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Nonequilibrium Casimir pressures in liquids under shear

  • J. M. Ortiz de Zárate
  • T. R. Kirkpatrick
  • J. V. SengersEmail author
Regular Article
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Abstract.

In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find that in shear nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that currently available computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin and do not probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes. Even more importantly, we find that in actual experimental conditions, shear-induced pressure enhancements are caused by viscous heating and not by thermal velocity fluctuations. Hence, isothermal computer simulations are irrelevant for the interpretation of experimental shear-induced pressure enhancements.

Graphical abstract

Keywords

Flowing Matter: Liquids and Complex Fluids 

References

  1. 1.
    M. Kardar, R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994)Google Scholar
  4. 4.
    T.R. Kirkpatrick, J.K. Bhattacharje, J.V. Sengers, Phys. Rev. Lett. 119, 030603 (2017)ADSCrossRefGoogle Scholar
  5. 5.
    J.R. Dorfman, T.R. Kirkpatrick, J.V. Sengers, Annu. Rev. Phys. Chem. 45, 213 (1994)ADSCrossRefGoogle Scholar
  6. 6.
    J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)Google Scholar
  7. 7.
    J.F. Lutsko, J.W. Dufty, Phys. Rev. A 32, 3040 (1985)ADSCrossRefGoogle Scholar
  8. 8.
    J.F. Lutsko, J.W. Dufty, Phys. Rev. E 66, 041206 (2002)ADSCrossRefGoogle Scholar
  9. 9.
    J.V. Sengers, J.M. Ortiz de Zárate, J. Non-Newton. Fluid Mech. 165, 925 (2010)CrossRefGoogle Scholar
  10. 10.
    K. Kawasaki, J.D. Gunton, Phys. Rev. A 8, 2048 (1973)ADSCrossRefGoogle Scholar
  11. 11.
    T. Yamada, K. Kawasaki, Prog. Theor. Phys. (Japan) 53, 111 (1975)ADSCrossRefGoogle Scholar
  12. 12.
    M.H. Ernst, B. Cichocki, J.R. Dorfman, J. Sharma, H. van Beijeren, J. Stat. Phys. 18, 237 (1978)ADSCrossRefGoogle Scholar
  13. 13.
    H. Wada, S.I. Sasa, Phys. Rev. E 67, 065302(R) (2003)ADSCrossRefGoogle Scholar
  14. 14.
    J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 77, 026306 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 79, 046308 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    J.M. Ortiz de Zárate, J.V. Sengers, J. Stat. Phys. 144, 774 (2011)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    J.M. Ortiz de Zárate, J.V. Sengers, J. Stat. Phys. 150, 540 (2013)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    D.J. Evans, Phys. Rev. A 23, 1988 (1981)ADSCrossRefGoogle Scholar
  19. 19.
    S.H. Lee, P.T. Cummings, J. Chem. Phys. 99, 3919 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    S.H. Lee, P.T. Cummings, J. Chem. Phys. 101, 6206 (1994)ADSCrossRefGoogle Scholar
  21. 21.
    G. Marcelli, B.D. Todd, R.J. Sadus, Phys. Rev. E 63, 021204 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    J. Ge, G. Marcelli, B.D. Todd, R.J. Sadus, Phys. Rev. E 64, 021201 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    J. Ge, B.D. Todd, G. Wu, R.J. Sadus, Phys. Rev. E 67, 061201 (2003)ADSCrossRefGoogle Scholar
  24. 24.
    A. Ahmed, P. Mausbach, R.J. Sadus, Phys. Rev. E 82, 011201 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    A. Varghese, G. Gompper, R.G. Winkler, Phys. Rev. E 96, 062617 (2017)ADSCrossRefGoogle Scholar
  26. 26.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 110, 235902 (2013)ADSCrossRefGoogle Scholar
  27. 27.
    P.G. Drazin, W.H. Reid, Hydrodynamic Stability, 2nd edition (Cambridge University Press, Cambridge, UK, 2004)Google Scholar
  28. 28.
    B. Eckhardt, R. Pandit, Eur. Phys. J. B 33, 373 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edition (Pergamon, London, 1987)Google Scholar
  30. 30.
    P.J. Schmid, D.S. Henningson, Stability and Transition in Shear Flows (Springer, Berlin, 2001)Google Scholar
