Numerical investigation of the translational motion of bubbles: The comparison of capabilities of the time-resolved and the time-averaged methods

In the present study, the accuracies of two different numerical approaches used to model the translational motion of acoustic cavitational bubble in a standing acoustic field are compared. The less accurate but less computational demanding approach is to decouple the equation of translational motion from the radial oscillation, and solve it by calculating the time-averaged forces exerted on the bubble for one acoustic cycle. The second approach is to solve the coupled ordinary differential equations directly, which provides more accurate results with higher computational effort. The investigations are carried out in the parameter space of the driving frequency, pressure amplitude and equilibrium radius. Results showed that both models are capable to reveal stable equilibrium positions; however, in the case of oscillatory solutions, the difference in terms of translational frequency may be more than three fold, and the amplitude of translational motion obtained by the time-averaged method is roughly 1.5 times higher compared to the time-resolved solution at particular sets of parameters. This observation implies that where the transient behaviour is important, the time-resolved approach is the proper choice for reliable results.     

An inverse method to fast-track the calculation of phase diagrams for sonoluminescing bubbles

A sound driven air bubble can be transformed into an argon bubble emitting light pulses stably. The very foundation to investigate the sonoluminescing bubble is to accurately determine the ambient radius and gas composition in the interior. The conventional approach is to model the air-to-argon transformation process through a large number of bubble dynamics simulations to obtain the physical parameters of the ultimate argon bubble. In this paper, we propose a highly efficient method to pinpoint this information in a phase diagram. The method is based on the diffusive equilibrium for each species inside the bubble and derives the ambient radius and composition inversely. To calculate the former parameter, the bisection algorithm is employed to consecutively narrow down the searching range until the equilibria is approached. Afterward, several cycles of full dynamics simulations are conducted to refine the composition. The method is validated using published experimental data. The calculated ambient radii deviate from the test results by less than 1 μm, which falls within the margin of measurement error. The advantages of this method over the semi-analytical approach reported by Hilgenfeldt et al. [J. Fluid Mech. 365 (1998)] are also discussed. Our study provides a standard procedure to calculate the ambient radius and composition and is beneficial for the numerical simulation of sonoluminescing bubbles.     

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     

声场中气泡群的动力学特性

以水为工作介质,考虑了液体的轻微可压缩性,研究了声场中气泡群的动力学特性,对单一型和混合型气泡群内微泡的初始半径、气泡的数目及声频率和声压对气泡动力学特性进行了数值研究．分析了各参数对气泡运动特性和气泡崩溃时所产生压力脉冲的影响．研究了单一型气泡群内气泡动力学的混沌特性,分析了气泡处于混沌特性下两次崩溃压力脉冲特征,结果表明：适合的参数有利于提高声空化处理效果．     

Effect of nonlinear translations on the pulsation of cavitation bubbles

The pulsations and translations of cavitation bubbles obey combined ordinary differential equations, and their nonlinearities are studied by the bifurcation diagram and the phase diagram in a strong ultrasonic field. Bubble pulsation can change regularly or irregularly with changing driving pressure in the time domain. The bifurcation diagrams of the pulsation versus driving pressure show that the pulsations and translations of bubbles have nonlinear characteristics, and the nonlinear translations of bubbles can disorder the pulsations for certain parameters. Disorder of the pulsation can also be caused by nonlinear pulsation itself. In addition, the phase diagrams also show that the nonlinear translations make a large contribution to the pulsations. The same result can also be obtained when the ambient radii of two bubbles are different.     

Air bubbles under vertical vibrations

This paper reports on an experimental study of the splitting instability of an air bubble a few centimetres in diameter placed in a sealed cylindrical cell filled with liquid and submitted to vertical oscillations. The response of the bubble to the oscillations is observed with a high-speed video camera. It is found that the bubble dynamics is closely associated with the acceleration of the cell Γ. For small acceleration values, the bubble undergoes minor shape deformations. With increasing acceleration values, these deformations are amplified and for sufficiently large Γ the bubble becomes toroidal. The bubble may then become unstable and split into smaller parts. The onset of bubble division is studied and its dependency on physical parameters such as the fluid viscosity, the fluid surface tension and the initial size of the bubble is presented. It is found that the criterion for the bubble splitting process is associated with a threshold based on the acceleration of the oscillations. Above this threshold, the number of bubbles present in the cell is observed to grow until a final steady state is reached. Data analysis reveals that the final bubble size may be characterized in terms of Bond number.     

