A two-dimensional nonlinear model for the generation of stable cavitation bubbles

Bubbles appear by acoustic cavitation in a liquid when rarefaction pressures attain a specific threshold value in a liquid. Once they are created, the stable cavitation bubbles oscillate nonlinearly and affect the ultrasonic field. Here we present a model developed for the study of bubble generation in a liquid contained in a two-dimensional cavity in which a standing ultrasonic field is established. The model considers dissipation and dispersion due to the bubbles. It also assumes that both the ultrasonic field and the bubble oscillations are nonlinear. The numerical experiments predict where the bubbles are generated from a population of nuclei distributed in the liquid and show how they affect the ultrasonic field.     

两种气泡混合的声空化

将非线性声波方程和改进的Rayleigh-Plesset方程联立可以描述空化环境中的声场及相应的气泡动力学特征. 用时域有限差分方法模拟了圆柱形容器内两种气泡相互混合时的空化情况. 在烧杯内的稳态背景声场形成过程中, 瓶壁耗散吸收扮演了重要的角色. 在稳态背景声场的基础上, 分析了混合气泡与声场的相互作用、气泡之间的相互作用、混合情况下的频谱特性. 结果表明: 两种气泡平衡半径都不太大时, 气泡与声场的相互作用不强, 声场及气泡的行为也比较规律; 相反, 当其中一种气泡平衡半径相对比较大时, 声场与气泡具有较强的非线性相互作用, 声场及气泡的行为表现出复杂的特性.     

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.     

Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.     

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.     

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.     

Generation and control of acoustic cavitation structure

The generation and control of acoustic cavitation structure are a prerequisite for application of cavitation in the field of ultrasonic sonochemistry and ultrasonic cleaning. The generation and control of several typical acoustic cavitation structures (conical bubble structure, smoker, acoustic Lichtenberg figure, tailing bubble structure, jet-induced bubble structures) in a 20–50 kHz ultrasonic field are investigated. Cavitation bubbles tend to move along the direction of pressure drop in the region in front of radiating surface, which are the premise and the foundation of some strong acoustic cavitation structure formation. The nuclei source of above-mentioned acoustic cavitation structures is analyzed. The relationship and mutual transformation of these acoustic cavitation structures are discussed.     

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.     

Selective aggregation by ultrasonic standing waves through gas nuclei on the particle surface

Gas nuclei in water are usually too small to be directly observed. They will grow into bubbles under the negative pressure, which is called cavitation (heterogeneous cavitation). In this study, the gas nuclei in the hydrophilic and hydrophobic silica particle suspension were investigated using the transient cavitation threshold measured by a high-intensity focused ultrasound (HIFU). The transient cavitation bubbles were also observed by a high-speed camera. The results showed that the nuclei only exist on the surface of hydrophobic particles. Furthermore, the aggregation experiments revealed that the aggregates were only formed in the hydrophobic silica suspension by ultrasonic standing waves (USW) at 200 kHz. This distinct difference was mainly due to the formation of gas nuclei on hydrophobic silica particles, which grew and coalesced into stable bubbles under the 200 kHz USW. The aggregation process in suspension was observed by a CCD camera. Moreover, the cavitation thresholds and acoustic radiation forces were analyzed to explain the mechanism of the acoustic aggregation. This study showed a very promising acoustic method for the selective aggregation of hydrophobic particles, which might be efficiently used in the mineral separation industry.     

