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Effective equations for wave propagation in bubbly liquids

Published online by Cambridge University Press:  20 April 2006

Russel E. Caflisch ,
Michael J. Miksis ,
George C. Papanicolaou  and
Lu Ting
Russel E. Caflisch
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York 10012
Michael J. Miksis
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York 10012 Present address: Department of Mathematics, Duke University, Durham, North Carolina, 27706.
George C. Papanicolaou
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York 10012
Lu Ting
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York 10012
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Abstract

We derive a system of effective equations for wave propagation in a bubbly liquid. Starting from a microscopic description, we obtain the effective equations by using Foldy's approximation in a nonlinear setting. We discuss in detail the range of validity of the effective equations as well as some of their properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 259 - 273
Copyright
© 1985 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.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1984 Wave propagation in bubbly liquids at small and finite volume fraction. Courant Institute Preprint.
Caflisch, R. E. 1985 Global existence for a nonlinear theory of bubbly liquids. Commun. Pure Appl. Maths (To appear.)
Carstensen, E. L. & Flody, L. L. 1947 Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Am. 19, 481–501.Google Scholar
D'Agostino, L. & Brennen, C. E.1983 On the acoustical dynamics of bubble bounds. Preprint.
Domenico, S. N. 1982 Acoustic wave propagation in air-bubble curtains in water. Geophys 47, 345–353.Google Scholar
Drew, D. A. & Cheng, L.-Y. 1982 Wave propagation in bubbly liquids. In Macroscopic Properties of Disordered Media (ed. R. Burridge, S. Childress & G. C. Papanicolaou). Lecture Notes in Physics, vol. 154, pp. 85–96. Springer.
Drumheller, D. S. & Bedford, A. 1979 A theory of bubbly liquids. J. Acoust Soc. Am. 66, 197–208.Google Scholar
Foldy, L. L. 1945 The multiple scattering of waves. Phys. Rev. 67, 107–119.Google Scholar
Hsieh, D. Y. 1982 Some aspects of dynamics of bubbly liquids. Appl. Sci. Res. 38, 305–312.Google Scholar
Hrushlov, E. I. & Marchenko, V. A. 1974 Boundary value problem in regions with fine-grained boundaries. Naukova Kumka, Kiev.
Keller, J. B. & Miksis, M. 1980 Bubble oscillation of large amplitude. J. Acoust. Soc. Am. 68, 628–633.Google Scholar
Miksis, M. J. & Ting, L. 1984 Nonlinear radial oscillations of a gas bubble including thermal effects. J. Acoust. Soc. Am. 76, 897–905.Google Scholar
Ozawa, S. 1983 On an elaboration of M. Kac's theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles. Commun. Math. Phys. 91, 473–487.Google Scholar
Papanicolaou, G. C. & Varadhan, S. R. S. 1980 Diffusion in regions with many small holes. In Stochastic Differential Systems (ed. B. Grigelionis). Lecture Notes in Control and Information Sciences, vol. 25, pp. 190–206. Springer.
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 145–185.Google Scholar
Prosperetti, A. 1984 Bubble phenomena in sound fields. Ultrasonic 23, 69–77, 115–124.Google Scholar
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29, 925–933.Google Scholar
Van Wijngaarden, L. 1968 On equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33, 465–474.Google Scholar
Van Wijngaarden, L. 1972 One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–394.Google Scholar
Wallis, G. B. 1969 One-Dimensional Two-Phase Flow. McGraw-Hill.