Nonlinear dynamics and acoustic emissions of interacting cavitation bubbles in viscoelastic tissues

The cavitation-mediated bioeffects are primarily associated with the dynamic behaviors of bubbles in viscoelastic tissues, which involves complex interactions of cavitation bubbles with surrounding bubbles and tissues. The radial and translational motions, as well as the resultant acoustic emissions of two interacting cavitation bubbles in viscoelastic tissues were numerically investigated. Due to the bubble–bubble interactions, a remarkable suppression effect on the small bubble, whereas a slight enhancement effect on the large one were observed within the acoustic exposure parameters and the initial radii of the bubbles examined in this paper. Moreover, as the initial distance between bubbles increases, the strong suppression effect is reduced gradually and it could effectively enhance the nonlinear dynamics of bubbles, exactly as the bifurcation diagrams exhibit a similar mode of successive period doubling to chaos. Correspondingly, the resultant acoustic emissions present a progressive evolution of harmonics, subharmonics, ultraharmonics and broadband components in the frequency spectra. In addition, with the elasticity and/or viscosity of the surrounding medium increasing, both the nonlinear dynamics and translational motions of bubbles were reduced prominently. This study provides a comprehensive insight into the nonlinear behaviors and acoustic emissions of two interacting cavitation bubbles in viscoelastic media, it may contribute to optimizing and monitoring the cavitation-mediated biomedical applications.     

High-speed imaging of ultrasound driven cavitation bubbles in blind and through holes

The interest in application of ultrasonic cavitation for cleaning and surface treatment processes has increased greatly in the last decades. However, not much is known about the behavior of cavitation bubbles inside the microstructural features of the solid substrates. Here we report on an experimental study on dynamics of acoustically driven (38.5 kHz) cavitation bubbles inside the blind and through holes of PMMA plates by using high-speed imaging. Various diameters of blind (150, 200, 250 and 1000 µm) and through holes (200 and 1000 µm) were investigated. Gas bubbles are usually trapped in the holes during substrate immersion in the liquid thus preventing their complete wetting. We demonstrate that trapped gas can be successfully removed from the holes under ultrasound agitation. Besides the primary Bjerknes force and acoustic streaming, the shape oscillations of the trapped gas bubble seem to be a driving force for bubble removal out of the holes. We further discuss the bubble dynamics inside microholes for water and Cu²⁺ salt solution. It is found that the hole diameter and partly the type of liquid media influences the number, size and dynamics of the cavitation bubbles. The experiments also showed that a large amount of the liquid volume inside the holes can be displaced within one acoustic cycle by the expansion of the cavitation bubbles. This confirmed that ultrasound is a very effective tool to intensify liquid exchange processes, and it might significantly improve micro mixing in small structures. The investigation of the effect of ultrasound power on the bubble density distribution revealed the possibility to control the cavitation bubble distribution inside the microholes. At a high ultrasound power (31.5 W) we observed the highest bubble density at the hole entrances, while reducing the ultrasound power by a factor of ten shifted the bubble locations to the inner end of the blind holes or to the middle of the through holes.     

Dynamics of cavitational bubbles and design of a hydrodynamic cavitational reactor: cluster approach

In the present work, a cavity cluster of predetermined size has been considered to study the bubble dynamics in the hydrodynamic cavitation reactor. The effect of different operating and system parameters on the cavitational intensity has been numerically investigated. The yield of any cavitationally induced physical/chemical transformations depends not only on the collapse pressure of the cavities but also on the active volume of cavitation within the reactor. Empirical correlations have been developed to predict the collapse pressure and the active volume of cavitation as a function of different operating parameters based on the bubble dynamics studies. Recommendations are made for designing a cavitational reactor on the basis of the proposed empirical correlations. This work is a first step towards the designing and optimization of hydrodynamic cavitational reactor with cluster approach.     

