Stationary and transient Soret separation in a binary mixture with a consolute critical point

Regular Article
Part of the following topical collections:
  1. Non-isothermal transport in complex fluids


The stationary and transient Soret separation in a binary mixture with a consolute critical point is studied theoretically. The mixture is placed between two parallel plates kept at different temperatures. A polymer blend is used as a model system. Analytical solutions are constructed to describe the stationary separation in a binary mixture with variable Soret coefficient. The latter strongly depends on temperature and concentration and enhances near a consolute critical point due to reduced diffusion. As a result, a large concentration gradient is observed locally, while much smaller concentration variations are found in the rest of the layer. It is shown that complete separation can be obtained by applying a small temperature difference first, waiting for the establishment of stationary state, and then increasing this difference again. In this case, the critical temperature lies between hot and cold wall temperatures, while the mixture still remains in the one-phase region. When the initial (mean) temperature or concentration are shifted away from the near-critical values, the separation decreases. The analysis of transient behavior shows that the Soret separation occurs much faster than diffusion to the homogeneous state when the initial concentration is close to the critical one. It happens due to the decrease (increase) of the local relaxation time during the Soret (Diffusion) steps. The transient times of these steps become comparable for small temperature differences or off-critical initial concentrations. An unusual (non-exponential) separation dynamics is observed when the separation starts in the off-critical domain, and then enhances greatly when the system enters into the near-critical region. It is also found that the transient time decreases with increasing the applied temperature difference.

Graphical abstract


Topical Issue: Non-isothermal transport in complex fluids 


  1. 1.
    W. Köhler, K. Morozov, J. Nonequilib. Thermodyn. 41, 151 (2016)ADSCrossRefGoogle Scholar
  2. 2.
    J. Luettmer-Strathmann, J.V. Sengers, G.A. Olchowy, J. Chem. Phys. 103, 7482 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)Google Scholar
  4. 4.
    J.V. Sengers, J.M.H. Levelt Sengers, Annu. Rev. Phys. Chem. 37, 189 (1986)ADSCrossRefGoogle Scholar
  5. 5.
    J.V. Sengers, R.A. Perkins, Fluids near critical points. Experimental Thermodynamics, Volume IX: Advances in Transport Properties of Fluids (Royal Society of Chemistry, Cambridge, 2014) Chapt. 10Google Scholar
  6. 6.
    J. Luettmer-Strathmann, Lect. Notes Phys. 584, 24 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    W.M. Rutherford, J.G. Roof, J. Phys. Chem. 63, 1506 (1959)CrossRefGoogle Scholar
  8. 8.
    L.H. Cohen, M.L. Dingus, H. Meyer, Phys. Rev. Lett. 50, 1058 (1983)ADSCrossRefGoogle Scholar
  9. 9.
    L.H. Cohen, M.L. Dingus, H. Meyer, J. Low Temp. Phys. 61, 79 (1985)ADSCrossRefGoogle Scholar
  10. 10.
    J. Luettmer-Strathmann, J.V. Sengers, J. Chem. Phys. 104, 3026 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    G. Thomaes, J. Chem. Phys. 25, 32 (1956)ADSCrossRefGoogle Scholar
  12. 12.
    M.L.S. Matos Lopes, C.A. Nieto de Castro, J.V. Sengers, Int. J. Thermophys. 13, 283 (1992)ADSCrossRefGoogle Scholar
  13. 13.
    M. Giglio, A. Vendramini, Phys. Rev. Lett. 34, 561 (1975)ADSCrossRefGoogle Scholar
  14. 14.
    M. Giglio, A. Vendramini, Phys. Rev. Lett. 35, 168 (1975)ADSCrossRefGoogle Scholar
  15. 15.
    S. Wiegand, W. Köhler, Lect. Notes Phys. 584, 189 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    O. Ecenarro, J.A. Madariaga, J.L. Navarro, C.M. Santamaría, J.A. Carrión, J.M. Savirón, J. Phys.: Condens. Matter 5, 2289 (1993)ADSGoogle Scholar
  17. 17.
    W. Enge, W. Köhler, Phys. Chem. Chem. Phys. 6, 2373 (2004)CrossRefGoogle Scholar
  18. 18.
    A. Voit, A. Krekhov, W. Köhler, Phys. Rev. E 76, 011808 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    W. Köhler, A. Krekhov, W. Zimmermann, Adv. Polym. Sci. 227, 145 (2010)CrossRefGoogle Scholar
  20. 20.
    S.K. Das, M.E. Fisher, J.V. Sengers, J. Horbach, K. Binder, Phys. Rev. Lett. 97, 025702 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    J.C. Legros, Yu. Gaponenko, T. Lyubimova, V. Shevtsova, Eur. Phys. J. E 37, 89 (2014)CrossRefGoogle Scholar
  22. 22.
    I.I. Ryzhkov, I.V. Stepanova, Int. J. Heat Mass Transf. 86, 268 (2015)CrossRefGoogle Scholar
  23. 23.
    O.A. Khlybov, I.I. Ryzhkov, T.P. Lyubimova, Eur. Phys. J. E 38, 29 (2015)CrossRefGoogle Scholar
  24. 24.
    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. Van Vaerenbergh, Eur. Phys. J. E 38, 30 (2015)CrossRefGoogle Scholar
  25. 25.
    V. Shevtsova, C. Santos, V. Sechenyh, J.C. Legros, A. Mialdun, Micrograv. Sci. Technol. 25, 275 (2014)CrossRefGoogle Scholar
  26. 26.
    S. Enders, A. Stammer, B.A. Wolf, Macromol. Chem. Phys. 197, 2961 (1996)CrossRefGoogle Scholar
  27. 27.
    J.E. Mark (Editor), Polymer Data Handbook (Oxford University Press, New York, 1999)Google Scholar
  28. 28.
    D. Van Krevelen. Properties of Polymers, 4th edition (Elsevier, 2009)Google Scholar
  29. 29.
    A.D. Polyanin, V.F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations (CRC Press, 2003)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Computational Modelling SB RASKrasnoyarskRussia
  2. 2.Siberian Federal UniversityKrasnoyarskRussia

Personalised recommendations