Bubble population phenomena in acoustic cavitation

Theoretical treatments of the dynamics of a single bubble in a pressure field have been undertaken for many decades. Although there is still scope for progress, there now exists a solid theoretical basis for the dynamics of a single bubble. This has enabled useful classifications to be established, including the distinction between stable cavitation (where a bubble pulsates for many cycles) and transient cavitation (where the bubble grows extensively over time-scales of the order of the acoustic cycle, and then undergoes an energetic collapse and subsequent rebound and then, potentially, either fragmentation, decaying oscillation or a repeat performance). Departures from sphericity, such as shape and surface oscillations and jetting, have also been characterized. However, in most practical systems involving high-energy cavitation (such as those involving sonochemical, biological and erosive effects), the bubbles do not behave as the isolated entities modelled by this single-bubble theory: the cavitational effect may be dominated by the characteristics of the entire bubble population, which may influence, and be influenced by, the sound field.

The well established concepts that have resulted from the single-bubble theory must be reinterpreted in teh light of the bubble population, an appreciation of population mechanisms being necessary to apply our understanding of single-bubble theory to many practical applications of ‘power’ ultrasound. Even at a most basic level these single-bubble theories describe the response of the bubble to the local sound field at the position of the bubble, and that pressure field will be influenced by the way sound is scattered by neighbouring bubbles. The influence of the bubble population will often go further, a non-uniform sound field creating an inhomogeneous bubble distribution. Such a distribution can scatter, channel and focus ultrasonic beams, can acoustically shield regions of the sample, and elsewhere localize the cavitational activity to discrete ‘hot spots’. As a result, portions of the sample may undergo intense sonochemical activity, degassing, erosion, etc., whilst other areas remain relatively unaffected. Techniques exist to control such situations where they are desirable, and to eliminate this localization where a more uniform treatment of the sample is desired.     

Spatial-temporal dynamics of cavitation bubble clouds in 1.2 MHz focused ultrasound field

Cavitation bubbles have been recognized as being essential to many applications of ultrasound. Temporal evolution and spatial distribution of cavitation bubble clouds induced by a focused ultrasound transducer of 1.2 MHz center frequency are investigated by high-speed photography. It is revealed that at a total acoustic power of 72 W the cavitation bubble cloud first emerges in the focal region where cavitation bubbles are observed to generate, grow, merge and collapse during the initial 600 μs. The bubble cloud then grows upward to the post-focal region, and finally becomes visible in the pre-focal region. The structure of the final bubble cloud is characterized by regional distribution of cavitation bubbles in the ultrasound field. The cavitation bubble cloud structure remains stable when the acoustic power is increased from 25 W to 107 W, but it changes to a more violent form when the acoustic power is further increased to 175 W.     

Observations of the collapses and rebounds of millimeter-sized lithotripsy bubbles

Bubbles excited by lithotripter shock waves undergo a prolonged growth followed by an inertial collapse and rebounds. In addition to the relevance for clinical lithotripsy treatments, such bubbles can be used to study the mechanics of inertial collapses. In particular, both phase change and diffusion among vapor and noncondensable gas molecules inside the bubble are known to alter the collapse dynamics of individual bubbles. Accordingly, the role of heat and mass transport during inertial collapses is explored by experimentally observing the collapses and rebounds of lithotripsy bubbles for water temperatures ranging from 20 to 60 °C and dissolved gas concentrations from 10 to 85% of saturation. Bubble responses were characterized through high-speed photography and acoustic measurements that identified the timing of individual bubble collapses. Maximum bubble diameters before and after collapse were estimated and the corresponding ratio of volumes was used to estimate the fraction of energy retained by the bubble through collapse. The rebounds demonstrated statistically significant dependencies on both dissolved gas concentration and temperature. In many observations, liquid jets indicating asymmetric bubble collapses were visible. Bubble rebounds were sensitive to these asymmetries primarily for water conditions corresponding to the most dissipative collapses.     

