Energy analysis during acoustic bubble oscillations: Relationship between bubble energy and sonochemical parameters

In this work, energy analysis of an oscillating isolated spherical bubble in water irradiated by an ultrasonic wave has been theoretically studied for various conditions of acoustic amplitude, ultrasound frequency, static pressure and liquid temperature in order to explain the effects of these key parameters on both sonochemistry and sonoluminescence. The Keller–Miksis equation for the temporal variation of the bubble radius in compressible and viscous medium has been employed as a dynamics model. The numerical calculations showed that the rate of energy accumulation, dE/dt, increased linearly with increasing acoustic amplitude in the range of 1.5–3.0 atm and decreased sharply with increasing frequency in the range 200–1000 kHz. There exists an optimal static pressure at which the power w is highest. This optimum shifts toward a higher value as the acoustic amplitude increases. The energy of the bubble slightly increases with the increase in liquid temperature from 10 to 60 °C. The results of this study should be a helpful means to explain a variety of experimental observations conducted in the field of sonochemistry and sonoluminescence concerning the effects of operational parameters.     

A comprehensive numerical analysis of heat and mass transfer phenomenons during cavitation sono-process

The present study treats the effects of mass transport, heat transfer and chemical reactions heat on the bubble dynamics by spanning a range of ambient bubble radii. The thermodynamic behavior of the acoustic bubble was shown for three wave frequencies, 355, 515 and 1000 kHz. The used acoustic amplitude ranges from 1 to 3 atm. It has been demonstrated that the ambient bubble radius, R₀, of the maximal response (i.e., maximal bubble temperature and pressure, T_max and P_max) is shifted toward lower values if the acoustic amplitude (at fixed frequency) or the ultrasonic frequency (at fixed amplitude) are increased. The range of the ambient bubble radius narrows as the ultrasonic frequency increases. Heat exchange at the bubble interface was found to be the most important mechanism within the bubble internal energy balance for acoustic amplitudes lower than 2.5 and 3 atm for ultrasonic frequencies of 355 and 515 kHz, respectively. For acoustic amplitudes greater or equal to 2.5 and 3 atm, corresponding to 355 and 515 kHz, respectively, mass transport mechanism (i.e., evaporation and condensation of water vapor) becomes dominant compared to the other mechanisms. At 1000 kHz, the mechanism of heat transfer persists to be dominant for all the used acoustic amplitudes (from 1 to 3 atm). Practically, all the above observations were maintained for bubbles at and around the optimum bubble radius, whereas no significant impact of the three energetic mechanisms was observed for bubbles of too lower and too higher values of R₀ (limits of the investigated ranges of R₀).     

Optimum bubble temperature for the sonochemical production of oxidants

Numerical simulations of bubble oscillations in liquid water irradiated by an ultrasonic wave are performed for various acoustic amplitudes and various ambient pressures. In the numerical simulations, effect of non-equilibrium evaporation and condensation of water vapor at the bubble wall and that of chemical reactions of gases and vapor inside a bubble are taken into account. The oxidants such as OH radicals, O radicals, H(2)O(2) molecules, and O(3) molecules are created from water vapor inside a heated bubble when a bubble collapses strongly. They are dispersed into the liquid and solutes are oxidized by the oxidants, which is called sonochemical reactions. The computer simulations have revealed that there exists the optimum bubble temperature, which is about 5500 K, for the production of the oxidants inside an air bubble because at higher bubble temperature the oxidants are strongly consumed inside a bubble by oxidizing nitrogen. Correspondingly, there exists an optimum acoustic amplitude for the production of the oxidants, which is about 2.2 atm when the ultrasonic frequency is 140 kHz and the ambient pressure is 1 atm. For an oxygen bubble, on the other hand, the amount of the oxidants created inside a bubble becomes nearly independent of the bubble temperature at the collapse above about 6000 K because nitrogen is absent.     

Theoretical prediction of the yield of strong oxides under acoustic cavitation

Considering liquid viscosity, surface tension, and liquid compressibility, the effects of dynamical behaviors of cavitation bubbles on temperature and the amount of oxides inside the bubble are numerically investigated by acoustic field,regarding water as a work medium. The effects of acoustic frequency, acoustic pressure amplitude, and driving waveforms on bubble temperature and the number of oxides inside the bubbles by rapid collapse of cavitation bubbles are analysed.The results show that the changes of acoustic frequency, acoustic pressure amplitude, and driving waveforms not only have an effect on temperature and the number of oxides inside the bubble, but also influence the degradation species of pollution,which provides guidance for improving the degradation of water pollution.     

