单泡超声空化仿真模型的建立及其动力学过程模拟*

为了模拟单泡超声空化的动力学特性,建立了单泡超声空化的有限元仿真模型,基于流体动力学控制方程和流体体积分数模型,利用有限元分析软件模拟了超声驱动下水中单泡的空化动力学过程。结果表明:单泡随时间的演化规律是先缓慢膨胀到最大后迅速塌缩;泡内压强与气体密度变化与单泡体积变化成反比;在膨胀阶段,泡外压强与气体密度沿着泡的径向向外递减;在压缩阶段,泡外在声压垂直方向的压强与气体密度要大于声压激励方向的压强和气体密度。该文分析结果将为超声空化动力学过程模拟及研究提供参考。     

Investigation of noninertial cavitation produced by an ultrasonic horn

This paper reports on noninertial cavitation that occurs beyond the zone close to the horn tip to which the inertial cavitation is confined. The noninertial cavitation is characterized by collating the data from a range of measurements of bubbles trapped on a solid surface in this noninertial zone. Specifically, the electrochemical measurement of mass transfer to an electrode is compared with high-speed video of the bubble oscillation. This gas bubble is shown to be a "noninertial" event by electrochemical surface erosion measurements and "ring-down" experiments showing the activity and motion of the bubble as the sound excitation was terminated. These measurements enable characterization of the complex environment produced below an operating ultrasonic horn outside of the region where inertial collapse can be detected. The extent to which solid boundaries in the liquid cause the frequencies and shapes of oscillatory modes on the bubble wall to differ from their free field values is discussed.     

超声场下刚性界面附近溃灭空化气泡的速度分析

为了揭示刚性界面附近气泡空化参数与微射流的相互关系, 从两气泡控制方程出发, 利用镜像原理, 建立了考虑刚性壁面作用的空化泡动力学模型. 数值对比了刚性界面与自由界面下气泡的运动特性, 并分析了气泡初始半径、气泡到固壁面的距离、声压幅值和超声频率对气泡溃灭的影响. 在此基础上, 建立了气泡溃灭速度和微射流的相互关系. 结果表明: 刚性界面对气泡振动主要起到抑制作用; 气泡溃灭的剧烈程度随气泡初始半径和超声频率的增加而降低, 随着气泡到固壁面距离的增加而增加; 声压幅值存在最优值, 固壁面附近的气泡在该最优值下气泡溃灭最为剧烈; 通过研究气泡溃灭速度和微射流的关系发现, 调节气泡溃灭速度可以达到间接控制微射流的目的.     

超声珩磨区实际气体的单空泡动力学分析

为进一步揭示功率超声振动的珩磨机理,以珩磨液为工作介质,研究了功率超声珩磨环境中实际气体的单空泡动力学特性。基于Rayleigh-Plesset方程,应用实际气体绝热方程和范德瓦尔斯方程对其进行了修正,建立了功率超声珩磨环境中实际气体的单空泡动力学方程以及实际气体单空泡共振频率方程。并运用4~5阶RungeKutta法模拟了不同超声条件(声压幅值、空泡初始半径、振动频率)对泡壁的运动以及运动速度的影响。结果表明:较高的声压幅值,空泡理论共振半径R'0与初始半径R0的比值为102数量级以及较低的超声频率有利于超声珩磨磨削区空化效应的发生。     

气泡在超声场中绕圈运动的高速摄影及其图像分析

借助高速摄影和图像分析技术对首次发现的附壁气泡的绕圈现象进行了实验研究,重点研究游移气泡的运动轨迹、附壁气泡的布阵过程、气泡的来源以及气泡的振动细节.研究发现游移绕圈气泡的运动轨迹呈现出不稳定、不规则、不光滑的特点.阵列气泡源于游移气泡,而游移气泡变成阵列气泡的方式主要是通过合并增大体积,从而减小所受的Bjerknes力,降低活性的方式实现的.游移气泡源于ALF(acoustic lichtenberg figure)空化云中大量空泡的合并,使以径向振动为主的空泡逐渐过渡到以表面波动为主的气泡.阵列气泡在Bjerknes力的作用下呈现出规则的表面波动,而体积更小受力更大的游移空泡的表面完全失稳,呈现极不规则的形貌,并对附近阵列气泡的表面波动产生影响.阵列气泡呈现出十分规则的排布,相邻阵列气泡之间的振动相位是相反的,表现为相互排斥.     