Ultrasonic cavitation at liquid/solid interface in a thin Ga–In liquid layer with free surface

Cavitation in thin layer of liquid metal has potential applications in chemical reaction, soldering, extraction, and therapeutic equipment. In this work, the cavitation characteristics and acoustic pressure of a thin liquid Ga–In alloy were studied by high speed photography, numerical simulation, and bubble dynamics calculation. A self-made ultrasonic system with a TC4 sonotrode, was operated at a frequency of 20 kHz and a max output power of 1000 W during the cavitation recording experiment. The pressure field characteristic inside the thin liquid layer and its influence on the intensity, types, dimensions, and life cycles of cavitation bubbles and on the cavitation evolution process against experimental parameters were systematically studied. The results showed that acoustic pressure inside the thin liquid layer presented alternating positive and negative characteristics within 1 acoustic period (T). Cavitation bubbles nucleated and grew during the negative-pressure stage and shrank and collapsed during the positive-pressure stage. A high bubble growth speed of 16.8 m/s was obtained and evidenced by bubble dynamics calculation. The maximum absolute pressure was obtained at the bottom of the thin liquid layer and resulted in the strongest cavitation. Cavitation was divided into violent and weak stages. The violent cavitation stage lasted several hundreds of acoustic periods and had higher bubble intensity than the weak cavitation stage. Cavitation cloud preferentially appeared during the violent cavitation stage and had a life of several acoustic periods. Tiny cavitation bubbles with life cycles shorter than 1 T dominated the cavitation field. High cavitation intensities were observed at high ultrasonication power and when Q235B alloy was used because such conditions lead to high amplitudes on the substrate and further high acoustic pressure inside the liquid.     

An acoustic backscattering technique for the detection of transient cavitation produced by microsecond pulses of ultrasound

An acoustic backscattering technique for detecting transient cavitation produced by 10-microseconds-long pulses of 757-kHz ultrasound is described. The system employs 10-microseconds-long, 30-MHz center frequency tone bursts that scatter from cavitation microbubbles. Experiments were performed with suspensions of hydrophobic polystyrene spheres in ultraclean water. Transient cavitation threshold pressures measured with the active cavitation detector (ACD) were always less than or equal to those measured using a passive acoustic detection scheme. The measured cavitation thresholds decreased with increasing dissolved gas content and increasing suspended particle concentration. Results also show that ultrasonic irradiation of the polystyrene sphere suspensions by the ACD lowered the threshold pressure measured with the passive detector. A possible mechanism through which suspensions of hydrophobic particles might nucleate bubbles is presented.     

The mechanism of interaction between focused ultrasound and microbubbles in blood-brain barrier opening in mice

The activation of bubbles by an acoustic field has been shown to temporarily open the blood-brain barrier (BBB), but the trigger cause responsible for the physiological effects involved in the process of BBB opening remains unknown. Here, the trigger cause (i.e., physical mechanism) of the focused ultrasound-induced BBB opening with monodispersed microbubbles is identified. Sixty-seven mice were injected intravenously with bubbles of 1-2, 4-5, or 6-8 μm in diameter and the concentration of 10(7) numbers/ml. The right hippocampus of each mouse was then sonicated using focused ultrasound (1.5 MHz frequency, 100 cycles pulse length, 10 Hz pulse repetition frequency, 1 min duration). Peak-rarefactional pressures of 0.15, 0.30, 0.45, or 0.60 MPa were applied to identify the threshold of BBB opening and inertial cavitation (IC). Our results suggest that the BBB opens with nonlinear bubble oscillation when the bubble diameter is similar to the capillary diameter and with inertial cavitation when it is not. The bubble may thus have to be in contact with the capillary wall to induce BBB opening without IC. BBB opening was shown capable of being induced safely with nonlinear bubble oscillation at the pressure threshold and its volume was highly dependent on both the acoustic pressure and bubble diameter.     

Modeling bubble dynamics and radical kinetics in ultrasound induced microalgal cell disruption

Microalgal cell disruption induced by acoustic cavitation was simulated through solving the bubble dynamics in an acoustical field and their radial kinetics (chemical kinetics of radical species) occurring in the bubble during its oscillation, as well as calculating the bubble wall pressure at the collapse point. Modeling results indicated that increasing ultrasonic intensity led to a substantial increase in the number of bubbles formed during acoustic cavitation, however, the pressure generated when the bubbles collapsed decreased. Therefore, cumulative collapse pressure (CCP) of bubbles was used to quantify acoustic disruption of a freshwater alga, Scenedesmus dimorphus, and a marine alga, Nannochloropsis oculata and compare with experimental results. The strong correlations between CCP and the intracellular lipid fluorescence density, chlorophyll-a fluorescence density, and cell particle/debris concentration were found, which suggests that the developed models could accurately predict acoustic cell disruption, and can be utilized in the scale up and optimization of the process.     

