The effects of nonlinear wave propagation on the stability of inertial cavitation

TL;DR

This paper investigates how nonlinear wave propagation affects inertial cavitation, revealing that it reduces bubble size, causes earlier collapse, and alters stability thresholds, which is crucial for improving ultrasound treatment safety.

Contribution

It introduces a model incorporating nonlinear wave effects via Burgers' equation, providing new insights into cavitation dynamics and stability thresholds.

Findings

Reduced maximum bubble size during inertial cavitation

Earlier inertial collapse compared to classical models

Altered stability thresholds and bifurcation behavior

Abstract

In the context of forecasting temperature and pressure fields in high-intensity focussed ultrasound, the accuracy of predictive models is critical for the safety and efficacy of treatment. In such fields inertial cavitation is often observed. Classically, estimations of cavitation thresholds have been based on the assumption that the incident wave at the surface of a bubble was the same as in the far-field, neglecting the effect of nonlinear wave propagation. By modelling the incident wave as a solution to Burgers' equation using weak shock theory, the effects of nonlinear wave propagation on inertial cavitation are investigated using both numerical and analytical techniques. From radius-time curves for a single bubble, it is observed that there is a reduction in the maximum size of a bubble undergoing inertial cavitation and that the inertial collapse occurs earlier in contrast with the classical case. Corresponding stability thresholds for a bubble whose initial radius is slightly below the critical Blake radius are calculated. Bifurcation diagrams and frequency-response curves are presented associated with the loss of stability. The consequences and physical implications of the results are discussed with respect to the classical results.