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Non-local fluctuation phenomena in liquids

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Abstract.

Fluids in non-equilibrium steady states exhibit long-range fluctuations which extend over the entire system. They can be described by non-equilibrium thermodynamics and fluctuating hydrodynamics that assume local equilibrium for the thermophysical properties as a function of space and time. The experimental evidence for the consistency between this assumption of local equilibrium in the equations and the non-local fluctuation phenomena observed is reviewed.

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References

  1. S. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (Dover, New York, 1984)

  2. D. Bedeaux, S. Kjelstrup, J.V. Sengers (Editors), Non-equilibrium Thermodynamics with Applications (IUPAC, Royal Society of Chemistry, Cambridge, 2016)

  3. S. Kjelstrup, D. Bedeaux, E. Johannessen. J. Gross, Non-Equilibrium Thermodynamics for Engineers (World Scientific, Singapore, 2010)

  4. D. Bedeaux, S. Kjelstrup, J.V. Sengers, in ref. 2, Chapt. 1, pp. 1--20

  5. L. Onsager, Phys. Rev. 37, 405 (1931) 38

    Article  ADS  Google Scholar 

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

  7. J.V. Sengers, J.M. Ortiz de Zárate, J. Non-Newton. Fluid Mech. 165, 925 (2010)

    Article  Google Scholar 

  8. J.R. Dorfman, T.R. Kirkpatrick, J.V. Sengers, Annu. Rev. Chem. Phys. 45, 213 (1994)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 89, 022145 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. L.D. Landau, E.M. Lifshitz, Statistical Physics (Pergamon, London, 1958)

  15. L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959)

  16. R.F. Fox, G.E. Uhlenbeck, Phys. Fluids 13, 1893 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  17. R.F. Fox, Phys. Rep. 48, 179 (1978)

    Article  ADS  Google Scholar 

  18. J.M. Ortiz de Zárate, J.V. Sengers, in ref. 2, Chapt. 2, pp. 21--38

  19. M.G. Velarde, R.S. Schechter, Phys. Fluids 15, 1707 (1972)

    Article  ADS  Google Scholar 

  20. R. Schmitz, E.G.D. Cohen, J. Stat. Phys. 39, 285 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  21. R.D. Mountain, Rev. Mod. Phys. 38, 205 (1966)

    Article  ADS  Google Scholar 

  22. R.D. Mountain, J.M. Deutch, J. Chem. Phys. 50, 1103 (1969)

    Article  ADS  Google Scholar 

  23. B.J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976)

  24. J.P. Boon, S. Yip, Molecular Hydrodynamics (Mc-Graw-Hill, New York, 1980)

  25. M.E. Fisher, J. Math. Phys. 5, 944 (1964)

    Article  ADS  Google Scholar 

  26. M.E. Fisher, H. Au-Yang, Physica A 101, 255 (1980)

    Article  ADS  Google Scholar 

  27. K. Binder, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz, Vol. 8 (Academic Press, London, 1983) pp. 1--474

  28. M.E. Fisher, P.-G. de Gennes, C.R. Acad. Sci. Paris 287, 207 (1978)

    Google Scholar 

  29. M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994)

  30. A. Gambassi, S. Dietrich, Soft Matter 7, 1247 (2011)

    Article  ADS  Google Scholar 

  31. K. Kawasaki, Ann. Phys. (N.Y.) 61, 1 (1970)

    Article  ADS  Google Scholar 

  32. H.C. Burstyn, J.V. Sengers, J.K. Bhattacharjee, R.A. Ferrell, Phys. Rev. A 28, 1567 (1983)

    Article  ADS  Google Scholar 

  33. J.V. Sengers, R.A. Perkins, in Advances in Transport Properties of Fluids, edited by M.J. Assael, A.R.H. Goodwin, V. Vesovic, W.A. Wakeham, (IUPAC, Royal Society of Chemistry, Cambridge, 2014) pp. 337--361

