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.     

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.     

A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter

The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit. The shock wave consists of a zero rise time positive spike that falls to 0 at 1 microsecond followed by a negative pressure component 6 microseconds long with amplitudes scaled to +1000 and -160 bars, P+ and P-, respectively. This pressure wave drives the Gilmore-Akulichev formulation for bubble dynamics; the zero-order effect of gas diffusion on bubble response is included. The negative pressure component of a 1000-bar shock wave will cause a preexisting bubble in the 1- to 10-microns range to expand to over 100 times its initial size, R0, for 250 microseconds, with a peak radius of approximately 1400 microns, then collapse very violently, emitting far UV or soft x-ray photons (black body). Gas diffusion does not appreciably mitigate the amplitude of the pressure wave radiated at the primary collapse, but does significantly reduce the collapse temperature. Diffusion also increases the bubble radius from R0 up to 40 microns and extends the duration of ringing following the primary collapse, assuming that the bubble does not break up or shed microbubbles. Results are sensitive to P+/P- and to the duration of the negative pressure cycle but not to rise time.     

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

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

Microimplosions: cavitation collapse and shock wave emission on a nanosecond time scale

A streak camera with high spatial and temporal resolution was used for imaging the dynamics of the violent collapse in single-bubble sonoluminescence. The high pressure in the last phase of the bubble collapse leads to the emission of a shock wave, which is launched with a shock velocity of almost 4000 m/s. The shock amplitude decays much faster than approximately 1/r. From the strongly nonlinear propagation the pressure in the vicinity of the bubble can be calculated to be in the range of 40-60 kbar.     

Shock wave-inertial microbubble interaction: a theoretical study based on the Gilmore formulation for bubble dynamics

The Gilmore formulation for bubble dynamics coupled with zeroth-order gas diffusion were used to investigate theoretically the cavitation activity produced by a modified XL-1 lithotripter [J. Acoust. Soc. Am. 105, 1997-2009 (1999)]. The model calculation confirms many of the basic features in bubble dynamics observed experimentally, in particular the strong secondary shock wave emission generated by in situ lithotripter shock wave-inertial microbubble interaction. In addition, shock wave-inertial microbubble interaction produced by a Dornier HM-3, the most commonly used clinical lithotripter, was evaluated. It was shown that the forced collapse of inertial microbubbles with strong secondary shock wave emission could be produced consistently, provided that an appropriate preceding shock wave and interpulse delay were used. Further, it was demonstrated that truncation of the tensile stress of the lithotripter shock wave could significantly reduce the large expansion of the bubble following shock wave-inertial microbubble interaction, which may alleviate the risk for vascular injury during shock wave exposure.     

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.     

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.     

Focusing of an oscillating shock wave emitted by a toroidal bubble cloud

An analysis of pressure-field dynamics is performed for an axially symmetric problem of interaction between a shock wave and a “free” bubble system (toroidal cluster) giving rise to a steady oscillating shock wave. The results of a numerical study of near-axis wave structure are presented for a focusing shock wave emitted by a bubble cluster. It is shown that the wave reflected from the axis has irregular structure. The Mach disk developing on the axis has a core of finite thickness with a nonuniform radial pressure distribution. The evolution of the Mach-disk core is analyzed, and the maximum pressure in the core is computed as a function of the gas volume fraction in the cluster. The effect of geometric parameters of the toroidal bubble cloud on the cumulative effect is examined.     

Laser-induced cavitation bubbles and shock waves in water near a concave surface

The interplay among the cavitation structures and the shock waves following a nanosecond laser breakdown in water in the vicinity of a concave surface was visualized with high-speed shadowgraphy and schlieren cinematography. Unlike the generation of the main cavitation bubble near a flat or a convex surface, the concave surface refocuses the emitted shock waves and causes secondary cavitation near the acoustic focus which is most pronounced when triggered by the shock wave released during the first main bubble collapse. The shock wave propagation, reflection from the concave surface and its scattering on the dominant cavity is clearly resolvable on the shadowgraphs. The schlieren approach revealed the pressure build up in the last stage of the collapse and the first stage of the rebound. A persistent low-density watermark is left behind the first collapse. The observed effects are important wherever cavities collapse near indented surfaces, such as in cavitation peening, cavitation erosion and ophthalmology.     

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.     

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。     

Dynamics of laser-induced bubble collapse visualized by time-resolved optical shadowgraph

Abstract  

Following the first shock wave generation and the successive single bubble expansion after the breakdown by the Nd:YAG laser pulse with 35 mJ and 10 ns in distilled water, the strong secondary shock wave is generated at the instant of the bubble collapse. The single bubble expands up to 0.59 mm in radius, and then closes up by the pressure difference between the ambient liquid pressure at 10² kPa and the vapor pressure inside the bubble at 2 kPa. The maximum pressure up to 3 GPa is attained without the strong rebounding surface motion at about 93 μs after the laser shedding. We present time-resolved velocity measurements for estimating the extreme peak pressures of the first and second shock waves with the Rankine–Hugoniot analysis.     

