Coupled resonance of bubbles in spherical cavitation clouds

Zhang Peng-Li^{1,2}, Lin Shu-Yu^{1}, Zhu Hua-Ze^{2}, Zhang Tao^{2}

1. Institute of Applied Acoustics Shaanxi Normal University, Xi'an 710062, China;
2. College of Science, Xi'an University of Science and Technology, Xi'an 710054, China

The interaction between bubbles in bubble group mainly acts on the other bubble through radiation sound pressure between the bubbles. In this paper, based on the bubble dynamics equation in bubble clouds, the equation of bubble wall motion is linearly reduced, the expression of bubble resonance frequency in spherical bubble group is obtained and the correction coefficient of bubble resonance frequency and single bubble are given. Furthermore, the effects of the initial radius, the number of bubbles and the distance between bubbles on the resonance frequency are discussed. The results show that the phase of bubbles is taken into account. Considering the interaction between bubbles, the resonance frequency of bubbles in spherical bubble group is obviously less than that of single bubble. With the decrease of the number of bubbles in bubble group, the distance between bubbles increases, the interaction between bubbles in bubble group decreases, and the resonance frequency of bubbles returns to the resonance frequency of Minnaert single bubble. At the same time, the resonance frequency of bubbles in bubble group changes gradient with the increase of the distance between bubbles and the number of bubbles. However, when the number of bubbles increases a certain value, the resonant frequency of the bubble is almost constant. When the bubble group has a certain radius, the more the number of bubbles, the smaller the resonance frequency of the bubble is, but there exists a critical value. It is also found that a smaller correction coefficient is held by the bubble group with larger initial radius, which indicates the same number of bubble groups. Under the same bubble spacing, the interaction of small bubbles with smaller bubbles is more significant, and the resonance frequency of the bubble is obviously affected. Because the frequency and amplitude of driving sound pressure can only be given values in ultrasonic cavitation, the resonant frequency of cavitation bubbles will be reduced by properly injecting air bubbles into liquid, which makes most of cavitation bubbles undergo intense non-linear oscillating steady-state cavitation. Therefore, the occurrence of cavitation can be effectively suppressed.

Project supported by the National Natural Science Foundation of China (Grant Nos. 50875132, 60573172) and the Industrial Public Relation Project of Shaanxi Technology Committee, China (Grant Nos. 2015GY182, 2016GY-041).