Analysis of multi-bubble pulsations by the finite element method and bubble dynamics equations

Bubbles are widely used in industrial production, biomedical engineering, and many other fields. The analysis of the response of bubble clusters under acoustic waves is significant for the application of bubbles. In this paper, different bubble dynamics models are used to calculate the instantaneous radius of multi-bubbles, and the results corresponding to the different models are compared with those by the finite element method. In addition, the effect of bubble interactions on bubble pulsation is analyzed at different distances, and the effect of incident acoustic direction on the bubble's instantaneous radius is also investigated. The results show that time delays, which have often been neglected in previous work, should be considered except when the bubble spacing is minimal. The results calculated by the finite element method indicate that the attraction and repulsion between bubbles are alternating, which is related to the velocity field between bubbles. Moreover, the suppression or promotion of bubble interactions for bubble pulsation is affected by bubble distance under the same acoustic excitation conditions. Finally, for a bubble cluster with large bubble distances, its total scattered field relating to the incident acoustic wave can be approximated as the interference field of multiple secondary acoustic sources with the same waveform and different phases. If these bubbles are in random motion, the total scattered sound intensity of the bubble cluster is proportional to the number of bubbles.