Gas bubble pulsation in a semiconfined space subjected to ultrasound

In the case of ultrasound application in biological tissues, gas bubbles might form and collapse within cells, in the intercellular spaces and on tissue surfaces. In this work the effect of confined space on the behavior of the gas bubble in the presence of ultrasonic field is studied. A numerical model for bubble pulsation in a planar liquid layer, bounded by two rigid walls, is developed. Surface tension at the interface between the host liquid and the gas in the bubble is considered as well. A mathematical statement and solution technique based on the boundary integral method are presented. In some cases, the bubble divides into two symmetrical parts and high-velocity jets are generated, aimed at the walls. The final velocity of the jets strongly depends on the surface tension of the host liquid. Two new parameters that predict the occurrence of jet formation are developed.     

Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.     

A new pressure formulation for gas-compressibility dampening in bubble dynamics models

We formulated a pressure equation for bubbles performing nonlinear radial oscillations under ultrasonic high pressure amplitudes. The proposed equation corrects the gas pressure at the gas–liquid interface on inertial bubbles. This pressure formulation, expressed in terms of gas-Mach number, accounts for dampening due to gas compressibility during the violent collapse of cavitation bubbles and during subsequent rebounds. We refer to this as inhomogeneous pressure, where the gas pressure at the gas–liquid interface can differ to the pressure at the centre of the bubble, in contrast to homogenous pressure formulations that consider that pressure inside the bubble is spatially uniform from the wall to the centre. The pressure correction was applied to two bubble dynamic models: the incompressible Rayleigh–Plesset equation and the compressible Keller and Miksis equation. This improved the predictions of the nonlinear radial motion of the bubble vs time obtained with both models. Those simulations were also compared with other bubble dynamics models that account for liquid and gas compressibility effects. It was found that our corrected models are in closer agreement with experimental data than alternative models. It was concluded that the Rayleigh–Plesset family of equations improve accuracy by using our proposed pressure correction.     

Theoretical model of ice nucleation induced by acoustic cavitation. Part 1: Pressure and temperature profiles around a single bubble

This paper deals with the inertial cavitation of a single gas bubble in a liquid submitted to an ultrasonic wave. The aim was to calculate accurately the pressure and temperature at the bubble wall and in the liquid adjacent to the wall just before and just after the collapse. Two different approaches were proposed for modeling the heat transfer between the ambient liquid and the gas: the simplified approach (A) with liquid acting as perfect heat sink, the rigorous approach (B) with liquid acting as a normal heat conducting medium. The time profiles of the bubble radius, gas temperature, interface temperature and pressure corresponding to the above models were compared and important differences were observed excepted for the bubble size. The exact pressure and temperature distributions in the liquid corresponding to the second model (B) were also presented. These profiles are necessary for the prediction of any physical phenomena occurring around the cavitation bubble, with possible applications to sono-crystallization.     

双泡模型共振频率的超声空化动力学研究

该研究旨在研究双泡模型的自然共振频率对超声空化的影响,通过理论计算研究了自然共振频率的影响因素,以及单频超声和双频超声与自然共振频率的关系。研究结果表明：气泡初始半径是影响自然共振频率的主要因素;低频驱动下的非线性波动程度会比高频的更加剧烈,当驱动频率等于气泡自然共振频率时,超声空化的效果更好;双频超声取气泡自然共振频率时超声空化效果远远优于单频超声驱动。该研究在超声医学和理解超声空化特性方面有着重要的意义。     

Numerical investigation of the inertial cavitation threshold by dual-frequency excitation in the fluid and tissue

