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

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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.

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References

  1. J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)

  2. F. Croccolo, J.M. Ortiz de Zárate, J.V. Sengers, Eur. Phys. J. E 39, 125 (2016)

    Article  Google Scholar 

  3. P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. E 47, 1026 (1993)

    Article  ADS  Google Scholar 

  4. A. Vailati, M. Giglio, Phys. Rev. Lett. 77, 1484 (1996)

    Article  ADS  Google Scholar 

  5. A. Vailati, M. Giglio, Progr. Colloid Polym. Sci. 104, 76 (1997)

    Article  Google Scholar 

  6. D. Brogioli, A. Vailati, M. Giglio, Phys. Rev. E 61, R1 (2000)

    Article  ADS  Google Scholar 

  7. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Phys. Rev. E 76, 041112 (2007)

    Article  ADS  Google Scholar 

  8. F. Giavazzi, G. Savorana, A. Vailati, R. Cerbino, Soft Matter 12, 6588 (2016)

    Article  ADS  Google Scholar 

  9. S. Bonella, M. Ferrario, G. Ciccotti, Langmuir 33, 11281 (2017)

    Article  Google Scholar 

  10. A. Mialdun, C. Minetti, Y. Gaponenko, V. Shevtsova, F. Dubois, Microgravity Sci. Technol. 25, 83 (2013)

    Article  ADS  Google Scholar 

  11. V. Shevtsova, C. Santos, V. Sechenyh, J.C. Legros, A. Mialdun, Microgravity Sci. Technol. 25, 275 (2018)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. A. Vailati, M. Giglio, Phys. Rev. E 58, 4361 (1998)

    Article  ADS  Google Scholar 

  15. R. Cerbino, Y. Sun, A. Donev, A. Vailati, Sci. Rep. 5, 14486 (2015)

    Article  ADS  Google Scholar 

  16. J.S. Huang, W.I. Goldburg, A.W. Bjierkaas, Phys. Rev. Lett. 32, 921 (1974)

    Article  ADS  Google Scholar 

  17. K. Binder, D. Stauffer, Phys. Rev. Lett. 33, 1006 (1974)

    Article  ADS  Google Scholar 

  18. H.A. Furukawa, Adv. Phys. 34, 703 (1985)

    Article  ADS  Google Scholar 

  19. M. Carpineti, M. Giglio, Phys. Rev. Lett. 68, 3327 (1992)

    Article  ADS  Google Scholar 

  20. F. Croccolo, H. Bataller, Eur. Phys. J. E 39, 132 (2016)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  22. S.P. Trainoff, D.S. Cannell, Phys. Fluids 14, 1340 (2002)

    Article  ADS  Google Scholar 

  23. A. Vailati, R. Cerbino, S. Mazzoni, C.J. Takacs, D.S. Cannell, M. Giglio, Nat. Commun. 2, 290 (2011)

    Article  ADS  Google Scholar 

  24. D. Brogioli, A. Vailati, Phys. Rev. E 63, 012105 (2001)

    Article  ADS  Google Scholar 

  25. T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 110, 235902 (2013)

    Article  ADS  Google Scholar 

  26. T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 115, 035901 (2015)

    Article  ADS  Google Scholar 

  27. J.M. Ortiz de Zárate, T.R. Kirkpatrick, J.V. Sengers, Eur. Phys. J. E 38, 99 (2015)

    Article  Google Scholar 

  28. T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 93, 012148 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  29. T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 93, 032117 (2016)

    Article  ADS  Google Scholar 

  30. D. Ronis, I. Procaccia, Phys. Rev. A 26, 1812 (1982)

    Article  ADS  Google Scholar 

  31. B.M. Law, J.C. Nieuwoudt, Phys. Rev. A 40, 3880 (1989)

    Article  ADS  Google Scholar 

  32. J.C. Nieuwoudt, B.M. Law, Phys. Rev. A 42, 2003 (1990)

    Article  ADS  Google Scholar 

  33. D. Brogioli, F. Croccolo, A. Vailati, Phys. Rev. E 94, 022142 (2016)

    Article  ADS  Google Scholar 

  34. P.N. Segré, J.V. Sengers, Physica A 198, 46 (1993)

    Article  ADS  Google Scholar 

  35. W.B. Li, P.N. Segré, R.W. Gammon, J.V. Sengers, Physica A 204, 399 (1994)

    Article  ADS  Google Scholar 

  36. W.B. Li, P.N. Segré, R.W. Gammon, J.V. Sengers, J. Phys.: Condens. Matter A 6, 119 (1994)

    Google Scholar 

  37. A. Vailati, M. Giglio, Nature 390, 262 (1997)

    Article  ADS  Google Scholar 

  38. W.B. Li, K.J. Zhang, J.V. Sengers, R.W. Gammon, J.M. Ortiz de Zárate, Phys. Rev. Lett. 81, 5580 (1998)

    Article  ADS  Google Scholar 

  39. F. Giavazzi, A. Fornasieri, A. Vailati, R. Cerbino, Eur. Phys. J. E 39, 103 (2016)

    Article  Google Scholar 

  40. F. Croccolo, C. Giraudet, H. Bataller, R. Cerbino, A. Vailati, Microgravity Sci. Technol. 28, 467 (2016)

    Article  ADS  Google Scholar 

  41. H. Bataller, C. Giraudet, F. Croccolo, J.M. Ortiz de Zárate, Microgravity Sci. Technol. 28, 611 (2016)

    Article  ADS  Google Scholar 

  42. C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, EPL 111, 60013 (2015)

    Article  ADS  Google Scholar 

  43. J. Crank, The Mathematics of Diffusion (Oxford University, Oxford, 1975)

  44. C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1961)

  45. K. Zhang, M.E. Briggs, R.W. Gammon, J.V. Sengers, J.F. Douglas, J. Chem. Phys. 111, 2270 (1999)

    Article  ADS  Google Scholar 

  46. J. Rauch, W. Köhler, J. Phys. Chem. 119, 11977 (2003)

    Article  Google Scholar 

  47. F. Croccolo, D. Brogioli, Appl. Opt. 50, 3419 (2011)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy

    Marina Carpineti, Matteo Sabato & Alberto Vailati

  2. Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150 E2S-Université de Pau et des Pays de l’Adour, CNRS, TOTAL, F-64600, Anglet, France

    Fabrizio Croccolo

Authors
  1. Marina Carpineti
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  2. Matteo Sabato
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  3. Fabrizio Croccolo
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  4. Alberto Vailati
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Correspondence to Marina Carpineti.

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Carpineti, M., Sabato, M., Croccolo, F. et al. Kinetics of growth of non-equilibrium fluctuations during thermodiffusion in a polymer solution. Eur. Phys. J. E 42, 25 (2019). https://doi.org/10.1140/epje/i2019-11786-x

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