Journal of Statistical Physics

, Volume 29, Issue 1, pp 139–153 | Cite as

Kinetic theory of hydrodynamic flows, III. the torque on a rotating sphere or cylinder1

  • Henk van Beijeren
  • J. R. Dorfman


The extended Boltzmann equation introduced in previous papers is used to compute the torque exerted on a macroscopic sphere or cylinder placed in a dilute gas, when the mean free path of the gas molecules is small compared to the characteristic dimension of the sphere or cylinder. The usual hydrodynamic results are recovered in this kinetic theory calculation.

Key words

Boltzmann equation boundary conditions normal solutions rotating sphere or cylinder torque 


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  1. 1.
    H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:335 (1980).Google Scholar
  2. 2.
    H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:443 (1980).Google Scholar
  3. 3.
    J. R. Dorfman and H. van Beijeren, inStatistical Physics, Part B, B. Berne (ed.), Plenum Press, New York (1978); see also J. H. Herzigen and H. G. Kaper,Mathematical Theory of Transport in Gases, North-Holland, Amsterdam (1972).Google Scholar
  4. 4.
    L. Landau and E. M. Lifshitz,Fluid Mechanics, Pergamon Press, New York (1954).Google Scholar
  5. 5.
    H. Lamb,Hydrodynamics, Dover, New York (1945).Google Scholar
  6. 6.
    Y. Pomeau and P. Resibois,Phys. Rep. 19C:64 (1975).Google Scholar
  7. 7.
    J. T. Hynes,Ann. Rev. Phys. Chem. 28:301 (1977).Google Scholar
  8. 8.
    S. Yip,Ann. Rev. Phys. Chem. 30:547 (1979).Google Scholar
  9. 9.
    E. Hauge and A. Martin-Löf,J. Stat. Phys. 7:259 (1973).Google Scholar
  10. 10.
    J. T. Hynes, R. Kapral, and M. Weinberg,J. Chem. Phys. 67:3256 (1977).Google Scholar
  11. 11.
    J. R. Lebenhaft and R. Kapral,J. Chem. Phys. 74:6888 (1981).Google Scholar
  12. 12.
    Cf, L. Landau and E. M. Lifshitz,Mechanics, 3rd ed., Pergamon Press, New York (1975), pp. 126–129.Google Scholar
  13. 13.
    Cf. I. S. Gradshteyn and I. M. Ryzhik,Tables of Integrals, Series and Products, Academic Press, New York (1965).Google Scholar
  14. 14.
    Cf. H. Lamb,Hydrodynamics, Dover, New York (1945), p. 588. The torque on a cylinder rotating in a rarefied gas has been computed by A. Gervois and Y. Pomeau,Phys. Fluids 17:2292 (1974).Google Scholar
  15. 15.
    J. T. Hynes and J. M. Deutch, inPhysical Chemistry: An Advance Treatise, Vol. IIB, H. Eyring, D. Henderson, and W. Jost (eds.), McGraw-Hill, New York (1975); see also N. Corngold,Phys. Rev. A 6:1570 (1972).Google Scholar
  16. 16.
    R. I. Cukier, R. Kapral, J. R. Lebenhaft, and J. R. Mehaffey,J. Chem. Phys. 73:5244 (1980).Google Scholar
  17. 17.
    T. Keyes and J. M. Mercer (private communication).Google Scholar
  18. 18.
    J. M. Mercer, The kinetic theory of Brownian motion, Ph.D. dissertation, Yale University (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Henk van Beijeren
    • 1
  • J. R. Dorfman
    • 2
  1. 1.Institute for Theoretical PhysicsR. W. T. H.AachenWest Germany
  2. 2.Institute for Physical Science and Technology and Department of Physics and AstronomyUniversity of MarylandMaryland

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