黏弹性介质包裹的液体腔内球状泡群耦合振动模型

A model of coupled oscillation of bubble cluster in liquid cavity wrapped by viscoelastic medium

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,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.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4μm的范围内;驱动频率增大,气泡振动不稳定区的声压阈值也随之增大,且不稳定区域有减小的趋势;随着气泡数密度的增加,气泡不稳定区域逐渐向无规则的斑图状分布,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大于4μm范围内气泡的惯性空化阈值受频率和气泡数密度的影响显著.

Considering the interactions between bubbles in a multi-bubble system in a liquid micro-cavity,a spherical bubble cluster in a liquid cavity is modeled in order to describe the dynamical effect of the viscoelastic medium outside the liquid cavity on the oscillation of bubbles,and the coupled equations of bubbles are obtained.Subsequently,the acoustic response characteristics of bubbles are investigated by analyzing the radial oscillation,the stability of the non-spherical shape of bubbles and the threshold of inertial cavitation.The results show that the confinement of the cavity and the bubble cluster facilitates the suppression of bubble oscillation,however,it might enhance the nonlinear properties of bubbles to a certain extent.From the acoustic response curve at 1 MHz,it is found that the main resonance peaks shift leftward with the increase of 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 bubble radius,and bubble number density,while the effect of the cavity radius is enhanced with the increase of the driving pressure.There is a minimum unstable driving acoustic pressure threshold,depending on the initial bubble radius,and the unstable regions are mainly located in a range of less than 4μm.With the increase in bubble number density,the strip-type stable region scattered of the unstable region in the map is gradually transformed into a random patch-like distribution,which indicates that the bubble oscillation under high acoustic pressure is more sensitive to the parameters,and it is very susceptible to interference,produces unstable oscillation and then collapses.When the bubble equilibrium radius is in a range greater than 4μm,the influences of frequency and bubble number density on the inertial thresholds are particularly significant.