ANZIAM J. 46(E) ppC102--C116, 2005.

Coupled nonlinear oscillations of microbubbles

A. Ooi

R. Manasseh
(Received 30 October 2004, revised 10 February 2005)

Abstract

The coupling effects on the acoustic signature from nonlinear oscillations of a group of microbubbles is investigated. In general, exploring this phenomenon would require solving a set of (linearly) coupled nonlinear ordinary differential equations (\lowercase {ODE}s). However, assuming that the initial conditions of all bubbles are identical and that all bubbles are equi-distant from each other simplifies the governing equations to just a single \lowercase {ODE}. Numerical data obtained by solving this \lowercase {ODE} is used to investigate the effects of bubble population size on the subharmonics and ultraharmonics of the system. As the number of bubbles is increased, the natural frequency and the damping of the system decreases. There is a slight shift in the frequencies at which the maximum bubble oscillation occur. The amplitude of oscillations near the main resonance are significantly reduced as the number of bubble increases.

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Authors

A. Ooi
Dept. Mechanical & Manufacturing Engineering, University of Melbourne, Victoria, Australia. mailto:a.ooi@unimelb.edu.au
R. Manasseh
CSIRO, Highett, Melbourne, Australia.

Published March 21, 2005. ISSN 1446-8735

References

  1. Yuan, H., Prosperetti, A., Popinet, S., Zaleski, S. Growth and collapse of a vapor bubble in a narrow tube {J. Acoust. Soc. Am.}, 106 (2): 674--681, 2000.
  2. Liu, R., Yang, J., Leningk, R., Bonanno, J., Grodzinski, P. Self-contained, fully integrated biochip for sample preparation, polymerase chain reaction amplification, and DNA microarray detection {Anal. Chem.}, 76: 1824--1831, 2004.
  3. Manasseh, R., LaFontaine, R. F., Davy, J., Shepherd, I. C., and Zhu, Y. Passive acoustic bubble sizing in sparged systems. {Exp. Fluids}, 30(6):672--682, 2001.
  4. Hilgenfeldt, S., Lohse, D., Zomack, M. Response of bubble to diagnostic ultrasound: a unifying theoretical approach. {Euro. Physical J. B}, 4: 247--255, 1998.
  5. J. Allen, D. Kruse, P. Dayton, and K. Ferrara. Effect of coupled oscillations on microbubble behaviour. {J. Acoust. Soc. Am.}, 114(3):1678--1690, 2003.
  6. Frauscher, F., Klauser, A., Halpern, E., Detection of prostate cancer with a microbubble ultrasound contrast agent. {Lancet}, 357: 1849--1850, 2001.
  7. W. Lauterborn. Numerical investigation of nonlinear oscillations of gas bubbles in liquids. {J. Acoust. Soc. Am.}, 59(2): 283--293, 1976.
  8. N. de Jong, R. Cornet and C. Lancee. Higher harmonics of vibrating gas-filled microspheres. Part one: simulations. {Ultrasonics.}, 32(6):447--453, 1994.
  9. R. Manasseh, A. Nikolovska, A. Ooi, and S. Yoshida. Anisotropy in the sound field generated by a bubble chain. To appear in {J. Sound and Vibration}, 2004.
  10. K. Vokurka Comparison of Rayleigh's, Herring's and Gilmore's Models of Gas Bubbles. {Acustica}, 59:214--219, 1986.
  11. Tolstoy, I. Superresonant systems of scatterers. i. {J. Acoust. Soc. Am.}, 80(1):282--294, 1986.
  12. Doinikov, A. A. and Zavtrak, S. T. On the mutual interaction of two gas bubbles in a sound field. {Phys. Fluids}, 7(8): 1923--1930, 1995.
  13. R. Mettin, I. Akhatov, U. Parlitz and C. D. Ohl and W. Lauterborn. Bjeknes forces between small cavitation bubbles in a strong acoustic field. {Physical Review E}, 56(3):2924--2931, 1997.
  14. Ida, M. A characteristic frequency of two mutually interacting gas bubbles in an acoustic field. {Physics Letters A}, 297(3--4): 210--217, 2002.
  15. J. Keller and M. Miksis. Bubble oscillations of large amplitude. {J. Acoust. Soc. Am.}, 68(2):628--633, 1980.
  16. Hilgenfeldt, S., Siegfried, G., Lohse, D. A simple explanation of light emission in sonoluminescence. {Nature}, 398: 402--405, 1999.
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