Factors Governing the Secondary Bjerknes Force Between Ultrasonically Excited Bubbles

Abstract

Studying the governing parameters and mechanistic principles underlying ultrasound-induced inter-bubble interactions can provide a critical theoretical foundation for advancing engineering applications: coalescence control of bubbles, optimization of cavitation field distributions, and reconfiguration of acoustic energy radiation patterns. This study investigates the governing factors of the secondary Bjerknes force acting between ultrasonically excited bubbles and its manifestations. The results demonstrate that dynamic modifications of the secondary Bjerknes force systematically depend on both ultrasonic excitation parameters and bubble conditions. Within the R₁₀–R₂₀ parameter space, this force distribution is divided into four distinct regions according to the linear resonance radius of bubbles. Critically, inter-bubble distance exhibits no significant correlation with the spatial patterning of force distribution. The magnitude of the secondary Bjerknes force increases positively with both decreasing inter-bubble separation and increasing ultrasonic pressure amplitudes. Furthermore, all bubble pairs universally undergo two sign inversions as ultrasonic frequency increases.