Skip to main content
SpringerLink
Log in

Kinetic Theory of Granular Fluids: Hard and Soft Inelastic Spheres

  • Chapter
Dynamics: Models and Kinetic Methods for Non-equilibrium Many Body Systems

Part of the book series: NATO Science Series ((NSSE,volume 371))

Abstract

The basic concept that rapid granular flows can be considered as a collection of particles with short range interactions, moving ballistically and suffering instantaneous and inelastic binary collisions, is formulated in Haff’s seminal paper Grain flow as a fluid mechanical phenomenon [1].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.K. Haff, J. Fluid Mech. 134, 401 (1983).

    Article  ADS  MATH  Google Scholar 

  2. J.T. Jenkins and S.B. Savage, J. Fluid Mech. 130, 187 (1983).

    Article  ADS  MATH  Google Scholar 

  3. C.K.K. Lun, S.B. Savage, D.J. Jeffrey, and N. Chepurniy, J. Fluid Mech. 140, 223 (1984).

    Article  ADS  MATH  Google Scholar 

  4. J.T. Jenkins and M.W. Richman, Arch. Rat. Fluid Mech. 192, 313 (1988).

    ADS  MATH  Google Scholar 

  5. M.A. Hopkins and M.Y. Louge, Phys. Fluids A 3, 47 (1991).

    Article  ADS  Google Scholar 

  6. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993); I. Goldhirsch, M-L. Tan, and G. Zanetti, J. Scient. Comp. 8, 1 (1993).

    Article  ADS  Google Scholar 

  7. S. McNamara, Phys. Fluids A 5, 3056 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. S. McNamara and W.R. Young, Phys. Rev. E 50, R28 (1994); S. McNamara and W.R. Young, Phys. Rev. E 53, 5089 (1996).

    Article  ADS  Google Scholar 

  9. S.E. Esipov and T. Pöschel, J. Stat. Phys. 86, 1385 (1997).

    Article  ADS  MATH  Google Scholar 

  10. P. Deltour and J.-L. Barrat, J. Phys. I (France) 7, 137 (1997).

    Article  Google Scholar 

  11. D.R. Williams and F.C. MacKintosh, Phys. Rev. E 54, R9 (1996).

    Article  ADS  Google Scholar 

  12. T.P.C. van Noije, M.H. Ernst, R. Brito, and J.A.G. Orza, Phys. Rev. Lett. 79, 411 (1997); T.P.C. van Noije, R. Brito, and M.H. Ernst, Phys. Rev. E 57, R4891 (1998); J.A.G. Orza, R. Brito, T.P.C. van Noije, and M.H. Ernst, Int. J. Mod. Phys. C 8, 953 (1997).

    Article  ADS  Google Scholar 

  13. T.P.C. van Noije and M.H. Ernst, Phys. Rev. E submitted, June 1999; T.P.C. van Noije, Ph.D. thesis, Universiteit Utrecht, September 1999.

    Google Scholar 

  14. A. Puglisi, V. Loreto, U. Marini Bettolo Marconi, A. Petri, and A. Vulpiani, Phys. Rev. Lett. 81, 3848 (1998).

    Article  ADS  Google Scholar 

  15. M.R. Swift, M. Boamfă, S.J. Cornell, and A. Maritan, Phys. Rev. Lett. 80, 4410 (1998).

    Article  ADS  Google Scholar 

  16. G. Peng and T. Ohta, Phys. Rev. E 58, 4737 (1998).

    Article  ADS  Google Scholar 

  17. R. Brito and M.H. Ernst, Europhys. Lett. 43, 497 (1998); Int. J. Mod. Phys. C 9, 1339 (1998).

    Article  ADS  Google Scholar 

  18. T.P.C. van Noije, M.H. Ernst, E. Trizac, and I. Pagonabarraga, Phys. Rev. E 59, 4326 (1999).

    Article  ADS  Google Scholar 

  19. J.A Orza, R. Brito, and M.H. Ernst, preprint August 1999.

    Google Scholar 

  20. C. Bizon, M.D. Shattuck, J.B. Swift, and H.L. Swinney, this volume, p. 361.

    Google Scholar 

  21. S. Luding and S. McNamara, Granular Matter, to appear.

    Google Scholar 

  22. S. Luding and H.J. Herrmann, Chaos, 9, 25 (1999).

    Article  Google Scholar 

  23. H.M. Jaeger, S.R. Nagel, and R.P. Behringer, Rev. Mod. Phys. 68, 1259 (1996).

    Article  ADS  Google Scholar 

  24. T. Pöschel, Dynamik Granularer Systeme, Habilitationsschrift, Humboldt Universität, Berlin, November 1998.

    Google Scholar 

  25. S. Luding, Die Physik kohäsionsloser granularer Medien, Habilitationsschrift, Universität Stuttgart (Logos Verlag, Berlin, 1998).

