Unknown characteristic frequency of a multibubble system in a sound field; Theoretical prediction and numerical verification using an improved CIP-CUP

Ida, Masato

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.