A novel explanation for the reversal of sign 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 Letter, 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, (2002) 210], gives an interpretation, which differs from previous ones (e.g., by Doinikov and Zavtrak [Phys. Fluids 7, (1995) 1923]), of the phenomenon. It is shown for example that the reversal that occurs when one bubble is smaller than and another is larger than a resonance size is due to the second-highest transition frequency of the smaller bubble, which cannot be given by the traditional naturalfrequency analysis.