Oscillation and Migration of Bubbles within Ultrasonic Field

The oscillation and migration of bubbles within an intensive ultrasonic field are important issues concerning acoustic cavitation in liquids.We establish a selection map of bubble oscillation mode related to initial bubble radius and driving sound pressure under 20 kHz ultrasound and analyze the individual-bubble migration induced by the combined effects of pressure gradient and acoustic streaming.Our results indicate that the pressure threshold of stable and transient cavitation decreases with the increasing initial bubble radius.At the pressure antinode,the Bjerknes force dominates the bubble migration, resulting in the large bubbles gathering toward antinode center,whereas small bubbles escape from antinode.By contrast,at the pressure node,the bubble migration is primarily controlled by acoustic streaming,which effectively weakens the bubble adhesion on the container walls,thereby enhancing the cavitation effect in the whole liquid.     

含气泡液体中气泡振动的研究

研究了含气泡液体中单个气泡在驱动声场一定情况下的振动过程. 让每次驱动声场作用的时间特别短, 使气泡半径发生微小变化后再将其变化反馈到气泡群对驱动声场的散射作用中去, 从而可以得到某单个气泡周围受气泡散射影响后的声场, 接着再让气泡在该声场作用下做短时振动, 如此反复. 通过这样的方法, 研究了液体中单个气泡的振动情况并对其半径变化进行了数值模拟, 结果发现, 在液体中含有大量气泡的情况下, 某单个气泡的振动过程明显区别于液体中只有一个气泡的情况. 由于大量气泡和驱动声场的相互作用, 使气泡半径的变化存在多种不同的振动情况, 在不同的气泡大小和含量的情况下, 半径变化过程分别表现为: 在平衡位置附近振荡的过程; 周期性的空化过程; 一次空化过程后保持某一大小振荡的过程; 增长后维持某一大小振荡的过程等. 所以, 对于含气泡液体中气泡振动的研究, 在驱动声场一定的情况下, 必须考虑气泡含量的因素. 关键词： 含气泡液体 超声空化 散射 数值模拟     

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.     

球状泡群内气泡的耦合振动

振动气泡形成辐射场影响其他气泡的运动, 故多气泡体系中气泡处于耦合振动状态. 本文在气泡群振动模型的基础上, 考虑气泡间耦合振动的影响, 得到了均匀球状泡群内振动气泡的动力学方程, 以此为基础分析了气泡的非线性声响应特征. 气泡间的耦合振动增加了系统对每个气泡的约束, 降低了气泡的自然共振频率, 增强了气泡的非线性声响应. 随着气泡数密度的增加, 振动气泡受到的抑制增强; 增加液体静压力同样可抑制泡群内气泡的振动, 且存在静压力敏感区(1–2 atm, 1 atm=1.01325×10⁵ Pa); 驱动声波对气泡振动影响很大, 随着声波频率的增加, 能够形成空化影响的气泡尺度范围变窄. 在同样的声条件、泡群尺寸以及气泡内外环境下, 初始半径小于5 μm 的气泡具有较强的声响应. 气泡耦合振动会削弱单个气泡的空化影响, 但可延长多气泡系统空化泡崩溃发生的时间间隔和增大作用范围, 整体空化效应增强.     

Energy analysis during acoustic bubble oscillations: Relationship between bubble energy and sonochemical parameters

In this work, energy analysis of an oscillating isolated spherical bubble in water irradiated by an ultrasonic wave has been theoretically studied for various conditions of acoustic amplitude, ultrasound frequency, static pressure and liquid temperature in order to explain the effects of these key parameters on both sonochemistry and sonoluminescence. The Keller–Miksis equation for the temporal variation of the bubble radius in compressible and viscous medium has been employed as a dynamics model. The numerical calculations showed that the rate of energy accumulation, dE/dt, increased linearly with increasing acoustic amplitude in the range of 1.5–3.0 atm and decreased sharply with increasing frequency in the range 200–1000 kHz. There exists an optimal static pressure at which the power w is highest. This optimum shifts toward a higher value as the acoustic amplitude increases. The energy of the bubble slightly increases with the increase in liquid temperature from 10 to 60 °C. The results of this study should be a helpful means to explain a variety of experimental observations conducted in the field of sonochemistry and sonoluminescence concerning the effects of operational parameters.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller–Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 μm diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Bubble acoustical scattering cross section under multi-frequency acoustic excitation

The acoustical scattering cross section is usually employed to evaluate the scattering ability of the bubbles when they are excited by the incident acoustic waves. This parameter is strongly related to many important applications of performance prediction for search sonar or underwater telemetry, acoustical oceanography, acoustic cavitation, volcanology, and medical and industrial ultrasound. In the present paper, both the analytical and numerical analysis results of the acoustical scattering cross section of a single bubble under multi-frequency excitation are obtained. The nonlinear characteristics(e.g.,harmonics, subharmonics, and ultraharmonics) of the scattering cross section curve under multi-frequency excitation are investigated compared with single-frequency excitation. The influence of several paramount parameters(e.g., bubble equilibrium radius, acoustic pressure amplitude, and acoustic frequencies) in the multi-frequency system on the predictions of scattering cross section is discussed. It is shown that the combination resonances become significant in the multi-frequency system when the acoustic power is big enough, and the acoustical scattering cross section is promoted significantly within a much broader range of bubble sizes and acoustic frequencies due to the generation of more resonances.     

