Collective bubble dynamics near a surface in a weak acoustic standing wave field

The transport of bubbles to a neighboring surface is very important in surface chemistry, bioengineering, and ultrasonic cleaning, etc. This paper proposes a multi-bubble transport method by using an acoustic standing wave field and establishes a model that explains the multi-bubble translation by expressing the balance between Bjerknes forces and hydrodynamic forces on a bubble in a liquid medium. Results indicated that the influence of primary Bjerknes force, secondary Bjerknes force, and buoyancy force on the bubble translation depends on the position of the target bubble in the acoustic field. Moreover, it was found that increasing the size of a bubble or pressure amplitude can accelerate the bubble motion and enhance the bubble-bubble interaction. The secondary Bjerknes force between two bubbles can switch from an attractive one when they oscillate in phase to a repulsive one when the bubble oscillations are out of phase. These findings provide an insight into the multi-bubble translation near a surface and can be applied to future bubble motion control studies, especially in drug delivery, sonoporation, and ultrasonic cleaning.     

Toward efficient interactions of bubbles and coal particles induced by stable cavitation bubbles under 600 kHz ultrasonic standing waves

The interactions of bubbles and coal particles in 600 kHz ultrasonic standing waves (USW) field has been investigated. A high-speed camera was employed to record the phenomena occurred under the USW treatment. The formation and behaviors of cavitation bubbles were analyzed. Under the driving of these cavitation bubbles, whose size is from several microns to dozens of microns, coal particles were aggregated and then attracted by large bubbles due to the acoustic radiation forces. The results of USW-assisted flotation show a significant improvement in recoveries at 600 kHz, which indicates that the interactions of bubbles and particles in the USW field are more efficient than that in the conventional gravitational field. Furthermore, the sound pressure distribution of the USW was measured and predicted by a hydrophone. The analysis of gravity and buoyancy, primary and secondary Bjerknes forces shows that bubble-laden particles can be attracted by the rising bubbles under large acoustic forces. This study highlights the potential for USW technology to achieve efficient bubble-particle interactions in flotation.     

Interaction of two bubbles with distortion in an acoustic field

Expression of the secondary Bjerknes force of two bubbles is obtained by considering the distrotion of two bubbles. The secondary Bjerknes forces in different acoustic fields are simulated, and the influence factors are analyzed and discussed. It is shown that the distortion of a bubble has an important influence on the interaction of two bubbles. The strength and even the directions of the secondary Bjerknes force of two bubbles with distortion differ considerably from the predictions of the sherical symmetry theory. The results show that when two bubbles oscillated stably in an acoustic field, the secondary Bjerknes force of two bubbles with distortion is several times more than that of two spherical bubbles in the same condition. The secondary Bjerknes force of two bubble with distortion has more interaction distance than that of two spherical bubbles. The secondary Bjerknes force of two bubbles with distortion depends on the distance of two bubbles, the shape mode of two bubbles, the equilibrium radii of two bubbles and the driving acoustic filed. The nonspherical distortion effects of the secondary Bjerknes has an importance on understanding the structure formation of bubbles and evolution process of bubble group in an acoustic field.     

An Euler–Lagrange method considering bubble radial dynamics for modeling sonochemical reactors

Unsteady numerical computations are performed to investigate the flow field, wave propagation and the structure of bubbles in sonochemical reactors. The turbulent flow field is simulated using a two-equation Reynolds-Averaged Navier–Stokes (RANS) model. The distribution of the acoustic pressure is solved based on the Helmholtz equation using a finite volume method (FVM). The radial dynamics of a single bubble are considered by applying the Keller–Miksis equation to consider the compressibility of the liquid to the first order of acoustical Mach number. To investigate the structure of bubbles, a one-way coupling Euler–Lagrange approach is used to simulate the bulk medium and the bubbles as the dispersed phase. Drag, gravity, buoyancy, added mass, volume change and first Bjerknes forces are considered and their orders of magnitude are compared. To verify the implemented numerical algorithms, results for one- and two-dimensional simplified test cases are compared with analytical solutions. The results show good agreement with experimental results for the relationship between the acoustic pressure amplitude and the volume fraction of the bubbles. The two-dimensional axi-symmetric results are in good agreement with experimentally observed structure of bubbles close to sonotrode.     

