Comptes Rendus
Fluctuating hydrodynamics and concentration fluctuations in ternary mixtures
Comptes Rendus. Mécanique, Volume 341 (2013) no. 4-5, pp. 399-404.

We use fluctuating hydrodynamics to derive expressions for the spatial and temporal spectra of concentration fluctuations in a ternary liquid mixture in equilibrium. Our results agree with those found by other investigators who have used a procedure in which arbitrary initial values are adopted. Our method of using fluctuating hydrodynamics has the advantage that it can also be extended to deal with fluctuations in systems out of equilibrium.

Published online:
DOI: 10.1016/j.crme.2013.01.018
Keywords: Ternary fluids, Fluctuating hydrodynamics, Concentration fluctuations, Correlation functions, Ternary diffusion coefficients

José M. Ortiz de Zárate 1; Jorge Luis Hita 1; Jan V. Sengers 2

1 Departamento de Física Aplicada I, Universidad Complutense, Madrid, Spain
2 Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA
@article{CRMECA_2013__341_4-5_399_0,
     author = {Jos\'e M. Ortiz de Z\'arate and Jorge Luis Hita and Jan V. Sengers},
     title = {Fluctuating hydrodynamics and concentration fluctuations in ternary mixtures},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {399--404},
     publisher = {Elsevier},
     volume = {341},
     number = {4-5},
     year = {2013},
     doi = {10.1016/j.crme.2013.01.018},
     language = {en},
}
TY  - JOUR
AU  - José M. Ortiz de Zárate
AU  - Jorge Luis Hita
AU  - Jan V. Sengers
TI  - Fluctuating hydrodynamics and concentration fluctuations in ternary mixtures
JO  - Comptes Rendus. Mécanique
PY  - 2013
SP  - 399
EP  - 404
VL  - 341
IS  - 4-5
PB  - Elsevier
DO  - 10.1016/j.crme.2013.01.018
LA  - en
ID  - CRMECA_2013__341_4-5_399_0
ER  - 
%0 Journal Article
%A José M. Ortiz de Zárate
%A Jorge Luis Hita
%A Jan V. Sengers
%T Fluctuating hydrodynamics and concentration fluctuations in ternary mixtures
%J Comptes Rendus. Mécanique
%D 2013
%P 399-404
%V 341
%N 4-5
%I Elsevier
%R 10.1016/j.crme.2013.01.018
%G en
%F CRMECA_2013__341_4-5_399_0
José M. Ortiz de Zárate; Jorge Luis Hita; Jan V. Sengers. Fluctuating hydrodynamics and concentration fluctuations in ternary mixtures. Comptes Rendus. Mécanique, Volume 341 (2013) no. 4-5, pp. 399-404. doi : 10.1016/j.crme.2013.01.018. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.01.018/

[1] M.M. Bou-Ali; J.K. Platten Metrology of the thermodiffusion coefficients in a ternary system, J. Non-Equilib. Thermodyn., Volume 30 (2005), p. 385

[2] A. Leahy-Dios; M.M. Bou-Ali; J.K. Platten; A. Firoozabadi Measurements of molecular and thermal diffusion coefficients in ternary mixtures, J. Chem. Phys., Volume 122 (2005), p. 234502

[3] D.A. Ivanov; T. Grossmann; J. Winkelmann Comparison of mutual diffusion coefficient data in a ternary liquid mixture obtained by various experimental techniques, Fluid Phase Equilib., Volume 228–229 (2005), p. 283

[4] D.A. Ivanov; J. Winkelmann Measurement of diffusion in ternary liquid mixtures by light scattering technique and comparison with Taylor dispersion data, Int. J. Thermophys., Volume 29 (2008), p. 1921

[5] T. Grossmann; J. Winkelmann Ternary diffusion coefficients of cyclohexane + toluene + methanol by Taylor dispersion measurements at 298.15 K. Part 1. Toluene rich area, J. Chem. Eng. Data, Volume 54 (2009), pp. 405-410

[6] T. Grossmann; J. Winkelmann Ternary diffusion coefficients of cyclohexane + toluene + methanol by Taylor dispersion measurements at 298.15 K. Part 2. Low toluene rich area, J. Chem. Eng. Data, Volume 54 (2009), pp. 485-490

[7] P. Blanco; M.M. Bou-Ali; J.K. Platten; D.A. de Mezquía; J.A. Madariaga; C. Santamaría Thermodiffusion coefficients of binary and ternary hydrocarbon mixtures, J. Chem. Phys., Volume 132 (2010), p. 114506

[8] A. Königer; H. Wunderlicht; W. Köhler Measurement of diffusion and thermal diffusion in ternary fluid mixtures using a two-color optical beam deflection technique, J. Chem. Phys., Volume 132 (2010), p. 174506

[9] V. Sechenyh; J.C. Legros; V. Shevtsova Measurements of optical properties in ternary mixture: cyclohexane–toluene–methanol, J. Chem. Eng. Data, Volume 57 (2012), p. 1036

[10] A. Mialdun, C. Minetti, Y. Gaponenko, V. Shevtsova, F. Dubois, Analysis of the thermal performance of SODI instrument for DCMIX configuration, Microgravity Sci. Technol. (2013) published online, . | DOI

[11] S.R. de Groot; P. Mazur Non-Equilibrium Thermodynamics, North-Holland, Amsterdam, 1962