Finite-amplitude vibration of a bubble and sonoluminescence

Numerical solutions of the differential equation for a bubble performing finite-amplitude vibration are given in detail for a variety of situations. The results demonstrate that in lower acoustic pressure (maximum Mach number very low) its vibration has bounce. When acoustic pressure is in excess of 1.18atm and the instantaneous radius of the bubble approaches its equivalent Van der Waals radius, the maximum velocity and acceleration on the surface of a bubble have a huge increase in a very short period, which seems to favour the sonoluminescence. In vacuum environment (0.1atm), an intensive sonoluminescence could be generated.     

球状泡群内气泡的耦合振动

振动气泡形成辐射场影响其他气泡的运动, 故多气泡体系中气泡处于耦合振动状态. 本文在气泡群振动模型的基础上, 考虑气泡间耦合振动的影响, 得到了均匀球状泡群内振动气泡的动力学方程, 以此为基础分析了气泡的非线性声响应特征. 气泡间的耦合振动增加了系统对每个气泡的约束, 降低了气泡的自然共振频率, 增强了气泡的非线性声响应. 随着气泡数密度的增加, 振动气泡受到的抑制增强; 增加液体静压力同样可抑制泡群内气泡的振动, 且存在静压力敏感区(1–2 atm, 1 atm=1.01325×10⁵ Pa); 驱动声波对气泡振动影响很大, 随着声波频率的增加, 能够形成空化影响的气泡尺度范围变窄. 在同样的声条件、泡群尺寸以及气泡内外环境下, 初始半径小于5 μm 的气泡具有较强的声响应. 气泡耦合振动会削弱单个气泡的空化影响, 但可延长多气泡系统空化泡崩溃发生的时间间隔和增大作用范围, 整体空化效应增强.     

Effects of modulation wave shape on modulation frequency discrimination with electrical hearing

Amplitude modulations of pulsitile stimulation can be used to convey pitch information to cochlear implant users. One variable in designing cochlear implant speech processors is the choice of modulation waveform used to convey pitch information. Modulation frequency discrimination thresholds were measured for 100 Hz modulations with four waveforms (sine, sawtooth, a sharpened sawtooth, and square). Just-noticeable differences (JNDs) were similar for all but the square waveform, which often produced larger JNDs. The results suggest that a sine, sawtooth, and sharpened sawtooth waveforms are likely to provide similar pitch discrimination within a speech processing strategy.     

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.     

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。     

Theoretical model of ice nucleation induced by inertial acoustic cavitation. Part 2: Number of ice nuclei generated by a single bubble

In the preceding paper (part 1), the pressure and temperature fields close to a bubble undergoing inertial acoustic cavitation were presented. It was shown that extremely high liquid water pressures but quite moderate temperatures were attained near the bubble wall just after the collapse providing the necessary conditions for ice nucleation. In this paper (part 2), the nucleation rate and the nuclei number generated by a single collapsing bubble were determined. The calculations were performed for different driving acoustic pressures, liquid ambient temperatures and bubble initial radius. An optimal acoustic pressure range and a nucleation temperature threshold as function of bubble radius were determined. The capability of moderate power ultrasound to trigger ice nucleation at low undercooling level and for a wide distribution of bubble sizes has thus been assessed on the theoretical ground.     

Theoretical estimation of sonochemical yield in bubble cluster in acoustic field

In order to learn more about the physical phenomena occurring in cloud cavitation, the nonlinear dynamics of a spherical cluster of cavitation bubbles and cavitation bubbles in cluster in an acoustic field excited by a square pressure wave are numerically investigated by considering viscosity, surface tension, and the weak compressibility of the liquid.The theoretical prediction of the yield of oxidants produced inside bubbles during the strong collapse stage of cavitation bubbles is also investigated. The effects of acoustic frequency, acoustic pressure amplitude, and the number of bubbles in cluster on bubble temperature and the quantity of oxidants produced inside bubbles are analyzed. The results show that the change of acoustic frequency, acoustic pressure amplitude, and the number of bubbles in cluster have an effect not only on temperature and the quantity of oxidants inside the bubble, but also on the degradation types of pollutants, which provides a guidance in improving the sonochemical degradation of organic pollutants.     

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.     

On the physical origin of conical bubble structure under an ultrasonic horn

The cavitation field generated by an ultrasonic horn at low frequency and high power is known to self-organize into a conical bubble structure. The physical mechanism at the origin of this bubble structure is investigated using numerical simulations and acoustic pressure measurements. The thin bubbly layer lying at horn surface is shown to act as a nonlinear thickness resonator that amplifies acoustic pressure and distorts acoustic waveform. This mechanism explains the self-stabilization of the conical bubble structure as well as the generation of shock wave and the focusing at very short distance.     

