Radial oscillation and translational motion of a gas bubble in a micro-cavity

According to classical nucleation theory, a gas nucleus can grow into a cavitation bubble when the ambient pressure is negative. Here, the growth process of a gas nucleus in a micro-cavity was simplified to two “events”, and the full confinement effect of the surrounding medium of the cavity was considered by including the bulk modulus in the equation of state. The Rayleigh–Plesset-like equation of the cavitation bubble in the cavity was derived to model the radial oscillation and translational motion of the cavitation bubble in the local acoustic field. The numerical results show that the nucleation time of the cavitation bubble is sensitive to the initial position of the gas nucleus. The cavity size affects the duration of the radial oscillation of the cavitation bubble, where the duration is shorter for smaller cavities. The equilibrium radius of a cavitation bubble grown from a gas nucleus increases with increasing size of the cavity. There are two possible types of translational motion: reciprocal motion around the center of the cavity and motion toward the cavity wall. The growth process of gas nuclei into cavitation bubbles is also dependent on the compressibility of the surrounding medium and the magnitude of the negative pressure. Therefore, gas nuclei in a liquid cavity can be excited by acoustic waves to form cavitation bubbles, and the translational motion of the cavitation bubbles can be easily observed owing to the confining influence of the medium outside the cavity.     

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.     

Influence of rigid wall on the nonlinear pulsation of nearby bubble

This paper mainly focuses on the nonlinear pulsation of a bubble near the rigid wall. Dynamics of near-wall bubble and free bubble are discussed and compared in details. Investigation reveals as the driving acoustic pressure amplitude increases, nonlinear pulsation of bubble becomes intense gradually. Besides, decreasing the viscosity of host liquid is advantageous for the nonlinear pulsation of bubble. Bifurcation diagrams of bubble radius show acoustic reflection of the rigid wall makes the initial bifurcation appear at low driving acoustic amplitude and on bubble with small ambient radius, and makes the bifurcation still exist for bubble in high-viscosity liquids. That indicates the rigid wall will produce enhancement on the nonlinearity of nearby bubble. As the bubble approaches the wall, the enhancement becomes strong. Moreover, research on the influence of driving frequency shows the rigid wall makes the frequency band corresponding to chaos around the resonant frequency of free bubble shift downward.     

方波驱动下双气泡的动力学行为*

探索方波驱动下双气泡的脉动规律,能够促进方波在声空化工程中的实际应用。本文通过数值求解双气泡耦合方程组,研究了方波驱动下双气泡的动力学行为,得到了多种条件下不同时刻两个气泡半径的数值,并以此计算出气泡间的次Bjerknes力。研究表明,增大驱动频率会使得两个气泡膨胀时能达到的最大半径和次Bjerknes力减小。当两个气泡的平衡半径不同时,其中一个气泡的剧烈收缩会使得另一个气泡产生一个振动方向相反的声脉冲。随着两个气泡平衡半径差距的增加,气泡收缩的时间间隔增大。此外,当驱动声压幅值逐渐增大时,气泡脉动规律也会发生很大的变化。     

On the dynamics of moving single bubble sonoluminescence

It is well known that the primary Bjerknes force is the origin of the trapping of sonoluminescing bubble in the sound field in liquid. In the present Letter, the quantitative investigation of the behavior of hydrodynamic force on the moving sonoluminescing (SL) bubble introduces the new role of stabilizing the trajectory motion of the bubble for primary Bjerknes force. Using a complete force balanced radial-translational dynamics, it is analytically discussed that by increasing the bubble distance from the antinode of the sound field the increase of the magnitude of inward Bjerknes force, controls the size of the domain of the bubble trajectory. At this time the wake produced by the rapid variation of the bubble's relative translational velocity to the surrounding liquid, changes the bubble direction of motion through the effect of history force. The required momentum for accelerating the SL bubble around the central antinode is produced by the added mass force at the bubble collapse. It is revealed in a re-examination of the coupled radial-translational dynamics for a trapping bubble that because of the bubble lower translational acceleration caused due to the lower added mass force and the bubble attraction towards the acoustic antinodes in presence of inward Bjerknes force, the small bubble will be trapped at the antinode of the sound field.     

