Numerical simulations for sonochemistry

Numerical simulations for sonochemistry are reviewed including single-bubble sonochemistry, influence of ultrasonic frequency and bubble size, acoustic field, and sonochemical synthesis of nanoparticles. The theoretical model of bubble dynamics including the effect of non-equilibrium chemical reactions inside a bubble has been validated from the study of single-bubble sonochemistry. By the numerical simulations, it has been clarified that there is an optimum bubble temperature for the production of oxidants inside an air bubble such as OH radicals and H₂O₂ because at higher temperature oxidants are strongly consumed inside a bubble by oxidizing nitrogen. Unsolved problems are also discussed.     

Influence of ultrasonic frequency on multibubble sonoluminescence

Computer simulations of bubble oscillations are performed under conditions of multibubble sonoluminescence (MBSL) in water for various ultrasonic frequencies. The range of the ambient bubble radius for sonoluminescing bubbles narrows as the ultrasonic frequency increases; at 20 kHz it is 0.1-100 microm while at 1 MHz it is 0.1-3 microm. At 1 MHz, any sonoluminescing bubble disintegrates into a mass of smaller bubbles in a few or a few tens of acoustic cycles, while at 20 kHz and 140 kHz some sonoluminescing bubbles are shape stable. The mechanism of the light emission also depends on the ultrasonic frequency. As the ultrasonic frequency increases, the amount of water vapor trapped inside bubbles at the collapse decreases. As a result, MBSL originates mainly in plasma emissions at 1 MHz while it originates in chemiluminescence of OH radicals and plasma emissions at 20 kHz.     

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).     

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.     

Effects of ultrasound frequency and acoustic amplitude on the size of sonochemically active bubbles – Theoretical study

Numerical simulation of chemical reactions inside an isolated spherical bubble of oxygen has been performed for various ambient bubble radii at different frequencies and acoustic amplitudes to study the effects of these two parameters on the range of ambient radius for an active bubble in sonochemical reactions. The employed model combines the dynamic of bubble collapse with the chemical kinetics of single cavitation bubble. Results from this model were compared with some experimental results presented in the literature and good apparent trends between them were observed. The numerical calculations of this study showed that there always exists an optimal ambient bubble radius at which the production of oxidizing species at the end of the bubble collapse attained their upper limit. It was shown that the range of ambient radius for an active bubble increased with increasing acoustic amplitude and decreased with increasing ultrasound frequency. The optimal ambient radius decreased with increasing frequency. Analysis of curves showing optimal ambient radius versus acoustic amplitude for different ultrasonic frequencies indicated that for 200 and 300 kHz, the optimal ambient radius increased linearly with increasing acoustic amplitude up to 3 atm. However, slight minima of optimal radius were observed for the curves obtained at 500 and 1000 kHz.     

Insights into numerical simulation of controlled ultrasonic waveforms driving single cavitation bubble activity

A computational study treating cavitation phenomenon within a single bubble undergoing various controlled ultrasonic waveforms is presented in this paper. Numerical simulations using sinusoidal, square, triangular and sawtooth waves crossing an aqueous media, saturated with oxygen, are conducted upon various operational conditions of frequency and amplitude. Bubble radius, temperature and pressure were estimated over time for 64 combined cases. The obtained results show that at relatively low acoustic pressure, i.e. 1.5 and 2 atm, the square wave is proved to generate the highest temperature and pressure inside the bubble, while triangular and sawtooth ones remain the less interesting waveforms for sonochemical application within the same operational conditions. At higher amplitudes above 2.5 atm, this trend is changed, especially at low frequencies, i.e. 200 and 300 kHz, where square wave showed some limitations in attaining the optimal values of the strong collapse within one acoustic cycle.     

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.     

Temperature and pressure dependence of sonoluminescence

The dependence of sonoluminescence on ambient pressure and temperature is measured. As water is cooled, there occurs a 100-fold increase in light emission which can be accompanied by only slight changes in the ambient radius of the pulsating bubble. This suggests that water vapor trapped in the collapsing bubble is a key parameter for this system. For fixed concentration of gases in water, the maximum intensity of sonoluminescence decreases as the ambient pressure is lowered below 1 atm.     

