Numerical investigations on nonlinear dynamic responses of multiple bubbles interacting with ultrasonic traveling waves in fluid

This study investigates the nonlinear dynamic behaviors of multiple bubbles driven by ultrasonic traveling waves in fluid. A theoretical model in the Lagrangian framework is developed to describe the radial oscillations and translational motions of the bubbles. The model accounts for the primary Bjerknes force, secondary Bjerknes force, and viscous drag acting on the bubbles. The validity of the model is confirmed through comparisons with benchmark solutions. The effects of several factors on bubble dynamics are investigated, including the initial inter-bubble distance, the initial radii of bubbles, and the pressure amplitude and excitation frequency of traveling waves. It is found that bubble pairs driven by traveling waves exhibit six typical types of translational motion. For a chain of three bubbles, various types of translational motion are observed, with either bubble pairs dominating or all three bubbles fully coupled. The configuration of a bubble chain can be decomposed into a bubble pair and a single bubble through enhancement or suppression of bubble pulsation. The chaotic motions of bubble chains are gradually induced as the pressure amplitude of traveling waves increases. Additionally, variations in the excitation frequency of traveling waves enable bubble chains to transit between stable and chaotic configurations.