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Kinetics of growth of non-equilibrium fluctuations during thermodiffusion in a polymer solution

  • Marina CarpinetiEmail author
  • Matteo Sabato
  • Fabrizio Croccolo
  • Alberto Vailati
Regular Article
  • 51 Downloads
Part of the following topical collections:
  1. Thermal Non-Equilibrium Phenomena in Soft Matter

Abstract.

A thermal diffusion process occurring in a binary liquid mixture is accompanied by long ranged non-equilibrium concentration fluctuations. The amplitude of these fluctuations at large length scales can be orders of magnitude larger than that of equilibrium ones. So far non-equilibrium fluctuations have been mainly investigated under stationary or quasi-stationary conditions, a situation that allows to achieve a detailed statistical characterization of their static and dynamic properties. In this work we investigate the kinetics of growth of non-equilibrium concentration fluctuations during a transient thermodiffusion process, starting from a configuration where the concentration of the sample is uniform. The use of a large molecular weight polymer solution allows to attain a slow dynamics of growth of the macroscopic concentration profile. We focus on the development of fluctuations at small wave vectors, where their amplitude is strongly limited by the presence of gravity. We show that the growth rate of non-equilibrium fluctuations follows a power law \( R_f(q,t)\propto \frac{1}{t}\) as a function of time, without any typical time scale and independently of the wave vector. We formulate a phenomenological model that allows to relate the rate of growth of non-equilibrium fluctuations to the growth of the macroscopic concentration profile in the absence of arbitrary parameters.

