Numerical study of the effect of liquid compressibility on acoustic droplet vaporization

In acoustic droplet vaporization (ADV), a cavitated bubble grows and collapses depending on the pressure amplitude of the acoustic pulse. During the bubble collapse, the surrounding liquid is compressed to high pressure, and liquid compressibility can have a significant impact on bubble behavior and ADV threshold. In this work, a one-dimensional numerical model considering liquid compressibility is presented for ADV of a volatile microdroplet, extending our previous Rayleigh-Plesset based model [Ultrason. Chem. 71 (2021) 105361]. The numerical results for bubble motion and liquid energy change in ADV show that the liquid compressibility highly inhibits bubble growth during bubble collapse and rebound, especially under high acoustic frequency conditions. The liquid compressibility effect on the ADV threshold is quantified with varying acoustic frequencies and amplitudes.     

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.     

Interpreting the influence of liquid temperature on cavitation collapse intensity through bubble dynamic analysis

The violent collapse of inertial bubbles generates high temperature inside and emits strong impulsive pressure. Previous tests on sonoluminescence and cavitation erosion showed that the influence of liquid temperature on these two parameters is different. In this paper, we conducted a bubble dynamic analysis to explore the mechanism of the temperature effect and account for the above difference. The results show that the increase of vapor at higher liquid temperatures changes both the external compression pressure and the internal cushion and is responsible for the variation of bubble collapse intensity. The different trends of the collapsing temperature and emitted sound pressure are caused by the energy distribution during the bubble collapse. Moreover, a series of simulations are conducted to establish the distribution map of the optimum liquid temperature where the collapse intensity is maximized. The relationship between the collapse intensity and the radial dynamics of the bubble is discussed and the reliable indicator is identified. This study provides a clear picture of how the thermodynamic process changes cavitation aggressiveness and enriches the understanding of this complex thermal-hydrodynamic phenomenon.     

Phase transitions of perfluorocarbon nanoemulsion induced with ultrasound: A mathematical model

While ultrasound has been used in many medical and industrial applications, only recently has research been done on phase transformations induced by ultrasound. This paper presents a numerical model and the predicted results of the phase transformation of a spherical nanosized droplet of perfluorocarbon in water. Such a model has applications in acoustic droplet vaporization, the generation of gas bubbles for medical imaging, therapeutic delivery and other biomedical applications.The formation of a gas phase and the subsequent bubble dynamics were studied as a function of acoustic parameters, such as frequency and amplitude, and of the physical aspects of the perfluorocarbon nanodroplets, such as chemical species, temperature, droplet size and interfacial energy. The model involves simultaneous applications of mass, energy and momentum balances to describe bubble formation and collapse, and was developed and solved numerically. It was found that, all other parameters being constant, the maximum bubble size and collapse velocity increases with increasing ultrasound amplitude, droplet size, vapor pressure and temperature. The bubble size and collapse velocity decreased with increasing surface tension and frequency. These results correlate with experimental observations of acoustic droplet vaporization.     

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.     

Numerical modelling of acoustic cavitation threshold in water with non-condensable bubble nuclei

Numerical modelling of acoustic cavitation threshold in water is presented taking into account non-condensable bubble nuclei, which are composed of water vapor and non-condensable air. The cavitation bubble growth and collapse dynamics are modeled by solving the Rayleigh-Plesset or Keller-Miksis equation, which is combined with the energy equations for both the bubble and liquid domains, and directly evaluating the phase-change rate from the liquid and bubble side temperature gradients. The present work focuses on elucidating acoustic cavitation in water with a wide range of cavitation thresholds (0.02–30 MPa) reported in the literature. Computations for different nucleus sizes and acoustic frequencies are performed to investigate their effects on bubble growth and cavitation threshold. The numerical predictions are observed to be comparable to the experimental data in the previous works and show that the cavitation threshold in water has a wide range depending on the bubble nucleus size.     

