Damping Constants and the Definition of Models for Cavitation Bubbles

Abstract

Two simple models—the stable cavity and the transient cavity—have been proposed as suitable representations of physical bubbles found in acoustic cavitation. Heretofore, both models have suffered from a lack of precision in their definitions. A mathematical formulation of equations of motion for a cavity has been used to study the damping of free oscillations of cavities owing to heat conduction, viscosity, and acoustic radiation. It was found that the thermal-damping constant of a cavity is a function of amplitude at the start of a cycle and that this function has a maximum. This maximum marks a transition between stable and transient cavities; for stable cavities, the thermal-damping constant increases with amplitude, while for transient cavities it decreases with amplitude. The results of this calculation suggest a fundamental definition for stable and transient cavities and a criterion for the range of their usefulness as models for physical bubbles. [Work supported by Acoustics Programs (Code 468), U. S. Office of Naval Research.]