  34. R. Perl, R.A. Ferrell, Phys. Rev. A 6, 2358 (1972)

    Article  ADS  Google Scholar 

  35. H.C. Burstyn, J.V. Sengers, Phys. Rev. A 27, 1071 (1983)

    Article  ADS  Google Scholar 

  36. J.V. Sengers, J.M. Ortiz de Zárate, T.R. Kirkpatrick, in ref. 2, Chapt. 3, pp. 39--60

  37. S. Kjelstrup, D. Bedeaux, in ref. 2, Chapt. 4, pp. 61--77

  38. A.-M.S. Tremblay, M. Arai, E.D. Siggia, Phys. Rev. A 23, 1451 (1981)

    Article  ADS  Google Scholar 

  39. I. Pagonabarraga, J.M. Rubí, Phys. Rev. E 49, 267 (1994)

    Article  ADS  Google Scholar 

  40. P.N. Segrè, R.W. Gammon, J.V. Sengers, B.M. Law, Phys. Rev. A 45, 714 (1992)

    Article  ADS  Google Scholar 

  41. J.M. Ortiz de Zárate, J.V. Sengers, J. Stat. Phys. 115, 1341 (2004)

    Article  ADS  Google Scholar 

  42. T.R. Kirkpatrick, J.R. Dorfman, E.G.D. Cohen, Phys. Rev. A 26, 995 (1982)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. B.M. Law, J.V. Sengers, J. Stat. Phys. 57, 531 (1989)

    Article  ADS  Google Scholar 

  45. B.M. Law, P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. A 41, 816 (1990)

    Article  ADS  Google Scholar 

  46. T.R. Kirkpatrick, J.R. Dorfman, Phys. Rev. E 92, 022109 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  47. J.M. Ortiz de Zárate, R. Pérez Cordón, J.V. Sengers, Physica A 291, 113 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  51. W.B. Li, K.J. Zhang, J.V. Sengers, J.M. Ortiz de Zárate, J. Chem. Phys. 112, 9139 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. R.S. Schechter. M.G. Velarde, J.K. Platten, in Advances in Chemical Physics, edited by I. Prigogine, S.A. Rice, Vol. 26, (Wiley, New York, 1974) pp. 265--301

  54. M. Lücke, W. Barton, P. Büchel, F. Fütterer, St. Hollinger, Ch. Jung, in Evolution of Spontaneous Structures in Dissipative Continuous Systems, edited by P.H. Busse, S.C. Müller (Springer, Berlin, 1998) pp. 128--196

  55. J.V. Sengers, J.M. Ortiz de Zárate, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, edited by W. Köhler, S. Wiegand (Springer, Berlin, 2002) pp. 121--145

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

    Article  ADS  Google Scholar 

  57. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Phys. Rev. E 76, 41112 (2007)

    Article  ADS  Google Scholar 

  58. A. Oprisan, A.L. Payne, Opt. Commun. 290, 100 (2013)

    Article  ADS  Google Scholar 

  59. P.N. Segrè, R. Schmitz, J.V. Sengers, Physica 195, 31 (1993)

    Article  Google Scholar 

  60. P.N. Segrè, J.V. Sengers, Physica A 198, 46 (1993)

    Article  ADS  Google Scholar 

  61. J.M. Ortiz de Zárate, J.V. Sengers, Physica A 300, 25 (2001)

    Article  ADS  Google Scholar 

  62. J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 66, 036305 (2002)

    Article  ADS  Google Scholar 

  63. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Appl. Opt. 45, 2166 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  67. 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)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  69. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Ann. N.Y. Acad. Sci. 1077, 365 (2006)

    Article  ADS  Google Scholar 

  70. J.M. Ortiz de Zárate, F. Peluso, J.V. Sengers, Eur. Phys. J. E 15, 319 (2004)

    Article  Google Scholar 

  71. J.M. Ortiz de Zárate, J.M. Fornés, J.V. Sengers, Phys. Rev. E 74, 046305 (2006)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  73. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961)