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.     

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).     

超声场下刚性界面附近溃灭空化气泡的速度分析

为了揭示刚性界面附近气泡空化参数与微射流的相互关系, 从两气泡控制方程出发, 利用镜像原理, 建立了考虑刚性壁面作用的空化泡动力学模型. 数值对比了刚性界面与自由界面下气泡的运动特性, 并分析了气泡初始半径、气泡到固壁面的距离、声压幅值和超声频率对气泡溃灭的影响. 在此基础上, 建立了气泡溃灭速度和微射流的相互关系. 结果表明: 刚性界面对气泡振动主要起到抑制作用; 气泡溃灭的剧烈程度随气泡初始半径和超声频率的增加而降低, 随着气泡到固壁面距离的增加而增加; 声压幅值存在最优值, 固壁面附近的气泡在该最优值下气泡溃灭最为剧烈; 通过研究气泡溃灭速度和微射流的关系发现, 调节气泡溃灭速度可以达到间接控制微射流的目的.     

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.     

Segregation of vapor and gas in a sonoluminescing bubble

Computer simulations of bubble oscillations in water are performed for various noble gases taking into account the segregation of water vapor and noble gas inside a collapsing bubble, which was predicted by Storey and Szeri [J. Fluid Mech. 396 (1999) 203]. It is clarified that the number of water vapor molecules dissociated inside a collapsing bubble is larger for heavier noble gases because of the lower thermal conductivity and the segregation of vapor and noble gas. It is also clarified that the temperature inside a helium bubble at the collapse increases considerably by the mixture segregation because a lesser amount of vapor is trapped inside a collapsing bubble. It is also clarified that multibubble sonoluminescence (MBSL) from heavier noble gases is brighter because of the lower ionization potential which results in the higher electron density and stronger plasma emissions.     

The evolution of the cavitation bubble driven by different sound pressure

In this paper, the relation between the ambient radius R(0) of the acoustic cavitation bubble and its driving pressure was investigated by an improved method. The evolution of the bubble was gained with a long-distance microscope and a bundle of 532 nm laser switched by an acousto-optic modulator. The ambient radius R(0) was determined by fitting the numerical calculation based on Rayleigh-Plesset equation to the experimental data. The results showed that as the sound pressure increased R(0) decreased at beginning and increased after the pressure reached to about 1.2 atm. Although the same rule was gotten from the relation between the maximum radius R(m) and the sound pressure, the ratio R(m)/R(0) varied monotonously with the sound pressure. It indicates that enhancing the sound pressure can increase the compression ratio of the bubble even if the mass inside the bubble is also increased.     

两种气泡混合的声空化

将非线性声波方程和改进的Rayleigh-Plesset方程联立可以描述空化环境中的声场及相应的气泡动力学特征. 用时域有限差分方法模拟了圆柱形容器内两种气泡相互混合时的空化情况. 在烧杯内的稳态背景声场形成过程中, 瓶壁耗散吸收扮演了重要的角色. 在稳态背景声场的基础上, 分析了混合气泡与声场的相互作用、气泡之间的相互作用、混合情况下的频谱特性. 结果表明: 两种气泡平衡半径都不太大时, 气泡与声场的相互作用不强, 声场及气泡的行为也比较规律; 相反, 当其中一种气泡平衡半径相对比较大时, 声场与气泡具有较强的非线性相互作用, 声场及气泡的行为表现出复杂的特性.     

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.     

