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Dynamical pressure for fluid mixtures with several temperatures

Published online by Cambridge University Press:  05 August 2009

Henri Gouin  and
Tommaso Ruggeri
Henri Gouin
Affiliation:
Université d'Aix-Marseille & M2P2, C.N.R.S. U.M.R. 6181, Case 322, Av. Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France
Tommaso Ruggeri
Affiliation:
Department of Mathematics and Research Center of Applied Mathematics C.I.R.A.M. University of Bologna, Via Saragozza 8, 40123-I Bologna, Italy
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Abstract

We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with the difference of temperatures between components even if bulk viscosities are null. The non-equilibrium dynamical pressure can be measured and may be convenient in several physical situations as for example in cosmological circumstances where a dynamical pressure played a major role in the evolution of the early universe.

Keywords

Fluid mixturesmulti-temperaturesdynamical pressureHamilton's principleMélanges de fluidesmulti-temperaturespression dynamiqueprinciple d'Hamilton
Type
Research Article
Information
Mechanics & Industry , Volume 10 , Issue 3-4: 19e Congrès français de mécanique (CFM 2009) , May 2009 , pp. 239 - 243
Copyright
© AFM, EDP Sciences, 2009

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References

M. Ishii, Thermo-fluid dynamic theory of two-phase flows, Paris, Eyrolles, 1975
S. Putterman, Super fluid hydrodynamics, Elsevier, New York, 1974
I. Müller, T. Ruggeri, Rational Extended Thermody- namics, Springer-Verlag, New York, 1998
Ruggeri, T., Simić, S., On the hyperbolic system of a mixture of Eulerian fluids: a comparison between single and multi-temperature models, Math. Meth. Appl. Sci. 30 (2007) 827–849 CrossRef
J. Serrin, Mathematical principles of classical fluid mechanics in Encyclopedia of Physics VIII/1, in: Flügge (éd.), Springer, Berlin, 1960
V.L. Berdichevsky, Variational principles of continuum mechanics, Nauka, Moscow, 1983
Gouin, H., Variational theory of mixtures in continuum mechanics, Eur. J. Mech. B/Fluids 9 (1990) 469–471
Gouin, H., Ruggeri, T., Mixture of fluids involving entropy gradients and acceleration waves in interfacial layers, Eur. J. Mech. B/Fluids 24 (2005) 596–613 CrossRef
Gouin, H., Ruggeri, T., Identification of an average temperature and a dynamical pressure in multi-temperature mixture of fluids, Phys. Rev. E 78 (2008) 016303 CrossRef
H. Gouin, T. Ruggeri, The Hamilton principle for fluid binary mixtures with two temperatures, Boll., Un. Math. It., 9, II (2009)
Gavrilyuk, S.L., Gouin, H., Perepechko, Yu.V., Hyperbolic models of homogeneous two-fluid mixtures, Meccanica 33 (1998) 161–175 CrossRef
Lhuillier, D., From Molecular mixtures to suspensions of particles, J. Physique II 5 (1995) 19–36 CrossRef
S.R. de Groot, W.A. van Leeuwen, Ch.G. van Weert, Relativistic kinetic theory, North-Holland, Amsterdam, 1980
Weinberg, S., Entropy generation and the survival of protogalaxies in an expanding universe, Astrophys. J. 168 (1971) 175–194 CrossRef