无阀微泵腔内气泡对周期驱动压力的影响

气泡的存在使无阀微泵的工作性能和使用寿命大大降低, 甚至无法正常工作. 为了合理地预测无阀微泵腔内气泡对周期驱动压力的影响, 给出了用来描述收缩管/扩张管型无阀压电微泵的数学模型, 包括泵腔体积变化、连续性方程、流体有效体积弹性模量以及锥管阻力系数的计算. 同时, 分析了腔内不同气泡体积对无阀微泵周期驱动压力的影响, 并对两个气泡进入无阀微泵泵腔时压力脉动过程进行了仿真和试验研究. 通过仿真结果与试验数据的比较表明, 所提出的存在气泡时无阀微泵数学模型及仿真方法是合理的. 关键词： 无阀微泵 气泡 压力脉动     

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.     

Experimental studies of bubble dynamics inside a corner

The dynamics of a bubble near a corner formed by two flat rigid boundaries (walls), is studied experimentally using a spark-generated bubble. The expansion, collapse, rebound, re-collapse and migration of the bubble, along with jetting and protrusion, are captured using a high-speed camera. Our experimental observations reveal the behaviour of the bubble in terms of the corner angle and the dimensionless standoff distances to the near and far walls in terms of the maximum bubble radius. The bubble remains approximately spherical during expansion except for its surface becoming flattened when in close proximity to a wall. When a bubble is initiated at the bisector of the two walls, the bubble becomes oblate along the bisector during the late stages of collapse. A jet forms towards the end of collapse, pointing to the corner. The closer the bubble to the two walls, the more oblate along the bisector the bubble becomes, and the wider the jet. A bubble initiated near one of the two walls is mainly influenced by the nearer wall. The jet formed is pointing to the near wall but inclined towards the corner. After the jet penetrates through the bubble surface, the bubble becomes a bubble ring, and a bubble protrusion forms following the jet. The bubble ring collapses and subsequently disappears, while the protrusion firstly expands, and then collapses and migrates to the corner.     

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。     

The effect of bulk viscosity on single bubble dynamics and sonoluminescence

In our previous paper, we derived a new single bubble model including the effect of bulk viscosity. To confront it to experiments, single bubble dynamics was measured here in 30% (v/v) glycerol-water mixture under different acoustic amplitudes and compared to models including or not the effect of bulk viscosity. The results showed that calculated bubble dynamics were not significantly affected by the bulk viscosity within the experimental conditions used in this study. However, there was a noticeable delay for the first rebound when bulk viscosity was considered. The corresponding sonoluminescence intensities were collected and compared with theoretical predictions. The results did not allow to discriminate between the two models (one includes the effect of bulk viscosity, the other does not), confirming the negligible effect of bulk viscosity in this condition (30% (v/v) glycerol-water mixture). Due to the instability of a single bubble in higher viscosity solutions, we could not implement experiments that can discriminate between the two models.     

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.     

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.     

Dynamics and measurement of cavitation bubble

Based on the introduction of international progress, our investigations on acoustic cavitation have been reported. Firstly we considered the cavity’s dynamics under the drive of the asymmetrical acoustic pressure. An aspheric dynamical model was proposed and a new stable and aspheric solution was found in numerical simulation of the theoretical framework of the aspheric model. Then, a dual Mie-scattering technique was developed to measure the cavity’s aspheric pulsation. A significant asynchronous pulsation signal between two Mie-scattering channels was caught in the case of large cavity driven by low acoustic pressure. As a direct deduction, we observed an evidence of cavity’s aspheric pulsation. Furthermore, we studied the dependency of the asynchronous pulsation signal on the various parameters, such as the amplitude and frequency of the driving acoustic pressure, and the surface tension, viscosity and gas concentration of the liquid. Finally, we introduced a new numeric imaging technique to measure the shapes of the periodic pulsation cavities. The time-resolution was in the order of 20 ns, one order of magnitude lower than that in the previous work, say, 200 ns.