Optical nucleation of bubble clouds in a high pressure spherical resonator

An experimental setup for nucleating clouds of bubbles in a high-pressure spherical resonator is described. Using nanosecond laser pulses and multiple phase gratings, bubble clouds are optically nucleated in an acoustic field. Dynamics of the clouds are captured using a high-speed CCD camera. The images reveal cloud nucleation, growth, and collapse and the resulting emission of radially expanding shockwaves. These shockwaves are reflected at the interior surface of the resonator and then reconverge to the center of the resonator. As the shocks reconverge upon the center of the resonator, they renucleate and grow the bubble cloud. This process is repeated over many acoustic cycles and with each successive shock reconvergence, the bubble cloud becomes more organized and centralized so that subsequent collapses give rise to stronger, better defined shockwaves. After many acoustic cycles individual bubbles cannot be distinguished and the cloud is then referred to as a cluster. Sustainability of the process is ultimately limited by the detuning of the acoustic field inside the resonator. The nucleation parameter space is studied in terms of laser firing phase, laser energy, and acoustic power used.     

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.     

The cavitation induced Becquerel effect and the hot spot theory of sonoluminescence

Over 150 years ago, Becquerel discovered the ultraviolet illumination of one of a pair of identical electrodes in liquid water produced an electric current, the phenomenon called the Becquerel effect. Recently, a similar effect was observed if the water surrounding one electrode is made to cavitate by focused acoustic radiation, which by similarity is referred to as the cavitation induced Becquerel effect. The current in the cavitation induced Becquerel effect was found to be semi-logarithmic with the standard electrode potential that is consistent with the oxidation of the electrode surface by the photo-decomposition theory of photoelectrochemistry. But oxidation of the electrode surface usually requires high temperatures, say as in cavitation. Absent high bubble temperatures, cavitation may produce vacuum ultraviolet (VUV) light that excites water molecules in the electrode film to higher H(2)O(*) energy states, the excited states oxidizing the electrode surface by chemical reaction. Solutions of the Rayleigh-Plesset equation during bubble collapse that include the condensation of water vapor show any increase in temperature or pressure of the water vapor by compression heating is compensated by the condensation of vapor to the bubble wall, the bubbles collapsing almost isothermally. Hence, the cavitation induced Becquerel effect is likely caused by cavitation induced VUV light at ambient temperature.     

Observations of the collapses and rebounds of millimeter-sized lithotripsy bubbles

Bubbles excited by lithotripter shock waves undergo a prolonged growth followed by an inertial collapse and rebounds. In addition to the relevance for clinical lithotripsy treatments, such bubbles can be used to study the mechanics of inertial collapses. In particular, both phase change and diffusion among vapor and noncondensable gas molecules inside the bubble are known to alter the collapse dynamics of individual bubbles. Accordingly, the role of heat and mass transport during inertial collapses is explored by experimentally observing the collapses and rebounds of lithotripsy bubbles for water temperatures ranging from 20 to 60 °C and dissolved gas concentrations from 10 to 85% of saturation. Bubble responses were characterized through high-speed photography and acoustic measurements that identified the timing of individual bubble collapses. Maximum bubble diameters before and after collapse were estimated and the corresponding ratio of volumes was used to estimate the fraction of energy retained by the bubble through collapse. The rebounds demonstrated statistically significant dependencies on both dissolved gas concentration and temperature. In many observations, liquid jets indicating asymmetric bubble collapses were visible. Bubble rebounds were sensitive to these asymmetries primarily for water conditions corresponding to the most dissipative collapses.     

