Phase properties and interaction force of acoustically interacting bubbles: A complementary study of the transition frequency

Abstract

The transition frequencies of multibubble systems in a sound field are reexamined to confirm their existence and further clarify their physical properties. We have recently suggested that a gas bubble interacting with a neighboring bubble in a sound field has up to three transition frequencies which invert the pulsation phase of the bubble, e.g., from in phase to out of phase with the driving sound [M. Ida, Phys. Lett. A 297, 210 (2002)]. The number is larger than that of the resonance frequencies of the double-bubble system, which also invert the pulsation phase of the bubbles. Namely, one of the three transition frequencies does not correspond to the resonance frequencies. We have furthermore suggested that the newly derived characteristic frequency plays a crucial role in the determination of the sign of the interaction force (the secondary Bjerknes force) acting between pulsating bubbles [M. Ida, Phys. Rev. E 67, 056617 (2003)]. More specifically, it has been shown that the height relation between the newly derived characteristic frequencies and the driving frequency determines the sign of the force, an interpretation which is different from the frequently cited explanation after Bjerknes that the resonance (or natural) frequencies of the interacting bubbles play a role in the determination of the sign. In the present paper, we attempt to resolve several points regarding the transition frequencies that had not been clarified in our previous papers. The results given are (1) further details of the characteristics of the transition frequencies, (2) the theoretical determination of the threshold distances for the appearance of the subtransition 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.