The role of the bubble–bubble interaction on radial pulsations of bubbles

Using a model that with or without considering the interaction between bubbles through the radiated pressure waves, numerical simulations of cavitation bubbles have been performed in order to study the effect of the bubble–bubble interaction on radial pulsations of bubbles. Comparing the results obtained by with or without considering the bubble–bubble interaction, it is suggested that the suppression or enlargement property of expansion ratios of bubbles due to the bubble–bubble interaction largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles (in multi-bubble environment, the last two aspects can be expressed using the coupling strength). The frequency response curve of expansion ratio decreases and shifts to left due to the bubble–bubble interaction and the larger the coupling strength is, the more the left-shifting is.     

Influence of rigid wall on the nonlinear pulsation of nearby bubble

This paper mainly focuses on the nonlinear pulsation of a bubble near the rigid wall. Dynamics of near-wall bubble and free bubble are discussed and compared in details. Investigation reveals as the driving acoustic pressure amplitude increases, nonlinear pulsation of bubble becomes intense gradually. Besides, decreasing the viscosity of host liquid is advantageous for the nonlinear pulsation of bubble. Bifurcation diagrams of bubble radius show acoustic reflection of the rigid wall makes the initial bifurcation appear at low driving acoustic amplitude and on bubble with small ambient radius, and makes the bifurcation still exist for bubble in high-viscosity liquids. That indicates the rigid wall will produce enhancement on the nonlinearity of nearby bubble. As the bubble approaches the wall, the enhancement becomes strong. Moreover, research on the influence of driving frequency shows the rigid wall makes the frequency band corresponding to chaos around the resonant frequency of free bubble shift downward.     

Phase transitions of perfluorocarbon nanoemulsion induced with ultrasound: A mathematical model

While ultrasound has been used in many medical and industrial applications, only recently has research been done on phase transformations induced by ultrasound. This paper presents a numerical model and the predicted results of the phase transformation of a spherical nanosized droplet of perfluorocarbon in water. Such a model has applications in acoustic droplet vaporization, the generation of gas bubbles for medical imaging, therapeutic delivery and other biomedical applications.The formation of a gas phase and the subsequent bubble dynamics were studied as a function of acoustic parameters, such as frequency and amplitude, and of the physical aspects of the perfluorocarbon nanodroplets, such as chemical species, temperature, droplet size and interfacial energy. The model involves simultaneous applications of mass, energy and momentum balances to describe bubble formation and collapse, and was developed and solved numerically. It was found that, all other parameters being constant, the maximum bubble size and collapse velocity increases with increasing ultrasound amplitude, droplet size, vapor pressure and temperature. The bubble size and collapse velocity decreased with increasing surface tension and frequency. These results correlate with experimental observations of acoustic droplet vaporization.     

Theoretical prediction of the yield of strong oxides under acoustic cavitation

Considering liquid viscosity, surface tension, and liquid compressibility, the effects of dynamical behaviors of cavitation bubbles on temperature and the amount of oxides inside the bubble are numerically investigated by acoustic field,regarding water as a work medium. The effects of acoustic frequency, acoustic pressure amplitude, and driving waveforms on bubble temperature and the number of oxides inside the bubbles by rapid collapse of cavitation bubbles are analysed.The results show that the changes of acoustic frequency, acoustic pressure amplitude, and driving waveforms not only have an effect on temperature and the number of oxides inside the bubble, but also influence the degradation species of pollution,which provides guidance for improving the degradation of water pollution.     

Dynamics of double bubbles under the driving of burst ultrasound

This paper investigates the pulsations and translation of bubbles in a double-bubble system driven by burst ultrasound. Results illustrate that for two identical bubbles, decreasing the frequency of burst or increasing its amplitude can enhance the pulsations and improve the translation velocities of bubbles. In a certain scope, large bubble brings about fast translation velocity, but the velocity will fall down for too large bubble, such as the bubble with ambient radius over about its resonance radius. When the ambient radii of two bubbles are different, translation of the large bubble is smaller than that of the small bubble. In addition, the effect of initial distance between bubbles is described as well. If burst serials are used, shortening the time interval between each burst and improving the acoustic amplitude of bursts are beneficial for the translations of bubbles.     

