Static versus dynamic analysis of the influence of gravity on concentration non-equilibrium fluctuations

  • Fabrizio CroccoloEmail author
  • Henri Bataller
  • Frank Scheffold
Regular Article
Part of the following topical collections:
  1. Thermal non-equilibrium phenomena in multi-component fluids


In a binary fluid mixture subject to gravity and a stabilizing concentration gradient, concentration non-equilibrium fluctuations are long-ranged. While the gradient leads to an enhancement of the respective equilibrium fluctuations, the effect of gravity is a damping of fluctuations larger than a “characteristic” size. This damping is visible both in the fluctuation power spectrum probed by static and the temporal correlation function probed by dynamic light scattering. One aspect of the “characteristic” size can be appreciated by the dynamic analysis; in fact at the corresponding “characteristic” wave vector q * one can observe a maximum of the fluctuation time constant indicating the more persistent fluctuation of the system. Also in the static analysis a “characteristic” size can be extracted from the crossover wave vector. According to common theoretical concepts, the result should be the same in both cases. In the present work we provide evidence for a systematic difference in the experimentally observed “characteristic” size as obtained by static and dynamic measurements. Our observation thus points out the need for a more refined theory of non-equilibrium concentration fluctuations.

Graphical abstract


Topical Issue: Thermal non-equilibrium phenomena in multi-component fluids 


  1. 1.
    J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, New York, 2006)Google Scholar
  2. 2.
    J. Oh, J.M. Ortiz de Zárate, J.V. Sengers, G. Ahlers, Phys. Rev. E 69, 021106 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    F. Balboa Usabiaga, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T.G. Fai, B.E. Griffith, C.S. Pekin, Multiscale Model. Simul. 10, 1369 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    A. Vailati, M. Giglio, Phys. Rev. E 58, 4361 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    K. Balakrishnan, A.L. Garcia, A. Donev, J.B. Bell, Phys. Rev. E 89, 013017 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    A. Donev, J.B. Bell, A. de la Fuente, A.L. Garcia, Phys. Rev. Lett. 106, 204501 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    F. Croccolo, F. Scheffold, H. Bataller, C. R. Méc. 341, 378 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    A. Vailati, R. Cerbino, S. Mazzoni, C.J. Takacs, D.S. Cannell, M. Giglio, Nat. Commun. 2, 290 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    C.J. Takacs, A. Vailati, R. Cerbino, S. Mazzoni, M. Giglio, D.S. Cannell, Phys. Rev. Lett. 106, 244502 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    A. Vailati, M. Giglio, Phys. Rev. Lett. 77, 1484 (1996)ADSCrossRefGoogle Scholar
  12. 12.
    A. Vailati, M. Giglio, Nature 390, 262 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Phys. Rev. E 76, 41112 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Appl. Opt. 45, 2166 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    J.M. Ortiz de Zárate, J.A. Fornés, J.V. Sengers, Phys. Rev. E 74, 046305 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    R.D. Mountain, J.M. Deutch, J. Chem. Phys. 50, 1103 (1969)ADSCrossRefGoogle Scholar
  17. 17.
    C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, submitted,
  18. 18.
    P.N. Segrè, J.V. Sengers, Physica A 198, 46 (1993)ADSCrossRefGoogle Scholar
  19. 19.
    P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. E 47, 1026 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    S. Trainoff, D.S. Cannell, Phys. Fluids 14, 1340 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    R. Cerbino, A. Vailati, Curr. Opin. Colloid Interface Sci. 14, 416 (2009) CrossRefGoogle Scholar
  22. 22.
    F. Giavazzi, R. Cerbino, J. Opt. 16, 083001 (2014) DOI:10.1088/2040-8978/16/8/083001 ADSCrossRefGoogle Scholar
  23. 23.
    G.S. Settles, Schlieren and Shadowgraph Techniques (Springer, Berlin, 2001)Google Scholar
  24. 24.
    F. Croccolo, D. Brogioli, Appl. Opt. 50, 3419 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    F. Croccolo, M.A. Arnaud, D. Bégué, H. Bataller, J. Chem. Phys. 135, 034901 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    F. Croccolo, F. Plantier, G. Galliero, G. Pijaudier-Cabot, M.Z. Saghir, F. Dubois, S. Van Vaerenbergh, F. Montel, H. Bataller, Rev. Sci. Instrum. 82, 126105 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    R. Cerbino, V. Trappe, Phys. Rev. Lett. 100, 188102 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    G. Cerchiari, F. Croccolo, F. Cardinaux, F. Scheffold, Rev. Sci. Instrum. 83, 106101 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    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

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Fabrizio Croccolo
    • 1
    • 2
    Email author
  • Henri Bataller
    • 1
  • Frank Scheffold
    • 2
  1. 1.Laboratoire des Fluides Complexes et leurs Réservoirs - UMR5150Université de Pau et des Pays de l’AdourAngletFrance
  2. 2.Department of PhysicsUniversity of FribourgFribourgSwitzerland

Personalised recommendations