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.     

II. Recirculation flow induced by a bubble stream rising in a viscous liquid

The recirculation flow induced by the rising motion of a bubble stream in a viscous fluid within an open-top rectangular enclosure is studied. The three-dimensional volume averaged conservation equations are solved by a control-volume method using a hybrid finite differencing scheme to describe the liquid phase hydrodynamics. The momentum exhange between the bubbles and the liquid phase is modeled with a source term equals to the volumetric buoyancy force acting on the gas in the bubble stream. The volumetric buoyancy force accounts for in line interactions between bubbles through the average gas volume fraction in the gas liquid column which depends on the size and the rising velocity of bubbles. The fluid flow within an open-top rectangular enclosure is further investigated by particle image velocimetry for a bubble stream rising in a water-glycerol solution. The measured fluid velocities in a vertical plane are compared with the predictions of the numerical model over a wide range of fluid viscosity (43 mPa s-800 mPa s) and gas flow rates. Finally, the recirculation flows resulting from the interaction of two neighbouring vertical bubble streams are studied. Received: 23 July 1997 / Revised: 19 December 1997 / Accepted: 11 May 1998     

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.     

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.     

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.     

非定常瞬态流动过程中的Lagrangian拟序结构与物质输运作用

从Lagrangian角度数值分析了圆柱瞬时起动过程中的非定常瞬态流动现象,如分离泡产生、破裂和涡脱落等及其产生的非定常效应,揭示了所列现象诱导的物质输运和迁移效应,首先采用双时间步长的特征线算子分裂算法数值模拟了圆柱起动过程中的瞬时流场,然后采用数值方法从流场中提取出Lagrangian拟序结构(LCSs),并根据非线性动力学理论研究了流动分离和旋涡演化过程中的物质输运作用,结果表明,圆柱瞬时起动后所产生的非定常阻力与相应瞬态现象中的物质输运有密切的关系:对称分离泡产生及其在流向方向的生长,能够使分离泡内压力升高且分布均匀,从而减小阻力;对称分离泡的失稳增强了分离泡与主流之间的物质输运作用,最终导致涡的脱落,并有利于推迟流动分离和减小分离区域,非定常流动中LCSs所描述的物质输运和迁移作用对流动控制的机理研究具有一定指导意义。     

Surface acoustic cavitation understood via nanosecond electrochemistry. Part III: Shear stress in ultrasonic cleaning

Acoustic cavitation is extensively used for cleaning purposes. However, little is known about the fundamental aspects of the cleaning process. Our previous electrochemical data suggested that acoustic bubbles were oscillating at a distance of only a few tens of nanometers above the surface [J. Phys. Chem. B 105 (2001) 12087; E. Maisonhaute, B.A. Brookes, R.G. Compton, J. Phys. Chem. B 106 (2002) 3166–3172]. The flow velocities resulting from the bubble collapse lead to important drag and shear forces on the surface, responsible for cleaning and/or eroding the latter. We review here the forces acting on an adsorbed particle located on the surface, and develop arguments to explain why small adsorbates are harder to remove by sonication. Then, experimental results on particle desorption and surface effects brought about by ultrasound are presented and shown to agree with our theoretical predictions.     

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.     

Visualization and minimization of disruptive bubble behavior in ultrasonic field

Although ultrasonic technology has been successfully adopted for semiconductor cleaning, a recent trend of extreme miniaturization of patterns calls for a novel process that can remove contaminant particles without damaging nanoscale patterns. Unstable bubble oscillations have been hypothesized to cause such surface damages, and here we show direct visualization results that a high acoustic pressure induces bubble instability leading to pattern damages. As a remedy for the conventional ultrasonic cleaning scheme, we introduce a novel cleaning system using dual transducers, in which one transducer generates bubbles with a high acoustic pressure in an acoustically isolated sub-chamber and the other drives the oscillation of bubbles around the cleaning area at a low acoustic pressure. The system is shown to achieve a high cleaning efficiency for submicron-sized particles while significantly suppressing the disruptive bubble instability thereby reducing the detachment of firmly attached nanoparticles. Comparison of the adhesion force of the firmly attached nanoparticles and the yield strength of nanopatterns allows us to anticipate that this scheme is capable of reducing damages of nanopatterns on semiconductor wafers and photomasks.     