超声波声孔效应中气泡动力学的研究

在超声快速制取组织细胞病理切片的过程中，发现激励信号对切片制取效果有明显的影响.为了掌握超声激励信号对组织细胞的影响规律，达到快速制取病理切片的最佳状态，从气泡空化模型入手，通过改变激励信号频率、声压、气泡初始半径和液体黏滞系数等参量，研究了声孔效应中气泡动力学激励机制.数值计算表明：空化泡振动随激励声压增强而升高，随液体黏滞系数增强而减弱；一定频率范围内空化泡振动能保持在膨胀、收缩和振荡的稳定空化状态，存在空化泡稳态振动的最佳激励频率；一定初始半径能保证空化泡产生稳定的振动，存在空化泡稳态振动幅度最大的初始半径.实际操作中，在频率、声压、初始半径和黏滞系数综合作用的若干空化阈内，声孔效应使超声快速法制取细胞组织切片获得最佳效果. 关键词： 声孔效应 超声空化 气泡振动 稳态空化域     

Theoretical prediction of the scattering of spherical bubble clusters under ultrasonic excitation

Due to the nonlinear vibration of ultrasound contrast agent bubbles, a nonlinear scattered sound field will be generated when bubbles are driven by ultrasound. A bubble cluster consists of numerous bubbles gathering in a spherical space. It has been noted that the forward scattering of a bubble cluster is larger than its backscattering, and some studies have experimentally found the angular dependence of a bubble cluster’s scattering signal. In this paper, a theory is proposed to explain the difference of acoustic scattering at different directions of a bubble cluster when it is driven by ultrasound, and predicts the angular distribution of scattered acoustic pressure under different parameters. The theory is proved to be correct under circumstances of small clusters and weak interactions by comparing theoretical results with numerical simulations. This theory not only sheds light on the physics of bubble cluster scattering, but also may contribute to the improvement of ultrasound imaging technology, including ultrasonic harmonic imaging and contrast-enhanced ultrasonography.     

Theoretical estimation of sonochemical yield in bubble cluster in acoustic field

In order to learn more about the physical phenomena occurring in cloud cavitation, the nonlinear dynamics of a spherical cluster of cavitation bubbles and cavitation bubbles in cluster in an acoustic field excited by a square pressure wave are numerically investigated by considering viscosity, surface tension, and the weak compressibility of the liquid.The theoretical prediction of the yield of oxidants produced inside bubbles during the strong collapse stage of cavitation bubbles is also investigated. The effects of acoustic frequency, acoustic pressure amplitude, and the number of bubbles in cluster on bubble temperature and the quantity of oxidants produced inside bubbles are analyzed. The results show that the change of acoustic frequency, acoustic pressure amplitude, and the number of bubbles in cluster have an effect not only on temperature and the quantity of oxidants inside the bubble, but also on the degradation types of pollutants, which provides a guidance in improving the sonochemical degradation of organic pollutants.     

非水液体中由修正的刹管法所产生的瞬态单一空化气泡的发光研究

在除水之外的7种非水液体和甘油的水溶液中，用修正的刹管法产生了有效直径达厘米量级的较大的瞬态单一空化气泡，这些气泡在崩溃时几乎都产生不同强度的光辐射。在其中的6种液体中，其光辐射强度与该液体的饱和蒸汽压和粘度是相关的。但在乙二醇和丙二醇中的气泡发光并不遵循这个规律，两者中的气泡发光都很强，但乙二醇中的发光强度的变化显示出某种非通常的规律性。本文还对瞬态单一气泡与通常的稳态单一气泡的发光特性进行了比较。     

含气泡液体中的非线性声传播

考虑到分布在液体中的气泡是声波在含气泡液体中传播时引起非线性的一个很重要的因素,本文研究了声波在含气泡液体中的非线性传播.将气体含量的影响引入到声波在液体中传播的方程中,从而得到声波在气液混合物中传播的数学模型.通过对该模型进行数值模拟发现,气体含量、驱动声场声压幅值及驱动声场作用时间均会影响到气液混合物中的声场分布及声压幅值大小.液体中的气泡会"阻滞"液体中声场的传播并将能量"聚集"在声源附近.对于连续大功率的驱动声场来说,液体中的气泡会"阻滞"气液混合物中声场及其能量的传播.     

声场中双空化泡的运动特性

空化泡的运动特性是声场作用下的动力学行为,受空化泡初始半径,声压幅值,驱动声压频率,液体特性等众多因素的影响,是个复杂工程。本文从双空化泡运动方程出发,考虑到液体粘滞系数、空化泡辐射阻尼项的影响,研究了不同初始半径、驱动声压频率、驱动声压幅值、液体粘滞系数下空化泡泡壁的运动情况,研究结果表明不同初始半径、外界驱动声压频率、驱动声压幅值、液体粘滞系数均会对空化泡的膨胀比和空化泡的溃灭时间有一定影响。     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller-Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 mum diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.