Abstract
The classical viscothermal problem of infinitesimal, planar acoustic-wave propagation in a single-component Newtonian fluid is extended to more general multicomponent materials that are diffusive, reacting and viscoelastic. The attenuation and dispersion of the sound wave are determined by solving the linearized (first-order) equations of mass, linear momentum, energy and chemical kinetics. General results are obtained in the form of a biquadratic characteristic equation (called the Kirchhoff-Langevin equation) for the complex propagation coefficient ≁ ≡ - (α + i ω/c), where α is the attenuation coefficient, ⊂ is the phase speed of the progressive wave and ω is the angular frequency.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. D. Coleman and V. J. Mizel, J. Chem. Phys. 40, 1116–1125, 1964.
C. A. Truesdell, J. Rational Mech. and Analysis 2, 643–741, October, 1953.
E. Buckingham, Phys. Rev. 4, 345, 1914
E. Buckingham, Phil. Mag. (6) 42, 696, 1921.
P. Biquard, Ann. Phys. (11) 6, 195–304, 1936.
J. Thoen, E. Vangeel and W. Van Dael, Physica, 45, 339–356, 1969.
M. Eigen and L. deMaeyer, “Relaxation Methods,” in Technique of Organic Chemistry, 2nd ed., edited by S. L. Friess, E. S. Lewis and A. Weissberger, (Interscience, New York, 1963), Vol. VIII/2, pp. 895–1054.
R. Haase, Thermodynamics of Irreversible Processes, Addison-Wesley Publishing Co., Reading, Mass., 1969;
S. R. deGroot and P. Mazur, Nonequilibrium Thermodynamics, North-Holland, Amsterdam, 1969.
L. S. Garcia-Colin and S. M. T. De la Selva, Physica, Utrecht 75, 37, 1974.
T. S. Margulies and W. H. Schwarz, J. Chem. Phys. 77, No. 2, 1005, 15 July 1982.
W. Jost, Z. Naturforsch. Teil A2, 159, 1947; Z. Phys. Chem. 195, 317, 1950.
G. W. Castellan, Ber. Bunsenges Phys. Chem. 67, 898, 1963.
R. M. Mazo, J. Chem. Phys. 28, 1225, 1958.
T. S. Margulies and W. H. Schwarz, paper presented at the 107th Acoustical Society of America Meeting, Norfolk, VA 6–10 May 1984; “Acoustic Wave Propagation in Fluids with Coupled Chemical Reaction,” U.S. Nuclear Regulatory Commission, NUREG-0935, August 1984.
O. J. Heilman, Mat.-Fys. Medd. K. Dans. Vidensk. Selsk. 38, 1, 1972.
M. Kohler, Z. Physik 127, 40–48, 1949.
J. Meixner, Acustica 2, 101–109, 1952.
E. Goldman, J. Acoust. Soc. Am. 41, 93–99 (1967).
G. S. Wang Chang and G. E. Uhlenbeck, in Studies in Statistical Mechanics, edited by J. de Boer and G. E. Uhlenbeck, North-Holland, Amsterdam, 1970. Vol. V, 1.
J. D. Foch and G. W. Ford, in Studies in Statistical Mechanics, edited by J. de Boer and G. E. Uhlenbeck, North-Holland, Amsterdam 1970, Vol. V, 103.
J. D. Foch, Jr., G. E. Uhlenbeck and M. F. Losa, Phys. Fluids 13, 1224–1232, 1972.
A. Fick, Ann. Physik, 94, 59, 1855.
Ming-Nan Huang, Ph.D. Thesis, The Johns Hopkins University, 1973.
E. Goldman and L. Sirovich, Phys. Fluids 10, 1928–1940.
G. J. Prangsma, R. M. Jonkman and J. J. M. Beenakker, Physica 48, 323–330, 1970.
E. Goldman and L. Sirovich, Phys. Fluids 12, 245–247, 1969.
M. Greenspan, J. Acoust. Soc. Amer. 28, 644–648, 1956.
M. Greenspan, in Physical Acoustics, edited by W. P. Mason, Academic Press, 1965, Vol. II.
E. Meyer and G. Sessler, Z. Physik. 149, 15–39, 1957.
B. D. Coleman and W. Noll, “Simple Fluids with Fading Memory,” in “Second-Order Effects in Elasticity, Plasticity, and Fluid Dynamics,” edited by M. Reiner and D. Abir, International Symposium, Haifa, Israel, April 23–27, 1962.
B. D. Coleman and W. Noll, “Foundations of Linear Viscoelasticity,” Rev. of Modern Physics 33, 239, 1961.
J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley and Sons, Inc. (1980).
R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, Volume 2: Kinetic Theory, John Wiley and Sons (1977).
F. Bueche, J. Chem. Phys. 22, 603, 1954.
P. E. Rouse, Jr., J. Chem. Phys. 21, 1272, 1953.
B. H. Zimm, J. Chem. Phys. 24, 269, 1956.
A. J. Barlow, G. Harrison and J. Lamb, Proc. R. Soc. Lond. 282, 228, 1964.
J. L. Hunter and P. R. Derdul, J. Acoust. Soc. Am. 42, 1041, 1967.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Margulies, T.S., Schwarz, W.H. (1985). Acoustic Wave Propagation in Fluids. In: Davis, S.H., Lumley, J.L. (eds) Frontiers in Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46543-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-46543-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46545-1
Online ISBN: 978-3-642-46543-7
eBook Packages: Springer Book Archive