Alternative interpretation of the sign reversal of secondary Bjerknes force acting between two pulsating gas bubbles

It is known that in a certain case, the secondary Bjerknes force (which is a radiation force acting between pulsating bubbles) changes, e.g., from attraction to repulsion, as the bubbles approach each other. In this paper, a theoretical discussion of this phenomenon for two spherical bubbles is described. The present theory based on analysis of the transition frequencies of interacting bubbles [M. Ida, Phys. Lett. A 297, 210 (2002)] provides an interpretation, different from previous ones (e.g., by Doinikov and Zavtrak [Phys. Fluids 7, 1923 (1995)]), of the phenomenon. It is shown, for example, that the reversal that occurs when one bubble is smaller and the other is larger than a resonance size is due to the second-highest transition frequency of the smaller bubble, which cannot be obtained using traditional natural-frequency analysis.