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Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks

Phys. Fluids 28, 3485 (1985); doi:10.1063/1.865302

Issue Date: December 1985

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J. T. Jenkins and M. W. Richman
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York 14853
Grad's method of moments is employed to derive balance laws and constitutive relations for plane flows of a dense gas consisting of identical, rough, inelastic, circular disks. Two temperatures are involved; these are proportional to the kinetic energies associated with fluctuations in translational velocity and spin, respectively. When the single particle velocity distribution function is assumed to be close to a two-temperature Maxwellian, two distinct theories are obtained. One applies when the particles are almost smooth and the collisions between them are nearly elastic; the other applies to nearly elastic particles that, in a collision, almost reverse the relative velocity of their points of contact. I both cases energy is nearly conserved in collisions. Physics of Fluids is copyrighted by The American Institute of Physics.
History: Received 26 April 1985; accepted 29 August 1985
Permalink: http://dx.doi.org/10.1063/1.865302
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KEYWORDS and PACS

Keywords
PACS
  • 51.10.+y
    Kinetic and transport theory of fluids; physical properties of gases Kinetic and transport theory
  • 05.20.Dd
    Statistical physics and thermodynamics Statistical mechanics Kinetic theory
  • 05.60.+w
    Statistical physics and thermodynamics Transport processes: theory
  • YEAR: 1985

PUBLICATION DATA

ISSN:
0031-9171 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (17)
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  1. C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Shepurniy, J. Fluid Mech. 140, 233 (1984).
  2. J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985).
  3. These experiments are being carried by N. L. Ackermann and his coworkers at Clarkson University.
  4. G. W. Hawkins, in Mechanics of Granular Materials, edited by J. T. Jenkins and M. Satake (Elsevier, Amsterdam, 1983), p. 305;
  5. C. W. Campbell and C. E. Brennen, ibid., p. 313;
  6. O. R. Walton, ibid., p. 327.
  7. C. S. Campbell and C. E. Brennen, in Deformation and Failure of Granular Materials, edited by P. A. Vermeer and H. J. Luger (Balkema, Rotterdam, 1982), p. 515.
  8. C. S. Campbell and C. E. Brennen, J. Appl. Mech. 52, 172 (1985).
  9. C. S. Campbell and C. E. Brennen, J. Fluid Mech. 151, 167 (1985).
  10. C. S. Campbell and A. Gong, submitted to J. Fluid Mech.
  11. H. Grad, Comm. Pure Appl. Math. 2, 331 (1949).
  12. W. Goldsmith, Impact (Arnold, London, 1960), Chap. 2.
  13. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (The University Press, Cambridge, 1970), 3rd ed., Secs. 16.1–16.21.
  14. L. Verlet and D. Levesque, Mol. Phys. 46, 969 (1982).
  15. N. F. Carnahan and K. E. Starling, J. Chem. Phys. 51, 635 (1969).
  16. F. Reif, Fundamentals of Statistical Mechanics and Thermal Physics (McGraw-Hill, New York, 1965), Chap. 14.
  17. B. J. McCoy, S. I. Sandler, and J. S. Dahler, J. Chem. Phys. 45, 3485 (1966).
  18. See AIP document no. PAPS PFLDA-28-3485-14 for 14 pages of the detailed calculation. Order by PAPS number and journal reference from American Institute of Physics, Physics Auxiliary Publication Service, 335 East 45th Street, New York, NY 10017. The price is $1.50 for each microfiche or $5.00 for photocopies of up to 30 pages, and $0.15 for each additional page over 30 pages. Airmail additional. Make checks payable to American Institute of Physics. [EPAPS]
  19. E. G. D. Cohen, Phys. Today 37 (1), 64 (1984).

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