Effect of vortex fluid motion on nonspherical oscillations of a gas bubble

Article
First Online:
Received:
Revised:
  • 41 Downloads

Abstract

This paper studies the effect of the vortex fluid motion produced by periodic radial oscillations of a weakly nonspherical gas bubble on the variation in the small initial deviation from the spherical shape of this bubble. It is shown that the most intense vortex motion of the fluid occurs in the boundary layer (near field), and in the far field, the vortex fluid motion rapidly transforms to potential motion. The ranges of problem parameters in which vortex motion in the far field flow does not affect bubble oscillations and the ranges in which accounting for this motion is necessary for a qualitatively correct description of the oscillations are determined

Key words

periodic action stability of spherical bubble shape deviation effect of vortex motion vorticity 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. F. Gaitan, L. A. Crum, C. C. Church, and R. A. Roy, “Sonoluminescence and bubble dynamics for a single, stable cavitation bubble,” J. Acoust. Soc. Am., 91, 3166–3183 (1992).ADSCrossRefGoogle Scholar
  2. 2.
    S. J. Putterman and K. P. Weninger, “Sonoluminescence: How bubbles turn sound into light,” Annu. Rev. Fluid Mech., 32, 445–476 (2000).ADSCrossRefGoogle Scholar
  3. 3.
    C. C. Wu and P. H. Roberts, “Bubble shape instability and sonoluminescence,” Phys. Lett., A, 250, 131–136 (1998).ADSCrossRefGoogle Scholar
  4. 4.
    Y. Hao and A. Prosperetti, “The effect of viscosity on the spherical stability of oscillating gas bubbles,” Phys. Fluids, 11, No. 6, 1309–1317 (1999).MATHMathSciNetADSCrossRefGoogle Scholar
  5. 5.
    L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, Pergamon Press, Oxford-Elmsford, New York (1987).Google Scholar
  6. 6.
    A. A. Aganin, M. A. Il’gamov, and D. Yu. Toporkov, “Effect of fluid viscosity on the decay of small distortions of a gas bubble from a spherical shape,” J. Appl. Mech. Tech. Phys., 47, No. 2, 175–182 (2006).MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    A. Prosperetti, “Viscous effects on perturbed spherical flows,” Quart. Appl. Math., 34, 339–352 (1977).MATHGoogle Scholar
  8. 8.
    S. Hilgenfeldt, D. Lohse, and M. Brenner, “Phase diagrams for sonoluminescing bubbles,” Phys. Fluids, 8, No. 11, 2808–2826 (1996).MATHADSCrossRefGoogle Scholar
  9. 9.
    J. B. Keller and M. Miksis, “Bubble oscillations of large amplitude,” J. Acoust. Soc. Am., 68, 628–633 (1980).MATHADSCrossRefGoogle Scholar
  10. 10.
    A. A. Aganin and N. A. Khismatullina, “Liquid vorticity computation in nonspherical bubble dynamics,” Int. J. Numer. Methods Fluids, 48, 115–133 (2005).MATHADSCrossRefGoogle Scholar
  11. 11.
    E. Hairer, S. Norsett, and G. Wanner, Solving Ordinary Differential Equations. Nonstiff Problems, Springer, Berlin (1993).Google Scholar
  12. 12.
    O. V. Voinov, “Effect of viscosity on the dynamics of bubble perturbations in a liquid,” J. Appl. Mech. Tech. Phys., 50, No. 6, 915–917 (2009).MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    G. Birkhoff, “Stability of spherical bubbles,” Quart. Appl. Math., 13, 451–453 (1956).MATHMathSciNetGoogle Scholar

Copyright information

© MAIK/Nauka 2010

Authors and Affiliations

  1. 1.Institute of Mechanics and EngineeringKazan’ Scientific Center, Russian Academy of SciencesKazan’Russia

Personalised recommendations