Abstract
Gas mixtures of heavy plus light molecules can apparently support several different sorts of sound waves (the most recent such prediction is that of Campa and Cohen). The origin of the first such predictions is reviewed, along with the development of the two-temperature hydrodynamic equations which govern these mixtures at moderate wavenumbers and frequencies. Light scattering in the two-temperature regime is also discussed. Experiments in both sound propagation and light scattering are shown to confirm the existence of a two-temperature regime, and two simultaneous sound modes, in these disparate-mass gas mixtures.
Similar content being viewed by others
References
A. Campa and E. G. D. Cohen,Phys. Rev. Lett. 61:853 (1988).
R. J. Huck and E. A. Johnson,Phys. Rev. Lett. 44:142 (1980).
R. J. Huck and E. A. Johnson,Arch. Mech. (Warsaw)32:703 (1980).
J. D. Foch and G. W. Ford, inStudies in Statistical Mechanics, Vol. 5, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1970), p. 101.
S. Chapman and T. G. Cowling,Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, 1970).
H. Grad, inRarefied Gas Dynamics, Vol. 3, F. M. Devienne, ed. (Pergamon, New York, 1960), p. 100.
C. J. Goebel, S. M. Harris, and E. A. Johnson,Phys. Fluids 19:627 (1976).
E. A. Johnson,Arch. Mech. (Warsaw)28:803 (1976).
C. J. Goebel, S. M. Harris, and E. A. Johnson, inRarefied Gas Dynamics, Vol. 51, J. L. Potter, ed. (American Institute of Aeronautics and Astronautics, New York, 1977), Part I, p. 109.
H. Grad,Commun. Pure Appl. Math. 11:331 (1949); inHandbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1958), Vol. XII, Section 28, p. 267.
J. P. Boon and S. Yip,Molecular Hydrodynamics (McGraw-Hill, New York, 1980).
C. D. Boley and S. Yip,Phys. Fluids 15:1424 (1972);Phys. Fluids 15:1433 (1972);J. Phys. (Paris)33:Cl-43 (1972).
N. A. Clark,Phys. Rev. A 12:2092 (1975).
E. W. Washburn, ed.,International Critical Tables (McGraw-Hill, New York, 1930), Vol. VII, pp. 7–8.
L. Letamendia, J. P. Chabrat, G. Nouchi, J. Rouch, C. Vaucamps, and S.-H. Chen,Phys. Rev. A 24:1574 (1981).
L. Letamendia, P. Joubert, J. P. Chabrat, J. Rouch, C. Vaucamps, C. D. Boley, S. Yip, and S.-H. Chen,Phys. Rev. A 25:481 (1982).
J. R. Bowler,Harmonie modes in binary monatomic gas mixtures, Ph.D. thesis, University of Surrey, United Kingdom (1984).
J. R. Bowler and E. A. Johnson,Phys. Rev. Lett. 54:329 (1985).
J. R. Bowler and E. A. Johnson,Proc. R. Soc. Lond. A 408:79 (1986).
E. A. Johnson,Phys. Rev. A 27:1146 (1983).
R. J. Huck and E. A. Johnson, inRarefied Gas Dynamics, S. S. Fisher, ed. (American Institute of Astronautics and Aeronautics, New York, 1981), p. 452.
J. D. Foch, G. E. Uhlenbeck, and M. Fuentes Losa,Phys. Fluids 15:1224 (1972).
E. G. D. Cohen, inTrends in Applications of Pure Mathematics to Mechanics, E. Kroner and K. Kirchgasser, eds. (Springer-Verlag, Berlin, 1986), p. 2; B. Kamgar-Parsi, E. G. D. Cohen, and I. M. de Schepper,Phys. Rev. A 35:4781 (1987); B. Kamgar-Parsi and E. G. D. Cohen,Physica A 138:249 (1986).
B. Kamgar-Parsi and E. G. D. Cohen,Int. J. Thermophys. 7:395 (1986), and private communication.
K. G. Budden and M. Eve,Proc. R. Soc. Lond. A 342:175 (1975) and references therein.
J. G. Plona,Appl. Phys. Lett. 36:259 (1981).
M. A. Ricci, D. Rocca, G. Ruocco, and R. Vallauri,Phys. Rev. Lett. 61:1958 (1988).
J. Bosse, G. Jacucci, M. Ronchetti, and W. Schirmacher,Phys. Rev. Lett. 57:3277 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Johnson, E.A. Two-temperature hydrodynamics and multiple sound modes in disparate-mass gas mixtures. J Stat Phys 57, 647–664 (1989). https://doi.org/10.1007/BF01022826
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01022826