Towards an understanding and control of cavitation activity in 1 MHz ultrasound fields

Various industrial processes such as sonochemical processing and ultrasonic cleaning strongly rely on the phenomenon of acoustic cavitation. As the occurrence of acoustic cavitation is incorporating a multitude of interdependent effects, the amount of cavitation activity in a vessel is strongly depending on the ultrasonic process conditions. It is therefore crucial to quantify cavitation activity as a function of the process parameters. At 1 MHz, the active cavitation bubbles are so small that it is becoming difficult to observe them in a direct way. Hence, another metrology based on secondary effects of acoustic cavitation is more suitable to study cavitation activity. In this paper we present a detailed analysis of acoustic cavitation phenomena at 1 MHz ultrasound by means of time-resolved measurements of sonoluminescence, cavitation noise, and synchronized high-speed stroboscopic Schlieren imaging. It is shown that a correlation exists between sonoluminescence, and the ultraharmonic and broadband signals extracted from the cavitation noise spectra. The signals can be utilized to characterize different regimes of cavitation activity at different acoustic power densities. When cavitation activity sets on, the aforementioned signals correlate to fluctuations in the Schlieren contrast as well as the number of nucleated bubbles extracted from the Schlieren Images. This additionally proves that signals extracted from cavitation noise spectra truly represent a measure for cavitation activity. The cyclic behavior of cavitation activity is investigated and related to the evolution of the bubble populations in the ultrasonic tank. It is shown that cavitation activity is strongly linked to the occurrence of fast-moving bubbles. The origin of this “bubble streamers” is investigated and their role in the initialization and propagation of cavitation activity throughout the sonicated liquid is discussed. Finally, it is shown that bubble activity can be stabilized and enhanced by the use of pulsed ultrasound by conserving and recycling active bubbles between subsequent pulsing cycles.     

球状泡群内气泡的耦合振动

振动气泡形成辐射场影响其他气泡的运动, 故多气泡体系中气泡处于耦合振动状态. 本文在气泡群振动模型的基础上, 考虑气泡间耦合振动的影响, 得到了均匀球状泡群内振动气泡的动力学方程, 以此为基础分析了气泡的非线性声响应特征. 气泡间的耦合振动增加了系统对每个气泡的约束, 降低了气泡的自然共振频率, 增强了气泡的非线性声响应. 随着气泡数密度的增加, 振动气泡受到的抑制增强; 增加液体静压力同样可抑制泡群内气泡的振动, 且存在静压力敏感区(1–2 atm, 1 atm=1.01325×10⁵ Pa); 驱动声波对气泡振动影响很大, 随着声波频率的增加, 能够形成空化影响的气泡尺度范围变窄. 在同样的声条件、泡群尺寸以及气泡内外环境下, 初始半径小于5 μm 的气泡具有较强的声响应. 气泡耦合振动会削弱单个气泡的空化影响, 但可延长多气泡系统空化泡崩溃发生的时间间隔和增大作用范围, 整体空化效应增强.     

超声空化及其声流结构实验研究*

超声空化及其声流效应在医学、化工和能源等领域得到广泛应用。本文采用高速摄像和粒子图像测速系统分别研究了超声场下的空化形态和声流场结构的时空演化规律。实验研究了50W,100W,200W和250W等四种不同输入功率对18kHz的超声变幅杆附近空化及其声流场的影响。研究结果表明：（1）在变幅杆下端面处观察到由大量空化气泡均匀分布组成的倒置锥形空泡结构,并且锥形空泡结构为稳态流动结构。（2）在超声变幅杆附近产生了两种不同的声流形式,第一种是变幅杆底端的射流型声流,第二种是变幅杆两侧的回旋流。此外,通过研究空泡与声流场中最大速度点之间的空间对应关系,发现声流是因为空泡流动带动而产生的。（3）空间位置和输入功率能显著影响射流型声流的流场结构,但是对回旋流的影响十分微弱。     

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.     

