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Ida, Masato
Physical Review E, 72(3), p.036306_1 - 036306_7, 2005/09
Times Cited Count：14 Percentile：53.94(Physics, Fluids & Plasmas)The resonance frequencies and oscillation phases of three acoustically coupled bubbles are examined to show that avoided crossings can appear in a multibubble system. Via a simple coupled oscillator model, we show that if at least three bubbles exist, it is possible for their resonance frequencies to experience an avoided crossing. Furthermore, by focusing our attention on the oscillation phases and based on analysis of the transition frequencies [Ida, Phys. Lett. A 297, 210 (2002); Ida, J. Phys. Soc. Jpn. 71, 1214 (2002)] of the coupled bubbles, we show that a distinct state exchange takes place between the bubbles at a point in the avoided crossing region, where a resonance frequency of the triple-bubble system crosses with a transition frequency.
Ida, Masato
Physics of Fluids, 17(9), p.097107_1 - 097107_13, 2005/09
Times Cited Count：16 Percentile：52.73(Mechanics)The transition frequencies of multibubble systems in a sound field are reexamined theoretically to confirm their existence and further clarify their physical properties. Via a forced coupled oscillator model, the following results are obtained: (1) further details of the characteristics of the transition frequencies, (2) the theoretical determination of the threshold distances for the appearance of the sub-transition frequencies, (3) a simple understanding of the sign reversal of the interaction force, and (4) the clarification of several similarities and differences among the natural, resonance, and transition frequencies in double-bubble cases. The present effort enforces our claim that transition frequencies causing no resonance response exist in multibubble systems and thoroughly clarifies the physical effects of the transition frequencies and their roles in the sign reversal of the interaction force.
Ida, Masato
Proceedings of 6th World Congress on Computational Mechanics in conjunction with 2nd Asian-Pacific Congress on Computational Mechanics (CD-ROM), p.1 - 11, 2004/09
The existence of the "transition frequencies" of two acoustically coupled gas bubbles has been verified by direct numerical simulation. The theory described by Ida [Phys. Lett. A 297 (2002) 210] predicted that a bubble in the double-bubble system has three transition frequencies, some of which makes the phase difference between the bubble's volume oscillation and an external sound 
without accompanying resonance response of the bubble. In a more recent paper [Ida, Phys. Rev. E 67 (2003) 056617], it was suggested theoretically that one of the transition frequencies may cause the sign reversal of the secondary Bjerknes force acting between pulsating bubbles. In the present study, we employ a direct numerical simulation technique that uses the compressible Navier-Stokes equations with a surface-tension term as the governing equations to investigate the transition frequencies of two coupled bubbles. The numerical results clearly exhibit the existence of the theoretically predicted characteristic frequency.
