The Rayleigh-like collapse of a conical bubble

Key to the dynamics of the type of bubble collapse which is associated with such phenomena as sonoluminescence and the emission of strong rebound pressures into the liquid is the role of the liquid inertia. Following the initial formulation of the collapse of an empty spherical cavity, such collapses have been termed "Rayleigh-like." Today this type of cavitation is termed "inertial," reflecting the dominant role of the liquid inertia in the early stages of the collapse. While the inertia in models of spherical bubble collapses depends primarily on the liquid, experimental control of the liquid inertia has not readily been achievable without changing the liquid density and, consequently, changing other liquid properties. In this paper, novel experimental apparatus is described whereby the inertia at the early stages of the collapse of a conical bubble can easily be controlled. The collapse is capable of producing luminescence. The similarity between the collapses of spherical and conical bubbles is investigated analytically, and compared with experimental measurements of the gas pressures generated by the collapse, the bubble wall speeds, and the collapse times.     

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.     

A dual passive cavitation detector for localized detection of lithotripsy-induced cavitation in vitro

A passive cavitation detector (PCD) identifies cavitation events by sensing acoustic emissions generated by the collapse of bubbles. In this work, a dual passive cavitation detector (dual PCD), consisting of a pair of orthogonal confocal receivers, is described for use in shock wave lithotripsy. Cavitation events are detected by both receivers and can be localized to within 5 mm by the nature of the small intersecting volume of the focal areas of the two receivers in association with a coincidence detection algorithm. A calibration technique, based on the impulse response of the transducer, was employed to estimate radiated pressures at collapse near the bubble. Results are presented for the in vitro cavitation fields of both a clinical and a research electrohydraulic lithotripter. The measured lifetime of the primary growth-and-collapse of the cavitation bubbles increased from 180 to 420 microseconds as the power setting was increased from 12 to 24 kV. The measured lifetime compared well with calculations based on the Gilmore-Akulichev formulation for bubble dynamics. The radiated acoustic pressure 10 mm from the collapsing cavitation bubble was measured to vary from 4 to 16 MPa with increasing power setting; although the trends agreed with calculations, the predicted values were four times larger than measured values. The axial length of the cavitation field correlated well with the 6-dB region of the acoustic field. However, the width of the cavitation field (10 mm) was significantly narrower than the acoustic field (25 mm) as bubbles appeared to be drawn to the acoustic axis during the collapse. The dual PCD also detected signals from "rebounds," secondary and tertiary growth-and-collapse cycles. The measured rebound time did not agree with calculations from the single-bubble model. The rebounds could be fitted to a Rayleigh collapse model by considering the entire bubble cloud as an effective single bubble. The results from the dual PCD agreed well with images from high-speed photography. The results indicate that single-bubble theory is sufficient to model lithotripsy cavitation dynamics up to time of the main collapse, but that upon collapse bubble cloud dynamics becomes important.     

激光空泡在文丘里管中运动的动力学特性

以水为工作介质,在不同文丘里管入口压力下,利用YAG激光器产生的激光轰击水中的金属靶材产生空泡,借助高速摄像系统记录激光空泡在文丘里管中的运动过程,并采用流体动力学模拟对文丘里管中的流场特性和空泡的溃灭特性进行分析.结果表明:激光空泡在文丘里管中的运动,其形状变化可分为产生阶段、挤压阶段、溃灭初始阶段和溃灭阶段等四个阶段.空泡的溃灭取决于流场状态,当流动为层流时,空泡不发生溃灭;当流动为湍流时,空泡发生溃灭,且湍流程度越剧烈,溃灭现象越显著.搭建的激光空泡生成与运动系统能够实现空泡的定点溃灭.     