Study on the bubble transport mechanism in an acoustic standing wave field

The use of bubbles in applications such as surface chemistry, drug delivery, and ultrasonic cleaning etc. has been enormously popular in the past two decades. It has been recognized that acoustically-driven bubbles can be used to disturb the flow field near a boundary in order to accelerate physical or chemical reactions on the surface. The interactions between bubbles and a surface have been studied experimentally and analytically. However, most of the investigations focused on violently oscillating bubbles (also known as cavitation bubble), less attention has been given to understand the interactions between moderately oscillating bubbles and a boundary. Moreover, cavitation bubbles were normally generated in situ by a high intensity laser beam, little experimental work has been carried out to study the translational trajectory of a moderately oscillating bubble in an acoustic field and subsequent interactions with the surface. This paper describes the design of an ultrasonic test cell and explores the mechanism of bubble manipulation within the test cell. The test cell consists of a transducer, a liquid medium and a glass backing plate. The acoustic field within the multi-layered stack was designed in such a way that it was effectively one dimensional. This was then successfully simulated by a one dimensional network model. The model can accurately predict the impedance of the test cell as well as the mode shape (distribution of particle velocity and stress/pressure field) within the whole assembly. The mode shape of the stack was designed so that bubbles can be pushed from their injection point onto a backing glass plate. Bubble radial oscillation was simulated by a modified Keller–Miksis equation and bubble translational motion was derived from an equation obtained by applying Newton’s second law to a bubble in a liquid medium. Results indicated that the bubble trajectory depends on the acoustic pressure amplitude and initial bubble size: an increase of pressure amplitude or a decrease of bubble size forces bubbles larger than their resonant size to arrive at the target plate at lower heights, while the trajectories of smaller bubbles are less influenced by these factors. The test cell is also suitable for testing the effects of drag force on the bubble motion and for studying the bubble behavior near a surface.     

Saser (Sound Amplification by Stimulated Emission of Radiation)

A theoretical scheme of a saser (Sound Amplification by Stimulated Emission of Radiation) is proposed. A liquid with gas bubbles is used as the active medium. Pumping is performed with an alternating electric field or mechanical vibrations of the resonator. Phase bunching of initially incoherent radiators (bubbles) occurs under the action of acoustic radiation forces. The proposed scheme is similar to that of a free-electron laser. Two models of an active medium are studied. In the first model it is assumed that all bubbles have the same radius. In the second model a continuous distribution of bubble radii is studied. The starting values for sasers with square and cylindrical resonators are calculated. It is shown that in all cases studied these conditions are identical, to within a numerical factor. The operation of a saser in a nonlinear regime and the directional pattern of a saser in the saturation regime are studied. Zh. Tekh. Fiz. 67, 92–100 (April 1997)     

Effect of dissolved gases in water on acoustic cavitation and bubble growth rate in 0.83 MHz megasonic of interest to wafer cleaning

Changes in the cavitation intensity of gases dissolved in water, including H₂, N₂, and Ar, have been established in studies of acoustic bubble growth rates under ultrasonic fields. Variations in the acoustic properties of dissolved gases in water affect the cavitation intensity at a high frequency (0.83 MHz) due to changes in the rectified diffusion and bubble coalescence rate. It has been proposed that acoustic bubble growth rates rapidly increase when water contains a gas, such as hydrogen faster single bubble growth due to rectified diffusion, and a higher rate of coalescence under Bjerknes forces. The change of acoustic bubble growth rate in rectified diffusion has an effect on the damping constant and diffusivity of gas at the acoustic bubble and liquid interface. It has been suggested that the coalescence reaction of bubbles under Bjerknes forces is a reaction determined by the compressibility and density of dissolved gas in water associated with sound velocity and density in acoustic bubbles. High acoustic bubble growth rates also contribute to enhanced cavitation effects in terms of dissolved gas in water. On the other hand, when Ar gas dissolves into water under ultrasound field, cavitation behavior was reduced remarkably due to its lower acoustic bubble growth rate. It is shown that change of cavitation intensity in various dissolved gases were verified through cleaning experiments in the single type of cleaning tool such as particle removal and pattern damage based on numerically calculated acoustic bubble growth rates.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

