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Attenuation and dispersion of sound in bubbly fluids via the Kramers—Kronig relations

Published online by Cambridge University Press:  26 April 2006

S. Temkin
S. Temkin
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08855-0909, USA
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Abstract

Sound propagation in a dilute bubble–liquid mixture is studied by means of the Kramers–Kronig relationships, which relate the real and imaginary parts of the general susceptibility of a linear medium. These relationships are adopted for the case of acoustic waves, where they become coupled integral equations. A simple but approximate procedure is used to obtain from these equations the phase speed of sound waves for the case when the attenuation coefficient is independently known. The procedure can be used to obtain the speed of propagation of sound waves in acoustic media having internal dissipation, but is here applied only to fluids containing radially pulsating bubbles. Approximate results for the speed of propagation and for the attenuation per wavelength are obtained for this case on the basis of a first-order estimate for the attenuation coefficient. These results are the same as those derived previously on the basis of model equations for bubbly liquids. They therefore provide additional support for those equations, while indicating some of their limitations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 211 , February 1990 , pp. 61 - 72
Copyright
© 1990 Cambridge University Press

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References

Batchelor, G. K. 1969 Compression waves in a suspension of gas bubbles in liquid. Fluid Dyn. Trans. 4, 425–445. Institute of Fundamental Technical Research, Polish Academy of Science, Warsaw.Google Scholar
Beltzer, A. 1988 Acoustics of Solids. Springer.
Beltzer, A. & Brauner, N. 1987 The dynamic response of random composites by a causal differential method. Mech. Mat. 6, 337–395.Google Scholar
Brauner, N. & Beltzer, A. 1985 High-frequency elastic waves in random composites via the Kramers—Kronig relations. Appl. Phys. Lett. 46, 243–245.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, C. & Ting, L. 1985 Effective equations for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273Google Scholar
Carstensen, E. L. & Foldy, L. L. 1947 Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Am. 19, 481–501.Google Scholar
Clay, C. S. & Medwin, H. 1987 Acoustical Oceanography: Principles and Applications. Wiley.
Commander, K. W. & Prosperetti, A. 1989 Linear pressure waves in bubbly liquids: comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732–746.Google Scholar
Devin, Jr. C. 1959 Survey of thermal, radiation, and viscous damping of pulsating air-bubbles in water. J. Acoust. Soc. Am. 31, 1654–1667.Google Scholar
Drumheller, D. S. & Bedford, A. 1979 A theory of bubbly liquids. J. Acoust. Soc. Am. 66, 197–208.Google Scholar
Eller, A. I. 1970 Damping constants of pulsating bubbles. J. Acoust. Soc. Am. 47, 1469–1470.Google Scholar
Fox, F. E., Curley, S. R. & Larson, G. S. 1955 Phase velocity and absorption measurements in water containing air bubbles. J. Acoust. Soc. Am. 27, 534–539, 1955.Google Scholar
Herzfeld, K. F. 1930 Propagation of sound in suspensions. Phil. Mag. 9, 741–751, 752–768.Google Scholar
Kennard, E. H. 1943 Radial motion of water surrounding a sphere of gas in relation to pressure waves In Underwater Explosion Research, Vol. II. The Gas Globe, Office of Naval Research.
Kittel, C. 1958 Elements of Statistical Physics, 206–210. Wiley.
Landau, L. D. & Lifshitz, E. M. 1958 Statistical Physics, pp. 391–402. Pergamon.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, pp. 299. Pergamon.
Meyer, E. Von & Skudrzyk, E. 1953 Uber die akustischen eigenschaften von gasbalsenschleiern in wasser. Acustica 3, 435–440.Google Scholar
Minnaert, M. 1933 On musical air-bubbles and the sounds of running water. Phil. May. 16 (7), 235–248.Google Scholar
Morfey, C. L. & Howell, G. P. 1980 Speed of sound in air as a function of frequency and humidity. J. Acoust. Soc. Am. 68, 1525–1527.Google Scholar
O'Donnell, M., Jaynes, E. T. & Miller, J. G. 1981 Kramers—Kronig relationship between ultrasonic attenuation and phase velocity. J. Acoust. Soc. Am. 69, 696–701.Google Scholar
Pippard, A. B. 1978 The Physics of Vibration, Vol. 1, pp. 107–113. Cambridge University Press.
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 145–185.Google Scholar
Prosperetti, A. 1977 Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids. J. Acoust. Soc. Am. 61, 17–27.Google Scholar
Prosperetti, A. 1986 Physics of acoustic cavitation. In Frontiers in Physical Acoustics (ed. D. Sette), pp. 145–188. North Holland.
Prosperetti, A. 1987 Bubble dynamics in oceanic ambient noise. NATO Advanced Research Workshop, La Spezia, 15–19 June 1987.
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29, 925–933.Google Scholar
Thorpe, S. A. 1982 On the clouds of bubbles formed by breaking wind waves in deep water, and their role in air-sea gas transfer.. Proc. R. Soc. Lond. A 304, 155–210.Google Scholar
Wijngaarden, L. Van 1968 On the equations of motion for mixtures of liquids and gas bubbles. J. Fluid Mech. 33, 465–474.Google Scholar
Wijngaarden, L. Van 1972 One dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–396.Google Scholar
Woods, L. C. 1975 The Thermodynamics of Fluid Systems, pp. 270–278. Oxford University Press.