The characterization of acoustic cavitation bubbles - an overview

Acoustic cavitation, in simple terms, is the growth and collapse of preexisting microbubbles under the influence of an ultrasonic field in liquids. The cavitation bubbles can be characterized by the dynamics of oscillations and the maximum temperatures and pressures reached when they collapse. These aspects can be studied both experimentally and theoretically for a single bubble system. However, in a multibubble system, the formation of bubble streamers and clusters makes it difficult to characterize the cumulative properties of these bubbles. In this overview, some recently developed experimental procedures for the characterization of acoustic cavitation bubbles have been discussed.     

Quantitative observations of cavitation activity in a viscoelastic medium

Quantitative experimental observations of single-bubble cavitation in viscoelastic media that would enable validation of existing models are presently lacking. In the present work, single bubble cavitation is induced in an agar gel using a 1.15 MHz high intensity focused ultrasound transducer, and observed using a focused single-element passive cavitation detection (PCD) transducer. To enable quantitative observations, a full receive calibration is carried out of a spherically focused PCD system by a bistatic scattering substitution technique that uses an embedded spherical scatterer and a hydrophone. Adjusting the simulated pressure received by the PCD by the transfer function on receive and the frequency-dependent attenuation of agar gel enables direct comparison of the measured acoustic emissions with those predicted by numerical modeling of single-bubble cavitation using a modified Keller-Miksis approach that accounts for viscoelasticity of the surrounding medium. At an incident peak rarefactional pressure near the cavitation threshold, period multiplying is observed in both experiment and numerical model. By comparing the two sets of results, an estimate of the equilibrium bubble radius in the experimental observations can be made, with potential for extension to material parameter estimation. Use of these estimates yields good agreement between model and experiment.     

Controlled cavitation in microfluidic systems

We report on cavitation in confined microscopic environments which are commonly called microfluidic or lab-on-a-chip systems. The cavitation bubble is created by focusing a pulsed laser into these structures filled with a light-absorbing liquid. At the center of a 20 microm thick and 1 mm wide channel, pancake-shaped bubbles expand and collapse radially. The bubble dynamics compares with a two-dimensional Rayleigh model and a planar flow field during the bubble collapse is measured. When the bubble is created close to a wall a liquid jet is focused towards the wall, resembling the jetting phenomenon in axisymmetry. The jet flow creates two counter-rotating vortices which stir the liquid at high velocities. For more complex geometries, e.g., triangle- and square-shaped structures, the number of liquid jets recorded correlates with the number of boundaries close to the bubble.     

Characterisation of the acoustic cavitation cloud by two laser techniques

An experimental investigation of the size and volumetric concentration of acoustic cavitation bubbles is presented. The cavitation bubble cloud is generated at 20 kHz by an immersed horn in a rectangular glass vessel containing bi-distilled water. Two laser techniques, laser diffraction and phase Doppler interferometry, are implemented and compared. These two techniques are based on different measuring principles. The laser diffraction technique analyses the light pattern scattered by the bubbles along a line-of-sight of the experimental vessel (spatial average). The phase Doppler technique is based on the analysis of the light scattered from single bubbles passing through a set of interference fringes formed by the intersection of two laser beams: bubble size and velocity distributions are extracted from a great number of single-bubble events (local and temporal average) but only size distributions are discussed here. Difficulties arising in the application of the laser diffraction technique are discussed: in particular, the fact that the acoustic wave disturbs the light scattering patterns even when there are no cavitation bubbles along the measurement volume. As a consequence, a procedure has been developed to correct the raw data in order to get a significant bubble size distribution. After this data treatment has been applied the results from the two measurement techniques show good agreement. Under the emitter surface, the Sauter mean diameter D(3, 2) is approximately 10 microm by phase Doppler measurement and 7.5 microm by laser diffraction measurement at 179 W. Note that the mean measured diameter is much smaller than the resonance diameter predicted by the linear theory (about 280 microm). The influence of the acoustic power is investigated. Axial and radial profiles of mean bubble diameters and void fraction are also presented.     