  31. 31.
    N. Tillmark, P. Alfredson, J. Fluid Mech. 235, 89 (1992)ADSCrossRefGoogle Scholar
  32. 32.
    J.R. Dorfman, T.R. Kirkpatrick, H. van Beijeren, Contemporary Kinetic Theory of Matter (Cambridge University Press, Cambridge) in printGoogle Scholar
  33. 33.
    F. Daviaud, J. Hegseth, P. Berge, Phys. Rev. Lett. 69, 2511 (1992)ADSCrossRefGoogle Scholar
  34. 34.
    O. Dauchot, E. Daviaud, Phys. Fluids 7, 335 (1995)ADSCrossRefGoogle Scholar
  35. 35.
    S. Bottin, F. Daviaud, P. Manneville, O. Dauchot, Europhys. Lett. 43, 171 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    A. Prigent, G. Gregoire, H. Chate, O. Dauchot, Physica D 174, 100 (2003)ADSCrossRefGoogle Scholar
  37. 37.
    M. Couliou, R. Monchaux, Phys. Fluids 27, 034101 (2015)ADSCrossRefGoogle Scholar
  38. 38.
    L. Klotz, G. Lemoult, I. Frontczak, L.S. Tuckerman, J.E. Wesfreid, Phys. Rev. Fluids 2, 043904 (2017)ADSCrossRefGoogle Scholar
  39. 39.
    L. Klotz, J. Wesfreid, J. Fluid Mech. 829, R4 (2017)ADSCrossRefGoogle Scholar
  40. 40.
    R. Monchaux, private communicationGoogle Scholar
  41. 41.
    Revised Supplementary Release on Properties of Liquid Water at 0.1 MPa, IAPWS SR6-08 (2011), available at www.iapws.org
  42. 42.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 93, 012148 (2016)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    J.J. Brey, J. Chem. Phys. 79, 4585 (1983)ADSCrossRefGoogle Scholar
  44. 44.
    H. van Beijeren, J.R. Dorfman, Physica 68, 437 (1973)ADSCrossRefGoogle Scholar
  45. 45.
    J.W. Dufty, Mol. Phys. 100, 2331 (2002)ADSCrossRefGoogle Scholar
  46. 46.
    J.J. Erpenbeck, W. Wood, J. Stat. Phys. 24, 455 (1981)ADSCrossRefGoogle Scholar
  47. 47.
    H. van Beijeren, Phys. Lett. A 105, 191 (1984)ADSCrossRefGoogle Scholar
  48. 48.
    T.R. Kirkpatrick, Phys. Rev. Lett. 53, 1735 (1984)ADSCrossRefGoogle Scholar
  49. 49.
    T.R. Kirkpatrick, Phys. Rev. A 32, 3130 (1985)ADSCrossRefGoogle Scholar
  50. 50.
    T.R. Kirkpatrick, J.C. Nieuwoudt, Phys. Rev. A 33, 2651 (1986)ADSCrossRefGoogle Scholar
  51. 51.
    A.L. Garcia, M. Malek Mansour, G.C. Lie, M. Mareschal, E. Clementi, Phys. Rev. A 36, 4348 (1987)ADSCrossRefGoogle Scholar
  52. 52.
    F.J. Alexander, A.L. Garcia, B.J. Adler, Phys. Fluids 6, 3854 (1994)ADSCrossRefGoogle Scholar
  53. 53.
    G. Gompper, T. Ihle, D.M. Kroll, R.C. Winkler, Adv. Polym. Sci. 221, 1 (2009)Google Scholar
  54. 54.
    C.-C. Huang, A. Varghese, G. Gompper, R.C. Winkler, Phys. Rev. E 91, 013310 (2015)ADSCrossRefGoogle Scholar
  55. 55.
    A. Varghese, C.-C. Huang, R.G. Winkler, G. Gompper, Phys. Rev. E 92, 053002 (2015)ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    J.W. Dufty, J. Lutsko, in Recent Developments in Nonequilibrium Thermodynamics: Fluids and Related Topics, edited by J. Casas-Vázquez, D. Jou, J.M. Rub\'i, Lect. Notes Phys., 253 (Springer, Berlin, 1986) pp. 47--84Google Scholar
  57. 57.
    R.A. Burton, Heat, Bearings, and Lubrication (Springer, New York, 2000) Chapt. 2Google Scholar
  58. 58.
    R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edition (Wiley, New York, 2002) Chapt. 10Google Scholar
  59. 59.
    E.W. Lemon, E.W. Bell, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0 (National Institute of Standards and Technology, Gaithersburg, MD, 2018)Google Scholar
  60. 60.
    Ch. Teagler, R. Span, W.A. Wagner, J. Phys. Chem. Ref. Data 28, 779 (1999)ADSCrossRefGoogle Scholar
  61. 61.
    T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 115, 035901 (2015)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • J. M. Ortiz de Zárate
    • 1
  • T. R. Kirkpatrick
    • 2
  • J. V. Sengers
    • 2
    Email author
  1. 1.Departamento de Estructura de la Materia, Facultad de FísicaUniversidad ComplutenseMadridSpain
  2. 2.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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