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Considering the interactions between bubbles in a multi-bubble system in a liquid micro-cavity, a model of a spherical bubble cluster in a liquid cavity was developed to describe the dynamical effect of the viscoelastic medium outside the liquid cavity on the oscillation of bubbles, and the coupled equations of bubbles in the spherical cluster were obtained. Subsequently, the acoustic response characteristics of the bubbles were investigated by analyzing the radial oscillation, the stability of the non-spherical shape of bubbles and the threshold of inertial cavitation. The results showed that the confinement of the cavity and the bubble cluster promoted the suppression of bubble oscillation, however, to a certain extent, it might enhance the nonlinear properties of bubbles. According to the acoustic response curves at 1 MHz, it is found that the main resonance peaks shift left when increasing the bubble number, which means a minor resonant radius can be obtained. The nonlinear stability of bubbles in a confined environment is mainly determined by acoustic pressure amplitude and frequency, the initial radius of the bubble, and the bubble number density, while the effect of the cavity radius is enhanced with the increase of the driving pressure. There was a minimum unstable driving acoustic pressure threshold, depending on the initial radius of the bubbles, and the unstable regions were mainly located in the range of less than 4 μm. With the increase in driving acoustic frequency, the unstable region tends to decrease due to the increasing pressure threshold of instability. With the increase in bubble number density, the strip-type stable region scattered in the unstable region in the map was gradually transformed to a random patch-like distribution, which indicates that the bubble oscillation under high acoustic pressure is more sensitive to the parameters, and it is extremely easily perturbed to generate unstable oscillation and then collapse. A lower inertial cavitation threshold was obtained in the range of 1 μm ~ 4 μm of bubble equilibrium radius, and it was less affected by parameters and easier to excite inertial cavitation, whereas the threshold increased in the range greater than 4 μm. Comparing with influences of these parameters, the frequency and bubble number density were more critical on the inertial thresholds.
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Keywords:
- spherical bubble cluster /
- liquid cavity /
- cavitation bubbles /
- coupled oscillation
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