Flow of an electrically conducting bubble liquid in the field of an electromagnetic force

Physical processes accompanying the flow of a conducting bubble liquid in crossed electric and magnetic fields are considered. Based on the general equations of mechanics of multiphase media, we develop a one-dimensional model of the flow of and heat exchange in a compressible bubble liquid when the phases are not in thermal and velocity equilibrium. The model is numerically investigated. It is demonstrated that, when the bubble liquid flows along the electromagnetic force vector, the bubbles lag behind the carrying flow and are compressed and warmed up. This causes oscillations of the bubble volume, as well as oscillations of the parameters of both the disperse and carrying phase. In particular, the compression of the bubbles reduces the volumetric gas content, as well as increases the effective conductivity of the flow and the electromagnetic force in the downstream direction. This sets conditions for crisis of the bubble flow when the electromagnetic force expels the bubbles against the main stream. On the basis of the solutions obtained, the efficiency of a gas compressor is calculated.     

Interaction of a bubble and a bubble cluster in an ultrasonic field

Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.     

Circular motion of submillimeter-sized acoustic bubbles attached to a boundary by high-speed image analysis

The circular motion of submillimeter-sized bubbles attached to a boundary in an 18.5 kHz ultrasonic field are investigated experimentally by high-speed photography and image analysis. It is found that the vibration of gas bubbles with diameters of 0.2–0.4 mm is between spherical radial vibration and regular surface fluctuation. Different from the circular motion of suspended bubbles in water, the circular motion of gas bubbles attached to a boundary presents some new characteristics. These bubbles attached to a boundary (wandering bubbles) will rotate around a fixed bubble array (holding bubbles). Both the wondering bubbles and holding bubbles are “degas” bubbles. The primary Bjerknes force acting on wandering bubbles in the acoustic wave field and the secondary Bjerknes force between the wandering bubbles and the holding bubbles strongly affects the circular motion. The circling and residence behavior of gas bubbles is described and analyzed in detail, which is helpful to understand and improve industrial applications such as ultrasonic cleaning, sonochemical treatment, aeration and cavitation reduction.     

Modeling of surface cleaning by cavitation bubble dynamics and collapse

Surface cleaning using cavitation bubble dynamics is investigated numerically through modeling of bubble dynamics, dirt particle motion, and fluid material interaction. Three fluid dynamics models; a potential flow model, a viscous model, and a compressible model, are used to describe the flow field generated by the bubble all showing the strong effects bubble explosive growth and collapse have on a dirt particle and on a layer of material to remove. Bubble deformation and reentrant jet formation are seen to be responsible for generating concentrated pressures, shear, and lift forces on the dirt particle and high impulsive loads on a layer of material to remove. Bubble explosive growth is also an important mechanism for removal of dirt particles, since strong suction forces in addition to shear are generated around the explosively growing bubble and can exert strong forces lifting the particles from the surface to clean and sucking them toward the bubble. To model material failure and removal, a finite element structure code is used and enables simulation of full fluid–structure interaction and investigation of the effects of various parameters. High impulsive pressures are generated during bubble collapse due to the impact of the bubble reentrant jet on the material surface and the subsequent collapse of the resulting toroidal bubble. Pits and material removal develop on the material surface when the impulsive pressure is large enough to result in high equivalent stresses exceeding the material yield stress or its ultimate strain. Cleaning depends on parameters such as the relative size between the bubble at its maximum volume and the particle size, the bubble standoff distance from the particle and from the material wall, and the excitation pressure field driving the bubble dynamics. These effects are discussed in this contribution.     