Experimental investigation of the impact on nearby solid boundary during laser-generated bubble collapse

Cavitation damage has been considered as being responsible for many effects in hydraulic machinery and biological medicine. In order to better understand the cavity interaction with nearby solid surfaces, the impact loading induced by the high-speed liquid-jet and subsequent jet flow during the final stage of the bubble collapse in a static fluid is investigated by focusing a Q-switched pulsed laser into water. By means of a new method based on a fibre-coupling optical beam deflection technique, a detailed experimental study has been made to clarify the relationship of the impact pressure against a solid boundary as a function of the dimensionless γ that is generally used to describe the bubble dynamics with its definition γ= s/R_{max}(R_{max} being the maximum bubble radius and s denoting the distance of the cavity inception from the boundary). The experimental results are shown that for γ in the range of about 0.67 to 0.95 with a pulsed laser energy 230mJ, the transient pressure applied on the solid surface is maximum; while for γ>1 or γ<0.67, it is gradually decreased. By combination of our experimental results with the other work that detected the acoustic emission during the bubble collapse at different γ, it is concluded that in this range of 0.67－0.95, the destructive effect due to a liquid-jet and the following jet flow impact actually outweighs the well-known effect of shock wave emission and plays a vital role during the cavitation bubble collapse.     

Nonlinear dynamics of a cavitation bubble pair near a rigid boundary in a standing ultrasonic wave field

The dynamics of a micrometer-sized bubble pair in water near a rigid boundary under standing ultrasonic wave excitation is investigated in this study. The viscous effect in the boundary layer at the air-water interface is considered following the viscous correction model. The evolution of the bubble surface at the collapsing stage of the bubble pair is presented for different parameter sets. The field pressure near the rigid boundary, which is induced by the oscillating bubble pair, and the high-speed water jet at the collapse stage, form the main focus of the analysis. This reveals that a horizontal configuration of the bubble pair retards the strength of the bubble jet towards the boundary, whilst a vertical configuration, especially with differently-sized bubbles, can enhance the bubble collapse. This study may help to understand the interaction of multiple bubbles in an acoustic field and its application to surface cleaning.     

Fundamental study of sterilization effects on marine Vibrio sp. in a cylindrical water chamber with supply of only underwater shock waves

The effect of shock sterilization on marine Vibrio sp. is investigated by carrying out a bio-experiment based on a bubble-shockwave interaction. In the experiments, underwater shock waves with different strength and frequencies are produced by a high-voltage power supply in a cylindrical water chamber. The bio-experimental results show marine Vibrio sp. is completely inactivated in a short time by a 1.0-Hz electric discharge. However, a high sterilization effect requires a strong and high frequency of the bubble motion, and it also depends on the lifetime of the bubble. Subsequently, by an experiment with an air gap to prevent the underwater shock waves entering the cell suspension, it is found that the introduction of a strong shock pressure is not entirely required to obtain the effective sterilization. On the other hand, the direct effect of the sterilization by rebound shock wave resulting from the bubble-shock wave interaction is examined in the experiments. The results suggest that free radicals mainly contribute to killing marine bacteria, and direct mechanical effects of the bubble motion are not responsible. In addition, the creation of the OH radical is indirectly confirmed by measuring the H₂O₂ concentration. Finally, the Herring equation is solved to investigate the condition of free radical generation when considering the effect of thermal conductivity at the bubble interface. As a result, the effective sterilization conditions based on the bubble-shock wave interaction are clearly obtained.     

Conditions of the Formation of a Shock Wave under Cavitation in Hydrocarbon Solutions

Doklady Physics - We carried out a numerical study of the appearance of a shock wave during the collapse of a bubble in a hydrocarbon aqueous solution. The conditions for the appearance of a shock...     

超声波降解有机物溶液的气泡动力学研究

在超声波降解有机物溶液过程中,超声空化产生的高温高压以及空化泡振荡产生的激波在有机物溶液的降解中发挥重要作用.本文通过对超声波作用下气泡动力学的研究,讨论了超声波声压、频率、气泡初始半径等参量对有机物溶液降解效率的影响.研究发现,存在使降解效率极大的声压和频率。在空化稳定的情况下,存在一个使降解效率极大的气泡初始半径,降解效率随着黏滞系数的增大而减小。研究还发现,双频超声作用的空化效果比单频超声作用时强,与双频超声作用下有机物溶液降解率较大这一实验结果一致。      

空化单气泡外围压强分布

关键词：     

Cavitation erosion by shockwave self-focusing of a single bubble

The ability of cavitation bubbles to effectively focus energy is made responsible for cavitation erosion, traumatic brain injury, and even for catalyse chemical reactions. Yet, the mechanism through which material is eroded remains vague, and the extremely fast and localized dynamics that lead to material damage has not been resolved. Here, we reveal the decisive mechanism that leads to energy focusing during the non-spherical collapse of cavitation bubbles and eventually results to the erosion of hardened metals. We show that a single cavitation bubble at ambient pressure close to a metal surface causes erosion only if a non-axisymmetric energy self-focusing is at play. The bubble during its collapse emits shockwaves that under certain conditions converge to a single point where the remaining gas phase is driven to a shockwave-intensified collapse. We resolve the conditions under which this self-focusing enhances the collapse and damages the solid. High-speed imaging of bubble and shock wave dynamics at sub-picosecond exposure times is correlated to the shockwaves recorded with large bandwidth hydrophones. The material damage from several metallic materials is detected in situ and quantified ex-situ via scanning electron microscopy and confocal profilometry. With this knowledge, approaches to mitigate cavitation erosion or to even enhance the energy focusing are within reach.