Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-03T04:52:42.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Variational determination of the coefficient of sound dispersion in binary gas mixtures

Published online by Cambridge University Press:  21 April 2006

P. Riesco-Chueca  and
J. Fernandez De La Mora
P. Riesco-Chueca
Affiliation:
Yale University, Department of Mechanical Engineering, Box 2159 Y.S., New Haven, CT 06520-2159, USA
J. Fernandez De La Mora
Affiliation:
Yale University, Department of Mechanical Engineering, Box 2159 Y.S., New Haven, CT 06520-2159, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The propagation of plane linear acoustic wave in a mixture of inert gases is considered by means of a variational formulation of the Boltzmann equations, through which the sound speed c is expressed with errors of order ε2 in terms of trial functions determined with errors of order ε. This feature allows the exact determination of the coefficient of sound dispersion d2 ≡ [dc/dω2] at zero frequency (ω = 0), in terms of trial functions known from the Chapman—Enskog theory. Explicit results for d2 are given for all combinations of noble gases from He to Xe, assumed to interact through the Lennard—Jones potential. Comparison with previous approximate descriptions and with experiments is made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 205 - 221
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bernstein, I. B. 1969 Phys. Fluids. 12, 64.
Bethe, H. A. & Salpeter, E. E. 1957 Handbuch der Physik (ed. S. Flüge), vol. 35, p. 208. Springer.
Cercignani, C. 1969 J. Stat. Phys. 1, 297.
Cercignani, C. & Pagani, C. D. 1966 Phys. Fluids 9, 1167.
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
de la Mora, J. Fernandez & Fernandez-Feria, R. 1987 Phys. Fluids 30, 740.
de la Mora, J. Fernandez & Puri, A. 1986 J. Fluid Mech. 168, 369.
Fernandez-Feria, R. & de la Mora, J. Fernandez 1986 Two-fiuid theory for monoatomic gases and the propagation of sound in binary mixtures. In Rarefied Gas Dynamics (ed. V. Boffi & C. Cercignani), vol. 1, p. 25. Stuttgart: Teubner.
Foch, J. D. & Ford, G. W. 1970 The dispersion of sound in monoatomic gases. In Studies in Statistical Mechanics (ed. de Boer & Uhlenbeck). North-Holland.
Foch, J. D. & Losa, M. Fuentes 1972 Phys. Rev. Lett. 28, 1315.
Foch, J. D., Uhlenbeck, G. E. & Losa, M. Fuentes 1972 Phys. Fluids 15, 1224.
Losa, M. Fuentes 1972 Experimental investigation of sound propagation in binary mixtures of noble gases. Ph.D. thesis, University of Colorado.
Goldman, E. B. 1968 J. Acoust. Soc. Am. 44, 708.
Greenspan, M. 1956 J. Acoust. Soc. Am. 28, 644.
Greenspan, M. 1965 Transmission of sound waves in gases at very low pressures. In Physical Acoustics (ed. W. P. Mason). Academic.
Hogervorst, W. 1971 Physica 51, 59.
Huck, R. J. & Johnson, E. A. 1980 Physical properties of double-sound modes in disparate-mass gas mixtures. In Rarefied Gas Dynamics (ed. S. S. Fisher), p. 452. American Inst. of Aeronautics and Astronautics.
Sirovich, L. & Thurber, J. K. 1965 J. Acoust. Soc. Am. 37, 329.