无界弹性介质球形液体空腔中的气泡的动力学

Dynamics of bubbles in spherical liquid cavity wrapped by elastic medium

构建了弹性介质包裹的液体腔内的气泡振动模型,并基于压力平衡关系得到了腔内液体中气核发展成为空化泡的Blake阈值以及液体腔临界半径表达式.体积模量、泡核半径及表面张力系数等因素可影响Blake阈值压力和气泡大小,形成触发或抑制空化发生的控制条件相关的参数空间.基于拉格朗日方程推导了考虑腔外介质弹性影响的气泡动力学方程,并基于此分析了激励声波频率、介质体积模量、腔内液体体积等因素对气泡振动行为的影响,结果表明:在声场驱动下,泡核快速生长到新的平衡半径后振荡;气泡平衡半径与超声无关,但会影响气泡动力学行为.当超声频率与气泡固有振荡频率相当时,气泡在几个周期的剧烈振动后崩溃,同时在腔内液体中形成明显的压力起伏变化.高频超声驱动下气泡的响应相对较弱,气泡主要表现为自由振荡.

The cavitation effects occur in the ultrasound therapy technology.With the development of ultrasound therapy technology,cavitation effect in biological tissues has attracted more and more attention.The aim of the present study is to discuss the factors affecting cavitation nucleation and dynamics in tissues,and to provide a theoretical reference for the application of cavitation effects to ultrasound therapy.A model is developed for the cavitation inception in a spherical liquid cavity wrapped by an elastic medium.The Blake threshold value and the critical radius of the liquid cavity for the generation of spherical bubbles are obtained by the pressure equilibrium relationship.The effects of the excitation frequency,the volume modulus of the medium and the volume of the liquid in the cavity on the bubble vibration behavior are analyzed by deriving a bubble dynamic equation that consider the elastic effect of the medium outside the cavity using Lagrange equation.It is shown that the volume modulus,initial radius of bubble nucleus and surface tension can affect the Blake threshold pressure and bubble size,and those form a parameter reference for the control conditions that trigger or inhibit cavitation.The gas core can rapidly grow to a new equilibrium radius and oscillate under the action of an acoustic wave,and the bubble equilibrium radius is independent of the external field,but it can affect the bubble dynamic behavior.When the frequency of the ultrasonic signal is equal to the natural oscillation frequency of the bubble,the bubble collapses after several periods of intense vibration,and the pressure fluctuation in the liquid in the cavity is obvious.The response of bubbles under high frequency ultrasonic driving is relatively weak,and the oscillations of bubbles are dominated by free oscillation.