The acoustic emissions of cavitation bubbles in stretched vortices

Pairs of unequal strength, counter-rotating vortices were produced in order to examine the inception, dynamics, and acoustic emission of cavitation bubbles in rapidly stretching vortices. The acoustic signatures of these cavitation bubbles were characterized during their inception, growth, and collapse. Growing and collapsing bubbles often produced a sharp, broadband, pop sound. The spectrum of these bubbles, and the peak resonant frequency can generally be related to quiescent flow bubble dynamics and corresponding resonant frequencies. However, some elongated cavitation bubbles produced a short tonal burst, or chirp, with frequencies on the order of a few kilohertz. Theses frequencies are too low to be related to resonant frequencies of a bubble in a quiescent flow. Instead, the frequency content of the acoustic signal during bubble inception and growth is related to the volumetric oscillations of the bubble while it interacted with vortical flow that surrounds the bubble (i.e., the resonant frequency of the vortex-bubble system). A relationship was determined between the observed peak frequency of the oscillations, the highly stretched vortex properties, and the water nuclei content. It was found that different cavitation spectra could relate to different flow and fluid properties and therefore would not scale in the same manner.     

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.     

Enhancement of oscillation amplitude of cavitation bubble due to acoustic wake effect in multibubble environment

Acoustic cavitation occurs in ultrasonic treatment causing various phenomena such as chemical synthesis, chemical decomposition, and emulsification. Nonlinear oscillations of cavitation bubbles are assumed to be responsible for these phenomena, and the neighboring bubbles may interact each other. In the present study, we numerically investigated the dynamic behavior of cavitation bubbles in multi-bubble systems. The results reveal that the oscillation amplitude of a cavitation bubble surrounded by other bubbles in a multi-bubble system becomes larger compared with that in the single-bubble case. It is found that this is caused by an acoustic wake effect, which reduces the pressure near a bubble surrounded by other bubbles and increases the time delay between the bubble contraction/expansion cycles and sound pressure oscillations. A new parameter, called “cover ratio” is introduced to quantitatively evaluate the variation in the bubble oscillation amplitude, the time delay, and the maximum bubble radius.     

A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound

Cavitation often occurs in therapeutic applications of medical ultrasound such as shock-wave lithotripsy (SWL) and high-intensity focused ultrasound (HIFU). Because cavitation bubbles can affect an intended treatment, it is important to understand the dynamics of bubbles in this context. The relevant context includes very high acoustic pressures and frequencies as well as elevated temperatures. Relative to much of the prior research on cavitation and bubble dynamics, such conditions are unique. To address the relevant physics, a reduced-order model of a single, spherical bubble is proposed that incorporates phase change at the liquid-gas interface as well as heat and mass transport in both phases. Based on the energy lost during the inertial collapse and rebound of a millimeter-sized bubble, experimental observations were used to tune and test model predictions. In addition, benchmarks from the published literature were used to assess various aspects of model performance. Benchmark comparisons demonstrate that the model captures the basic physics of phase change and diffusive transport, while it is quantitatively sensitive to specific model assumptions and implementation details. Given its performance and numerical stability, the model can be used to explore bubble behaviors across a broad parameter space relevant to therapeutic ultrasound.     

Effects of medium viscoelasticity on bubble collapse strength of interacting polydisperse bubbles