The two-phase flow at gas-evolving electrodes: Bubble-driven and Lorentz-force-driven convection

We observe electrolysis with gas evolution, a phenomenon occurring in a number of industrial scale electrochemical processes. Here, water electrolysis takes place in a small undivided electrolysis cell consisting of vertical electrodes embedded in a larger glass vessel which contains a dilute NaOH solution. Fluid flow velocities are measured by particle image velocimetry with fluorescent tracers, while size distribution and velocities of the bubbles are determined from bubble shadow images obtained with a high speed camera. Coalescence phenomena are observed in the flow and explain the relatively wide distribution of bubble sizes. Depending on the gap width and the current density, bubbles ascending near the electrodes form two discernible bubble curtains (low average void fraction, wide gaps) or a flow profile more akin to a channel flow (high average void fraction, small gaps). If the flow consists of separate bubble curtains, instabilities develop not unlike to those of a single phase wall jet. Finally, the influence of different wall parallel Lorentz force configurations on the velocity distribution in the cell is investigated. These Lorentz forces are generated by permanent magnets mounted behind the electrodes. Depending on gap width, current density, and magnet configuration, liquid phase velocities can be increased by several times compared to the baseline case.     

Numerical analysis of the effect of bubble distribution on multiple-bubble behavior

Understanding multiple-bubble behavior in a megasonic field is essential for efficient megasonic nanodevice cleaning without pattern damage. In this study, we numerically studied the effects of equilibrium radius and initial void fraction on multiple-bubble behavior and induced pressure. We analyzed the nonspherical collapse, coalescence, and breakup of bubbles in a megasonic field using a compressible, locally homogeneous model of a gas-liquid two-phase medium. Bubbles were simulated with a uniform equilibrium radius or with a bubble size distribution. Our results indicate that the bubble behavior and induced pressure depended mainly on the initial void fraction. For the case of bubbles with uniform equilibrium radius, small bubbles generated high wall pressure at large initial void fractions. When there was a size distribution, bubbles with small equilibrium radii contributed little to the wall pressure because of the damping effect of the oscillation of larger bubbles. Furthermore, the addition of a large bubble suppressed the resonant behavior of the bubbles that induced high wall pressure.     

Characterization of an acoustic cavitation bubble structure at 230 kHz

A generic bubble structure in a 230 kHz ultrasonic field is observed in a partly developed standing wave field in water. It is characterized by high-speed imaging, sonoluminescence recordings, and surface cleaning tests. The structure has two distinct bubble populations. Bigger bubbles (much larger than linear resonance size) group on rings in planes parallel to the transducer surface, apparently in locations of driving pressure minima. They slowly rise in a jittering, but synchronous way, and they can have smaller satellite bubbles, thus resembling the arrays of bubbles observed by Miller [D. Miller, Stable arrays of resonant bubbles in a 1-MHz standing-wave acoustic field, J. Acoust. Soc. Am. 62 (1977) 12]. Smaller bubbles (below and near linear resonance size) show a fast "streamer" motion perpendicular to and away from the transducer surface. While the bigger bubbles do not emit light, the smaller bubbles in the streamers show sonoluminescence when they pass the planes of high driving pressure. Both bubble populations exhibit cleaning potential with respect to micro-particles attached to a glass substrate. The respective mechanisms of particle removal, though, might be different.     

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.     

Qualitative and quantitative flow visualization of bubble motions in a plane bubble plume

Overall, as well as individual, bubble behavior of a plane bubble plume which is confined by two parallel plates is investigated by means of several qualitative and quantitative flow visualization methods. These include observation, measurement of time-averaged void distribution, surface tufts and particle imaging velocimetry. Several kinds of unstable motion of the bubble convection, which depend on the free surface initial height and on the gas flow rate, are observed. The bubble motion along the bubble plume is precisely measured by an image-processing method which also delivers velocity vectors, number density and size of the bubbles.     

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.     

Physical forces exerted by microbubbles on a surface in a traveling wave field

The effect of a wave with a varying traveling component on the bubble activity as well as the physical force generated by microbubbles on a surface has been studied. The acoustic emission from a collection of bubbles is measured in a 928 kHz sound field. Particle removal tests on a surface, which actually measures the applied physical force by the bubbles on that surface, indicate a very strong dependence on the angle of incidence. In other words, when the traveling wave component is maximized, the average physical force applied by microbubbles reaches a maximum. Almost complete particle removal for 78 nm silica particles was obtained for a traveling wave, while particle removal efficiency was reduced to only a few percent when a standing wave was applied. This increase in particle removal for a traveling wave is probably caused by a decrease in bubble trapping at nodes and antinodes in a standing wave field.