Scaling the nonlinear dynamics of bubble clouds in an ultrasound field*

The dynamics of bubble clouds induced by high-intensity focused ultrasound are investigated. The regime studied, where the cloud size is similar to the ultrasound wavelength, is motivated by a recently proposed ultrasound-based lithotripter. High-speed images show that the cloud is asymmetrical; bubbles nearest the source grow to a larger radius than the distal ones. Similar structures of clouds are observed in numerical simulations that mimic the experiment. To elucidate the structure, a parametric study is conducted for plane ultrasound waves with various amplitudes and diffuse clouds with different initial void fractions. Based on an analysis of the kinetic energy of liquid induced by bubble oscillations, a new scaling parameter is introduced to characterize the dynamics. The new parameter generalizes the cloud interaction parameter originally introduced by d'Agostino and Brennen (1989). The dynamic interaction parameter controls the energy localization and consequent anisotropy of the cloud. The amplitude of the far-field, bubble-scattered acoustics is likewise correlated with the parameter. These findings not only shed light on the physics of cloud cavitation, but may also be of use to quantification of the effects of cavitation on outcomes of lithotripsy.