Collapse dynamics of smectic-A bubbles

The collapse dynamics of smectic-A bubbles are analyzed experimentally and theoretically. Each bubble is expanded from a flat film stretched at the end of a hollow cylinder and deflated through a pressure release by means of a capillary tube. Its total collapse time can be varied between 0.1s and 20s by suitably choosing the length and the internal diameter of the capillary. This experiment allowed us to show that the collapse takes place in two steps: an initial one, which lasts a fraction of a second, where the meniscus destabilizes and fills up with focal conics, followed by a much longer period during which the bubble collapses and exchanges material with the meniscus. By measuring simultaneously the Laplace pressure and the internal pressure inside the bubble, we were able to fully characterize the shear-thinning behavior of the smectic phase within the meniscus. We emphasize that this method is generic and could be applied as well to other systems such as soap bubbles, on condition that inertial effects are negligible.     

Multiple observations of cavitation cluster dynamics close to an ultrasonic horn tip

Bubble dynamics in water close to the tip of an ultrasonic horn (～23 kHz, 3 mm diameter) have been studied using electrochemistry, luminescence, acoustics, light scattering, and high-speed imaging. It is found that, under the conditions employed, a large bubble cluster (～1.5 mm radius) exists at the tip of the horn. This cluster collapses periodically every three to four cycles of the fundamental frequency of the horn. Following the collapse of the cluster, a short-lived cloud of small bubbles (each tens of microns in diameter) was observed in the solution. Large amplitude pressure emissions are also recorded, which correlate temporally with the cluster collapse. Bursts of surface erosion (measured in real time using an electrochemical technique) and multibubble sonoluminescence emission both also occur at a subharmonic of the fundamental frequency of the horn and are temporally correlated with the bubble cluster collapse and the associated pressure wave emission.     

Bubble creation and collapse during excimer laser ablation of weak absorbing polymers

We present evidence suggesting that XeCl laser ablation of a weakly absorbing poly-methyl-methacrylate (PMMA) polymer, done by chemical, thermal bond breaking of the polymer chain or optical breakdown of the material, which involves plasma generation, creates a cloud of small asymmetric near the surface bubbles, which subsequently expand and aggregate during the same laser pulse duration or in subsequent pulses depending on the laser pulse energy. When a critical volume is reached each bubble collapses in a high pressure and temperature central point and rebounds ejecting a hot jet of material on the non-irradiated area of the polymer and creating craters on the surface. A characteristic bipolar pressure wave corresponding to the bubble collapse, explosion and rebound is observed. The number density of the craters on the surface is a function of the laser pulse sequence number and the laser pulse energy density.     

Numerical investigation of shock-induced bubble collapse dynamics and fluid–solid interactions during shock-wave lithotripsy

In this paper we investigate the bubble collapse dynamics under shock-induced loading near soft and rigid bio-materials, during shock wave lithotripsy. A novel numerical framework was developed, that employs a Diffuse Interface Method (DIM) accounting for the interaction across fluid–solid-gas interfaces. For the resolution of the extended variety of length scales, due to the dynamic and fine interfacial structures, an Adaptive Mesh Refinement (AMR) framework for unstructured grids was incorporated. This multi-material multi-scale approach aims to reduce the numerical diffusion and preserve sharp interfaces. The presented numerical framework is validated for cases of bubble dynamics, under high and low ambient pressure ratios, shock-induced collapses, and wave transmission problems across a fluid–solid interface, against theoretical and numerical results. Three different configurations of shock-induced collapse applications near a kidney stone and soft tissue have been simulated for different stand-off distances and bubble attachment configurations. The obtained results reveal the detailed collapse dynamics, jet formation, solid deformation, rebound, primary and secondary shock wave emissions, and secondary collapse that govern the near-solid collapse and penetration mechanisms. Significant correlations of the problem configuration to the overall collapse mechanisms were found, stemming from the contact angle/attachment of the bubble and from the properties of solid material. In general, bubbles with their center closer to the kidney stone surface produce more violent collapses. For the soft tissue, the bubble movement prior to the collapse is of great importance as new structures can emerge which can trap the liquid jet into induced crevices. Finally, the tissue penetration is examined for these cases and a novel tension-driven tissue injury mechanism is elucidated, emanating from the complex interaction of the bubble/tissue interaction during the secondary collapse phase of an entrapped bubble in an induced crevice with the liquid jet.     