An acoustic switch

The benefits derived from the development of acoustic transistors which act as switches or amplifiers have been reported in the literature. Here we propose a model of acoustic switch. We theoretically demonstrate that the device works: the input signal is totally restored at the output when the switch is on whereas the output signal nulls when the switch is off. The switch, on or off, depends on a secondary acoustic field capable to manipulate the main acoustic field. The model relies on the attenuation effect of many oscillating bubbles on the main travelling wave in the liquid, as well as on the capacity of the secondary acoustic wave to move the bubbles. This model evidences the concept of acoustic switch (transistor) with 100% efficiency.     

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.     

方波驱动下双气泡的动力学行为*

探索方波驱动下双气泡的脉动规律,能够促进方波在声空化工程中的实际应用。本文通过数值求解双气泡耦合方程组,研究了方波驱动下双气泡的动力学行为,得到了多种条件下不同时刻两个气泡半径的数值,并以此计算出气泡间的次Bjerknes力。研究表明,增大驱动频率会使得两个气泡膨胀时能达到的最大半径和次Bjerknes力减小。当两个气泡的平衡半径不同时,其中一个气泡的剧烈收缩会使得另一个气泡产生一个振动方向相反的声脉冲。随着两个气泡平衡半径差距的增加,气泡收缩的时间间隔增大。此外,当驱动声压幅值逐渐增大时,气泡脉动规律也会发生很大的变化。     

Sonoluminescence and dynamics of cavitation bubble populations in sulfuric acid

The detailed link of liquid phase sonochemical reactions and bubble dynamics is still not sufficiently known. To further clarify this issue, we image sonoluminescence and bubble oscillations, translations, and shapes in an acoustic cavitation setup at 23 kHz in sulfuric acid with dissolved sodium sulfate and xenon gas saturation. The colour of sonoluminescence varies in a way that emissions from excited non-volatile sodium atoms are prominently observed far from the acoustic horn emitter (“red region”), while such emissions are nearly absent close to the horn tip (“blue region”). High-speed images reveal the dynamics of distinct bubble populations that can partly be linked to the different emission regions. In particular, we see smaller strongly collapsing spherical bubbles within the blue region, while larger bubbles with a liquid jet during collapse dominate the red region. The jetting is induced by the fast bubble translation, which is a consequence of acoustic (Bjerknes) forces in the ultrasonic field. Numerical simulations with a spherical single bubble model reproduce quantitatively the volume oscillations and fast translation of the sodium emitting bubbles. Additionally, their intermittent stopping is explained by multistability in a hysteretic parameter range. The findings confirm the assumption that bubble deformations are responsible for pronounced sodium sonoluminescence. Notably the observed translation induced jetting appears to serve as efficient mixing mechanism of liquid into the heated gas phase of collapsing bubbles, thus potentially promoting liquid phase sonochemistry in general.     

Modeling non-spherical oscillations and stability of acoustically driven shelled microbubbles

The oscillation and destruction of microbubbles under ultrasound excitation form the basis of contrast enhanced ultrasound imaging and microbubble assisted drug and gene delivery. A typical microbubble has a size of a few micrometers and consists of a gas core encapsulated by a shell. These bubbles can be driven into surface mode oscillations, which not only contribute to the measured acoustic signal but can lead to bubble destruction. Existing models of surface model oscillations have not considered the effects of a bubble shell. In this study a model was developed to study the surface mode oscillations in shelled bubbles. The effects of shell viscosity and elasticity on the surface mode oscillations were modeled using a Boussinesq-Scriven approach. Simulation was conducted using the model with various bubble sizes and driving acoustic pressures. The occurrence of surface modes and the number of ultrasound cycles needed for the occurrence were calculated. The simulation results show a significant difference between shelled bubbles and shell free bubbles. The shelled bubbles have reduced surface mode amplitudes and a narrower bubble size range within which these modes develop compared to shell free bubbles. The clinical implications were also discussed.     

非球形效应对强声场中次Bjerknes力的影响

考虑了非球形气泡在声场中的形状振动,推导了非球形气泡和球形气泡之间的次Bjerknes力方程,数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力,并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明:当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时,在第一个声驱动周期内,非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大,在大小上是两个球形气泡次Bjerkens力的数倍,且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.     

