The Kirkwood–Bethe hypothesis for bubble dynamics, cavitation, and underwater explosions

Abstract

Pressure-driven bubble dynamics is a major topic of current research in fluid dynamics, driven by innovative medical therapies, sonochemistry, material treatments, and geophysical exploration. First proposed in 1942, the Kirkwood–Bethe hypothesis provides a simple means to close the equations that govern pressure-driven bubble dynamics as well as the resulting flow field and acoustic emissions in spherical symmetry. The models derived from the Kirkwood–Bethe hypothesis can be solved using standard numerical integration methods at a fraction of the computational cost required for fully resolved simulations. Here, the theoretical foundation of the Kirkwood–Bethe hypothesis and contemporary models derived from it are gathered and reviewed, as well as generalized to account for spherically symmetric, cylindrically symmetric, and planar one-dimensional domains. In addition, the underpinning assumptions are clarified and new results that scrutinize the predictive capabilities of the Kirkwood–Bethe hypothesis with respect to the complex acoustic impedance experienced by curved acoustic waves and the formation of shock waves are presented. Although the Kirkwood–Bethe hypothesis is built upon simplifying assumptions and lacks some basic acoustic properties, models derived from it are able to provide accurate predictions under the specific conditions associated with pressure-driven bubble dynamics, cavitation, and underwater explosions.