A Level-Set Based Free-Surface Tracking Method for the Simulation of Bubble Collapse and Jetting in Generalized Newtonian Fluids

Predictive simulations of aspherical bubble collapse and jetting are known to be particularly challenging. Under the influence of an external pressure perturbation, bubbles can also undergo prolonged oscillations with potentially large variations in their size and shape. Simulation techniques must robustly represent these large variations while maintaining accuracy. The challenge of nonlinear rheology introduces additional challenges. To do this, we design a new level-set-based free-surface tracking technique. The bubble contents are assumed to be inviscid and spatially homogeneous, governed by a polytropic gas equation of state. A least-squares methodology enforces the normal pressure jump and shear-free boundary conditions precisely at the sharp bubble-liquid interface. Constraints maintain a divergence-free velocity. Numerical tests on spherically symmetric configurations on rectangular meshes demonstrate that the method accurately predicts the bubble response to impulsive and time-periodic pressure perturbations in a generalized Newtonian fluid over multiple growth and collapse cycles. Asymmetries remain small throughout the course of computations. Demonstrations of aspherical bubble dynamics and jetting next to a rigid wall illustrate the formulation's ability to represent complex topological features, including interface breakup in shear-thinning/thickening fluids. These simulations are used to study the influence of shear-thinning and shear-thickening rheology on cavitation damage in tissue-mimicking soft materials. Simulations of growth and collapse of a spherically symmetric vapor bubble that fully incorporate the phase change dynamics, illustrate the flexibility and robustness of our implementation.