Abstract.
The definitions of thermodiffusion and Soret coefficients for a binary mixture include a concentration prefactor x(1 - x), when mole fraction x is used, or w(1 - w), when mass fraction w is used. In this paper the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the thermodiffusion and the Soret coefficients invariant upon changing in the concentration representation, using either mole fraction or mass faction. Then, it is shown how this invariance property can be extended to ternary mixtures by using appropriate concentration prefactors in matrix form. The paper is completed with some considerations about alternative definitions of thermodiffusion coefficients, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, use of molar concentrations and, finally, extension to multi-component mixtures.
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
W. Köhler, K.I. Morozov, J. Non-Equilib. Thermodyn. 41, 151 (2016)
S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962
Y. Demirel, Nonequilibrium Thermodynamics (Elsevier, Amsterdam, 2002)
G. Lebon, D. Jou, J. Casas-Vázquez, Understanding Nonequilibrium Thermodynamics (Springer, 2008)
S. Kjelstrup, D. Bedeaux, E. Johannessen, J. Gross, Non-Equilibrium Thermodynamics for Engineers (World Scientific, Singapore, 2010)
J.K. Platten, P. Costesèque, Eur. Phys. J. E 15, 235 (2004)
A. Vailati, M. Giglio, Phys. Rev. E 58, 4361 (1998)
R. Taylor, R. Krishna, Multicomponent Mass Transfer (Wiley, New York, 1993)
P.S. Belton, H.J.V. Tyrrell, Z. Naturforsch. 26, 48 (1971)
S. Wiegand, H. Ning, R. Kita, J. Non-Equilib. Thermodyn. 32, 193 (2007)
H. Cabrera, F. Cordido, A. Velásquez, P. Moreno, E. Sira, S.A. López-Rivera, C.R. Mec. 341, 372 (2013)
B. Hafskjold, Eur. Phys. J. E 40, 4 (2017)
S. Di Lecce, T. Albrecht, F. Bresme, Sci. Rep. 7, 44833 (2017)
W. Köhler, B. Müller, J. Chem. Phys. 103, 4367 (1995)
A. Mialdun, V.M. Shevtsova, Int. J. Heat Mass Transfer 51, 3164 (2008)
F. Croccolo, H. Bataller, F. Scheffold, J. Chem. Phys. 137, 234202 (2012)
F.A. Furtado, A.J. Silveira, C.R.A. Abreu, F.W. Tavares, Brazil. J. Chem. Eng. 32, 683 (2015)
S.R. De Groot, Physica 9, 699 (1942)
R. Delgado-Buscalioni, M. Khayet, J.M. Ortiz de Zárate, F. Croccolo, Eur. Phys. J. E 40, 51 (2017)
J.K. Platten, M.M. Bou-Ali, P. Costesèque, J.F. Dutrieux, W. Köhler, C. Leppla, S. Wiegand, G. Wittko, Philos. Mag. 83, 1965 (2003)
A. Mialdun, C. Minetti, Y. Gaponenko, V. Shevtsova, F. Dubois, Microgravity Sci. Technol. 25, 83 (2013)
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, Microgravity Sci. Technol. 28, 79 (2016)
G. Galliero, H. Bataller, J.P. Bazile, J. Diaz, F. Croccolo, H. Hoang, R. Vermorel, P.A. Artola, B. Rousseau, V. Vesovic, M.M. Bou-Ali, J.M. Ortiz de Zárate, S. Xu, K. Zhang, F. Montel, A. Verga, O. Minster, npj microgravity 3, 20 (2017)
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)
P. Costesèque, A. Mojtabi, J.K. Platten, C.R. Mec. 339, 275 (2011)
V. Shevtsova, V. Sechenyh, A. Nepomnyashchy, J.C. Legros, Philos. Mag. 91, 3498 (2011)
L.J.T.M. Kempers, J. Chem. Phys. 90, 6541 (1998)
H. Bataller, T. Triller, B. Pur, W. Köhler, J.M. Ortiz de Zárate, F. Croccolo, Eur. J. Phys. E 40, 35 (2017)
K. Ghorayeb, A. Firoozabadi, AIChe J. 46, 883 (2000)
M.M. Bou-Ali, A. Ahadi, D. Alonso de Mezquia, Q. Galand, M. Gebhardt, O. Khlybov, W. Köhler, M. Larrañaga, J.C. Legros, T. Lyubimova, A. Mialdun, I. Ryzhkov, M.Z. Saghir, V. Shevtsova, S.V. Vaerenbergh, Eur. Phys. J. E 38, 30 (2015)
M. Gebhardt, W. Köhler, J. Chem. Phys. 143, 164511 (2015)
R. Piazza, A. Parola, J. Phys.: Condens. Matter 20, 153102 (2008)
C.B. Mast, D. Braun, Phys. Rev. Lett. 104, 188102 (2010)
H. Matsuura, S. Iwaasa, Y. Nagasaka, J. Chem. Eng. Data 60, 3621 (2015)
S. Duhr, D. Braun, PNAS 26, 19678 (2006)
S. Iacopini, R. Rusconi, R. Piazza, Eur. Phys. J. E 19, 59 (2006)
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. Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures. Eur. Phys. J. E 42, 43 (2019). https://doi.org/10.1140/epje/i2019-11803-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2019-11803-2