[12] R. Taylor; R. Krishna Multicomponent Mass Transfer, Wiley, 1993

[13] Y. Demirel Nonequilibrium Thermodynamics, Elsevier, Amsterdam, 2002

[14] F. Vázquez; M. López de Haro Fluctuating hydrodynamics and irreversible thermodynamics, J. Non-Equilib. Thermodyn., Volume 26 (2001), pp. 279-290

[15] J.M. Ortiz de Zárate; J.V. Sengers Hydrodynamic Fluctuations in Fluids and Fluid Mixtures, Elsevier, Amsterdam, 2006

[16] M. López de Haro; J.A. del Río; F. Vázquez Light-scattering spectrum of a viscoelastic fluid subjected to an external temperature gradient, Rev. Mex. Fis. Suppl., Volume 48 (2002) no. 1, pp. 230-237

[17] R.F. Fox; G.E. Uhlenbeck Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations, Phys. Fluids, Volume 13 (1970), pp. 1893-1902

[18] L.D. Landau; E.M. Lifshitz Fluid Mechanics, Pergamon, London, 1959 (Chapter XVII)

[19] R.D. Mountain Spectral distribution of scattered light in a simple fluid, Rev. Mod. Phys., Volume 38 (1966), pp. 205-214

[20] R.D. Mountain; J.M. Deutch Light scattering from binary solutions, J. Chem. Phys., Volume 50 (1969), pp. 1103-1108

[21] J.P. Boon; S. Yip Molecular Hydrodynamics, McGraw–Hill, New York, 1980 (Chapter 5)

[22] B.J. Berne; R. Pecora Dynamic Light Scattering, Wiley, New York, 1976 (Chapter 10)

[23] J.P. Hansen; I.R. McDonald Theory of Simple Liquids, Academic Press, London, 1986 (Chapter 8)

[24] C. Cohen; J.W.H. Sutherland; J.M. Deutch Hydrodynamic correlation functions for binary mixtures, Phys. Chem. Liquids, Volume 2 (1971), pp. 213-235

[25] F. Croccolo; D. Brogioli; A. Vailati; M. Giglio; D.S. Cannell Nondiffusive decay of gradient-driven fluctuations in a free-diffusion process, Phys. Rev. E, Volume 76 (2007), p. 041112

[26] C.J. Takacs; A. Vailati; R. Cerbino; S. Mazzoni; M. Giglio; D.S. Cannell Thermal fluctuations in a layer of liquid CS2 subjected to temperature gradients with and without the influence of gravity, Phys. Rev. Lett., Volume 106 (2011), p. 244502

[27] B.M. Law; J.V. Sengers Fluctuations in fluids out of thermal equilibrium, J. Stat. Phys., Volume 57 (1989), pp. 531-547

[28] H.N.W. Lekkerkerker; W.G. Laidlaw Spectral analysis of light scattered by a ternary mixture, J. Chem. Soc., Faraday Trans., Volume 2 (1974) no. 70, pp. 1088-1097

[29] J. van der Elsken; A. Bot Rayleigh–Brillouin scattering from multicomponent mixtures: the Landau–Placzek ratio, J. Appl. Phys., Volume 66 (1989), pp. 2118-2121

[30] D.A. Ivanov; J. Winkelmann Multiexponential decay autocorrelation function in dynamic light scattering in near-critical ternary liquid mixture, J. Chem. Phys., Volume 125 (2006), p. 104507

[31] A. Bardow On the interpretation of ternary diffusion measurements in low-molecular weight fluids by dynamic light scattering, Fluid Phase Equilib., Volume 251 (2007), pp. 121-127

[32] M.G. Velarde; R.S. Schechter Thermal diffusion and convective instability. II. An analysis of the convected fluxes, Phys. Fluids, Volume 15 (1972), pp. 1707-1714

[33] J.V. Sengers; J.M. Ortiz de Zárate Nonequilibrium concentration fluctuations in binary liquid systems induced by the Soret effect (W. Köhler; S. Wiegand, eds.), Thermal Nonequilibrium Phenomena in Fluid Mixtures, Lect. Notes Phys., vol. 584, Springer, Berlin, 2002, pp. 121-145

[34] J.M. Ortiz de Zárate; J.A. Fornés; J.V. Sengers Long-wavelength nonequilibrium concentration fluctuations induced by the Soret effect, Phys. Rev. E, Volume 74 (2006), p. 046305

[35] T.O. Ziebold; R.E. Ogilvie Ternary diffusion in Copper–Silver–Gold alloys, Trans. Metall. Soc. AIME, Volume 239 (1967), pp. 942-954

[36] F.J. Spera; A.F. Trial Verification of the Onsager reciprocal relations in a molten silicate, Science, Volume 259 (1993) no. 5092, pp. 204-206

[37] D.G. Miller Application of irreversible thermodynamics to electrolyte solutions. II. Ionic coefficients Iij for isothermal vector processes in ternary systems, J. Phys. Chem., Volume 71 (1967), p. 616

[38] T.K. Kett; D.K. Anderson Ternary isothermal diffusion and the validity of the Onsager reciprocal relations in nonassociating systems, J. Phys. Chem., Volume 73 (1969), pp. 1268-1274

[39] Z. Sun; C.H. Wang Quasielastic light scattering from semidilute ternary polymer solutions of polystyrene and poly(methyl methacrylate) in benzene, Macromolecules, Volume 29 (1996), pp. 2011-2018

Cited by Sources:

Comments - Policy