Role of the channel geometry on the bubble pinch-off in flow-focusing devices

The formation of bubbles by flow focusing of a gas and a liquid in a rectangular channel is shown to depend strongly on the channel aspect ratio. Bubble breakup consists in a slow linear 2D collapse of the gas thread, ending in a fast 3D pinch-off. The 2D collapse is predicted to be stable against perturbations of the gas-liquid interface, whereas the 3D pinch-off is unstable, causing bubble polydispersity. During 3D pinch-off, a scaling w_(m) approximately tau(1/3) between the neck width w_(m) and the time tau before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity.     

Dependence of the characteristics of bubbles on types of sonochemical reactors

Computer simulations of bubble oscillations in liquid water irradiated by an ultrasonic wave have revealed that the characteristic of bubbles depends on types of sonochemical reactors: a horn-type reactor and a standing-wave type reactor. When the acoustic amplitude is large at 20 kHz, the bubble content is mostly water vapor even at the end of the bubble collapse and the temperature inside a bubble at the collapse is relatively low. On the other hand, when the acoustic amplitude is relatively low, the bubble content is mostly noncondensable gas at the end of the bubble collapse and the bubble temperature is relatively high. In a horn-type sonochemical reactor, the former type of bubbles are dominant because many bubbles exist near the horn-tip where the acoustic amplitude is large, while in a standing-wave type reactor the latter type of bubbles are dominant because the Bjerknes force gathers bubbles at a region where acoustic amplitude is relatively low.     

Bubble proliferation in the cavitation field of a shock wave lithotripter

Lithotripter shock waves (SWs) generated in non-degassed water at 0.5 and 2 Hz pulse repetition frequency (PRF) were characterized using a fiber-optic hydrophone. High-speed imaging captured the inertial growth-collapse-rebound cycle of cavitation bubbles, and continuous recording with a 60 fps camcorder was used to track bubble proliferation over successive SWs. Microbubbles that seeded the generation of bubble clouds formed by the breakup of cavitation jets and by bubble collapse following rebound. Microbubbles that persisted long enough served as cavitation nuclei for subsequent SWs, as such bubble clouds were enhanced at fast PRF. Visual tracking suggests that bubble clouds can originate from single bubbles.     

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.     

Interaction between phases in the liquid–gas system

This work analyzes the equilibrium between a liquid and a gas over this liquid separated by an interface. Various gas forms exist inside the liquid: dissolved gas molecules attached to solvent molecules, free gas molecules, and gaseous bubbles. Thermodynamic equilibrium is maintained between two phases; the first phase is the liquid containing dissolved and free molecules, and the second phase is the gas over the liquid and bubbles inside it. Kinetics of gas transition between the internal and external gas proceeds through bubbles and includes the processes of bubbles floating up and bubble growth as a result of association due to the Smoluchowski mechanism. Evolution of a gas in the liquid is considered using the example of oxygen in water, and numerical parameters of this system are given. In the regime under consideration for an oxygen–water system, transport of oxygen into the surrounding air proceeds through micron-size bubbles with lifetimes of hours. This regime is realized if the total number of oxygen molecules in water is small compared with the numbers of solvated and free molecules in the liquid.     

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.     

螺旋桨空化噪声连续谱仿真算法

螺旋桨空化噪声连续谱由大量空泡随机崩溃所辐射噪声叠加而成。据此,考虑到空泡初始崩溃时刻的随机性和各空泡辐射噪声频谱的相似性,对四种情况空化辐射噪声连续谱特性分别进行了理论分析表明,可依据空泡半径和初始崩溃时间的统计性质,采用蒙特卡罗方法对空化噪声连续谱波形进行仿真建模,模型参数为空泡半径期望值、差异度和随机度,分别相应于确定辐射噪声的基准波形、各空泡噪声频谱相似程度和大量空泡的随机崩溃过程。该方法输入参数物理意义明确,控制简单,能较好地仿真空化噪声连续谱的特性,仿真结果与理论分析吻合较好。     

Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results.

