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Linear acoustic properties of bubbly liquids near the natural frequency of the bubbles using numerical simulations

Published online by Cambridge University Press:  26 April 2006

A. S. Sangani
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA
R. Sureshkumar
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA

Abstract

We consider the problem of determining linear acoustic properties of bubbly liquids near the natural frequency of the bubbles. Since the effective wavelength and attenuation length are of the same order of magnitude as the size of the bubbles, we devise a numerical scheme to determine these quantities by solving exactly the multiple scattering problem among many interacting bubbles. It is shown that the phase speed and attenuation are finite at natural frequency even in the absence of damping due to viscous, thermal, nonlinear, and liquid compressibility effects, thus validating a recent theory (Sangani 1991). The results from the numerical scheme are in good agreement with the theory but considerably higher than the experimental values for frequencies greater than the natural frequency. The discrepancy with experiments remains even after accounting for the effect of polydispersity, finite liquid compressibility, and non-adiabatic thermal changes.

Type
Research Article
Copyright
© 1993 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards.
Bensoussan, A., Lions, J.-L. & Papanicolaou, G. C. 1978 Studies in Mathematics and Its Applications, vol. 5. North-Holland.
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985a Effective equation for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985b Wave propagation in bubbly liquids at finite volume fraction. J. Fluid Mech. 160, 1.Google Scholar
Carstensen, E. L. & Foldy, L. L. 1947 Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Am. 19, 481.Google Scholar
Commander, K. W. & Prosperetti, A. 1989 Linear pressure waves in bubbly liquids: Comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732.Google Scholar
Foldy, L. L. 1945 The multiple scattering of waves. Phys. Rev. 67, 107.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. 19, 481.Google Scholar
Hasimoto, H. 1959 On the periodic fundamental singular solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317.Google Scholar
Hobson, E. W. 1931 The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press.
Keller, J. B. 1977 Effective behavior of heterogeneous media. Statistical Mechanics and Statistic Methods in Theory and Application (ed. U. Landman), p. 631. Plenum.
Kol'tsova, I. S., Krynskii, L. O., Mikhalov, I. G. & Pokrovskaya, I. E. 1979 Attenuation of ultrasonic sound waves in low-viscosity liquids containing gas bubbles. Akust. Zh. 25, 725. (English transl: Sov. Phys. Acoust. 25, 409.)Google Scholar
Mattern, K. & Felderhof, B. U. 1987 Self-consistent cluster expansion for wave propagation and diffusion-controlled reactions in a random medium. Physica A 143, 21.Google Scholar
Miksis, M. J. & Ting, L. 1987a Viscous effects on wave propagation in a bubbly liquid. Phys. Fluids 30, 1683.Google Scholar
Miksis, M. J. & Ting, L. 1987b Wave propagation in a multiphase media with viscous and thermal effects. ANS Proc. Natl Heat Transfer Conf., p. 145.
Prosperetti, A. 1984 Bubble phenomena in sound fields: part one. Ultrasonics 22, 69.Google Scholar
Rubinstein, J. 1985 Bubble interaction effects on waves in bubbly liquids. J. Acoust. Soc. Am. 77, 2061.Google Scholar
Ruggles, A. E., Scarton, H. A. & Lahey, R. T. 1986 An investigation of the propagation of pressure perturbations in bubbly air/water flows. In First Intl Multiphase Fluids Transients Symp. (ed. H. H. Safwat, J. Braun & U. S. Rohatgi). ASME.
Sanchez-Palencia, E. 1980 Non-Homogeneous Media and Vibration Theory. Lecture Notes in Physics, vol. 127. Springer.
Sangani, A. S. 1991 A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids. J. Fluid Mech. 232, 221.Google Scholar
Sangani, A. S. & Behl, S. 1989 The planar periodic singular solutions of Stokes and Laplace equations and their application to transport processes near porous surfaces. Phys. Fluids A 1, 21.Google Scholar
Sangani, A. S., Zhang, D. Z. & Prosperetti, A. 1991 The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion. Phys. Fluids A 3, 2955.Google Scholar
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29, 925.Google Scholar
Twersky, V. 1962 On scattering of waves by random distributions. I. Free-space scatterer formalism. J. Math. Phys. 3, 700.Google Scholar
Wijngaarden, L. van 1972 One-dimensional flow of liquids containing small bubbles. Ann. Rev. Fluid Mech. 4, 369.Google Scholar