Predicting complex nonspherical instability shapes of inertial cavitation bubbles in viscoelastic soft matter

Inertial cavitation in soft matter is an important phenomenon featured in a wide array of biological and engineering processes. Recent advances in experimental, theoretical, and numerical techniques have provided access to a world full of nonlinear physics, yet most of our quantitative understanding to date has been centered on a spherically symmetric description of the cavitation process in water. However, cavitation bubble growth and collapse rarely occur in a perfectly symmetrical fashion, particularly in soft materials. Predicting the onset of dynamically arising, nonspherical instabilities in soft matter has remained a significant, unresolved challenge, in part due to the additional constitutive complexities introduced by the surrounding nonlinear viscoelastic solid. Here, we provide a new theoretical framework capable of accurately predicting the onset of nonspherical instability shapes of a bubble in a soft material by explicitly accounting for all pertinent nonlinear interactions between the cavitation bubble and the solid surroundings. Comparison with high-resolution experimental images from laser-induced cavitation events in a polyacrylamide hydrogel show excellent agreement. Interestingly, and consistent with experimental findings, our model predicts the emergence of various dynamic instability shapes for circumferential bubble stretch ratios greater than 1, in contrast to most quasistatic investigations. Our new theoretical framework not only provides unprecedented insight into the cavitation dynamics in a soft, nonlinear solid, but also provides a quantitative means of interpreting bubble dynamics relevant to a wide array of engineering and medical applications as well as natural phenomena.