    Google Scholar 

  26. A. Goldshtein and M. Shapiro, J. Fluid Mech. 282, 75 (1995).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. N. Sela, I. Goldhirsch, and S.H. Noskowicz, Phys. Fluids 8, 2337 (1996), I. Goldhirsch and M-L. Tan, Phys. Fluids 8, 1752 (1996); N. Sela and I. Goldhirsch, J. Fluid. Mech. 361, 41 (1998).

    Article  ADS  MATH  Google Scholar 

  28. M.H. Ernst, J.R. Dorfman, W.R. Hoegy, and J.M.J. van Leeuwen, Physica 45, 127 (1969).

    Article  ADS  Google Scholar 

  29. J.J. Brey, J.W. Dufty, and A. Santos, J. Stat. Phys. 87, 1051 (1997); J.J. Brey, J.W. Dufty, C.S. Kim, and A. Santos, Phys. Rev. E 58, 4638 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. T.P.C. van Noije, M.H. Ernst, and R. Brito, Physica A 251, 266 (1998); T.P.C. van Noije and M.H. Ernst, Granular Matter 1, 57 (1998).

    Article  Google Scholar 

  31. M. Huthmann and A. Zippelius, Phys. Rev. E 56, R6275 (1997). M. Huthmann, T. Aspelmeier, and A. Zippelius, Phys. Rev. E 60, 654 (1999); T. Aspelmeier, M. Huthmann, and A. Zippelius, in Proceedings of 215th WE-Heraeus Seminar on Granular Gases, Bad Honnef (Germany), March 8-12 1999.

    Article  ADS  Google Scholar 

  32. N.V. Brilliantov and T. Pöschel, e-print cond-mat/9906404.

    Google Scholar 

  33. M. Huthmann, J.A.G. Orza, and R. Brito, preprint (1999).

    Google Scholar 

  34. M. Müller and H. J. Herrmann, in Physics of Dry Granular Media, H. J. Herrmann, J.-P. Hovi, and S. Luding. eds., (Kluwer Academic Publishers, Dordrecht, 1998).

    Google Scholar 

  35. J.J. Brey, M.J. Ruiz-Montero, and D. Cubero, Phys. Rev. E 54, 3664 (1996); J.J. Brey, D. Cubero, and M.J. Ruiz-Montero, Phys. Rev. E 59, 1256 (1999).

    Article  ADS  Google Scholar 

  36. J.M. Montanero and A. Santos, submitted to Granular Matter, July 1999.

    Google Scholar 

  37. N.V. Brilliantov, F. Spahn, J.M. Hertzsch, and T. Pöschel, Phys. Rev. E 53, 5382 (1996); T. Schwager and T. Pöschel, Phys. Rev. E 57, 650 (1996).

    Article  ADS  Google Scholar 

  38. G. Kuwabara and K. Kono, Jpn. J. Appl. Phys. 26, 1230 (1987).

    Article  ADS  Google Scholar 

  39. W.A.M. Morgado and I. Oppenheim, Phys. Rev. E 55, 1940 (1998).

    Article  ADS  Google Scholar 

  40. H. Hwang and K. Hutter, Continuum Mech. and Thermodynamics 7, 357 (1995).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  41. J. Trulsen, Astrophys. Space Sci. 12, 329 (1971); K.A. Hameen-Anttila, Astro-phys. Space Sci. 58, 477 (1978); P. Goldreich and S. Tremaine, ICARUS 34, 227 (1978).

