Bouncing Behavior of Microbubbles in Rigid Capillary Tube

This study systematically investigates the bouncing behavior and dynamics of microbubbles under ultrasound excitation within a rigid capillary. It aims to provide quantitative insights into their oscillation characteristics, migration trajectories, and phase modulation mechanisms for applications in microfluidics, contrast-enhanced ultrasound imaging, and controlled drug delivery. A high-speed imaging system was employed to track the motion of single-, double-, and triple-bubble systems in a viscoelastic medium inside a capillary with a 0.5 mm inner diameter. Under a 28 kHz ultrasound field, bubble dynamics were captured at 100,000 frames per second. Image processing techniques, including dynamic threshold segmentation and morphological operations, were applied to extract bubble contours and centroid trajectories. Spectral analysis via Fast Fourier Transform (FFT) was performed to identify oscillation frequencies and modulation characteristics. Experimental results showed that a single bubble exhibits periodic lateral migration with oscillation frequency slightly below the driving frequency, alongside an asymmetric sideband distribution in its spectrum. In the two-bubble system, five distinct dynamic stages were identified: initial suppression, accelerated migration, interaction dominance, position exchange, and a secondary approach to the wall. The bubbles oscillated at a common dominant frequency of 27.32 kHz but maintained phase difference. Modulation sidebands of approximately 0.3 kHz were observed, indicating nonlinear coupling. The three-bubble system exhibited more complex spatiotemporal evolution, including sequential migration and transitions between triangular and mirror-symmetric configurations. A notable sideband at 0.1 kHz suggested that multi-bubble synergy enhances nonlinear behavior. The tube diameter and fluid viscosity were found to influence the bouncing period through added mass effects and viscous energy dissipation, respectively. The period increased significantly with decreasing tube diameter and decreased with reducing fluid viscosity. Theoretical modeling incorporated the mirror bubble effect into the coupled Keller-Miksis equations to account for wall confinement, successfully simulating the oscillation and translation of confined microbubbles. Numerical analysis further indicated that interbubble distance, wall proximity, and medium viscosity modulate the system's dynamics. Specifically, the bubble resonance frequency is regulated by inter-bubble distance and wall confinement. The two-bubble system exhibits both in-phase and out-of-phase modes, with the latter being more sensitive to distance variations. Near the wall, the oscillation frequency decreases, and the phase difference attenuation accelerates. Increased medium viscosity weakens the phase coupling between bubbles, an effect particularly pronounced for smaller bubbles. This study not only enhances the understanding of multi-bubble synergistic effects in confined spaces but also provides a theoretical foundation and technical reference for optimizing ultrasound contrast agents, designing microfluidic devices, and developing targeted therapies in biomedicine.