Contributions to the acoustic excitation of bubbles released from a nozzle

It has recently been demonstrated that air bubbles released from a nozzle are excited into volume mode oscillations by the collapse of the neck of air formed at the moment of bubble detachment. A pulse of sound is caused by these breathing mode oscillations, and the sound of air-entraining flows is made up of many such pulses emitted as bubbles are created. This paper is an elaboration on a JASA-EL paper, which examined the acoustical excitation of bubbles released from a nozzle. Here, further details of the collapse of a neck of air formed at the moment of bubble formation and its implications for the emission of sound by newly formed bubbles are presented. The role of fluid surface tension was studied using high-speed photography and found to be consistent with a simple model for neck collapse. A re-entrant fluid jet forms inside the bubble just after detachment, and its role in acoustic excitation is assessed. It is found that for slowly-grown bubbles the jet does make a noticeable difference to the total volume decrease during neck collapse, but that it is not a dominant effect in the overall acoustic excitation.     

声场中水力空化泡的动力学特性

以水为工作介质,考虑了液体黏性、表面张力、可压缩性及湍流作用等情况,对文丘里管反应器中空化泡在声场作用下的动力学行为特性进行了数值研究.分析了超声波频率、声压及喉径比对空化泡运动特性以及空化泡崩溃时所形成泡温以及压力脉冲的影响.结果表明,超声将水力空化泡运动调制成稳态空化,有利于增强空化效果. 关键词： 超声波 水力空化 湍流 气泡动力学     

Numerical investigation on acoustic cavitation characteristics of an air-vapor bubble: Effect of equation of state for interior gases

The cavitation dynamics of an air-vapor mixture bubble with ultrasonic excitation can be greatly affected by the equation of state (EOS) for the interior gases. To simulate the cavitation dynamics, the Gilmore-Akulichev equation was coupled with the Peng–Robinson (PR) EOS or the Van der Waals (vdW) EOS. In this study, the thermodynamic properties of air and water vapor predicted by the PR and vdW EOS were first compared, and the results showed that the PR EOS gives a more accurate estimation of the gases within the bubble due to the less deviation from the experimental values. Moreover, the acoustic cavitation characteristics predicted by the Gilmore-PR model were compared to the Gilmore-vdW model, including the bubble collapse strength, the temperature, pressure and number of water molecules within the bubble. The results indicated that a stronger bubble collapse was predicted by the Gilmore-PR model rather than the Gilmore-vdW model, with higher temperature and pressure, as well as more water molecules within the collapsing bubble. More importantly, it was found that the differences between both models increase at higher ultrasound amplitudes or lower ultrasound frequencies while decreasing as the initial bubble radius and the liquid parameters (e.g., surface tension, viscosity and temperature of the surrounding liquid) increase. This study might offer important insights into the effects of the EOS for interior gases on the cavitation bubble dynamics and the resultant acoustic cavitation-associated effects, contributing to further optimization of its applications in sonochemistry and biomedicine.     

Shock wave interaction with laser-generated single bubbles

The interaction of a lithotripter shock wave (LSW) with laser-generated single vapor bubbles in water is investigated using high-speed photography and pressure measurement via a fiber-optic probe hydrophone. The interaction leads to nonspherical collapse of the bubble with secondary shock wave emission and microjet formation along the LSW propagation direction. The maximum pressure amplification is produced during the collapse phase of the bubble oscillation when the compressive pulse duration of the LSW matches with the forced collapse time of the bubble.     

Comparison of electrohydraulic lithotripters with rigid and pressure-release ellipsoidal reflectors. II. Cavitation fields.

Dramatically different cavitation was produced by two separate acoustic pulses that had different shapes but similar duration, frequency content, and peak positive and negative pressure. Both pulses were produced by a Dornier HM-3 style lithotripter: one pulse when the ellipsoidal reflector was rigid, the other when the reflector was pressure release. The cavitation, or bubble action, generated by the conventional rigid-reflector pulse was nearly 50 times longer lived and 3-13 times stronger than that produced by the pressure-release-reflector pulse. Cavitation durations measured by passive acoustic detection and high-speed video agreed with calculations based on the Gilmore equation. Cavitation intensity, or destructive potential, was judged (1) experimentally by the size of pits in aluminum foil detectors and (2) numerically by the calculated amplitude of the shock wave emitted by a collapsing bubble. The results indicate that the trailing positive spike in the pressure-release-reflector waveform stifles bubble growth and mitigates the collapse, whereas the trough after the positive spike in the rigid-reflector waveform triggers inertially driven growth and collapse. The two reflectors therefore provide a tool to compare effects in weakly and strongly cavitating fields and thereby help assess cavitation's role in lithotripsy.     