声驻波场中空化泡的动力学特性

以水为工作介质, 考虑了液体的可压缩性, 研究了驻波声场中空化泡的运动特性, 模拟了驻波场中各位置处空化泡的运动状态以及相关参数对各位置处空化泡在主Bjerknes力作用下运动方向的影响. 结果表明: 驻波声场中, 空化泡的运动状态分为三个区域, 即在声压波腹附近空化泡做稳态空化, 在偏离波腹处空化泡做瞬态空化, 在声压波节附近, 空化泡在主Bjerknes 力作用下, 一直向声压波节处移动, 显示不发生空化现象; 驻波场中声压幅值增加有利于空化的发生, 但声压幅值增加到一定上限时, 压力波腹区域将排斥空化泡, 并驱赶空化泡向压力波节移动, 不利于空化现象的发生; 当声频率小于初始空化泡的共振频率时, 声频率越高, 由于主Bjerknes 力的作用将有更多的空化泡向声压波节移动, 不利于空化的发生, 尤其是驻波场液面的高度不应是声波波长的1/4; 当声频率一定时, 空化泡初始半径越大越有利于空化现象的发生, 但当空化泡的初始半径超过声频率的共振半径时, 由于主Bjerknes力的作用将有更多的空化泡向声压波节移动, 不利于空化的发生.     

The impact of methanol mass transport on its conversion for the production of hydrogen and oxygenated reactive species in sono-irradiated aqueous solution

This study aims principally to assess numerically the impact of methanol mass transport (i.e., evaporation/condensation across the acoustic bubble wall) on the thermodynamics and chemical effects (methanol conversion, hydrogen and oxygenated reactive species production) of acoustic cavitation in sono-irradiated aqueous solution. This effect was revealed at various ultrasound frequencies (from 213 to 1000 kHz) and acoustic intensities (1 and 2 W/cm²) over a range of methanol concentrations (from 0 to 100%, v/v). It was found that the impact of methanol concentration on the expansion and compression ratios, bubble temperature, CH₃OH conversion and the molar productions inside the bubble is frequency dependent (either with or without consideration of methanol mass transport), where this effect is more pronounced when the ultrasound frequency is decreased. Alternatively, the decrease in acoustic intensity decreases clearly the effect of methanol mass transport on the bubble sono-activity. When methanol mass transfer is eliminated, the decrease of the bubble temperature, CH₃OH conversion and the molar yield of the bubble with the rise of methanol concentration was found to be more amortized as the wave frequency is reduced from 1 MHz to 213 kHz, compared to the case when the mass transport of methanol is taken into account. Our findings indicate clearly the importance of incorporating the evaporation and condensation mechanisms of methanol throughout the numerical simulations of a single bubble dynamics and chemical activity.     

Dynamics of double bubbles under the driving of burst ultrasound

This paper investigates the pulsations and translation of bubbles in a double-bubble system driven by burst ultrasound. Results illustrate that for two identical bubbles, decreasing the frequency of burst or increasing its amplitude can enhance the pulsations and improve the translation velocities of bubbles. In a certain scope, large bubble brings about fast translation velocity, but the velocity will fall down for too large bubble, such as the bubble with ambient radius over about its resonance radius. When the ambient radii of two bubbles are different, translation of the large bubble is smaller than that of the small bubble. In addition, the effect of initial distance between bubbles is described as well. If burst serials are used, shortening the time interval between each burst and improving the acoustic amplitude of bursts are beneficial for the translations of bubbles.     

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1-4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.     