弱酸试纸法测量功率超声珩磨空化声场的研究*

为了简便、直观地测量功率超声珩磨磨削区的空化声场强度及分布情况,提出了利用弱酸PH试纸测量磨削区空化声场的方法。利用超声空化效应产生的弱酸空化泡在PH试纸表面溃灭后,形成深浅和分布不同的变色区域,间接地表征油石表面空化声场的强弱和分布规律。通过对比不同超声频率、测试距离和时间,得出了最佳测试距离和时间。结果表明,当超声频率为18.6 kHz,距离为10 mm时,测得油石表面的空化声场强度和分布最佳。该方法可形象地评价功率超声珩磨磨削区空化声场的强度和分布情况,具有一定的实际应用价值。     

An objective comparison of commercially-available cavitation meters

With a number of cavitation meters on the market which claim to characterise fields in ultrasonic cleaning baths, this paper provides an objective comparison of a selection of these devices and establishes the extent to which their claims are met. The National Physical Laboratory’s multi-frequency ultrasonic reference vessel provided the stable 21.06 kHz field, above and below the inertial cavitation threshold, as a test bed for the sensor comparison. Measurements from these devices were evaluated in relation to the known acoustic pressure distribution in the cavitating vessel as a means of identifying the mode of operation of the sensors and to examine the particular indicator of cavitation activity which they deliver. Through the comparison with megahertz filtered acoustic signals generated by inertial cavitation, it was determined that the majority of the cavitation meters used in this study responded to acoustic pressure generated by the direct applied acoustic field and therefore tended to overestimate the occurrence of cavitation within the vessel, giving non-zero responses under conditions when there was known to be no inertial cavitation occurring with the reference vessel. This has implications for interpreting the data they provide in user applications.     

Grain fragmentation in ultrasonic-assisted TIG weld of pure aluminum

Under the action of acoustic waves during an ultrasonic-assisted tungsten inert gas (TIG) welding process, a grain of a TIG weld of aluminum alloy is refined by nucleation and grain fragmentation. Herein, effects of ultrasound on grain fragmentation in the TIG weld of aluminum alloy are investigated via systematic welding experiments of pure aluminum. First, experiments involving continuous and fixed-position welding are performed, which demonstrate that ultrasound can break the grain of the TIG weld of pure aluminum. The microstructural characteristics of an ultrasonic-assisted TIG weld fabricated by fixed-position welding are analyzed. The microstructure is found to transform from plane crystal, columnar crystal, and uniform equiaxed crystal into plane crystal, deformed columnar crystal, and nonuniform equiaxed crystal after application of ultrasound. Second, factors influencing ultrasonic grain fragmentation are investigated. The ultrasonic amplitude and welding current are found to have a considerable effect on grain fragmentation. The degree of fragmentation first increases and then decreases with an increase in ultrasonic amplitude, and it increases with an increase in welding current. Measurement results of the vibration of the weld pool show that the degree of grain fragmentation is related to the intensity of acoustic nonlinearity in the weld pool. The greater the intensity of acoustic nonlinearity, the greater is the degree of grain fragmentation. Finally, the mechanism of ultrasonic grain fragmentation in the TIG weld of pure aluminum is discussed. A finite element simulation is used to simulate the acoustic pressure and flow in the weld pool. The acoustic pressure in the weld pool exceeds the cavitation threshold, and cavitation bubbles are generated. The flow velocity in the weld pool does not change noticeably after application of ultrasound. It is concluded that the high-pressure conditions induced during the occurrence of cavitation, lead to grain fragmentation in a pure aluminum TIG weld during an ultrasonic-assisted TIG welding process.