Numerical analyses on nonlinear dynamic behaviors of bubble arrays driven by ultrasonic traveling waves

Bubbles are widely used as drug carriers, contrast agents, and wave sources in acoustic fields. Understanding their acoustic behavior is challenging but crucial for practical applications. This study develops a Lagrangian theoretical model to investigate the nonlinear dynamics of bubble arrays driven by ultrasonic traveling waves in fluid. The model describes large-amplitude radial oscillations of bubbles and their translational motions driven by Bjerknes forces and viscous drag. In this study, a two-dimensional bubble array with waves propagating perpendicularly is considered. The translational motions of bubbles are most significant in the wave propagation direction. The primary Bjerknes force governs the spatial configuration of the bubble array, which exhibits peak- and fold-like structures. Modal analysis identifies a dominant radial oscillation mode that governs the overall dynamics of the array. Time-histories of modal weight also reveal a modal transition for the array. Under dual-frequency excitation, the spatial configurations of bubble arrays retain features observed under single-frequency excitation. Nonuniform bubble radii shift the dominant radial oscillation modes of bubble arrays and confine modal frequencies within a specific range. These results elucidate the nonlinear mechanisms governing bubble array dynamics under traveling wave excitation.