Study on the bubble transport mechanism in an acoustic standing wave field

The use of bubbles in applications such as surface chemistry, drug delivery, and ultrasonic cleaning etc. has been enormously popular in the past two decades. It has been recognized that acoustically-driven bubbles can be used to disturb the flow field near a boundary in order to accelerate physical or chemical reactions on the surface. The interactions between bubbles and a surface have been studied experimentally and analytically. However, most of the investigations focused on violently oscillating bubbles (also known as cavitation bubble), less attention has been given to understand the interactions between moderately oscillating bubbles and a boundary. Moreover, cavitation bubbles were normally generated in situ by a high intensity laser beam, little experimental work has been carried out to study the translational trajectory of a moderately oscillating bubble in an acoustic field and subsequent interactions with the surface. This paper describes the design of an ultrasonic test cell and explores the mechanism of bubble manipulation within the test cell. The test cell consists of a transducer, a liquid medium and a glass backing plate. The acoustic field within the multi-layered stack was designed in such a way that it was effectively one dimensional. This was then successfully simulated by a one dimensional network model. The model can accurately predict the impedance of the test cell as well as the mode shape (distribution of particle velocity and stress/pressure field) within the whole assembly. The mode shape of the stack was designed so that bubbles can be pushed from their injection point onto a backing glass plate. Bubble radial oscillation was simulated by a modified Keller–Miksis equation and bubble translational motion was derived from an equation obtained by applying Newton’s second law to a bubble in a liquid medium. Results indicated that the bubble trajectory depends on the acoustic pressure amplitude and initial bubble size: an increase of pressure amplitude or a decrease of bubble size forces bubbles larger than their resonant size to arrive at the target plate at lower heights, while the trajectories of smaller bubbles are less influenced by these factors. The test cell is also suitable for testing the effects of drag force on the bubble motion and for studying the bubble behavior near a surface.     

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.     

Acoustic vibration of the amphibian eardrum studied by white noise analysis and holographic interferometry

The motion of the amphibian eardrum under free-field acoustic stimulation was investigated using time-averaged holography. We show that the amplitude is linearly related to sound pressure up to +/- 1000 nm. The frequency response of the eardrum shows broad resonance characteristics with a main peak between 1200-2200 Hz. The velocity of the tympanic membrane's motion at its resonance frequency matches the acoustic velocity of air particles. The resonance characteristics of the eardrum are also revealed by white noise stimulation. The power spectrum obtained by Fourier transformation of the autocorrelation of the response to noise resembles closely that obtained by holography.     

声场中双空化泡的运动特性

空化泡的运动特性是声场作用下的动力学行为,受空化泡初始半径,声压幅值,驱动声压频率,液体特性等众多因素的影响,是个复杂工程。本文从双空化泡运动方程出发,考虑到液体粘滞系数、空化泡辐射阻尼项的影响,研究了不同初始半径、驱动声压频率、驱动声压幅值、液体粘滞系数下空化泡泡壁的运动情况,研究结果表明不同初始半径、外界驱动声压频率、驱动声压幅值、液体粘滞系数均会对空化泡的膨胀比和空化泡的溃灭时间有一定影响。     

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.     

Bubble levitation and translation under single-bubble sonoluminescence conditions

Bubble levitation in an acoustic standing wave is re-examined for conditions relevant to single-bubble sonoluminescence. Unlike a previous examination [Matula et al., J. Acoust. Soc. Am. 102, 1522-1527 (1997)], the stable parameter space [Pa,R0] is accounted for in this realization. Forces such as the added mass force and drag are included, and the results are compared with a simple force balance that equates the Bjerknes force to the buoyancy force. Under normal sonoluminescence conditions, the comparison is quite favorable. A more complete accounting of the forces shows that a stably levitated bubble does undergo periodic translational motion. The asymmetries associated with translational motion are hypothesized to generate instabilities in the spherical shape of the bubble. A reduction in gravity results in reduced translational motion. It is hypothesized that such conditions may lead to increased light output from sonoluminescing bubbles.     