Inertial cavitation thresholds, which are defined as bubble growth by 2-fold from the equilibrium radius, by two types of ultrasonic excitation (at the classical single-frequency mode and dual-frequency mode) were calculated. The effect of the dual-frequency excitation on the inertial cavitation threshold in the different surrounding media (fluid and tissue) was studied, and the paramount parameters (driving frequency, amplitude ratio, phase difference, and frequency ratio) were also optimized to maximize the inertial cavitation. The numerical prediction confirms the previous experimental results that the dual-frequency excitation is capable of reducing the inertial cavitation threshold in comparison to the single-frequency one at the same output power. The dual-frequency excitation at the high frequency (i.e., 3.1 + 3.5 MHz vs. 1.1 + 1.3 MHz) is preferred in this study. The simulation results suggest that the same amplitudes of individual components, zero phase difference, and large frequency difference are beneficial for enhancing the bubble cavitation. Overall, this work may provide a theoretical model for further investigation of dual-frequency excitation and guidance of its applications for a better outcome.     

调频超声脉冲驱动微气泡运动偏移的研究

提出调频超声辐射力技术驱动微泡群,以加强微泡的吸附效率.基于改进的RP方程及粒子轨迹方程研究了微泡群整体的运动位移与调频信号的中心频率、调频范围、信号声压,以及微泡半径分布关系.研究结果表明调频信号在驱动半径具有宽泛分布的气泡群,以及半径分布远离谐振半径的气泡群时,作用效果好于传统正弦波信号.例如中心频率1 MHz、调频范围0.75 MHz的调频脉冲作用高斯分布（平均半径3.5 μm、均方差为1）的微泡群200 μs,可比同等声压的正弦波多约12%的微气泡产生位移30 μm. 关键词： 超声辐射力 调频波 高斯分布     

Generation of microbubbles from hollow cylindrical ultrasonic horn

In this study, we found that microbubbles with diameters of less than 100 μm can be easily generated by using a hollow cylindrical ultrasonic horn. Consecutive images of bubbles obtained by using high-speed and high-resolution cameras reveal that a capillary wave is formed on the gas–liquid interface under weak ultrasonic irradiation and that the wave head is detached in the form of bubbles by the fragmentation of the interface as the power of ultrasonic irradiation increases. Moreover, consecutive images of the bubble interface obtained by an ultra-high-speed camera indicate that the breakup of bubbles oscillating harmonically with the ultrasonic irradiation generates many microbubbles that are less than 100 μm in diameter. With regard to the orifice diameter of the horn end, we found that its optimum value varies with the ultrasonic power input. When the orifice diameter is small, the capillary wave generated from the horn end easily propagates all over the gas–liquid interface, thereby starting the generation of microbubbles at a lower ultrasonic power input. When the orifice diameter is large, the capillary wave is attenuated because of viscosity and surface tension. Hence, in this case, microbubble generation from the horn requires a higher ultrasonic power input. Furthermore, the maximum yield of microbubbles via primary and secondary bubble generation can be increased by increasing the gas flow rate.     

油-气-水三相流超声传感器持气率测量*

为探索油-气-水三相流持气率测量难题,该文开展了脉冲透射式超声传感器持气率测量动态实验研究。首先,利用超声传感器与光纤传感器组合,测取了油-气-水三相流中段塞流、混状流、泡状流的响应信号;其次,提取了超声脉冲信号的最大值序列来反映不同流型时超声传感器响应特性,同时,借助双头光纤传感器与相关测速法,计算得到了流体中气泡弦长序列;最后,结合流型与泡径信息,利用超声传感器测量了不同流型下持气率,并分析了不同流型持气率预测的误差来源,为其他油-气-水三相流持气率测量传感器设计提供了借鉴。     

Occurrence of transient cavitation in pulsed sawtooth ultrasonic fields

Thus far, studies conducted to assess the safety of diagnostic ultrasound have employed sinusoidal sound fields. To evaluate the influence of nonlinearly distorted acoustic fields, this article compares the responses of microbubbles of variable size, exposed to (1) a sinusoidal pulse and (2) a sawtooth pulse. The nonlinear oscillations of a spherical bubble in a viscous compressible liquid stimulated into motion by an ultrasonic pulse are predicted, using a theoretical model for bubble dynamics. The maximum gas pressures inside the bubble when it collapses under the influence of a sinusoid or a sawtooth are deduced. Experimental work on Drosophila larvae exposed to sinusoidal and to sawtooth fields is consistent with the theoretical analysis.     

