Skip to main content
    • Aa
    • Aa
  • Journal of Fluid Mechanics, Volume 570
  • January 2007, pp. 407-429

On the boundary integral method for the rebounding bubble

  • M. LEE (a1) (a2), E. KLASEBOER (a3) and B. C. KHOO (a2) (a4)
  • DOI:
  • Published online: 10 January 2007

The formation of a toroidal bubble towards the end of the bubble collapse stage in the neighbourhood of a solid boundary has been successfully studied using the boundary integral method. The further evolution (rebound) of the toroidal bubble is considered with the loss of system energy taken into account. The energy loss is incorporated into a mathematical model by a discontinuous jump in the potential energy at the minimum volume during the short collapse–rebound period accompanying wave emission. This implementation is first tested with the spherically oscillating bubble system using the theoretical Rayleigh–Plesset equation. Excellent agreement with experimental data for the bubble radius evolution up to three oscillation periods is obtained. Secondly, the incorporation of energy loss is tested with the motion of an oscillating bubble system in the neighbourhood of a rigid boundary, in an axisymmetric geometry, using a boundary integral method. Example calculations are presented to demonstrate the possibility of capturing the peculiar entity of a counterjet, which has been reported only in recent experimental studies.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T. B. Benjamin & A. T. Ellis 1966 The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries. Phil. Trans. R. Soc. Lond. A 260, 221240.

J. P. Best 1993 A The formation of toroidal bubbles upon the collapse of transient cavities. J. Fluid Mech. 251, 79107.

J. P. Best 1994 The rebound of toroidal bubbles. In Bubble Dynamics and Interface Phenomena (ed. J. R. Blake , J. M. Boulton-Stone & N. H. Thomas ), pp. 405412. Kluwer.

J. P. Best & A. Kucera 1992 A numerical investigation of non-spherical rebounding bubbles. J. Fluid Mech. 245, 137154.

J. R. Blake , B. B. Taib & G. Doherty 1986 Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479497.

J. M. Boulton-Stone 1993 A comparison of boundary integral methods for studying the motion of a two-dimensional bubble in an infinite fluid. Comput. Methods Appl. Mech. Engng 102, 213234.

E. A. Brujan , G. S. Keen , A. Vogel & J. R. Blake 2002 The final stage of the collapse of a cavitation bubble close to a rigid boundary. Phys. Fluids 14, 8592.

S. Buogo & G. B. Cannelli 2002 Implosion of an underwater spark-generated bubble and acoustic energy evaluation using the Rayleigh model. J. Acoust. Soc. Am. 111, 25942600.

C. F. Delale & M. Tunç 2004 A bubble fission model for collapsing cavitation bubbles. Phys. Fluids 16 (11), 42004203.

T. L. Geers & K. S. Hunter 2002 An integrated wave-effects model for an underwater explosion bubble. J. Acoust. Soc. Am. 111, 15841601.

E. Klaseboer , K. C. Hung , C. Wang , C. W. Wang , B. C. Khoo , P. Boyce , S. Debono & H. Charlier 2005 Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J. Fluid Mech. 537, 387413.

T. Kodama & Y. Tomita 2000 Cavitation bubble behaviour and bubble-shock wave interaction near a gelatine surface as a study of in vivo bubble dynamics. Appl. Phys. B 70, 139149.

W. Lauterborn 1972 High-speed photography of laser-induced breakdown in liquids. Appl. Phys. Lett. 21, 2729.

T. G. Leighton 1994 The Acoustic Bubble. Academic.

O. Lindau & W. Lauterborn 2003 Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall. J. Fluid Mech. 479, 327348.

Y. J. Liu & T. J. Rudolphi 1999 New identities for fundamental solutions and their applications to non-singular boundary element formulations. Comput. Mech. 24, 286292.

T. S. Lundgren & N. N. Mansour 1991 Vortex ring bubbles. J. Fluid Mech. 224, 177196.

A. Pearson , J. R. Blake & S. R. Otto 2004 Jets in bubbles. J. Engng Maths 48, 391412.

A. Philipp & W. Lauterborn 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75116.

S. J. Putterman & K. R. Weninger 2000 Sonoluminescence: how bubbles turn sound into light. Annu. Rev. Fluid Mech. 32, 445476.

Lord Rayleigh 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 9498.

Y. Tomita & A. Shima 1986 Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J. Fluid Mech. 169, 535564.

A. Vogel , W. Lauterborn & R. Timm 1989 Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary. J. Fluid Mech. 206, 299338.

C. Wang & B. C. Khoo 2004 An indirect boundary element method for three-dimensional explosion bubbles. J. Comput. Phys. 194, 451480.

Q. X. Wang , K. S. Yeo , B. C. Khoo & K. Y. Lam 1996 Nonlinear interaction between gas bubble and free surface. Comput. Fluids 25, 607628.

B. Ward & D. C. Emmony 1991 Interferometric studies of the pressure developed in a liquid during infrared-laser-induced cavitation bubble oscillation. Infrared Phys. 32, 489515.

S. G. Zhang & J. H. Duncan 1994 On the non-spherical collapse and rebound of a cavitation bubble. Phys. Fluids 6 (7), 23522362.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *