Effect of the ultrasonic standing wave frequency on the attractive mineralization for fine coal particle flotation

Froth flotation for mineral beneficiation is one of the most important separation techniques; however, it has several challenges for processing fine and ultrafine particles. Attractive mineralization between particles and bubbles by ultrasonic standing wave (USW) is a novel and high-efficiency method that could assist fine particle flotation. Frequency is an important ultrasound parameter, whose effectiveness mechanisms on the attractive mineralization did not compressively address. This study explored the effect of the USW field with various frequencies on the fine coal flotation for filling this gap. Herein, a high-speed camera and a focused beam reflectance measurement (FBRM) were used to analyze three sub-processes of the attractive mineralization, including the microbubbles’ formation, the conventional flotation bubbles (CFBs)’ dispersion, and the particles’ movement. It was found that the maximum flotation metallurgical responses were obtained under the highest examined USW frequency (600 kHz). However, the flotation outcomes by a low USW frequency (50 kHz) were even lower than the conventional flotation tests. Observation and theoretical calculation results revealed these results were originated from the influence of frequency on the carrier bubbles’ formation and the action of the secondary acoustic force during USW-assisted flotation. These outcomes demonstrated that frequency is a key factor determining the success of attractive mineralization for fine particles’ flotation.     

Effect of ultrasonic standing waves on flotation bubbles

Ultrasonic flotation was an effective method to float fine coal. In this study, the effects of the standing waves with different frequencies on ultrasonic flotation were investigated. The dynamic processes of bubble and coal-bubble were revealed by a high-speed camera. The results showed that under the action of Bjerknes force, bubble aggregates were formed within 450 ms and coal bubble aggregates were formed within 20 ms. The bubble aggregates were statistically analyzed by image processing method. The number of aggregates and small bubbles in the ultrasonic field at 100 kHz was greater than those at 80 and 120 kHz. Besides, 100 kHz ultrasonic flotation achieved the highest yields of clean coal (35.89%) and combustible recovery (45.77%). The cavitation bubbles acted as either a “medium” or an “inclusion”, entrapping and entraining the coal particles in the flotation pulp. It promoted the aggregation of bubbles with coal particles, so the flotation efficiency was effectively improved in the presence of ultrasonic standing waves.     

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.     

A novel flotation technique combining carrier flotation and cavitation bubbles to enhance separation efficiency of ultra-fine particles

In this paper, a novel flotation technique that combines nano-scale bubbles generated by hydrodynamic cavitation (HC) and carrier flotation is proposed to promote the flotation efficiency of a high-ash (43%) ultra-fine coal sample (<45 µm). We investigated the mechanism by which cavitation bubbles enhance the separation efficiency of carrier flotation using focused beam reflectance measurements, polarizing microscopy, and extended Derjaguin–Landau–Verwey–Overbeek theory. The carrier particles (polystyrene (PS)) and fine coal were pre-treated in a venturi tube and then floated in a laboratory mechanical flotation cell. The flotation results indicate that the presence of cavitation bubbles significantly improved the carrier flotation performance of high-ash ultra-fine coal. This improvement was attributed to the presence of highly hydrophobic PS, which creates additional gas nuclei in the flotation system. The nano-bubbles, which were produced by the venturi tube and adhered to the fine coal particle surfaces, were conducive to the agglomeration of fine coal particles into large aggregates. Moreover, the nano-bubbles functioned as “bridges” of interaction between the carrier particles and large aggregates of fine coal particles. This paper mainly focused on the effect of carrier (PS) and HC on high-ash fine coal. The influence of different HC intensities on carrier (PS) flotation was discussed. Two models for the interactions between the coal particles, nano-bubbles, and PS during cavitation were proposed and were proved using the E-DLVO theory.     

Interactions of bubbles in acoustic Lichtenberg figure

The evolution of acoustic Lichtenberg figure (ALF) in ultrasound fields is studied using high-speed photography. It is observed that bubbles travel along the branch to the aggregation region of an ALF, promoting the possibility of large bubble or small cluster formation. Large bubbles move away from the aggregation region while surrounding bubbles are attracted into this structure, and a bubble transportation cycle arises in the cavitation field. A simplified model consisting of a spherical cluster and a chain of bubbles is developed to explain this phenomenon. The interaction of the two units is analyzed using a modified expression for the secondary Bjerknes force in this system. The model reveals that clusters can attract bubbles on the chain within a distance of 2 mm, leading to a bubble transportation process from the chain to the bubble cluster. Many factors can affect this process, including the acoustic pressure, frequency, bubble density, and separation distance. The larger the bubble in the cluster, the broader the attraction region. Therefore, the presence of large bubbles might enhance the process in this system. Local disturbances in bubble density could destroy the ALF structure. The predictions of the model are in good agreement with the experimental phenomena.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The use of ultrasonic standing waves to enhance optical particle sizing equipment

Fluid dynamics modelling augmented with routines to simulate acoustic forces on aerosol particles has been used to investigate the potential of combining ultrasonic standing wave fields with optical particle analysis equipment. Simulations of particle dynamics in airstreams incorporating acoustic forces predict that particles in the 1-10 microns diameter range may be effectively focused to the velocity nodes of the standing wave field. Particles move to the velocity nodes within tens of milliseconds for acoustic frequencies of 10-100 kHz and at an acoustic energy density of 100 Jm-3. Larger particles are predicted to move to the velocity antinodes within similar times; however, there is a crossover region at approximately 15-20 microns particle diameter where longer times are predicted due to the competing forces driving particles to the vibration node and antinode. With sufficient transverse flow velocities the models predict that disturbances due to acoustic streaming can be overcome and a useful degree of focusing achieved for the aerosol particles. Results from a model demonstrating sampling and acoustic focusing of 3-9 microns aerosol particles to a 200 microns wide analysis area are presented.     

