Stability analysis of ring-like cavitation bubble cluster structure in standing wave field

Multi-cavitation bubble system can easily produce cavitation clouds with various structure types, including ring-like cavitation structures. Nonetheless, the evolutionary behavior of the structure and the physical mechanism of its formation are less investigated. In this work, high-speed photography and image analysis techniques are used to study the evolution of ring-like cavitation bubble aggregation structure in an ultrasonic cleaning tank with a frequency of 40 kHz. The ring-like structure usually appears near the pressure nodule, and its radius is less than a one-eighth wavelength. The structure involves establishment, stability and disappearance during an envelope wave period, and its morphology is stable. The ring-like cavitation structure exists as a bubble transport phenomenon, and the formed small bubble clusters flow to the outside of the ring and become discrete cavitation bubbles, or the bubble nuclei rejoin the cycle of bubble transport in the main accumulation area of the bubble. The size of the ring structure and the bubble accumulation area oscillate slightly, and there exists the whole structure rotation phenomenon, which depends on the interaction of the main sound field and the secondary radiation field with the bubbles. Furthermore, in this work, a mathematical model of two bubbles is used to investigate the physical mechanism behind the formation of a ring. It is found that the sound field is a key factor in ring formation. The ring chain model is used to analyze the structural stability by taking into account the time delay caused by the secondary acoustic radiation of the bubble. The numerical results show that the equivalent potential energy distribution of a ring bubble chain with a one-eighth wavelength in radius can stabilize each bubble in the potential well, and the radial distribution presents a ring-like barrier structure. The higher the sound pressure, the greater the equivalent potential, and the more the bubbles are clustered. The higher the driving sound field, the more complete the ring chain structure is. However, high sound pressure may cause the agglomeration of bubbles with high number density to disintegrate the stability of the ring aggregation of bubbles and evolve into other types of bubble aggregation structures. The theoretical results are in good consistence with the experimental phenomena.