Due to its physical and/or chemical effects, acoustic cavitation plays a crucial role in various emerging applications ranging from advanced materials to biomedicine. The cavitation bubbles usually undergo oscillatory dynamics and violent collapse within a viscoelastic medium, which are closely related to the cavitation-associated effects. However, the role of medium viscoelasticity on the cavitation dynamics has received little attention, especially for the bubble collapse strength during multi-bubble cavitation with the complex interactions between size polydisperse bubbles. In this study, modified Gilmore equations accounting for inter-bubble interactions were coupled with the Zener viscoelastic model to simulate the dynamics of multi-bubble cavitation in viscoelastic media. Results showed that the cavitation dynamics (e.g., acoustic resonant response, nonlinear oscillation behavior and bubble collapse strength) of differently-sized bubbles depend differently on the medium viscoelasticity and each bubble is affected by its neighboring bubbles to a different degree. More specifically, increasing medium viscosity drastically dampens the bubble dynamics and weakens the bubble collapse strength, while medium elasticity mainly affects the bubble resonance at which the bubble collapse strength is maximum. Differently-sized bubbles can achieve resonances and even subharmonic resonances at high driving acoustic pressures as the elasticity changes to certain values, and the resonance frequency of each bubble increases with the elasticity increasing. For the interactions between the size polydisperse bubbles, it indicated that the largest bubble generally has a dominant effect on the dynamics of smaller ones while in turn it is almost unaffected, exhibiting a pattern of destructive and constructive interactions. This study provides a valuable insight into the acoustic cavitation dynamics of multiple interacting polydisperse bubbles in viscoelastic media, which may offer a potential of controlling the medium viscoelasticity to appropriately manipulate the dynamics of multi-bubble cavitation for achieving proper cavitation effects according to the desired application.     

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.     

声场中水力空化泡的动力学特性

以水为工作介质,考虑了液体黏性、表面张力、可压缩性及湍流作用等情况,对文丘里管反应器中空化泡在声场作用下的动力学行为特性进行了数值研究.分析了超声波频率、声压及喉径比对空化泡运动特性以及空化泡崩溃时所形成泡温以及压力脉冲的影响.结果表明,超声将水力空化泡运动调制成稳态空化,有利于增强空化效果. 关键词： 超声波 水力空化 湍流 气泡动力学     

Optical cavitation probe using light scattering from bubble clouds

To understand the behaviour of systems containing clouds of bubbles (multibubble system) in real sonochemical reactors, a new diagnosis method, i.e., optical cavitation probe (OCP), has been proposed. When a laser beam is introduced into the cavitation bubble cloud, the scattered light intensity changes by the collective oscillation of cavitation bubbles. The frequency domain spectrum of the scattered light contains rich information on the cavitation bubble clouds, comparable with the acoustic emission spectra detected by a hydrophone. The significant merits of OCP, such as capability for spatially resolved, non-invasive measurement of the cavitation bubble clouds, robustness even in a violent cavitation field have been experimentally demonstrated.     

Effect of static pressure on acoustic energy radiated by cavitation bubbles in viscous liquids under ultrasound

The effect of static pressure on acoustic emissions including shock-wave emissions from cavitation bubbles in viscous liquids under ultrasound has been studied by numerical simulations in order to investigate the effect of static pressure on dispersion of nano-particles in liquids by ultrasound. The results of the numerical simulations for bubbles of 5 μm in equilibrium radius at 20 kHz have indicated that the optimal static pressure which maximizes the energy of acoustic waves radiated by a bubble per acoustic cycle increases as the acoustic pressure amplitude increases or the viscosity of the solution decreases. It qualitatively agrees with the experimental results by Sauter et al. [Ultrason. Sonochem. 15, 517 (2008)]. In liquids with relatively high viscosity (～200 mPa s), a bubble collapses more violently than in pure water when the acoustic pressure amplitude is relatively large (～20 bar). In a mixture of bubbles of different equilibrium radius (3 and 5 μm), the acoustic energy radiated by a 5 μm bubble is much larger than that by a 3 μm bubble due to the interaction with bubbles of different equilibrium radius. The acoustic energy radiated by a 5 μm bubble is substantially increased by the interaction with 3 μm bubbles.     

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.     

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.     

Modeling of interaction between therapeutic ultrasound propagation and cavitation bubbles

In medical applications of high intense focused ultrasound the mechanism of interaction between ultrasound waves and cavitation bubbles is responsible for several therapeutic effects as well as for undesired side effects. Based on a two-phase continuum approach for bubbly liquids, in this paper a numerical model is presented to simulate these interactions. The numerical results demonstrate the influence of the cavitation bubble cloud on ultrasound propagation. In the case of a lithotripter pulse an increased bubble density leads to significant changes in the tensile part of the pressure waveform. The calculations are verified by measurements with a fiber optical hydrophone and by experimental results of the bubble cloud dynamics.