Cone-like bubble formation in ultrasonic cavitation field

A new phenomenon in ultrasonic cavitation field is reported. Cavitation bubbles are observed to self-arrange in a cone-like macrostructure in the vicinity of transducer radiating surface. The cone-like macrostructure is stable while its branch-like pattern microstructure changes rapidly. The structure is constituted by moving bubbles which undergo attractive and repulsive Bjerknes forces caused by high acoustic pressure gradients and strongly nonlinear oscillations of cavitation bubbles. The cone-like bubble structure is a chemically active formation. Its remarkably high activity is confirmed by chemiluminescence experiments.     

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.     

Trapping cavitation bubbles with a self-focused laser beam

We observed that laser-induced cavitation bubbles in water can be trapped in a self-focused laser beam. Both optical imaging and acoustic detection have been utilized to confirm bubble trapping. Transverse and longitudinal trapping forces were measured to be as large as 87 and 11 pN, respectively. This result is contrary to conventional wisdom, since the mechanism of trapping in conventional optical tweezers implies that a low-index particle (a bubble being the limiting case) should be antitrapped.     

Physical and chemical effects of acoustic cavitation in selected ultrasonic cleaning applications

Acoustic cavitation in a liquid medium generates several physical and chemical effects. The oscillation and collapse of cavitation bubbles, driven at low ultrasonic frequencies (e.g., 20 kHz), can generate strong shear forces, microjets, microstreaming and shockwaves. Such strong physical forces have been used in cleaning and flux improvement of ultrafiltration processes. These physical effects have also been shown to deactivate pathogens. The efficiency of deactivation of pathogens is not only dependent on ultrasonic experimental parameters, but also on the properties of the pathogens themselves. Bacteria with thick shell wall are found to be resistant to ultrasonic deactivation process. Some evidence does suggest that the chemical effects (radicals) of acoustic cavitation are also effective in deactivating pathogens. Another aspect of cleaning, namely, purification of water contaminated with organic and inorganic pollutants, has also been discussed in detail. Strong oxidising agents produced within acoustic cavitation bubbles could be used to degrade organic pollutants and convert toxic inorganic pollutants to less harmful substances. The effect of ultrasonic frequency and surface activity of solutes on the sonochemical degradation efficiency has also been discussed in this overview.     

同步双脉冲激光致声研究

利用高速摄像机拍摄了同步双脉冲激光聚焦击穿水介质产生激光空泡的运动过程。分析了该条件下产生的四种典型激光声信号特性,初步计算了光声能量转换效率。研究结果表明:通过调节脉冲激光的能量差,可以控制激光声信号峰值间隔,提高激光声信号脉宽;两空泡之间无量纲距离为1.5时,溃灭过程中出现融合现象,融合过程中空泡热力学能转化为机械能,融合后形成的单个空泡能量变大,其溃灭产生的激光声信号主频降低;同步双脉冲激光聚焦击穿情况下的光声能量转换效率为6%~10%。     

A method for estimating time-dependent acoustic cross-sections of bubbles and bubble clouds prior to the steady state

Models for the acoustic cross-sections of gas bubbles undergoing steady-state pulsation in liquid have existed for some time. This article presents a theoretical scheme for estimating the cross-sections of single bubbles, and bubble clouds, from the start of insonation onward. In this period the presence of transients can significantly alter the cross-section from the steady-state value. The model combines numerical solutions of the Herring-Keller model with appropriate damping values to calculate the extinction cross-section of a bubble as a function of time in response to a continuous harmonic sound field (it is also shown how the model can be adapted to estimate the time-dependent scatter cross-section). The model is then extended to determine the extinction cross-section area of multiple bubbles of varying population distributions assuming no bubble-bubble interactions. The results have shown that the time taken to reach steady state is dependent on the closeness of the bubble to resonance, and on the driving pressure amplitude. In the response of the population as a whole, the time to reach steady state tends to decrease with increasing values of the driving pressure amplitude; and with the increasing values of the ratio of the numbers of bubbles having radii much larger than resonance to the number of resonant bubbles. The implications of these findings for the use of acoustic pulses are explored.