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高强度超声可激发生物组织空化，软组织常被当作黏弹性介质，因此，黏弹性介质中气泡动力学行为研究可为超声生物治疗提供理论支持。为探索组织液内多气泡动力学影响，我们构建了球形液体腔内的球状泡团模型，考虑了液体腔外黏弹性介质的动力学效应，得到了球状泡群内气泡耦合振动方程，并基于此分析了气泡的振动行为。结果表明，腔体以及泡群约束虽抑制了气泡振动，但在一定程度上还可以增强气泡的非线性振动特性，主要表现为在1 MHz的声波激励下，气泡的主共振响应半径在2 μm附近且随着气泡数密度的增加有减小的趋势。约束环境下气泡的非球形振动稳定性主要受驱动声波压力幅值和频率、气泡初始半径以及气泡数密度影响，而腔体半径的影响随驱动压力的增加而增强；存在最小不稳定驱动声压阈值，不同初始半径的气泡不稳定振动阈值压力不同且不稳定分布区主要分布在小于4 μm的范围内；随着驱动频率由20 kHz增加至1 MHz，气泡振动不稳定区的声压阈值由0.19 MPa增大至0.29 MPa，且不稳定区域有减小的趋势；随着气泡数密度的增加，气泡不稳定分布区域内散布的条带型稳定区逐渐向无规则的斑图状分布，表明高声压条件下气泡振动对条件参数更为敏感，极易受到扰动发生不稳定振动而崩溃。高频声波激励下平衡半径1 μm ~4 μm间的空化泡的惯性空化阈值较低，其中2 μm微泡的惯性空化阈值约为0.16 MPa，且受各参量的影响较小，更易于激发惯性空化；平衡半径大于4 μm范围内气泡的空化阈值受各参量的影响逐渐增强，而频率和气泡数密度的影响尤为显著。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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