鼓泡床中超声驻波的模拟及其对气泡的调制机理

采用计算流体动力学（CFD）的方法，数值生成了鼓泡床中一对声换能器以16kHz高频振动引发的超声场。数值计算是基于包括粘性影响的可压缩流体基本守恒方程，并耦合了水的状态方程。模拟结果表明，在本研究所用的几何布置和换能器与时间相关的速度入口边界条件下，反应器中形成了一个稳定的驻波声场；由于波的非线性以及水的粘性，压力波节点呈现出轻微的时间漂移性。模拟结果与前人的实验结果定性吻合。在模拟的声压分布的基础上，分析了驻波声场调制气泡的机理。如比较熟知，气泡在驻波声场作用下或者向压力波节点运动或者向压力波腹点运动，取决于气泡尺寸与共振尺寸的关系。     

Influence of bulk nanobubble concentration on the intensity of sonoluminescence

The present study mainly examined the effects of the volumetric concentration of nanobubbles (ultrafine bubbles) on the intensity of sonoluminescence (SL). The addition of nanobubbles at high acoustic amplitude enhanced the SL intensity for various bubble concentrations in comparison with that in pure water. This probably means that the resulting high amplitude is over the Blake threshold, and accordingly nanobubbles expand to some extent, leading to higher SL intensity. Therefore, nanobubbles have the potential to provide nucleation sites for sonochemistry. The influence of bubble size on the intensity of SL was also evaluated.     

Bubble size distribution in acoustic droplet vaporization via dissolution using an ultrasound wide-beam method

Performance and efficiency of numerous cavitation enhanced applications in a wide range of areas depend on the cavitation bubble size distribution. Therefore, cavitation bubble size estimation would be beneficial for biological and industrial applications that rely on cavitation. In this study, an acoustic method using a wide beam with low pressure is proposed to acquire the time intensity curve of the dissolution process for the cavitation bubble population and then determine the bubble size distribution. Dissolution of the cavitation bubbles in saline and in phase-shift nanodroplet emulsion diluted with undegassed or degassed saline was obtained to quantify the effects of pulse duration (PD) and acoustic power (AP) or peak negative pressure (PNP) of focused ultrasound on the size distribution of induced cavitation bubbles. It was found that an increase of PD will induce large bubbles while AP had only a little effect on the mean bubble size in saline. It was also recognized that longer PD and higher PNP increases the proportions of large and small bubbles, respectively, in suspensions of phase-shift nanodroplet emulsions. Moreover, degassing of the suspension tended to bring about smaller mean bubble size than the undegassed suspension. In addition, condensation of cavitation bubble produced in diluted suspension of phase-shift nanodroplet emulsion was involved in the calculation to discuss the effect of bubble condensation in the bubble size estimation in acoustic droplet vaporization. It was shown that calculation without considering the condensation might underestimate the mean bubble size and the calculation with considering the condensation might have more influence over the size distribution of small bubbles, but less effect on that of large bubbles. Without or with considering bubble condensation, the accessible minimum bubble radius was 0.4 or 1.7 μm and the step size was 0.3 μm. This acoustic technique provides an approach to estimate the size distribution of cavitation bubble population in opaque media and might be a promising tool for applications where it is desirable to tune the ultrasound parameters to control the size distribution of cavitation bubbles.     

Theoretical analysis of interaction between a particle and an oscillating bubble driven by ultrasound waves in liquid

A theoretical model is developed to describe the interaction of a particle and an oscillating bubble at arbitrary separation between them. The derivation of the model is based on the multipole expansion of the particle and bubble velocity potentials and the use of Lagrangian mechanics. The model consists of three coupled ordinary differential equations. One of them accounts for the pulsation of the bubble and the other two describe the translation of the bubble and particle in an infinite, incompressible liquid. The model here is accurate to order 1/d~(10), where d is the distance between the centers of the particle and bubble. The effects of the size and density of the particle are investigated, namely, the interaction between the particle and bubble changes from repulsion to attraction with the increment of the particle density, and the increment of the particle size makes the interaction between the particle and bubble stronger. It is demonstrated that the driving frequency and acoustic pressure amplitude can affect the interaction of the particle and bubble. It is shown that the correct modeling of the translational dynamics of the bubble and particle at small separation distances requires terms accurate up to the tenth order.