The propagation of ultrasound through a liquid induces the growth of inceptions and germs into bubbles. In a low frequency reactor, fragmentary transient bubbles emerge due to the acoustic driving. They violently collapse in one cycle and fragment into many smaller bubbles than in turn cavitate. This violent collapse is responsible for the mechanical effects of ultrasounds effects. The latter bubbles gather in a ball-shaped cloud and migrate to pressure antinodes. During their migration, their nonexplosive collapses mainly contribute to activate chemical reactions by producing OH. radicals. Mathematical modelling is performed as a new approach to predict the bubbles field. Through numerical simulation, we determinate emergence sites of mechanically active cavitation bubbles. Calculus are compared with aluminium foil degradation. The modelling of bubble migration allow us to have an insight on the privileged sites of the chemical reactions. Validation of the modelling is made through direct comparison with chemiluminescence photo. All experiments and computations are made in a 28.2 kHz sonoreactor.     

Time-resolved measurements of shock-induced cavitation bubbles in liquids

A novel experimental method for the measurement of cavitation bubble dynamics is presented. The method makes use of a collimated cw HeNe laser beam that is focused onto a photodiode. A cavitation bubble centered in the laser beam leads to refraction and thus changes the diode signal. With sufficient temporal resolution of the measurement, the evolution of the bubble dynamics, and in particular, the collapse, could be well resolved (limitation is only due to diode response and oscilloscope bandwidth). In the present work this is demonstrated with cavitation bubbles generated with high-power nanosecond and femtosecond laser pulses, respectively. Bubble evolution is studied in two different liquids (water and glycerine) and at different temperatures and pressures.     

Liquid compressibility effects during the collapse of a single cavitating bubble

The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied. While it is known that compressibility damps the amplitude of bubble rebounds, the extent to which this effect is accurately captured by weakly compressible versions of the Rayleigh-Plesset equation is unclear. To clarify this issue, partial differential equations governing conservation of mass, momentum, and energy are numerically solved both inside the bubble and in the surrounding compressible liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured. Results obtained with Rayleigh-Plesset type equations accounting for compressibility effects, proposed by Keller and Miksis [J. Acoust. Soc. Am. 68, 628-633 (1980)], Gilmore, and Tomita and Shima [Bull. JSME 20, 1453-1460 (1977)], are compared with those resulting from the full model. For strong collapses, the solution of the latter reveals that an important part of the energy concentrated during the collapse is used to generate an outgoing pressure wave. For the examples considered in this research, peak pressures are larger than those predicted by Rayleigh-Plesset type equations, whereas the amplitudes of the rebounds are smaller.     

Collective oscillations of fresh and salt water bubble plumes

Bubble plumes of various void fractions and sizes were produced by varying the flow velocity of a water jet impinging normally on a water surface. The bubbles entrained at the surface were carried downwards by the fluid flow to depths ranging from 33 to 65 cm, and formed roughly cylindrical plumes with diameters ranging from 12 to 27 cm. The acoustic emissions from the plumes were recorded onto digital audio tape using a hydrophone placed outside the cloud at distances ranging from 50 cm to 16.0 m. Closeup video images of the individual bubbles within the plume were also taken in order to gain knowledge of the bubble size distributions. The experiments were performed in both fresh-water and salt-water environments. The fresh-water clouds emitted sounds with a modal structure that was significantly different from that produced by the salt-water clouds. Furthermore, the smaller bubbles present in the salt-water clouds have a fundamental effect on the amplification of turbulence noise, generating sound at significant levels for frequencies up to several hundred Hertz.