Linear pressure waves in bubbly liquids: Comparison between theory and experiments

Recent work has rendered possible the formulation of a rigorous model for the propagation of pressure waves in bubbly liquids. The derivation of this model is reviewed heuristically, and the predictions for the small‐amplitude case are compared with the data sets of several investigators. The data concern the phase speed, attenuation, and transmission coefficient through a layer of bubbly liquid. It is found that the model works very well up to volume fractions of 1%–2% provided that bubble resonances play a negligible role. Such is the case in a mixture of many bubble sizes or, when only one or a few sizes are present, away from the resonant frequency regions for these sizes. In the presence of resonance effects, the accuracy of the model is severely impaired. Possible reasons for the failure of the model in this case are discussed.

[1]  Roelof Omta Oscillations of a cloud of bubbles of small and not so small amplitude , 1987 .

[2]  P. Waterman,et al.  MULTIPLE SCATTERING OF WAVES , 1961 .

[3]  Francis E. Fox,et al.  Phase Velocity and Absorption Measurements in Water Containing Air Bubbles , 1955 .

[4]  V. Twersky,et al.  Acoustic bulk parameters in distributions of pair‐correlated scatterers , 1978 .

[5]  Andrea Prosperetti,et al.  Bubble phenomena in sound fields: part one , 1984 .

[6]  Michael J. Miksis,et al.  Bubble Oscillations of Large Amplitude , 1980 .

[7]  Michael J. Miksis,et al.  Effective equations for wave propagation in bubbly liquids , 1985, Journal of Fluid Mechanics.

[8]  Joseph B. Keller,et al.  Stochastic equations and wave propagation in random media , 1964 .

[9]  Herman Medwin,et al.  In situ acoustic measurements of bubble populations in coastal ocean waters , 1970 .

[10]  M. Lax Multiple Scattering of Waves , 1951 .

[11]  L. van Wijngaarden,et al.  On the equations of motion for mixtures of liquid and gas bubbles , 1968, Journal of Fluid Mechanics.

[12]  V. Twersky On Scattering of Waves by Random Distributions. I. Free‐Space Scatterer Formalism , 1962 .

[13]  L. Foldy,et al.  The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers , 1945 .

[14]  Joseph B. Keller,et al.  Damping of Underwater Explosion Bubble Oscillations , 1956 .

[15]  E. L. Carstensen,et al.  Propagation of Sound Through a Liquid Containing Bubbles , 1947 .

[16]  A. Ruggles,et al.  The propagation of pressure perturbations in bubbly air/water flows , 1988 .

[17]  V. Twersky,et al.  Acoustic Bulk Parameters of Random Volume Distributions of Small Scatterers , 1964 .

[18]  E. Silberman Sound Velocity and Attenuation in Bubbly Mixtures Measured in Standing Wave Tubes , 1957 .

[19]  J. Macpherson,et al.  The Effect of Gas Bubbles on Sound Propagation in Water , 1957 .

[20]  Andrea Prosperetti,et al.  Nonlinear bubble dynamics , 1988 .

[21]  Andrea Prosperetti,et al.  Bubble dynamics in a compressible liquid. Part 1. First-order theory , 1986, Journal of Fluid Mechanics.

[22]  C. Brennen,et al.  Acoustical Absorption and Scattering Cross Sections of Spherical Bubble Clouds , 1988 .

[23]  Andrea Prosperetti,et al.  Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids , 1977 .