Abstract.
We discuss the gravity effects on the dynamics of composition fluctuations in a ternary mixture around the non-equilibrium quiescent state induced by thermodiffusion when subjected to a stationary temperature gradient. We found that the autocorrelation matrix of concentration fluctuations can be expressed as the sum of two exponentially decaying concentration modes. Without accounting for confinement, we obtained exact analytical expressions for the two decay rates which, as a consequence of gravity, display a wave-number-dependent mixing. The stability of the quiescent solution is also examined, as a function of the two solutal Rayleigh numbers used to express the decay rates. After having discussed the dynamics of the two concentration modes, we calculate the corresponding amplitudes. Consequences for optical experiments are discussed.
Graphical abstract
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
H.N.W. Lekkerkerker, W.G. Laidlaw, J. Chem. Soc., Faraday Trans. 2 70, 1088 (1974)
J. van der Elsken, A. Bot, J. Appl. Phys. 66, 2118 (1989)
D.A. Ivanov, J. Winkelmann, J. Chem. Phys. 125, 104507 (2006)
A. Bardow, Fluid Phase Equilib. 251, 121 (2007)
M.G. Velarde, R.S. Schechter, Phys. Fluids 15, 1707 (1972)
R.D. Mountain, Rev. Mod. Phys. 38, 205 (1966)
R.D. Mountain, J.M. Deutch, J. Chem. Phys. 50, 1103 (1969)
B.J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976)
J.P. Boon, S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980)
J.P. Hansen, I.R. McDonald, Theory of Simple liquids, 2nd edn. (Academic Press, London, 1986)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), 2nd revised English version, 1987
R.F. Fox, G.E. Uhlenbeck, Phys. Fluids 13, 1893 (1970)
J. Foch, Phys. Fluids 14, 893 (1971)
D. Ronis, I. Procaccia, Phys. Rev. A 26, 1812 (1982)
R. Schmitz, E.G.D. Cohen, J. Stat. Phys. 39, 285 (1985)
J.M. Ortiz de Zárate, J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (Elsevier, Amsterdam, 2006)
F. Croccolo, J.M. Ortiz de Zárate, J.V. Sengers, Eur. Phys. J. E 39, 125 (2016)
B.M. Law, R.W. Gammon, J.V. Sengers, Phys. Rev. Lett. 60, 1554 (1988)
P.N. Segrè, R.W. Gammon, J.V. Sengers, Phys. Rev. E 47, 1026 (1993)
W.B. Li, P.N. Segrè, R.W. Gammon, J.V. Sengers, Physica A 204, 399 (1994)
W.B. Li, K.J. Zhang, J.V. Sengers, R.W. Gammon, J.M. Ortiz de Zárate, Phys. Rev. Lett. 81, 5580 (1998)
W.B. Li, K.J. Zhang, J.V. Sengers, R.W. Gammon, J.M. Ortiz de Zárate, J. Chem. Phys. 112, 9139 (2000)
P.N. Segrè, J.V. Sengers, Physica A 198, 46 (1993)
A. Vailati, M. Giglio, Phys. Rev. Lett. 77, 1484 (1996)
J.M. Ortiz de Zárate, R. Pérez Cordón, J.V. Sengers, Physica A 291, 113 (2001)
J.M. Ortiz de Zárate, J.V. Sengers, Physica A 300, 25 (2001)
C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, Europhys. Lett. 111, 60013 (2015)
A. Vailati, R. Cerbino, S. Mazzoni, C.J. Takacs, D.S. Cannell, M. Giglio, Nat. Commun. 2, 290 (2011)
C. Giraudet, H. Bataller, Y. Sun, A. Donev, J.M. Ortiz de Zárate, F. Croccolo, Eur. Phys. J. E 39, 120 (2016)
J.M. Ortiz de Zárate, J.L. Hita, J.V. Sengers, C.R. Mec. 341, 399 (2013)
J.M. Ortiz de Zárate, C. Giraudet, H. Bataller, F. Croccolo, Eur. Phys. J. E 37, 77 (2014)
H. Bataller, C. Giraudet, F. Croccolo, J.M. Ortiz de Zárate, Micrograv. Sci. Technol. 28, 611 (2016)
F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012)
F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, D.S. Cannell, Appl. Opt. 45, 2166 (2006)
G. Galliero, H. Bataller, F. Croccolo, R. Vermorel, P. Artola, B. Rousseau, V. Vesovic, M. Bou-Ali, J.M. Ortiz de Zárate, K. Zhang, F. Montel, Micrograv. Sci. Technol. 28, 79 (2016)
I. Lizarraga, C. Giraudet, F. Croccolo, M.M. Bou-Ali, H. Bataller, Micrograv. Sci. Technol. 28, 267 (2016)
K. Balakrishnan, A.L. Garcia, A. Donev, J.B. Bell, Phys. Rev. E 89, 013017 (2014)
R. Taylor, R. Krishna, Multicomponent Mass Transfer (Wiley, New York, 1993)
J.M. Ortiz de Zárate, J.V. Sengers, J. Stat. Phys. 115, 1341 (2004)
H. Bataller, T. Triller, B. Pur, W. Köhler, J.M. Ortiz de Zárate, F. Croccolo, submitted to Eur. Phys. J. E
I. Ryzhkov, V. Shevtsova, Phys. Fluids 21, 014102 (2009)
I. Ryzhkov, Fluid Dyn. 48, 477 (2013)
T. Lyubimova, N. Zubova, Eur. J. Phys. E 38, 19 (2015)
T. Grossmann, J. Winkelmann, J. Chem. Eng. Data 54, 405 (2009)
T. Grossmann, J. Winkelmann, J. Chem. Eng. Data 54, 485 (2009)
A. Mialdun, V. Sechenyh, J.C. Legros, J.M. Ortiz de Zárate, V. Shevtsova, J. Chem. Phys. 139, 104903 (2013)
J.V. Sengers, J.M. Ortiz de Zárate, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, Lecture Notes in Physics, Vol. 584, edited by W. Köhler, S. Wiegand (Springer, Berlin, 2002) pp. 121--145
S.P. Trainoff, D.S. Cannell, Phys. Fluids 14, 1340 (2002)
M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)
A. Mialdun, C. Minetti, Y. Gaponenko, V. Shevtsova, F. Dubois, Micrograv. Sci. Technol. 25, 83 (2013)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Martínez Pancorbo, P., Ortiz de Zárate, J.M., Bataller, H. et al. Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures. Eur. Phys. J. E 40, 22 (2017). https://doi.org/10.1140/epje/i2017-11513-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2017-11513-9