scholar
  6. 6.
    J.K. Platten, P. Costesèque, Eur. Phys. J. E 15, 235 (2004)CrossRefGoogle Scholar
  7. 7.
    A. Vailati, M. Giglio, Phys. Rev. E 58, 4361 (1998)ADSCrossRefGoogle Scholar
  8. 8.
    R. Taylor, R. Krishna, Multicomponent Mass Transfer (Wiley, New York, 1993)Google Scholar
  9. 9.
    P.S. Belton, H.J.V. Tyrrell, Z. Naturforsch. 26, 48 (1971)ADSCrossRefGoogle Scholar
  10. 10.
    S. Wiegand, H. Ning, R. Kita, J. Non-Equilib. Thermodyn. 32, 193 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    H. Cabrera, F. Cordido, A. Velásquez, P. Moreno, E. Sira, S.A. López-Rivera, C.R. Mec. 341, 372 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    B. Hafskjold, Eur. Phys. J. E 40, 4 (2017)CrossRefGoogle Scholar
  13. 13.
    S. Di Lecce, T. Albrecht, F. Bresme, Sci. Rep. 7, 44833 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    W. Köhler, B. Müller, J. Chem. Phys. 103, 4367 (1995)ADSCrossRefGoogle Scholar
  15. 15.
    A. Mialdun, V.M. Shevtsova, Int. J. Heat Mass Transfer 51, 3164 (2008)CrossRefGoogle Scholar
  16. 16.
    F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    F.A. Furtado, A.J. Silveira, C.R.A. Abreu, F.W. Tavares, Brazil. J. Chem. Eng. 32, 683 (2015)CrossRefGoogle Scholar
  18. 18.
    S.R. De Groot, Physica 9, 699 (1942)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    R. Delgado-Buscalioni, M. Khayet, J.M. Ortiz de Zárate, F. Croccolo, Eur. Phys. J. E 40, 51 (2017)CrossRefGoogle Scholar
  20. 20.
    J.K. Platten, M.M. Bou-Ali, P. Costesèque, J.F. Dutrieux, W. Köhler, C. Leppla, S. Wiegand, G. Wittko, Philos. Mag. 83, 1965 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    A. Mialdun, C. Minetti, Y. Gaponenko, V. Shevtsova, F. Dubois, Microgravity Sci. Technol. 25, 83 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    G. Galliero, H. Bataller, F. Croccolo, R. Vermorel, P. Artola, B. Rousseau, V. Vesovic, M. Bou-Ali, J.M. Ortiz de Zárate, K. Zhang, F. Montel, Microgravity Sci. Technol. 28, 79 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    G. Galliero, H. Bataller, J.P. Bazile, J. Diaz, F. Croccolo, H. Hoang, R. Vermorel, P.A. Artola, B. Rousseau, V. Vesovic, M.M. Bou-Ali, J.M. Ortiz de Zárate, S. Xu, K. Zhang, F. Montel, A. Verga, O. Minster, npj microgravity 3, 20 (2017)CrossRefGoogle Scholar
  24. 24.
    P. Baaske, H. Bataller, M. Braibanti, M. Carpineti, R. Cerbino, F. Croccolo, A. Donev, W. Köhler, J.M. Ortiz de Zárate, A. Vailati, Eur. Phys. J. E 39, 119 (2016)CrossRefGoogle Scholar
  25. 25.
    P. Costesèque, A. Mojtabi, J.K. Platten, C.R. Mec. 339, 275 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    V. Shevtsova, V. Sechenyh, A. Nepomnyashchy, J.C. Legros, Philos. Mag. 91, 3498 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    L.J.T.M. Kempers, J. Chem. Phys. 90, 6541 (1998)ADSCrossRefGoogle Scholar
  28. 28.
    H. Bataller, T. Triller, B. Pur, W. Köhler, J.M. Ortiz de Zárate, F. Croccolo, Eur. J. Phys. E 40, 35 (2017)CrossRefGoogle Scholar
  29. 29.
    K. Ghorayeb, A. Firoozabadi, AIChe J. 46, 883 (2000)CrossRefGoogle Scholar
  30. 30.
    M.M. Bou-Ali, A. Ahadi, D. Alonso de Mezquia, Q. Galand, M. Gebhardt, O. Khlybov, W. Köhler, M. Larrañaga, J.C. Legros, T. Lyubimova, A. Mialdun, I. Ryzhkov, M.Z. Saghir, V. Shevtsova, S.V. Vaerenbergh, Eur. Phys. J. E 38, 30 (2015)CrossRefGoogle Scholar
  31. 31.
    M. Gebhardt, W. Köhler, J. Chem. Phys. 143, 164511 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    R. Piazza, A. Parola, J. Phys.: Condens. Matter 20, 153102 (2008)ADSGoogle Scholar
  33. 33.
    C.B. Mast, D. Braun, Phys. Rev. Lett. 104, 188102 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    H. Matsuura, S. Iwaasa, Y. Nagasaka, J. Chem. Eng. Data 60, 3621 (2015)CrossRefGoogle Scholar
  35. 35.
    S. Duhr, D. Braun, PNAS 26, 19678 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    S. Iacopini, R. Rusconi, R. Piazza, Eur. Phys. J. E 19, 59 (2006)CrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Facultad de Ciencias FísicasUniversidad ComplutenseMadridSpain

Personalised recommendations