Cavitation bubbles often appear as populations in a wide range of naval and biomedical applications. While the oscillations of an isolated spherical bubble are relatively well understood, the dynamics of multiple bubbles remain less characterized due to the large number of parameters associated with bubble size and spatial configuration. In the present study, we develop an energy budget framework for quantifying energy transfer and pressure work during the oscillations of spherical bubbles while conserving the total energy of the system. We focus on a two-bubble system in the dilute limit, in which bubbles interact weakly and largely maintain spherical symmetry. The energy budget framework uses the outputs of the coupled Keller–Miksis equations to evaluate individual energy components and their temporal evolution. Three key parameters—bubble size ratio, bubble–bubble distance, and driving pressure ratio—are observed to nonlinearly alter collapse time, energy concentration, and radiated acoustic energy. We show that stronger interactions, caused by larger size ratios or smaller separation distances, lead to reduced compression and less violent and delayed collapse, thereby lowering the energy concentrated in the bubble. We further determine scaling relationships for bubble dynamics and energy components at the instant of collapse based on the initial problem parameters. We identify the initial driving pressure conditions where the dominant energy reduction mechanism shifts from bubble–bubble interactions at low driving pressures to liquid compressibility at high pressures. The proposed framework and scaling relations provide a robust basis for incorporating bubble–bubble interactions and energy redistribution mechanisms into bubble cloud models, in the dilute limit.
Kim et al. (Sun,) studied this question.