    Article  ADS  Google Scholar 

  42. C.K.K. Lun and S.B. Savage, Acta Mechanica 63, 15 (1986).

    Article  MATH  Google Scholar 

  43. O.R. Walton and R.L. Braun, J. Rheol. 30, 949 (1986); Acta Mech. 63, 73 (1986).

    Article  ADS  Google Scholar 

  44. C.S. Campbell, Annu. Rev. Fluid Mech. 22, 57 (1990), C.S. Campbell and C.E. Brennen, J. Fluid Mech. 151, 167 (1985).

    Article  ADS  Google Scholar 

  45. H.J. Herrmann, Physica A 191, 263 (1992).

    Article  ADS  Google Scholar 

  46. S. Luding, E. Clement, A. Blumen, J. Rajchenbach, and J. Duran, Phys. Rev. E 50, 4113 (1994).

    Article  ADS  Google Scholar 

  47. S. Chen, Y. Deng, X. Nie, and Y. Tu, unpublished.

    Google Scholar 

  48. K. Kawasaki, in Phase Transitions and Critical Phenomena, Vol. 5A, C. Domb and M.S. Green, eds., (Academic Press, London, 1976).

    Google Scholar 

  49. T. Keyes, in Modern Theoretical Chemistry: Statistical Mechanics, B.J. Berne, ed., (Academic Press, New York, 1977).

    Google Scholar 

  50. B.J. Alder and W.E. Alley, Physics Today 37, 56 (1984); E.G.D. Cohen, Physics Today 37, 64 (1984).

    Article  ADS  Google Scholar 

  51. J.-P. Hansen and I.R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986).

    Google Scholar 

  52. J.R. Dorfman and H. van Beijeren, The Kinetic Theory of Gases, in Statistical Mechanics, Part B: Time-Dependent Processes, B.J. Berne, ed., (Plenum Press, New York, 1977), Chap. 3.

    Google Scholar 

  53. J.R. Dorfman and E.G.D. Cohen, Phys. Rev. Lett. 25, 1257 (1970).

    Article  ADS  Google Scholar 

  54. M.H. Ernst and J.R. Dorfman, Physica 61, 157 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  55. M.H. Ernst, E.H. Hauge, and J.M.J. van Leeuwen, Phys. Rev. A 4, 2055 (1971); M.H. Ernst and J.R. Dorfman, J. Stat. Phys. 15, 311 (1976).

    Article  ADS  Google Scholar 

  56. Y. Pomeau and P. Resibois, Phys. Rep. C 19, 63 (1975).

    Article  ADS  Google Scholar 

  57. J.R. Dorfman, T.R. Kirkpatrick, and J. Sengers, Ann. Rev. Phys. Chem. 45, 213 (1994).

    Article  ADS  Google Scholar 

  58. L. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon Press, London, 1959).

    Google Scholar 

  59. L. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, London, 1959), ch. 3, 17.

    Google Scholar 

  60. J.S. Langer, in: Solids Far from Equilibrium, C. Godrèche, ed., (Cambridge University Press, 1992), p. 297; J.K. Dhont, this volume, p. 73.

    Google Scholar 

  61. Holmes’ Principles of Physical Geology, D. Duff, ed., (Chapman and Hall, Boca Raton, U.S.A., 1994), p. 368.

    Google Scholar 

  62. S. Chapman and T.G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, London, 1970).

    Google Scholar 

  63. S.R. de Groot and P. Mazur, Non-equilibrium Thermodynamics (North Holland Publ. Co, Amsterdam, 1963) p. 100.

    Google Scholar 

  64. C.A. Marsh, G. Backx, and M.H. Ernst, Phys. Rev. E 56, 1676 (1997).

    Article  ADS  Google Scholar 

  65. H. van Beijeren and M.H. Ernst, Phys. Lett. A 43, 367 (1973); Physica 68, 437 (1973); Physica 70, 225 (1973).

    Article  ADS  Google Scholar 

  66. For a review, see E.G.D. Cohen, Physica A 194, 241 (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Utrecht, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    M. H. Ernst

Authors
  1. M. H. Ernst
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Physics, Marquette University, Milwaukee, WI, USA

    John Karkheck

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ernst, M.H. (2000). Kinetic Theory of Granular Fluids: Hard and Soft Inelastic Spheres. In: Karkheck, J. (eds) Dynamics: Models and Kinetic Methods for Non-equilibrium Many Body Systems. NATO Science Series, vol 371. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4365-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4365-3_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6554-9

  • Online ISBN: 978-94-011-4365-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation