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Choosing Hydrodynamic Fields

Published online by Cambridge University Press:  18 July 2011

J. W. Dufty  and
J. J. Brey
J. W. Dufty*
Affiliation:
Department of Physics, University of Florida, Gainesville, FL 32611, USA
J. J. Brey
Affiliation:
Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
*
⋆Corresponding author. E-mail: dufty@phys.ufl.edu

Abstract

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Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumptionthat a small set of fields provides a closed description on large space and time scales.Conditions governing the choice for these fields are discussed in the context of granularfluids and multi-component fluids. In the first case, the relevance of temperature orenergy as a hydrodynamic field is justified. For mixtures, the use of a total temperatureand single flow velocity is compared with the use of multiple species temperatures andvelocities.

Keywords

granular gaskinetic equations equationshydrodynamics

Information

Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 19 - 36
Copyright
© EDP Sciences, 2011

References

Brey, J. J., Dufty, J. W., Santos, A.. Dissipative dynamics for hard spheres. J. Stat. Phys., 87 (1997), 1051–1066. CrossRefGoogle Scholar
Brey, J. J., Ruiz-Montero, M. J.. Hydrodynamic character of the non-equipartition of kinetic energy in binary granular gases. Phys. Rev. E, 80 (2009), 041306. CrossRefGoogle Scholar
N. Brilliantov, T. Pöschel. Kinetic Theory of Granular Gases. Oxford, New York, 2004.
Dahl, S. R., M.Hrenya, C., Garzó, V., Dufty, J. W.. Kinetic temperatures for a granular mixture. Phys. Rev. E, 66 (2006), 04301. Google ScholarPubMed
J. W. Dufty. Granular Fluids. R. Meyers, ed. Encyclopedia of Complexity and Systems Science. Springer, Heidelberg, 2009. arXiv:0709.0479.
J. W. Dufty. Nonequilibrium Statistical Mechanics and Hydrodynamics for a Granular Fluid. B. Cichocki, M. Napiorkowski, J. Piasecki, eds. 2nd Warsaw School on Statistical Physics. Warsaw University Press, Warsaw, 2008. arXiv:0707.3714.
Dufty, J. W., Baskaran, A., Brey, J J.. Linear response and hydrodynamics for granular fluids. Phys. Rev. E, 77 (2008), 031310. CrossRefGoogle ScholarPubMed
J. W. Dufty, J. J. Brey. Origins of hydrodynamics for a granular gas. L. Pareschi,G. Russo, G. Toscani eds. Modelling and Numerics of Kinetic Dissipative Systems. Nova Science, NY, 2005; arXiv:cond-mat/0410133.
J. Ferziger, H. Kaper. Mathematical Theory of Transport Processes in Gases. North-Holland, Amsterdam, 1972.
D. Forster. Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions. Benjamin, Reading, MA, 1975.
Garzó, V., Dufty, J.. Homogeneous cooling state for a granular mixture. Phys. Rev. E, 60 (1999), 5706–5713. CrossRefGoogle ScholarPubMed
Goldhirsch, I.. Rapid Granular Flows. Annual Review of Fluid Mechanics, 35 (2003), 267–293. CrossRefGoogle Scholar
H. Grabert. Projection Operator Techniques in Nonequilibrium Statistical Mechanics. Springer, Berlin, 1982.
T. Halsey, A. Mehta, eds. Challenges in Granular Physics. World Scientific, Singapore, 2002.
Iddir, H. and Arastoopour, H.. Modeling of multitype particle flow using the kinetic theory approach. AIChe. J., 51 (2005), 1620–1632. CrossRefGoogle Scholar
Jenkins, J., Mancini, F.. Balance laws and constitutive relations for plane flows of a dense binary mixture of smooth nearly elastic circular disks. J. Appl. Mech., 54 (1987), 27–34. CrossRefGoogle Scholar
Jou, D., Casas-Vazquez, J., Lebon, G.. Extended Irreversible Thermodynamics. Rep. Prog. Phys., 51 (1988), 1105. CrossRefGoogle Scholar
Kadanoff, L. P.. Built upon sand: Theoretical ideas inspired by granular flows. Rev. Mod. Phys., 71 (1999), 435–444. CrossRefGoogle Scholar
Lutsko, J.. Approximate solution of the Enskog equation far from equilibrium. Phys. Rev. Lett., 78 (1997), 243-246. CrossRefGoogle Scholar
Lutsko, J.. Rheology of dense polydisperse granular fluids under shear. Phys. Rev. E, 70 (2004), 061101. CrossRefGoogle ScholarPubMed
Martin, P., Parodi, O., Pershan, P.. Unified Hydrodynamic Theory for Cristals, Liquids, and Normal Fluids. Phys. Rev. A, 6 (1972), 2401-2420. CrossRefGoogle Scholar
J. A. McLennan. Introduction to Nonequilibrium Statistical Mechanics. Prentice-Hall, New Jersey, 1989.
Montanero, J. M., Garzó, V.. Monte Carlo simulations of the homogeneous cooling state for a granular mixture. Granular Matter, 4 (2002), 17–24. CrossRefGoogle Scholar
A. Santos, J. Dufty. Strong breakdown of equipartition in uniform gas mixtures. M. S. Ivanov, A. K. Rebrov, eds. Rarefied Gas Dynamics. Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2007.
R. Zwanzig. Nonequilibrium Statistical Mechanics, Oxford, NY, 2001.
Zwanzig, R.. Memory Effects in Irreversible Thermodynamics. Phys. Rev., 124 (1961), 983–992. CrossRefGoogle Scholar