Theoretical estimation of the temperature and pressure within collapsing acoustical bubbles

Formation of highly reactive species such as OH, H, HO₂ and H₂O₂ due to transient collapse of cavitation bubbles is the primary mechanism of sonochemical reaction. The crucial parameters influencing the formation of radicals are the temperature and pressure achieved in the bubble during the strong collapse. Experimental determinations estimated a temperature of about 5000 K and pressure of several hundreds of MPa within the collapsing bubble. In this theoretical investigation, computer simulations of chemical reactions occurring in an O₂-bubble oscillating in water irradiated by an ultrasonic wave have been performed for diverse combinations of various parameters such as ultrasound frequency (20–1000 kHz), acoustic amplitude (up to 0.3 MPa), static pressure (0.03–0.3 MPa) and liquid temperature (283–333 K). The aim of this series of computations is to correlate the production of OH radicals to the temperature and pressure achieved in the bubble during the strong collapse. The employed model combines the dynamic of bubble collapse in acoustical field with the chemical kinetics of single bubble. The results of the numerical simulations revealed that the main oxidant created in an O₂ bubble is OH radical. The computer simulations clearly showed the existence of an optimum bubble temperature of about 5200 ± 200 K and pressure of about 250 ± 20 MPa. The predicted value of the bubble temperature for the production of OH radicals is in excellent agreement with that furnished by the experiments. The existence of an optimum bubble temperature and pressure in collapsing bubbles results from the competitions between the reactions of production and those of consumption of OH radicals at high temperatures.     

The size of active bubbles for the production of hydrogen in sonochemical reaction field

The sonication of aqueous solution generates microscopic cavitation bubbles that may growth and violently collapse to produce highly reactive species (i.e. OH, HO₂ and H₂O₂), hydrogen and emit light, sonoluminescence. The bubble size is a key parameter that influences the chemical activity of the system. This wok aims to study theoretically the size of active bubbles for the production of hydrogen in ultrasonic cavitation field in water using a single bubble sonochemistry model. The effect of several parameters such as frequency of ultrasound, acoustic intensity and liquid temperature on the range of sonochemically active bubbles for the production of hydrogen was clarified. The numerical simulation results showed that the size of active bubbles is an interval which includes an optimum value at which the production rate of H₂ is maximal. It was shown that the range of ambient radius for an active bubble as well as the optimum bubble radius for the production of hydrogen increased with increasing acoustic intensity and decreased with increasing ultrasound frequency and bulk liquid temperature. It was found that the range of ambient bubble radius dependence of the operational conditions followed the same trend as those reported experimentally for sonoluminescing bubbles. Comparison with literature data showed a good agreement between the theoretical determined optimum bubble sizes for the production of hydrogen and the experimental reported sizes for sonoluminescing bubbles.     

Study of single bubble sonoluminescence in phosphoric acid

Sonoluminescence (SL) radiation from different solutions of phosphoric acid has been studied in the framework of a hydro-chemical simulation. By calculating the phase diagrams of an SL bubble in different concentrations of phosphoric acid, the optimum solution for acquiring maximum SL emission has been specified as the solution of around 30 wt.% acid. It is shown that the SL temperature and the number of particles inside the bubble at the time of SL emission are two important factors determining the optimum solution. Numerical calculation of the SL intensity shows that the optimum solution has an intensity of about 20 times greater than that of water. Also, contributions of different energy sources in creation of thermal energy of the bubble have been calculated. The result indicates that the work of external driving pressure is the most important factor to determine the ultimate thermal energy of the bubble at the time of SL emission. Based on this result, we have reasoned out that in the determination of the optimum solution, the role of viscosity of the acid solutions is more important than the vapor pressure.     

Implosion of an underwater spark-generated bubble and acoustic energy evaluation using the Rayleigh model

The growth, collapse, and rebound of a vapor bubble generated by an underwater spark is studied by means of high-speed cinematography, simultaneously acquiring the emitted acoustic signature. Video recordings show that the growth and collapse phases are nearly symmetrical during the first two or three cycles, the bubble shape being approximately spherical. After 2-3 cycles the bubble behavior changes from a collapsing/rebounding regime with sound-emitting implosions to a pulsating regime with no implosions. The motion of the bubble wall during the first collapses was found to be consistent with the Rayleigh model of a cavity in an incompressible liquid, with the inclusion of a vapor pressure term at constant temperature within each bubble cycle. An estimate of the pressure inside the bubble is obtained measuring the collapse time and maximum radius, and the amount of energy converted into acoustical energy upon each implosion is deduced. The resulting value of acoustic efficiency was found to be in agreement with measurements based on the emitted acoustic pulse.