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.