A theoretical model for ice primary nucleation induced by acoustic cavitation

The modelling and simulation of ice nucleation triggered by acoustic cavitation was addressed in this study. The objective was to evaluate the number of nuclei generated by a single gas bubble and afterwards by a multi-bubble system as function of the acoustic pressure (ultrasound wave amplitude) and supercooling level (liquid temperature). According to our calculations, the nucleation could be initiated with moderated acoustic pressure amplitude (around one bar) even at low supercooling levels (around few degrees). These results may provide a sound basis for the control of ice crystal size and morphology which is a key issue in industrial freezing and freeze-drying processes.     

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.     

Insight into the impact of excluding mass transport,heat exchange and chemical reactions heat on the sonochemical bubble yield: Bubble size-dependency

Numerical simulations have been performed on a range of ambient bubble radii, in order to reveal the effect of mass transport, heat exchange and chemical reactions heat on the chemical bubble yield of single acoustic bubble. The results of each of these energy mechanisms were compared to the normal model in which all these processes (mass transport, thermal conduction, and reactions heat) are taken into account. This theoretical work was carried out for various frequencies (f: 200, 355, 515 and 1000 kHz) and different acoustic amplitudes (P_A: 1.5, 2 and 3 atm). The effect of thermal conduction was found to be of a great importance within the bubble internal energy balance, where the higher rates of production (for all acoustic amplitudes and wave frequencies) are observed for this model (without heat exchange). Similarly, the ignorance of the chemical reactions heat (model without reactions heat) shows the weight of this process into the bubble internal energy, where the yield of the main species (OH, H, O and H₂) for this model was accelerated notably compared to the complete model for the acoustic amplitudes greater than 1.5 atm (for f = 500 kHz). However, the lowest production rates were registered for the model without mass transport compared to the normal model, for the acoustic amplitudes greater than 1.5 atm (f = 500 kHz). This is observed even when the temperature inside bubble for this model is greater than those retrieved for the other models. On the other hand, it has been shown that, at the acoustic amplitude of 1.5 atm, the maximal production rates of the main species (OH, H, O and H₂) for all the adopted models appear at the same optimum ambient-bubble size (R₀ ~ 3, 2.5 and 2 µm for, respectively, 355, 500 and 1000 kHz). For P_A = 2 and 3 atm (f = 500 kHz), the range of the maximal yield of OH radicals is observed at the range of R₀ where the production of OH, O and H₂ is the lowest, which corresponds to the bubble temperature at around 5500 K. The maximal production rate of H, O and H₂ is shifted toward the range of ambient bubble radii corresponding to the bubble temperatures greater than 5500 K. The ambient bubble radius of the maximal response (maximal production rate) is shifted toward the smaller bubble sizes when the acoustic amplitude (wave frequency is fixed) or the ultrasound frequency (acoustic power is fixed) is increased. In addition, it is observed that the increase of wave frequency or the acoustic amplitude decrease cause the range of active bubbles to be narrowed (scenario observation for the four investigated models).     

水下等离子体声源的冲击波负压特性

基于修正的Rayleigh气泡脉动方程对水下等离子体声源放电产生的 强声冲击波的传播过程进行了分析; 利用Euler方程作为控制方程组, 建立了水下等离子体声源的聚束声场模型, 通过仿真计算获得的传播云图对冲击波负压的形成机理进行了直观的理论分析. 结果表明: 经过聚能反射罩反射汇聚得到的聚束波在反射稀疏波和水的惯性作用下, 聚束波周围水域产生了拉伸, 形成负压区, 如果拉伸力大于水的抗拉上限, 就会使得水中形成不连续现象, 即出现空化气泡; 此外聚能罩边缘处产生的衍射波进一步加剧了负压的产生, 边缘衍射波最终与拉伸波叠加, 使冲击波负压达到最大值; 通过对比仿真波形和实验波形, 从而验证和进一步揭示了冲击波负压的形成原因. 研究结果对认识水下冲击波的传播规律和进一步改进等离子体声源的设计具有指导意义. 关键词： 等离子体声源 冲击波负压 聚束声场模型 气泡     

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.     

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。     

Single bubble sonoluminescence driven by non-simple-harmonic ultrasounds

The dependence of the single bubble sonoluminescence (SBSL) on the waveforms of the driving ultrasound has been investigated by both experiment and numerical calculation. Three types of non-simple-harmonic waves, the rectangular, triangular and as well as the sinusoidal wave with a pulse, are used to drive the SBSL in our research. The triangular wave is the most effective, while the rectangular wave is the worst and the sinusoidal wave in the middle. However, the rectangular wave drives the brightest SBSL among those waves if the sound pressure amplitude keeps constant. When we use a simple-harmonic wave with a pulse as the driving sound, stable and periodic SBSL flashes have been observed. An increase in the flash intensity can be observed as the pulse is put at a suitable phase related to the sinusoidal wave. All of the observations are investigated numerically. Well qualitative agreements between the numerical simulations and the experimental measurements have been achieved.