Bubble acceleration in the ablative Rayleigh-Taylor instability

The highly nonlinear evolution of the single-mode Rayleigh-Taylor instability (RTI) at the ablation front of an accelerated target is investigated in the parameter range typical of inertial confinement fusion implosions. A new phase of the nonlinear bubble evolution is discovered. After the linear growth phase and a short constant-velocity phase, it is found that the bubble is accelerated to velocities well above the classical value. This acceleration is driven by the vorticity accumulation inside the bubble resulting from the mass ablation and vorticity convection off the ablation front. While the ablative growth rates are slower than their classical values in the linear regime, the ablative RTI grows faster than the classical RTI in the nonlinear regime for deuterium and tritium ablators.     

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.     

A dual passive cavitation detector for localized detection of lithotripsy-induced cavitation in vitro

A passive cavitation detector (PCD) identifies cavitation events by sensing acoustic emissions generated by the collapse of bubbles. In this work, a dual passive cavitation detector (dual PCD), consisting of a pair of orthogonal confocal receivers, is described for use in shock wave lithotripsy. Cavitation events are detected by both receivers and can be localized to within 5 mm by the nature of the small intersecting volume of the focal areas of the two receivers in association with a coincidence detection algorithm. A calibration technique, based on the impulse response of the transducer, was employed to estimate radiated pressures at collapse near the bubble. Results are presented for the in vitro cavitation fields of both a clinical and a research electrohydraulic lithotripter. The measured lifetime of the primary growth-and-collapse of the cavitation bubbles increased from 180 to 420 microseconds as the power setting was increased from 12 to 24 kV. The measured lifetime compared well with calculations based on the Gilmore-Akulichev formulation for bubble dynamics. The radiated acoustic pressure 10 mm from the collapsing cavitation bubble was measured to vary from 4 to 16 MPa with increasing power setting; although the trends agreed with calculations, the predicted values were four times larger than measured values. The axial length of the cavitation field correlated well with the 6-dB region of the acoustic field. However, the width of the cavitation field (10 mm) was significantly narrower than the acoustic field (25 mm) as bubbles appeared to be drawn to the acoustic axis during the collapse. The dual PCD also detected signals from "rebounds," secondary and tertiary growth-and-collapse cycles. The measured rebound time did not agree with calculations from the single-bubble model. The rebounds could be fitted to a Rayleigh collapse model by considering the entire bubble cloud as an effective single bubble. The results from the dual PCD agreed well with images from high-speed photography. The results indicate that single-bubble theory is sufficient to model lithotripsy cavitation dynamics up to time of the main collapse, but that upon collapse bubble cloud dynamics becomes important.     

Dependence of the characteristics of bubbles on types of sonochemical reactors

Computer simulations of bubble oscillations in liquid water irradiated by an ultrasonic wave have revealed that the characteristic of bubbles depends on types of sonochemical reactors: a horn-type reactor and a standing-wave type reactor. When the acoustic amplitude is large at 20 kHz, the bubble content is mostly water vapor even at the end of the bubble collapse and the temperature inside a bubble at the collapse is relatively low. On the other hand, when the acoustic amplitude is relatively low, the bubble content is mostly noncondensable gas at the end of the bubble collapse and the bubble temperature is relatively high. In a horn-type sonochemical reactor, the former type of bubbles are dominant because many bubbles exist near the horn-tip where the acoustic amplitude is large, while in a standing-wave type reactor the latter type of bubbles are dominant because the Bjerknes force gathers bubbles at a region where acoustic amplitude is relatively low.