- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Single-bubble sonoluminescence: Shape stability analysis of collapse dynamics in a semianalytical approach

Vladislav A. Bogoyavlenskiy*

  • Low Temperature Physics Department, Moscow State University, 119899 Moscow, Russia

  • *Electronic address: bogoyavlenskiy@usa.net
PDF

Phys. Rev. E 62, 2158 – Published 1 August, 2000

DOI: https://doi.org/10.1103/PhysRevE.62.2158

Abstract

This paper theoretically analyzes the hydrodynamic shape stability problem for sonoluminescing bubbles. We present a semianalytical approach to describe the evolution of shape perturbations in the strongly nonlinear regime of violent collapse. The proposed approximation estimating the damping rate produced by liquid viscosity is used to elucidate the influence of the collapse phase on subsequent evolution of the Rayleigh-Taylor instability. We demonstrate that time derivatives of shape perturbations grow significantly as the bubble radius vanishes, forming the dominant contribution to destabilization during the ensuing bounce phase. By this effect the Rayleigh-Taylor instability can be enhanced drastically, yielding a viable explanation of the upper threshold of driving pressure experimentally observed by Barber et al. [Phys. Rev. Lett. 72, 1380 (1994)].

View figure in article

References (42)

  1. D.F. Gaitan and L.A. Crum, in Frontiers in Nonlinear Acoustics, edited by M. Hamilton and D.T. Blackstock (Elsevier, New York, 1990), p. 459; D. F. Gaitan, Ph.D. thesis, University of Mississippi, 1990 (unpublished).
  2. D.F. Gaitan, L.A. Crum, R.A. Roy, and C.C. Church, J. Acoust. Soc. Am. 91, 3166 (1992).
  3. B.P. Barber and S.J. Putterman, Nature (London) 352, 318 (1991).
  4. R. Hiller, K. Weninger, S.J. Putterman, and B.P. Barber, Science 266, 248 (1994).
  5. B.P. Barber, C.C. Wu, R. Löfstedt, P.H. Roberts, and S.J. Putterman, Phys. Rev. Lett. 72, 1380 (1994).
  6. B.P. Barber, K. Weninger, R. Löfstedt, and S.J. Putterman, Phys. Rev. Lett. 74, 5276 (1995).
  7. R. Löfstedt, K. Weninger, S. Putterman, and B.P. Barber, Phys. Rev. E 51, 4400 (1995).
  8. B.P. Barber, R.A. Hiller, R. Löfstedt, S.J. Putterman, and K.R. Weninger, Phys. Rep. 281, 65 (1997).
  9. M.P. Brenner, D. Lohse, and T.F. Dupont, Phys. Rev. Lett. 75, 954 (1995).
  10. S. Hilgenfeldt, D. Lohse, and M.P. Brenner, Phys. Fluids 8, 2808 (1996); ibid.9, 2462(E) (1997).
  11. M.P. Brenner, D. Lohse, D. Oxtoby, and T.F. Dupont, Phys. Rev. Lett. 76, 1158 (1996).
  12. L. Kondic, C. Yuan, and C.K. Chan, Phys. Rev. E 57, R32 (1998).
  13. S. Hilgenfeldt, D. Lohse, and W.C. Moss, Phys. Rev. Lett. 80, 1332 (1998).
  14. R.G. Holt and D.F. Gaitan, Phys. Rev. Lett. 77, 3791 (1996).
  15. D.F. Gaitan and R.G. Holt, Phys. Rev. E 59, 5495 (1999).
  16. S.J. Putterman and P.H. Roberts, Phys. Rev. Lett. 80, 3666 (1998).
  17. M.P. Brenner, T. Dupont, S. Hilgenfeldt, and D. Lohse, Phys. Rev. Lett. 80, 3668 (1998).
  18. C.C. Wu and P.H. Roberts, Phys. Lett. A 250, 131 (1998); Phys. Fluids 10, 3227 (1998).
  19. Y. Hao and A. Prosperetti, Phys. Fluids 11, 1309 (1999); A. Prosperetti and Y. Hao, Philos. Trans. R. Soc. London, Ser. A 357, 203 (1999).
  20. V.A. Bogoyavlenskiy, Phys. Rev. E 60, 504 (1999).
  21. Lord Rayleigh, Philos. Mag. 34, 94 (1917).
  22. For a recent review, see S. Hilgenfeldt, M.P. Brenner, S. Grossmann, and D. Lohse, J. Fluid Mech. 365, 171 (1998), and references therein.
  23. M.S. Plesset, J. Appl. Mech. 16, 277 (1949).
  24. L. Trilling, J. Appl. Phys. 23, 14 (1952).
  25. A. Prosperetti, J. Fluid Mech. 222, 587 (1991).
  26. V. Kamath, A. Prosperetti, and F. Egolfopoulos, J. Acoust. Soc. Am. 94, 248 (1993).
  27. C.C. Wu and P.H. Roberts, Phys. Rev. Lett. 70, 3424 (1993); Proc. R. Soc. London, Ser. A 445, 323 (1994).
  28. L. Kondic, J.I. Gersten, and C. Yuan, Phys. Rev. E 52, 4976 (1995).
  29. V.Q. Vuong, A.J. Szeri, and D.A. Young, Phys. Fluids 11, 10 (1999).
  30. R. Löfstedt, B.P. Barber, and S.J. Putterman, Phys. Fluids A 5, 2911 (1993).
  31. R. Hiller, S.J. Putterman, and B.P. Barber, Phys. Rev. Lett. 69, 1182 (1992); ibid.B.P. Barber and S.J. Putterman, 69, 3839 (1992).
  32. H. Lamb, Hydrodynamics, 6th ed. (Dover Publications, New York, 1945).
  33. Lord Rayleigh, Proc. London Math. Soc. XIV, 170 (1883); G.I. Taylor, Proc. R. Soc. London, Ser. A 201, 192 (1950).
  34. M.S. Plesset, J. Appl. Phys. 25, 96 (1954).
  35. M.S. Plesset and T.P. Mitchell, Q. Appl. Math. 13, 419 (1956).
  36. G. Birkhoff, Q. Appl. Math. 12, 306 (1954); ibid.13, 451 (1956).
  37. A.I. Eller and L.A. Crum, J. Acoust. Soc. Am. 47, 762 (1970).
  38. H.W. Strube, Acustica 25, 289 (1971).
  39. A. Prosperetti, Q. Appl. Math. 34, 339 (1977); Ph.D. thesis, California Institute of Technology, Pasadena, California, 1974.
  40. A. Prosperetti, Atti Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Nat., Rend. 62, 196 (1977).
  41. The beginning of the violent collapse region is defined by the condition Pvel>Pext, yielding the estimation Vi≈2(P0/ρ)1/2∼20 m/s. Since for sonoluminescing bubbles the initial radius Ri∼40 μm, corresponding values of the liquid viscosity parameter α calculated from Eq. (11) are of the order of 100.
  42. Sonoluminescence is observed when the bubble wall velocity achieves supersonic speeds, (dR/dt)max=Mc, where c≈1.5×103 m/s is the sound speed in water and M∼2–4 is the Mach number. Since corresponding values of Ri are approximately 40 μm, the expression (dR/dt)/Ri is estimated as 4M×107 s−1∼108 s−1.

Outline

Information

Phys. Rev. E 62, 2158– Published 1 August, 2000
  • Received 29 December 1999

© 2000 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation