Physical investigation of acoustic waves induced by the oscillation and collapse of the single bubble

The objective of this paper is to apply both experimental and numerical methods to investigate acoustic waves induced by the oscillation and collapse of a single bubble. In the experiments, the schlieren technique is used to capture the temporal evolution of the bubble shapes, and the corresponding acoustic waves. The results are presented for the single bubble generated by a low-voltage bubble generator in the free field of water. During the numerical simulations, a three-dimensional (3D) weakly compressible model is introduced to investigate the single bubble dynamics, including the generation and propagation of acoustic waves. The results show that (1) Compression wave, rarefaction wave and shock wave are generated during expansion stage, collapse stage and rebound stage of the bubble respectively. (2) Compression waves are induced by the rapid expansion of the bubble and eventually steepen into one shock wave propagating outward in the liquid, then another strong shock wave is emitted at the final collapse stage. The velocity and pressure of the liquid field increases after the shock wave. (3) Rarefaction waves are generated during the collapse stage due to the contraction of the bubble. The rarefaction wave reduces the liquid pressure and its spatial distribution is dispersive. The pressure of these acoustic waves and their effect on the liquid velocity attenuate with the increase of propagation distance.     

Cavitation bubble behavior and bubble–shock wave interaction near a gelatin surface as a study of in vivo bubble dynamics

The collapse of a single cavitation bubble near a gelatin surface, and the interaction of an air bubble attached to a gelatin surface with a shock wave, were investigated. These events permitted the study of the behavior of in vivo cavitation bubbles and the subsequent tissue damage mechanism during intraocular surgery, intracorporeal and extracorporeal shock wave lithotripsy. Results were obtained with high-speed framing photography. The cavitation bubbles near the gelatin surface did not produce significant liquid jets directed at the surface, and tended to migrate away from it. The period of the motion of a cavitation bubble near the gelatin surface was longer than that of twice the Rayleigh's collapse time for a wide range of relative distance, L/R_max, excepting for very small L/R_max values (L was the stand-off distance between the gelatin surface and the laser focus position, and R_max was the maximum bubble radius). The interaction of an air bubble with a shock wave yielded a liquid jet inside the bubble, penetrating into the gelatin surface. The liquid jet had the potential to damage the gelatin. The results predicted that cavitation-bubble-induced tissue damage was closely related to the oscillatory bubble motion, the subsequent mechanical tissue displacement, and the liquid jet penetration generated by the interaction of the remaining gas bubbles with subsequent shock waves. The characteristic bubble motion and liquid jet formation depended on the tissue's mechanical properties, resulting in different damage mechanisms from those observed on hard materials.     

含气量对激光空泡在刚性壁面空蚀的影响

采用强脉冲激光器设计液体环境下刚性壁面空蚀实验平台,改变液体中含气量,利用高速相机观察不同含气量条件下激光空泡在壁面附近的脉动过程,并对刚性壁面造成的空蚀结果进行了观测。实验研究发现,随着液体中相对空气含量的提高,激光空泡脉动的最大尺寸增大,空泡的膨胀运动变剧烈,溃灭运动速度降低,空泡的溃灭强度降低,从而影响到溃灭冲击波和壁面微射流对刚性壁面的冲击速度,减弱了壁面空蚀,而液体中含气量的提高能够降低激光空泡对刚性壁面的空蚀程度。     

Investigation of cavitation bubble collapse in hydrophobic concave using the pseudopotential multi-relaxation-time lattice Boltzmann method

The interaction between cavitation bubble and solid surface is a fundamental topic which is deeply concerned for the utilization or avoidance of cavitation effect.The complexity of this topic is that the cavitation bubble collapse includes many extreme physical phenomena and variability of different solid surface properties.In the present work,the cavitation bubble collapse in hydrophobic concave is studied using the pseudopotential multi-relaxation-time lattice Boltzmann model(MRT-LB).The model is modified by involving the piecewise linear equation of state and improved forcing scheme.The fluid-solid interaction in the model is employed to adjust the wettability of solid surface.Moreover,the validity of the model is verified by comparison with experimental results and grid-independence verification.Finally,the cavitation bubble collapse in a hydrophobic concave is studied by investigating density field,pressure field,collapse time,and jet velocity.The superimposed effect of the surface hydrophobicity and concave geometry is analyzed and explained in the framework of the pseudopotential LBM.The study shows that the hydrophobic concave can enhance cavitation effect by decreasing cavitation threshold,accelerating collapse and increasing jet velocity.     

Modified shock waves for extracorporeal shock wave lithotripsy: a simulation based on the Gilmore formulation

Extracorporeal shock wave lithotripsy (SWL) is a reliable therapy for the treatment of urolithiasis. Nevertheless, improvements to enhance stone fragmentation and reduce tissue damage are still needed. During SWL, cavitation is one of the most important stone fragmentation mechanisms. Bubbles with a diameter between about 7 and 55 μm have been reported to expand and collapse after shock wave passage, forming liquid microjets at velocities of up to 400 m/s that contribute to the pulverization of renal calculi. Several authors have reported that the fragmentation efficiency may be improved by using tandem shock waves. Tandem SWL is based on the fact that the collapse of a bubble can be intensified if a second shock wave arrives tenths or even a few hundredths of microseconds before its collapse. The object of this study is to determine if tandem pulses consisting of a conventional shock wave (estimated rise time between 1 and 20 ns), followed by a slower second pressure profile (0.8 μs rise time), have advantages over conventional tandem SWL. The Gilmore equation was used to simulate the influence of the modified pressure field on the dynamics of a single bubble immersed in water and compare the results with the behavior of the same bubble subjected to tandem shock waves. The influence of the delay between pulses on the dynamics of the collapsing bubble was also studied for both conventional and modified tandem waves. For a bubble of 0.07 mm, our results indicate that the modified pressure profile enhances cavitation compared to conventional tandem waves at a wide range of delays (10-280 μs). According to this, the proposed pressure profile could be more efficient for SWL than conventional tandem shock waves. Similar results were obtained for a ten times smaller bubble.     

Dynamic behavior of a single bubble between the free surface and rigid wall

The objective of this paper is to apply high-speed photography and schlieren method to investigate the bubble dynamics between the free surface and a rigid wall. The temporal evolution of the bubble shape and the free surface motion are recorded by two synchronous high-speed cameras. Experiments are carried out for a single bubble generated at various normalized stand-off distances from bubble center to the free surface and to the rigid wall. The results show that (1) three distinctive patterns are identified with the morphology of the bubble and free surface, namely single toroidal bubble without spike (STB), single toroidal bubble with a spike (STBS) and double toroidal bubbles with a spike (DTBS). (2) The dynamic characteristics of the bubble at collapse and rebound stage vary evidently at different patterns, including the bubble shape variations and free surface motion. In detail, the schlieren images show the formation and propagation of shock waves, which explains the radiative process of bubble collapse energy. (3) Qualitative comparisons are carried out for the bubble and free surface at the same pattern. And quantitative analyses are conducted for the jet velocity, bubble collapse position, bubble collapse time and spike height, etc. for different values of bubble-rigid wall distance.     

Luminescence induced by spherically focused acoustic pulses in liquids

The determination of the phase of the bubble oscillation at the instant of light emission, which is a key issue for understanding the origin of cavitation luminescence of liquids, is discussed. The observation of luminescence in the course of the nucleation and growth of a bubble up to its collapse is performed in a bipolar wave consisting of a compression phase followed by a rarefaction phase in the regime of a two-fraction bubble cluster formation. The space-time distributions of the luminescence intensity and pressure and the dynamics of the cluster in water and a glycerin solution are investigated at the early stage of cavitation. A correlation between the maximal density of light flashes and the positive pressure pulses in the field of superposition of the initial and secondary cavitation compression waves is revealed. It is shown that the spherical focusing of acoustic pulses both away from the boundaries of the liquid and near its free surface makes it possible to compare the luminescence intensities for different rates of the pressure decrease.     

On the Formation of Centered Shock Waves in Gas Bubbles under the Conditions of Acoustic Cavitation

The possibility of the formation of centered shock waves in collapsing gas bubbles under the conditions of acoustic cavitation is considered. In this case, the overturning of the front of compression waves occurs at the instant the waves reach the center of the cavitation bubble, resulting in the highest possible temperatures and pressures inside the bubble. Examination of the magnetohydrodynamic equations has shown that the law of the motion of the wall of a bubble at the final stage of compression, described by the Rayleigh–Plesset equation, has a universal form and coincides with the condition of the formation of a spherically symmetric centered shock wave with the adiabatic constant = 5/3. For < 5/3, the collapse of a bubble occurs within a shorter time than it takes for a spherically symmetric centered shock wave to form. In this case, the overturning of the front of compression waves occurs earlier than they reach the center of the bubble, and shock waves are formed inside the bubble at different points. The most appropriate condition for the detection of centered shock waves is the cavitation in cryogenic fluids, such as helium, for which 5/3.     

A mechanistic analysis of stone fracture in lithotripsy

In vitro experiments and an elastic wave model were used to analyze how stress is induced in kidney stones by lithotripsy and to test the roles of individual mechanisms-spallation, squeezing, and cavitation. Cylindrical U30 cement stones were treated in an HM-3-style lithotripter. Baffles were used to block specific waves responsible for spallation or squeezing. Stones with and without surface cracks added to simulate cavitation damage were tested in glycerol (a cavitation suppressive medium). Each case was simulated using the elasticity equations for an isotropic medium. The calculated location of maximum stress compared well with the experimental observations of where stones fractured in two pieces. Higher calculated maximum tensile stress correlated with fewer shock waves required for fracture. The highest calculated tensile stresses resulted from shear waves initiated at the proximal corners and strengthened along the side surfaces of the stone by the liquid-borne lithotripter shock wave. Peak tensile stress was in the distal end of the stone where fracture occurred. Reflection of the longitudinal wave from the distal face of the stone--spallation-produced lower stresses. Surface cracks accelerated fragmentation when created near the location where the maximum stress was predicted.     

Shock wave emission upon spherical bubble collapse during cavitation-induced megasonic surface cleaning

When a gas bubble in a liquid interacts with an acoustic wave near a solid surface, the bubble first expands and then collapses. In this paper, a mathematical framework combining the Gilmore model and the method of characteristics is presented to model the shock wave emitted at the end of the bubble collapse. It allows to describe the liquid velocity at the shock front as a function of the radial distance to the bubble center in the case of spherical bubble collapse. Numerical calculations of the liquid velocity at the shock front have shown that this velocity increases with the acoustic amplitude and goes through a maximum as a function of the initial bubble radius. Calculations for different gas state equations inside the bubble show that the Van der Waals law predicts a slightly higher liquid velocity at the shock front than when considering a perfect gas law. Finally, decreasing the value of the surface tension at the bubble/liquid interface results in an increase of the liquid velocity at the shock front. Our calculations indicate that the strength of the shock waves emitted upon spherical bubble collapse can cause delamination of typical device structures used in microelectronics.     

Energy partitioning in laser-induced millimeter-sized spherical cavitation up to the fourth oscillation

To investigate the energy partitioning up to the fourth oscillation of a millimeter-scale spherical cavitation bubble induced by laser, we used nanosecond laser pulses to generate highly spherical cavitation bubbles and shadowgraphs to measure the radius-time curve. Using the extended Gilmore model and considering the continuous condensation of the vapor in the bubble, the time evolution of the bubble radius, bubble wall velocity, and pressure in the bubble is calculated till the 4th oscillation. Using Kirkwood-Bethe hypothesis, the evolution of velocity and pressure of shock wave at the optical breakdown, the first and second collapses are calculated. The shock wave energy at the breakdown and bubble collapse is directly calculated by numerical method. We found the simulated radius-time curve fits well with experimental data for the first four oscillations. The energy partition at the breakdown is the same as that in previous studies, the ratio of shock wave energy to bubble energy is about 2:1. In the first collapse and the second collapse, the ratio of shock wave energy to bubble energy is 14.54:1 and 2.81:1 respectively. In the third and fourth collapses, the ratio is less, namely than 1.5:1 and 0.42:1 respectively. The formation mechanism of the shock wave at the collapse is analyzed. The breakdown shock wave is mainly driven by the expansion of the supercritical liquid resulting from the thermalization of the energy of the free electrons in the plasma, and the collapse shock wave is mainly driven by the compressed liquid around the bubble.     

On the governing fragmentation mechanism of primary intermetallics by induced cavitation

One of the main applications of ultrasonic melt treatment is the grain refinement of aluminium alloys. Among several suggested mechanisms, the fragmentation of primary intermetallics by acoustic cavitation is regarded as very efficient. However, the physical process causing this fragmentation has received little attention and is not yet well understood. In this study, we evaluate the mechanical properties of primary Al₃Zr intermetallics by nano-indentation experiments and correlate those with in-situ high-speed imaging (of up to 1 Mfps) of their fragmentation process by laser-induced cavitation (single bubble) and by acoustic cavitation (cloud of bubbles) in water. Intermetallic crystals were chemically extracted from an Al-3 wt% Zr alloy matrix. Mechanical properties such as hardness, elastic modulus and fracture toughness of the extracted intermetallics were determined using a geometrically fixed Berkovich nano-diamond and cube corner indenter, under ambient temperature conditions. The studied crystals were then exposed to the two cavitation conditions mentioned. Results demonstrated for the first time that the governing fragmentation mechanism of the studied intermetallics was due to the emitted shock waves from the collapsing bubbles. The fragmentation caused by a single bubble collapse was found to be almost instantaneous. On the other hand, sono-fragmentation studies revealed that the intermetallic crystal initially underwent low cycle fatigue loading, followed by catastrophic brittle failure due to propagating shock waves. The observed fragmentation mechanism was supported by fracture mechanics and pressure measurements using a calibrated fibre optic hydrophone. Results showed that the acoustic pressures produced from shock wave emissions in the case of a single bubble collapse, and responsible for instantaneous fragmentation of the intermetallics, were in the range of 20–40 MPa. Whereas, the shock pressure generated from the acoustic cavitation cloud collapses surged up to 1.6 MPa inducing fatigue stresses within the crystal leading to eventual fragmentation.     

Problems of interpretation of holographic interferograms near shock wave fronts

A method of avoiding ambiguity in the interpretation of interferograms near a shock wave front is proposed. The method is based on combining the double-exposure schlieren method and holographic interferometry. Relations for calculating, on the basis of data obtained by analyzing double-exposure schlieren photographs, both the density at the shock wave front and the gradient of the density directly behind the front, which is necessary for calculating the shifts of the interference fringes near the shock wave front, are presented. Zh. Tekh. Fiz. 68, 88–91 (September 1998)     

Background Oriented Schlieren Method as an Optical Method to Study Shock Waves

Background oriented schlieren method is applied in diagnostics of shock waves in air. The method can be used for visualization of shock waves that are generated after explosion or due to motion at ultrasonic speeds. Experimental data make it possible to observe propagation of a shock wave in space, estimate the asymmetry of energy liberation in explosion, and determine parameters of shock wave.     

Quantitative measurements of acoustic emissions from cavitation at the surface of a stone in response to a lithotripter shock wave

Measurements are presented of acoustic emissions from cavitation collapses on the surface of a synthetic kidney stone in response to shock waves (SWs) from an electrohydraulic lithotripter. A fiber optic probe hydrophone was used for pressure measurements, and passive cavitation detection was used to identify acoustic emissions from bubble collapse. At a lithotripter charging voltage of 20 kV, the focused SW incident on the stone surface resulted in a peak pressure of 43 +/- 6 MPa compared to 23 +/- 4 MPa in the free field. The focused SW incident upon the stone appeared to be enhanced due to the acoustic emissions from the forced cavitation collapse of the preexisting bubbles. The peak pressure of the acoustic emission from a bubble collapse was 34 +/- 15 MPa, that is, the same magnitude as the SWs incident on the stone. These data indicate that stresses induced by focused SWs and cavitation collapses are similar in magnitude thus likely play a similar role in stone fragmentation.     

Surface damage as a result of cavitation erosion

Erosion is regarded as a result of the periodic loading of a surface with spherical waves generated at the sites of the collapse of cavitation bubbles. One feature of cavitation loading is the formation of a zone of intense failure at the center of the contact surface. Damage appears a consequence of the formation of longitudinal cleavage cracks under the contact zone, which comprise a system of small annular cracks coaxial to a deep channel crack. The damage zone (blister) occupies a small fraction of the crater surface (the contact zone with the shock wave). The depth of the longitudinal cracks is an order of magnitude smaller than the thickness of the hardened layer. The hardening and erosion processes occur simultaneously. Zh. Tekh. Fiz. 68, 110–114 (September 1998)     

Generation of intense x-rays during ejection of a fast water jet from a metal channel to atmosphere

The radiation processes associated with a supersonic water jet exhausting from a narrow channel are considered. It has been found for the first time that the output of the channel and the initial portion of the jet are sources of intense X-radiation, generation of which is related to cavitation processes in the water jet bulk and subsequent excitation of shock waves. The frequency of X-radiation depends on the types of atoms on a radiating surface (for a jet, it is water; for a channel, the metal atoms on the surface) and increases with the charge of atoms. The total X-ray activity of an experimental setup in the mode of jet exhaust reaches 0.1 Ci. It is found for the first time that the impact of shock acoustic waves, which are formed in the air as a result of cavitation jets of water, on distant screens leads to the generation of a quasi-coherent directional X-ray emission from the back side of these screens. The spatial parameters of this radiation depend on the shape and cross section of the screen and the spatial characteristics of the shock wave.     

The interaction of a laser-generated cavity with a solid boundary

In this paper new observations of a laser-generated cavitation bubble interacting with an inertial boundary are presented. Employing schlieren photography techniques and a thin film transducer placed on the surface of the boundary, the pressure stresses induced in the solid boundary and the surrounding fluid by collapsing bubbles, created very close to the solid surface, are experimentally measured. Liquid jet development, shock wave emission, and "splash" phenomena are identified. For different creation sites close to the boundary, the relevance of each of these phenomena with respect to potentially damaging pressure stresses in the boundary is speculated on.     

Effects of surface tension on the dynamics of a single micro bubble near a rigid wall in an ultrasonic field

Acoustic cavitation is a very important hydrodynamic phenomenon, and is often implicated in a myriad of industrial, medical, and daily living applications. In these applications, the effect mechanism of liquid surface tension on improving the efficiency of acoustic cavitation is a crucial concern for researchers. In this study, the effects of liquid surface tension on the dynamics of an ultrasonic driven bubble near a rigid wall, which could be the main mechanism of efficiency improvement in the applications of acoustic cavitation, were investigated at the microscale level. A synchronous high-speed microscopic imaging method was used to clearly record the temporary evolution of single acoustic cavitation bubble in the liquids with different surface tension. Meanwhile, the bubble dynamic characteristics, such as the position and time of bubble collapse, the size and stability of the bubbles, the speed of bubble boundaries and the micro-jets, were analyzed and compared. In the case of the single bubbles near a rigid wall, it was found that low surface tension reduces the stability of the bubbles in the liquid medium. Meanwhile, the bubbles collapse earlier and farther from the rigid wall in the liquids with lower surface tension. In addition, the surface tension has no significant influence on the speed of the first micro-jet, but it can substantially increase the speed of second and the third micro-jets after the first collapse of the bubble. These effects of liquid surface tension on the bubble dynamics can explain the mechanism of surfactants in numerous fields of acoustic cavitation for facilitating its optimization and application.     

Numerical study of the synergistic effect of cavitation and micro-abrasive particles

In ultrasonic-assisted machining, the synergistic effect of the cavitation effect and micro-abrasive particles plays a crucial role. Studies have focused on the investigation of the micro-abrasive particles, cavitation micro-jets, and cavitation shock waves either individually or in pairs. To investigate the synergy of shock waves and micro-jets generated by cavitation with micro-abrasive particles in ultrasonic-assisted machining, the continuous control equations of a cavitation bubble, shock wave, micro-jet, and micro-abrasive particle influenced by the dimensionless amount (R/R₀), a particle size-velocity–pressure model of the micro-abrasive particle was established. The effects of ultrasonic frequency, sound pressure amplitude, and changes in particle size on micro-abrasive particle velocity and pressure were numerically simulated. At an ultrasonic frequency of 20 kHz and ultrasonic sound pressure of 0.1125 MPa, a smooth spherical SiO₂ micro-abrasive particle (size = 5 µm) was obtained, with a maximum velocity of 190.3–209.4 m/s and pressure of 79.69–89.41 MPa. The results show that in the range of 5–50 μm, smaller particle sizes of the micro-abrasive particles led to greater velocity and pressure. The shock waves, micro-jets, and micro-abrasive particles were all positively affected by the dimensionless amount (R/R₀) of cavitation bubble collapse, the larger the dimensionless quantity, the faster their velocity and the higher their pressure.