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
Similar content being viewed by others
References
M. Kardar, R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999)
G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009)
M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994)
T.R. Kirkpatrick, J.K. Bhattacharje, J.V. Sengers, Phys. Rev. Lett. 119, 030603 (2017)
J.R. Dorfman, T.R. Kirkpatrick, J.V. Sengers, Annu. Rev. Phys. Chem. 45, 213 (1994)
J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)
J.F. Lutsko, J.W. Dufty, Phys. Rev. A 32, 3040 (1985)
J.F. Lutsko, J.W. Dufty, Phys. Rev. E 66, 041206 (2002)
J.V. Sengers, J.M. Ortiz de Zárate, J. Non-Newton. Fluid Mech. 165, 925 (2010)
K. Kawasaki, J.D. Gunton, Phys. Rev. A 8, 2048 (1973)
T. Yamada, K. Kawasaki, Prog. Theor. Phys. (Japan) 53, 111 (1975)
M.H. Ernst, B. Cichocki, J.R. Dorfman, J. Sharma, H. van Beijeren, J. Stat. Phys. 18, 237 (1978)
H. Wada, S.I. Sasa, Phys. Rev. E 67, 065302(R) (2003)
J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 77, 026306 (2008)
J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 79, 046308 (2009)
J.M. Ortiz de Zárate, J.V. Sengers, J. Stat. Phys. 144, 774 (2011)
J.M. Ortiz de Zárate, J.V. Sengers, J. Stat. Phys. 150, 540 (2013)
D.J. Evans, Phys. Rev. A 23, 1988 (1981)
S.H. Lee, P.T. Cummings, J. Chem. Phys. 99, 3919 (1993)
S.H. Lee, P.T. Cummings, J. Chem. Phys. 101, 6206 (1994)
G. Marcelli, B.D. Todd, R.J. Sadus, Phys. Rev. E 63, 021204 (2001)
J. Ge, G. Marcelli, B.D. Todd, R.J. Sadus, Phys. Rev. E 64, 021201 (2001)
J. Ge, B.D. Todd, G. Wu, R.J. Sadus, Phys. Rev. E 67, 061201 (2003)
A. Ahmed, P. Mausbach, R.J. Sadus, Phys. Rev. E 82, 011201 (2010)
A. Varghese, G. Gompper, R.G. Winkler, Phys. Rev. E 96, 062617 (2017)
T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 110, 235902 (2013)
P.G. Drazin, W.H. Reid, Hydrodynamic Stability, 2nd edition (Cambridge University Press, Cambridge, UK, 2004)
B. Eckhardt, R. Pandit, Eur. Phys. J. B 33, 373 (2003)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edition (Pergamon, London, 1987)
P.J. Schmid, D.S. Henningson, Stability and Transition in Shear Flows (Springer, Berlin, 2001)
N. Tillmark, P. Alfredson, J. Fluid Mech. 235, 89 (1992)
J.R. Dorfman, T.R. Kirkpatrick, H. van Beijeren, Contemporary Kinetic Theory of Matter (Cambridge University Press, Cambridge) in print
F. Daviaud, J. Hegseth, P. Berge, Phys. Rev. Lett. 69, 2511 (1992)
O. Dauchot, E. Daviaud, Phys. Fluids 7, 335 (1995)
S. Bottin, F. Daviaud, P. Manneville, O. Dauchot, Europhys. Lett. 43, 171 (1998)
A. Prigent, G. Gregoire, H. Chate, O. Dauchot, Physica D 174, 100 (2003)
M. Couliou, R. Monchaux, Phys. Fluids 27, 034101 (2015)
L. Klotz, G. Lemoult, I. Frontczak, L.S. Tuckerman, J.E. Wesfreid, Phys. Rev. Fluids 2, 043904 (2017)
L. Klotz, J. Wesfreid, J. Fluid Mech. 829, R4 (2017)
R. Monchaux, private communication
Revised Supplementary Release on Properties of Liquid Water at 0.1 MPa, IAPWS SR6-08 (2011), available at www.iapws.org
T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. E 93, 012148 (2016)
J.J. Brey, J. Chem. Phys. 79, 4585 (1983)
H. van Beijeren, J.R. Dorfman, Physica 68, 437 (1973)
J.W. Dufty, Mol. Phys. 100, 2331 (2002)
J.J. Erpenbeck, W. Wood, J. Stat. Phys. 24, 455 (1981)
H. van Beijeren, Phys. Lett. A 105, 191 (1984)
T.R. Kirkpatrick, Phys. Rev. Lett. 53, 1735 (1984)
T.R. Kirkpatrick, Phys. Rev. A 32, 3130 (1985)
T.R. Kirkpatrick, J.C. Nieuwoudt, Phys. Rev. A 33, 2651 (1986)
A.L. Garcia, M. Malek Mansour, G.C. Lie, M. Mareschal, E. Clementi, Phys. Rev. A 36, 4348 (1987)
F.J. Alexander, A.L. Garcia, B.J. Adler, Phys. Fluids 6, 3854 (1994)
G. Gompper, T. Ihle, D.M. Kroll, R.C. Winkler, Adv. Polym. Sci. 221, 1 (2009)
C.-C. Huang, A. Varghese, G. Gompper, R.C. Winkler, Phys. Rev. E 91, 013310 (2015)
A. Varghese, C.-C. Huang, R.G. Winkler, G. Gompper, Phys. Rev. E 92, 053002 (2015)
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--84
R.A. Burton, Heat, Bearings, and Lubrication (Springer, New York, 2000) Chapt. 2
R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edition (Wiley, New York, 2002) Chapt. 10
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)
Ch. Teagler, R. Span, W.A. Wagner, J. Phys. Chem. Ref. Data 28, 779 (1999)
T.R. Kirkpatrick, J.M. Ortiz de Zárate, J.V. Sengers, Phys. Rev. Lett. 115, 035901 (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ortiz de Zárate, J.M., Kirkpatrick, T.R. & Sengers, J.V. Nonequilibrium Casimir pressures in liquids under shear. Eur. Phys. J. E 42, 106 (2019). https://doi.org/10.1140/epje/i2019-11868-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2019-11868-9