- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Phenomenological viscous factor in the nonequilibrium distribution function for liquids

S. Morioka

  • Key Laboratory of Liquid Structure and Heredity of Materials, College of Materials Science and Engineering, Shandong University, Jinan, Shandong 250061, China

PDF

Phys. Rev. E 72, 051203 – Published 17 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.051203

Abstract

An improved formula of shear viscosity for liquids is presented by introducing a phenomenological viscous factor in the nonequilibrium term in the doublet distribution function, which improves an incomplete formula of shear viscosity presented in an early work of Born and Green. The phenomenological viscous factor effectively counts some higher-order interactions, and is constrained so that, in the limit of hard-sphere liquids, the magnitude of the improved formula of shear viscosity reduces to that of Enskog for dense fluids. The improved formula does not require any adjustable parameters except for the pair potential to describe liquids. In order to verify the improved formula, a liquid of Ar near the triple point is studied in detail. In addition, liquids of Pb in wide ranges of temperature are examined to test the temperature dependence of the phenomenological viscous factor. Here an available integral equation is employed to calculate the radial distribution function by prescribed pair potentials. One finds that the present formula is capable to describe the shear viscosity in accord with those of experimental data for both cases of Ar and Pb. The phenomenological viscous factor plays a crucial role in the evaluation of shear viscosity for liquids.

View figure in article

Article Text

References (36)

  1. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, 2nd ed. (Cambridge University Press, London, 1952).
  2. M. V. Tokarchuk, I. P. Omelyan, and A. E. Kobryn, Phys. Rev. E 62, 8021 (2000).
  3. J. G. Kirkwood, J. Chem. Phys. 14, 180 (1946); J. G. Kirkwood, F. P. Buff, and M. S. Green, ibid. 17, 988 (1949); S. A. Rice, J. G. Kirkwood, J. Ross, and R. W. Zwanzig, ibid. 31, 575 (1959); S. A. Rice and J. G. Kirkwood, ibid. 31, 901 (1959).
  4. S. A. Rice and A. R. Allnatt, J. Chem. Phys. 34, 2144 (1961); A. R. Allnatt and S. A. Rice, ibid. 34, 2156 (1961).
  5. S. A. Rice and P. Gray, The Statistical Mechanics of Simple Liquids (Interscience, New York, 1965), Chaps. 5 and 6.
  6. N. N. Bogoliubov, J. Phys. (Moscow) 10, 256 (1946); 10, 265 (1946); M. Born and H. S. Green, Proc. R. Soc. London, Ser. A 188, 10 (1946); J. G. Kirkwood, J. Chem. Phys. 3, 300 (1935); J. Yvon, Actualités Scientifiques et Industrielles (Hermann, Paris, 1935).
  7. P. Malbrunot, A. Boyer, E. Charles, and H. Abachi, Phys. Rev. A 27, 1523 (1983).
  8. R. Vogelsang and C. Hoheisel, Phys. Rev. A 39, 6391 (1989).
  9. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, New York, 1986), Chaps. 7–9.
  10. M. Born and H. S. Green, Proc. R. Soc. London, Ser. A 190, 455 (1947).
  11. M. Shimoji, Adv. Phys. 16, 705 (1967).
  12. Y. Waseda, The Structure of Non-Crystalline Materials (McGraw-Hill, New York, 1980), p. 202.
  13. S. Morioka, J. Non-Cryst. Solids 341, 46 (2004).
  14. B. J. Alder, D. M. Gass, and T. E. Wainwright, J. Chem. Phys. 53, 3813 (1970).
  15. Y. Rosenfeld and N. W. Ashcroft, Phys. Rev. A 20, 1208 (1979).
  16. J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).
  17. H. S. Green, The Molecular Theory of Fluids (North-Holland, Amsterdam, 1952), Chap. V.
  18. T. L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956), p. 214.
  19. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (Ref. [1]), p. 283.
  20. E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938), Chap. IV.
  21. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954), Chap. 8.
  22. J. A. Barker and D. Henderson, Rev. Mod. Phys. 48, 587 (1976).
  23. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Ref. [9]), Chap. 5.
  24. M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963); W. R. Smith and D. Henderson, Mol. Phys. 19, 411 (1970).
  25. J. K. Percus and G. J. Yevick, Phys. Rev. 110, 1 (1958).
  26. F. Mandel, R. J. Bearman, and M. Y. Bearman, J. Chem. Phys. 52, 3315 (1970).
  27. L. Verlet, Phys. Rev. 159, 98 (1967); 165, 201 (1968).
  28. J. L. Yarnell, M. J. Katz, R. G. Wenzel, and S. H. Koenig, Phys. Rev. A 7, 2130 (1973).
  29. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Ref. [9]), Chap. 1.
  30. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Ref. [21]), Table I-M in the Appendix.
  31. Y. Waseda, The Structure of Non-Crystalline Materials (Ref. [12]), Appendix 8.
  32. T. Iida and R. I. L. Guthrie, The Physical Properties of Liquid Metals, 1st ed. (Oxford University Press, New York, 1988).
  33. S. M. Foiles, Phys. Rev. B 32, 3409 (1985).
  34. T. Iida, Z. Morita, and S. Takeuchi, J. Jpn. Inst. Met. 39, 1169 (1975).
  35. E. Gebhardt and K. Köstlin, Z. Metallkd. 48, 636 (1957).
  36. F. Lado, S. M. Foiles, and N. W. Ashcroft, Phys. Rev. A 28, 2374 (1983).

Outline

Information

Phys. Rev. E 72, 051203– Published 17 November, 2005
  • Received 27 February 2005

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation