Energy Transfer during Strong Oscillations of a Spherical Bubble with Non-Ideal Gas Equations of State

Abstract

Spherical bubble oscillations are widely used to model cavitation phenomena in biomedical and naval hydrodynamic systems. During collapse, a sudden increase in surrounding pressure initiates the collapse of a cavitation bubble, followed by a rebound driven by the high internal gas pressure. While the ideal gas equation of state (EOS) is commonly used to describe the internal pressure and temperature of the bubble, it is limited in its capacity to capture molecular-level effects under highly compressed conditions. In the present study, we employ non-ideal EOS for the gas (the van der Waals EOS and its volume-limited case) to investigate bubble oscillations with a focus on energy redistribution. Bubble oscillation is modeled in two phases: collapse, described by the Keller-Miksis formulation, and rebound, where peak shock pressure is estimated using similitude-based relations. To assess the role of EOS in energy redistribution, we introduce a framework that quantifies energy components in the bubble-liquid system while conserving total energy, tailored to each EOS. Using this framework, we evaluate energy concentration, acoustic radiation, and shock propagation and statistically analyze their dependence on both the driving pressure and the EOS of gas. We statistically derive scaling relations of key bubble dynamics quantities, energy concentration and radiation, and shock pressure using the driving pressure ratio. This work provides a generalizable framework and set of scaling relations for predicting bubble dynamics and energy transfer, with potential applications in evaluating the impacts of cavitation phenomena in complex practical systems.