Nonlinear dynamics of a cavitation bubble pair near a rigid boundary in a standing ultrasonic wave field

The dynamics of a micrometer-sized bubble pair in water near a rigid boundary under standing ultrasonic wave excitation is investigated in this study. The viscous effect in the boundary layer at the air-water interface is considered following the viscous correction model. The evolution of the bubble surface at the collapsing stage of the bubble pair is presented for different parameter sets. The field pressure near the rigid boundary, which is induced by the oscillating bubble pair, and the high-speed water jet at the collapse stage, form the main focus of the analysis. This reveals that a horizontal configuration of the bubble pair retards the strength of the bubble jet towards the boundary, whilst a vertical configuration, especially with differently-sized bubbles, can enhance the bubble collapse. This study may help to understand the interaction of multiple bubbles in an acoustic field and its application to surface cleaning.     

Bubble nonlinear dynamics and stimulated scattering process

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller–Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition.     

Bubble motions confined in a microspace observed with stroboscopic technique

Dynamic motions of gas bubble confined in a microspace, i.e., in a channel of a microreactor, were observed with a video microscope and stroboscopic technique using a light emitting diode operated in a pulsed mode. There are many important phenomena related to the bubble dynamics synchronized with ultrasonic wave and continued for more than a few minutes. With the stroboscopic technique, the time-expanded bubble motions synchronized with ultrasound wave and the real time background images can be simultaneously observed. A number of interesting phenomena resulting from the dynamic motions of a microbubble in a microspace were observed; nonspherical bubble oscillation, rectified diffusion, emergence of cavitation, and microstreaming of different patterns depending on the input power of ultrasound. The observation technique described in this investigation could be a convenient tool for taming the bubble under a microscope to investigate the bubble dynamics in detail.     

Effects of radiator shapes on the bubble diving and dispersion of ultrasonic argon process

In this work, three ultrasonic radiators in different shapes have been designed in order to investigate the effects of radiator shapes on the argon bubble dispersion and diving as well as the degassing efficiency on magnesium melt. The radiator shape has a strong influence on the bubble diving and dispersion by ultrasound. A massive argon bubble slowly flows out from the radiator with the hemispherical cap, due to the covering hemispherical cap. Using a concave radiator can intensively crush the argon bubbles and drive them much deep into the water/melt, depending on the competition between the argon flow and opposite joint shear force from the concave surface. The evolution of wall bubbles involves the ultrasonic cavities carrying dissolved gas, migrating to the vessel wall, and escaping from the liquid. Hydrogen removal can be efficiently achieved using a concave radiator. The hydrogen content can be reduced from 22.3 μg/g down to 8.7 μg/g. Mechanical properties are significantly promoted, due to the structure refinement and efficient hydrogen removal.     

超声波作用下泡群的共振声响应

从球状泡群气泡动力学方程出发, 考虑泡群间次级声辐射的影响, 得到了声场中两泡群共同存在时气泡振动的动力学方程, 并以此为基础探讨声波驱动下双泡群振动系统的共振响应特征. 由于泡群间气泡间的相互作用, 系统存在低频共振和高频共振现象, 两不同共振频率的数值与泡群内气泡的本征频率相关. 泡群内气泡的本征频率又受到初始半径、泡群大小和泡群内气泡数量的影响. 气泡自由振动和驱动声波的耦合激起泡群内气泡的受迫振动, 气泡初始半径、气泡数密度和驱动声波频率等都会影响泡群内气泡的振动幅值和初相位. 关键词： 气泡群 共振 声响应 超声空化