Predicting Complex Non-spherical 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 into 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. However, cavitation bubble growth and collapse rarely occur in a perfectly symmetrical fashion, particularly in soft materials. Predicting the onset of dynamically arising, non-spherical instabilities 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 model capable of accurately predicting the onset of non-spherical instability shapes of a bubble in a soft material by explicitly accounting for all pertinent nonlinear interactions between the fluid-like cavitation bubble and the solid-like surroundings. Comparison against high-resolution experimental images from laser-induced cavitation events in a polyacrylamide (PA) hydrogel show excellent agreement. Interestingly, and consistent with experimental findings, our model predicts the emergence of various dynamic instability shapes for hoop stretch ratios greater than one in contrast to most quasi-static investigations. Our new theoretical framework not only provides unprecedented insight into the cavitation dynamics in a soft solid, but it also provides a quantitative means of interpreting bubble dynamics relevant to a wide array of engineering and medical applications as well as natural phenomena.