Journal of Fluid Mechanics


On the boundary integral method for the rebounding bubble

M. LEEa1a2, E. KLASEBOERa3 and B. C. KHOOa2a4

a1 Department of Mechanical Engineering, Sejong University, Seoul, 143-747 Korea

a2 Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

a3 Institute of High Performance Computing, 1 Science Park Road #01-01 The Capricorn, Singapore 117528

a4 Singapore-MIT Alliance, 4 Engineering Drive 3, Singapore 117576,,


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.

(Received February 02 2005)

(Revised June 08 2006)