  74. S. Mazzoni, R. Cerbino, A. Vailati, M. Giglio, D.S. Cannell, Ann. N.Y. Acad. Sci. 1077, 351 (2006)

    Article  ADS  Google Scholar 

  75. C.J. Takacs, A. Vailati, M. Giglio, D.S. Cannell, Phys. Rev. Lett. 106, 244502 (2011)

    Article  ADS  Google Scholar 

  76. M. Wu, G. Ahlers, D.S. Cannell, Phys. Rev. Lett. 75, 1743 (1995)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  78. Cédric Giraudet, Henri Bataller, Yifei Sun, Aleksandar Donev, José M. Ortiz de Zárate, Fabrizio Croccolo, Eur. Phys. J. E 39, 120 (2016)

    Google Scholar 

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

    Article  Google Scholar 

  80. M. Kardar, R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999)

    Article  ADS  Google Scholar 

  81. H.B.G. Casimir, Proc. K. Ned. Akad. Wet. B 51, 793 (1948)

    Google Scholar 

  82. F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012)

    Article  ADS  Google Scholar 

  83. F. Croccolo, F. Scheffold, H. Bataller, C. R. Méc. 341, 378 (2013)

    Article  Google Scholar 

  84. C. Giraudet, H. Bataller, F. Croccolo, Eur. Phys. J. E 37, 107 (2014)

    Article  Google Scholar 

  85. I. Lizarraga, C. Giraudet, F. Croccolo, M.M. Bou-Ali, H. Bataller, Micrograv. Sci. Technol. 28, 267 (2016)

    Article  Google Scholar 

  86. J.M. Ortiz de Zárate, C. Giraudet, H. Bataller, F. Croccolo, Eur. Phys. J. E 37, 77 (2014)

    Article  Google Scholar 

  87. P.M. Pancorbo, J.M. Ortiz de Zárate, H. Bataller, F. Croccolo, submitted to Eur. Phys. J. E

  88. F.B. Usabiaga, J.B. Bell, R. Delgado-Buscalioni, A. Donev, T.G. Fai, B.E. Griffith, C.S. Peskin, Multiscale Model. Simul. 10, 1369 (2012)

    Article  MathSciNet  Google Scholar 

  89. A. Donev, A.J. Nonaka, Y. Sun, T.G. Fai, A.L. Garcia, J.B. Bell, Commun. Appl. Math. Comput. Sci. 9, 47 (2014)

    Article  MathSciNet  Google Scholar 

  90. A.J. Nonaka, Y. Sun, J.B. Bell, A. Donev, Commun. Appl. Math. Comput. Sci. 10, 163 (2015)

    Article  MathSciNet  Google Scholar 

  91. A. Chaudhri, J.B. Bell, A.L. Garcia, A. Donev, Phys. Rev. E 90, 033014 (2014)

    Article  ADS  Google Scholar 

  92. A.K. Bhattacharjee, K. Balakrishnan, A.L. Garcia, J.B. Bell, A. Donev, J. Chem. Phys. 142, 224107 (2015)

    Article  ADS  Google Scholar 

  93. J.-P. Péraud, A. Nonaka, A. Chaudhri, J.B. Bell, A. Donev, A.L. Garcia, Phys. Rev. F 1, 074103 (2016)

    Google Scholar 

  94. S. Delong, Y. Sun, B.E. Griffith, E. Vanden-Eijnden, A. Donev, Phys. Rev. E 90, 063312 (2014)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire des Fluides Complexes et leurs Réservoirs, UMR 5150, Université de Pau et des Pays de l’Adour, 64600, Anglet, France

    F. Croccolo

  2. Centre National d’Etudes Spatiales (CNES), 2 Place Maurice Quentin, 75001, Paris, France

    F. Croccolo

  3. Departamento de Física Aplicada I, Facultad de Física, Universidad Complutense, 28040, Madrid, Spain

    J. M. Ortiz de Zárate

  4. Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA

    J. V. Sengers

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  1. F. Croccolo
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Croccolo, F., Ortiz de Zárate, J.M. & Sengers, J.V. Non-local fluctuation phenomena in liquids. Eur. Phys. J. E 39, 125 (2016). https://doi.org/10.1140/epje/i2016-16125-3

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