Numerical simulation of cavitation bubble dynamics induced by ultrasound waves in a high frequency reactor

The use of high frequency ultrasound in chemical systems is of major interest to optimize chemical procedures. Characterization of an open air 477 kHz ultrasound reactor shows that, because of the collapse of transient cavitation bubbles and pulsation of stable cavitation bubbles, chemical reactions are enhanced. Numerical modelling is undertaken to determine the spatio-temporal evolution of cavitation bubbles. The calculus of the emergence of cavitation bubbles due to the acoustic driving (by taking into account interactions between the sound field and bubbles' distribution) gives a cartography of bubbles' emergence within the reactor. Computation of their motion induced by the pressure gradients occurring in the reactor show that they migrate to the pressure nodes. Computed bubbles levitation sites gives a cartography of the chemical activity of ultrasound. Modelling of stable cavitation bubbles' motion induced by the motion of the liquid gives some insight on degassing phenomena.     

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.     

Physical and chemical effects of acoustic cavitation in selected ultrasonic cleaning applications

Acoustic cavitation in a liquid medium generates several physical and chemical effects. The oscillation and collapse of cavitation bubbles, driven at low ultrasonic frequencies (e.g., 20 kHz), can generate strong shear forces, microjets, microstreaming and shockwaves. Such strong physical forces have been used in cleaning and flux improvement of ultrafiltration processes. These physical effects have also been shown to deactivate pathogens. The efficiency of deactivation of pathogens is not only dependent on ultrasonic experimental parameters, but also on the properties of the pathogens themselves. Bacteria with thick shell wall are found to be resistant to ultrasonic deactivation process. Some evidence does suggest that the chemical effects (radicals) of acoustic cavitation are also effective in deactivating pathogens. Another aspect of cleaning, namely, purification of water contaminated with organic and inorganic pollutants, has also been discussed in detail. Strong oxidising agents produced within acoustic cavitation bubbles could be used to degrade organic pollutants and convert toxic inorganic pollutants to less harmful substances. The effect of ultrasonic frequency and surface activity of solutes on the sonochemical degradation efficiency has also been discussed in this overview.     

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.     

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.     

Enhancement of cavitation activity and particle removal with pulsed high frequency ultrasound and supersaturation

Megasonic cleaning as applied in leading edge semiconductor device manufacturing strongly relies 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 the cleaning liquid strongly depends on the sonication conditions. It is shown that cavitation activity as measured by means of ultraharmonic cavitation noise can be significantly enhanced when pulsed sonication is applied to a gas supersaturated liquid under traveling wave conditions. It is demonstrated that this enhancement coincides with a dramatic increase in particle removal and is therefore of great interest for megasonic cleaning applications. It is demonstrated that the optimal pulse parameters are determined by the dissolution time of the active bubbles, whereas the amount of cavitation activity depends on the ratio between pulse-off and pulse-on time as well as the applied acoustic power. The optimal pulse-off time is independent of the corresponding pulse-on time but increases significantly with increasing gas concentration. We show that on the other hand, supersaturation is needed to enable acoustic cavitation at aforementioned conditions, but has to be kept below values, for which active bubbles cannot dissolve anymore and are therefore lost during subsequent pulses. For the applicable range of gas contents between 100% and 130% saturation, the optimal pulse-off time reaches values between 150 and 340 ms, respectively. Full particle removal of 78 nm-diameter silica particles at a power density of 0.67 W/cm² is obtained for the optimal pulse-off times. The optimal pulse-off time values are derived from the dissolution time of bubbles with a radius of 3.3 μm and verified experimentally. The bubble radius used in the calculations corresponds to the linear resonance size in a 928 kHz sound field, which demonstrates that the recycling of active bubbles is the main enhancement mechanism. The optimal choice of the pulsing conditions however is constrained by the trade-off between the effective sonication time and the desire to have a sufficient amount of active bubbles at lower powers, which might be necessary if very delicate structures have to be cleaned.     

Theory of local electrification of cavitation bubbles: new approaches

The theory of local electrification of cavitation bubbles has been generalised. The major cases for a local electrification of bubbles in a cavitation field were considered; i.e., fragmentation and deformation of cavitation bubbles. The splitting of cavitation bubbles was considered taking into account surface tension, bubble perturbation, Stokes force and electrostatic forces between like charges on the wall of the collapsing neck of the fragment bubble. The problem of the uncompensated charge on the surface of the deformed cavitation bubble is solved. For this purpose radial deformations are considered in terms of the paraboloid of rotation and axial deformation approximated by one cavity hyperboloid of rotation. The maximum electric strength is accounted for. An explanation for some physical and physico-chemical effects in cavitation fields is proposed in terms of the electrical theory of the local electrification of cavitation bubbles.