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Collective oscillations in bubble clouds

Published online by Cambridge University Press:  06 June 2011

ZORANA ZERAVCIC ,
DETLEF LOHSE  and
WIM VAN SAARLOOS
ZORANA ZERAVCIC*
Affiliation:
Instituut Lorentz, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
DETLEF LOHSE
Affiliation:
Physics of Fluids Group, Mesa+ and Impact Research Institutes and Burgers Center for Fluid Dynamics, Department for Science and Technology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
WIM VAN SAARLOOS
Affiliation:
Instituut Lorentz, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands FOM Foundation, PO Box 3201, 3502 GA Utrecht, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

In this paper the collective oscillations of a bubble cloud in an acoustic field are theoretically analysed with concepts and techniques of condensed matter physics. More specifically, we will calculate the eigenmodes and their excitabilities, eigenfrequencies, densities of states, responses, absorption and participation ratios to better understand the collective dynamics of coupled bubbles and address the question of possible localization of acoustic energy in the bubble cloud. The radial oscillations of the individual bubbles in the acoustic field are described by coupled linearized Rayleigh–Plesset equations. We explore the effects of viscous damping, distance between bubbles, polydispersity, geometric disorder, size of the bubbles and size of the cloud. For large enough clusters, the collective response is often very different from that of a typical mode, as the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by ultrasound. The reason is the strong effect of viscosity on the collective mode response, which is surprising, as viscous damping effects are small for single-bubble oscillations in water. Localization of acoustic energy is only found in the case of substantial bubble size polydispersity or geometric disorder. The lack of localization for a weak disorder is traced back to the long-range 1/r interaction potential between the individual bubbles. The results of the present paper are connected to recent experimental observations of collective bubble oscillations in a two-dimensional bubble cloud, where pronounced edge states and a pronounced low-frequency response had been observed, both consistent with the present theoretical findings. Finally, an outlook to future possible experiments is given.

JFM classification

Drops and Bubbles: Bubble dynamics Acoustics: Waves in random media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 680 , 10 August 2011 , pp. 114 - 149
Copyright
Copyright © Cambridge University Press 2011

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