Skip to main content

The Soret coefficient from the Faxén theorem for a particle moving in a fluid under a temperature gradient

The European Physical Journal E volume 42, Article number: 55 (2019) Cite this article

Abstract.

We compute the Soret coefficient for a particle moving through a fluid subjected to a temperature gradient. The viscosity and thermal conductivity of the particle are in general different from those of the solvent and its surface tension may depend on temperature. We find that the Soret coefficient depends linearly on the derivative of the surface tension with respect to temperature and decreases in accordance with the ratios between viscosities and thermal conductivities of particle and solvent. Additionally, the Soret coefficient also depends on a parameter which gives the ratio between Marangoni and shear stresses, a dependence which results from the local stresses inducing a heat flux along the particle surface. Our results are compared to those obtained by using the Stokes value for the mobility in the calculation of the Soret coefficient and in the estimation of the radius of the particle. We show cases in which these differences may be important. The new expression of the Soret coefficient can systematically be used for a more accurate study of thermophoresis.

Graphical abstract

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

43,34 €

Price includes VAT (Finland)
Tax calculation will be finalised during checkout.

References

  1. R. Piazza, S. Iacopini, B. Triulzi, PCCP 6, 1616 (2004)

    ADS  Article  Google Scholar 

  2. W. Koehler, K.I. Morozov, J. Non-Equilib. Thermodyn. 41, 151 (2016)

    ADS  Google Scholar 

  3. M. Rahman, M. Saghir, Int. J. Heat Mass Transfer 73, 693 (2014)

    Article  Google Scholar 

  4. R. Piazza, A. Parola, J. Phys.: Condens. Matter 20, 153102 (2008)

    ADS  Google Scholar 

  5. J.K. Platten, J. Appl. Mech. 73, 5 (2006)

    ADS  Article  Google Scholar 

  6. O. Wilhelmsen, D. Bedeaux, D. Reguera, J. Chem. Phys. 142, 171103 (2015)

    ADS  Article  Google Scholar 

  7. D. Ross, L.E. Locascio, Anal. Chem. 74, 2556 (2002)

    Article  Google Scholar 

  8. I. Zahmatkesh, Int. Commun. Heat Mass Transfer 35, 369 (2008)

    Article  Google Scholar 

  9. C.J. Tsai, J.S. Lin, S.G. Aggarwal, D.R. Chen, Aerosol Sci. Technol. 38, 131 (2004)

    ADS  Article  Google Scholar 

  10. B.U. Lee, D.S. Byun, G.N. Bae, J.H. Lee, J. Aerosol Sci. 37, 1788 (2006)

    ADS  Article  Google Scholar 

  11. H.J. Keh, C.L. Ou, Aerosol Sci. Technol. 38, 675 (2004)

    ADS  Article  Google Scholar 

  12. D. Braun, A. Libchaber, Phys. Biol. 1, 1 (2004)

    ADS  Article  Google Scholar 

  13. G. Kucsko, P. Maurer, N.Y. Yao, M. Kubo, H. Noh, P. Lo, H. Park, M.D. Lukin, Nature 500, 54 (2013)

    ADS  Article  Google Scholar 

  14. J. Olarte-Plata, J.M. Rubi, F. Bresme, Phys. Rev. E 97, 052607 (2018)

    ADS  Article  Google Scholar 

  15. H. Faxen, Ark. Mat., Astron. Fys. 18, 1 (1924)

    Google Scholar 

  16. S.R. De Groot, P. Mazur, Non-Equilibrium Thermodynamics (Courier Corporation, 2013)

  17. J. Bafaluy, I. Pagonabarraga, J.M. Rubi, D. Bedeaux, Physica A 213, 277 (1995)

    ADS  Article  Google Scholar 

  18. R. Berker, Encyclopedia of Physics, Vol. VIII/2: Fluid Dynamics II (Springer-Verlag, 1963)

  19. J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics (Kluwer, Dordrecht, 1991)

  20. R. Zwanzig, J. Res. Natl. Bur. Std. (US) B 68, 143 (1964)

    Google Scholar 

  21. R.S. Subramanian, J. Fluid Mech. 153, 389 (1985)

    ADS  Article  Google Scholar 

  22. F.E. Torres, E. Herbolzheimer, Phys. Fluids A 5, 537 (1993)

    ADS  Article  Google Scholar 

  23. A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces (Interscience Publishers, New York, 1967).

  24. J. Harper, D. Moore, J. Pearson, J. Fluid Mech. 27, 361 (1967)

    ADS  Article  Google Scholar 

  25. P. Naumann, S. Datta, T. Sottmann, B. Arlt, H. Frielinghaus, S. Wiegand, J. Phys. Chem. B 118, 3451 (2014)

    Article  Google Scholar 

  26. A. van Veluwen, H.N. Lekkerkerker, C.G. de Kruif, A. Vrij, Faraday Discuss. 83, 59 (1987)

    Article  Google Scholar 

  27. W. Goldburg, Am. J. Phys. 67, 1152 (1999)

    ADS  Article  Google Scholar 

  28. B.J. Berne, R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover Publications, Mineola, NY, 2000)

  29. R. Pecora, J. Nanopart. Res. 2, 123 (2000)

    ADS  Article  Google Scholar 

  30. P.A. Hassan, S. Rana, G. Verma, Langmuir 31, 3 (2014)

    Article  Google Scholar 

  31. H.L. Fu, L. Gao, Int. J. Therm. Sci. 61, 61 (2012)

    Article  Google Scholar 

  32. P. Tillman, J.M. Hill, Int. J. Heat Mass Transfer 34, 399 (2007)

    Article  Google Scholar 

  33. X.F. Zhou, L. Gao, J. Appl. Phys. 100, 083503 (2008)

    ADS  Article  Google Scholar 

  34. B.E. Poling, J.M. Prausnitz, J.P. Oapos Connell, Properties of Gases and Liquids (McGraw Hill, 2007)

  35. A.A. Pádua, J.M. Fareleira, J.C. Calado, W.A. Wakeham, J. Chem. Eng. Data 41, 1488 (1996)

    Article  Google Scholar 

  36. T. Sottmann, R. Strey, J. Chem. Phys. 106, 8606 (1997)

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

  1. Departament de Física de la Matéria Condensada, Facultat de Física, Universitat de Barcelona, Avinguda Diagonal 647, 08028, Barcelona, Spain

    Andrés Arango-Restrepo & J. Miguel Rubi

  2. Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, Barcelona, Spain

    Andrés Arango-Restrepo

Authors
  1. Andrés Arango-Restrepo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Miguel Rubi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrés Arango-Restrepo.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Arango-Restrepo, A., Rubi, J.M. The Soret coefficient from the Faxén theorem for a particle moving in a fluid under a temperature gradient. Eur. Phys. J. E 42, 55 (2019). https://doi.org/10.1140/epje/i2019-11822-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2019-11822-y

Keywords

  • Topical issue: Thermal Non-Equilibrium Phenomena in Soft Matter