Graphical abstract

Keywords

Topical issue: Thermal Non-Equilibrium Phenomena in Soft Matter 

References

  1. 1.
    J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)Google Scholar
  2. 2.
    F. Croccolo, J.M. Ortiz de Zárate, J.V. Sengers, Eur. Phys. J. E 39, 125 (2016)CrossRefGoogle Scholar
  3. 3.
    P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. E 47, 1026 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    A. Vailati, M. Giglio, Phys. Rev. Lett. 77, 1484 (1996)ADSCrossRefGoogle Scholar
  5. 5.
    A. Vailati, M. Giglio, Progr. Colloid Polym. Sci. 104, 76 (1997)CrossRefGoogle Scholar
  6. 6.
    D. Brogioli, A. Vailati, M. Giglio, Phys. Rev. E 61, R1 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Phys. Rev. E 76, 041112 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    F. Giavazzi, G. Savorana, A. Vailati, R. Cerbino, Soft Matter 12, 6588 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    S. Bonella, M. Ferrario, G. Ciccotti, Langmuir 33, 11281 (2017)CrossRefGoogle Scholar
  10. 10.
    A. Mialdun, C. Minetti, Y. Gaponenko, V. Shevtsova, F. Dubois, Microgravity Sci. Technol. 25, 83 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    V. Shevtsova, C. Santos, V. Sechenyh, J.C. Legros, A. Mialdun, Microgravity Sci. Technol. 25, 275 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    D.A. de Mezquia, M. Larrañaga, M.M. Bou-Ali, J.A. Madariaga, C. Santamaría, J.K. Platten, Int. J. Therm. Sci. 92, 14 (2015)CrossRefGoogle Scholar
  13. 13.
    T. Triller, H. Bataller, M. Bou-Ali, M. Braibanti, F. Croccolo, J. Ezquerro, Q. Galand, J. Gavald, E. Lapeira, A. Lavern-Simavilla et al., Microgravity Sci. Technol. 30, 295 (2018)ADSCrossRefGoogle Scholar
  14. 14.
    A. Vailati, M. Giglio, Phys. Rev. E 58, 4361 (1998)ADSCrossRefGoogle Scholar
  15. 15.
    R. Cerbino, Y. Sun, A. Donev, A. Vailati, Sci. Rep. 5, 14486 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    J.S. Huang, W.I. Goldburg, A.W. Bjierkaas, Phys. Rev. Lett. 32, 921 (1974)ADSCrossRefGoogle Scholar
  17. 17.
    K. Binder, D. Stauffer, Phys. Rev. Lett. 33, 1006 (1974)ADSCrossRefGoogle Scholar
  18. 18.
    H.A. Furukawa, Adv. Phys. 34, 703 (1985)ADSCrossRefGoogle Scholar
  19. 19.
    M. Carpineti, M. Giglio, Phys. Rev. Lett. 68, 3327 (1992)ADSCrossRefGoogle Scholar
  20. 20.
    F. Croccolo, H. Bataller, Eur. Phys. J. E 39, 132 (2016)CrossRefGoogle Scholar
  21. 21.
    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
  22. 22.
    S.P. Trainoff, D.S. Cannell, Phys. Fluids 14, 1340 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    A. Vailati, R. Cerbino, S. Mazzoni, C.J. Takacs, D.S. Cannell, M. Giglio, Nat. Commun. 2, 290 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    D. Brogioli, A. Vailati, Phys. Rev. E 63, 012105 (2001)ADSCrossRefGoogle Scholar
  25. 25.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 110, 235902 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 115, 035901 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    J.M. Ortiz de Zárate, T.R. Kirkpatrick, J.V. Sengers, Eur. Phys. J. E 38, 99 (2015)CrossRefGoogle Scholar
  28. 28.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 93, 012148 (2016)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 93, 032117 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    D. Ronis, I. Procaccia, Phys. Rev. A 26, 1812 (1982)ADSCrossRefGoogle Scholar
  31. 31.
    B.M. Law, J.C. Nieuwoudt, Phys. Rev. A 40, 3880 (1989)ADSCrossRefGoogle Scholar
  32. 32.
    J.C. Nieuwoudt, B.M. Law, Phys. Rev. A 42, 2003 (1990)ADSCrossRefGoogle Scholar
  33. 33.
    D. Brogioli, F. Croccolo, A. Vailati, Phys. Rev. E 94, 022142 (2016)ADSCrossRefGoogle Scholar
  34. 34.
    P.N. Segré, J.V. Sengers, Physica A 198, 46 (1993)ADSCrossRefGoogle Scholar
  35. 35.
    W.B. Li, P.N. Segré, R.W. Gammon, J.V. Sengers, Physica A 204, 399 (1994)ADSCrossRefGoogle Scholar
  36. 36.
    W.B. Li, P.N. Segré, R.W. Gammon, J.V. Sengers, J. Phys.: Condens. Matter A 6, 119 (1994)Google Scholar
  37. 37.
    A. Vailati, M. Giglio, Nature 390, 262 (1997)ADSCrossRefGoogle Scholar
  38. 38.
    W.B. Li, K.J. Zhang, J.V. Sengers, R.W. Gammon, J.M. Ortiz de Zárate, Phys. Rev. Lett. 81, 5580 (1998)ADSCrossRefGoogle Scholar
  39. 39.
    F. Giavazzi, A. Fornasieri, A. Vailati, R. Cerbino, Eur. Phys. J. E 39, 103 (2016)CrossRefGoogle Scholar
  40. 40.
    F. Croccolo, C. Giraudet, H. Bataller, R. Cerbino, A. Vailati, Microgravity Sci. Technol. 28, 467 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    H. Bataller, C. Giraudet, F. Croccolo, J.M. Ortiz de Zárate, Microgravity Sci. Technol. 28, 611 (2016)ADSCrossRefGoogle Scholar
  42. 42.
    C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, EPL 111, 60013 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    J. Crank, The Mathematics of Diffusion (Oxford University, Oxford, 1975)Google Scholar
  44. 44.
    C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1961)Google Scholar
  45. 45.
    K. Zhang, M.E. Briggs, R.W. Gammon, J.V. Sengers, J.F. Douglas, J. Chem. Phys. 111, 2270 (1999)ADSCrossRefGoogle Scholar
  46. 46.
    J. Rauch, W. Köhler, J. Phys. Chem. 119, 11977 (2003)CrossRefGoogle Scholar
  47. 47.
    F. Croccolo, D. Brogioli, Appl. Opt. 50, 3419 (2011)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Marina Carpineti
    • 1
    Email author
  • Matteo Sabato
    • 1
  • Fabrizio Croccolo
    • 2
  • Alberto Vailati
    • 1
  1. 1.Dipartimento di FisicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Laboratoire des Fluides Complexes et leurs RéservoirsIPRA, UMR5150 E2S-Université de Pau et des Pays de l’Adour, CNRS, TOTALAngletFrance

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