Refined secondary Bjerknes force equation for double bubbles with pulsation, translation, and deformation

Abstract

The secondary Bjerknes force (SBF) is the time-averaged interaction between two bubbles driven in a sound field. We derived a refined formula for the interaction force, incorporating the radial vibration and translational and deformational motions of the bubble. The coupling of pulsation, translation, and deformation enhances the interaction between bubbles but also weakens their stability, making it easier for bubbles to merge or break during motion. The effects of the coupling mode on the magnitude and direction of SBFs coupled with pulsation, translation, and deformation were numerically analyzed and studied. Under certain sound-field conditions, the SBF increased with increasing pressure amplitude, initial radius, and initial velocity, while decreased as the distance increased. In addition, the SBF irregularly increased with increasing frequency.