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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
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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

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