Modeling acoustic emissions and shock formation of cavitation bubbles

Despite significant progress in understanding and foretelling pressure-driven bubble dynamics, models that faithfully predict the emitted acoustic waves and the associated shock formation of oscillating or collapsing bubbles have received comparably little attention. We propose a numerical framework using a Lagrangian wave tracking approach to model the acoustic emissions of pressure-driven bubbles based on the Kirkwood-Bethe hypothesis and under the assumption of spherical symmetry. This modeling approach is agnostic to the equation of the state of the liquid and enables the accurate prediction of pressure and velocity in the vicinity of pressure-driven bubbles, including the formation and attenuation of shock fronts. We validate and test this new numerical framework by comparison with solutions of the full Navier-Stokes equations and by considering a laser-induced cavitation bubble as well as pressure-driven microbubbles in excitation regimes relevant to sonoluminescence and medical ultrasound, including different equations of state for the liquid. A detailed analysis of the bubble induced flow field as a function of the radial coordinate r demonstrates that the flow velocity u is dominated by acoustic contributions during a strong bubble collapse and, hence, decays predominantly with u infinity r(-1), contrary to the frequently postulated decay with u infinity r(-2) in an incompressible fluid.