Evolutionary mechanism of Y-branches in acoustic Lichtenberg figures just below the water surface

Abstract

The acoustic Lichtenberg figure (ALF) in an ultrasonic cleaner with a frequency of 28 kHz at different power levels was observed using high-speed photography. The nonlinear response of the cavitation structure was analyzed by the entropy spectrum in the ALF images, which showed the modulation influence of the primary acoustic field, exhibiting the fluctuations of the bubble distribution with time. Typical Y-branches predict the paths by which surrounding bubbles are attracted and converge into the structure, the branches are curved due to bubble-bubble interactions, and the curvature increases as the bubbles are approaching the main chain. The average travelling speed of bubbles along the branches is about 1.1 m/s, almost independent of power level of the ultrasonic cleaner. A theoretical model consisting of free bubbles and a straight bubble chain of finite length was developed to explore the evolutionary mechanism of branching. It was found that the bubble trajectories showed a bending tendency similar to the experimentally observed Y-branches, and the stationary straight bubble chain parallel to the main chain could evolve into a curved chain and eventually become a branch of the main chain. The theoretical predictions agree well with the experimental results, verifying the evolutionary mechanism of Y-branches in ALF.