Relationship between the radial dynamics and the chemical production of a harmonically driven spherical bubble

The violent collapse of vapor bubbles in cryogenic liquids

Vapor bubbles in cryogenic fluids may collapse violently under subcooled and pressurized conditions. Despite important implications for engineering applications such as cavitation erosion in liquid propellant rocket engines, these intense phenomena are still largely unexplored. In this paper, we systematically investigate the ambient conditions leading to the occurrence of violent collapses in liquid nitrogen and analyze their thermodynamic characteristics. Using Brenner's time ratio χ, the regime of violent collapse is identified in the ambient pressure-temperature parameter space. Complete numerical simulations further refine the prediction and illustrate two classes of collapses. At 1 < χ < 10, the collapse is impacted by significant thermal effects and attains only moderate wall velocity. Only when χ > 10 does the collapse show more inertial features. A mechanism analysis pinpoints a critical time when the surrounding liquid enters supercritical state. The ultimate collapse intensity is shown to be closely associated with the dynamics at this moment. Our study provides a fresh perspective to the treatment of cavitation in cryogenic fluids. The findings can be instrumental in engineering design to mitigate adverse effects arising from intense cavitational activities.

Influence of interactions between bubbles on physico-chemical effects of acoustic cavitation

Ultrasound technology has been extensively used as one of the efficient and economic methodology to achieve the desired outcomes in many applications by harnessing the physico-chemical effects of acoustic cavitation. However, the cavitation-associated effects, primarily determined by the oscillatory dynamics of cavitation bubbles, are considerably complex and still remain poorly understood. The main objective of this study was to perform a numerical analysis of the acoustic cavitation (i.e., the cavitation dynamics, the resultant temperature, pressure and chemical yields within collapsing bubbles), particularly focusing on the influence of the interactions between bubbles. A comprehensive model was developed to simulate the acoustic cavitation dynamics via combining the influences of mass transfer, heat conduction and chemical reactions as well as the interaction effects between bubbles. The results demonstrated that only the large bubble exerts a greater impact on the small one in a two-bubble system. Specifically, within parameter ranges covered this study, there are noticeable decreases in the expansion ratio of the small bubble, the resultant temperature, pressure and molar yields of free radicals, hence weakening the cavitation intensity and cavitation- associated physico-chemical effects. Moreover, the influences of the interactions between bubbles were further assessed quantitatively under various parameters, such as the ultrasound amplitude PA and frequency f, the distance between bubbles d0, the initial radius of the large bubble R20, as well as the liquid properties (e.g., surface tension σ and viscosity μ). It was found that the suppression effect can be amplified when subjected to ultrasound with an increased PA and/or a decreased f, probably due to a stronger cavitation intensity under this condition. Additionally, the suppression effect is also enhanced with a decrease in d0, σ and μ, but with R20 increasing. This study can contribute to deepening knowledge about acoustic cavitation and the resultant physical and/or chemical effects, potentially further facilitating the ultrasound-assisted various applications involving acoustic cavitation.

Numerical investigation on the influence of dual-frequency coupling parameters on acoustic cavitation and its analysis of the enhancement and attenuation effect

To understand the effect of coupling parameters between two ultrasonic waves on acoustic cavitation, in this work, Keller-Miksis equation was introduced to built a bubble dynamics model that was used to describe the dynamic evolution of bubble and to discuss the effect of dual-frequency coupling parameters, such as frequency difference f (5 ∼ 280 kHz), phase difference φ (0 ∼ 7π/4 rad), and power allocation ratio β (0 ∼ 9), on acoustic cavitation in the presence of two ultrasonic waves irradiation. The enhancement and attenuation effect of cavitation have also been analyzed in detail by comparing the different dual-frequency combinations with single-frequency mode. It was found that all coupling parameters have a significant impact on acoustic cavitation, where the smaller values of f and φ were employed when β = 1, the stronger cavitation intensity was observed. Nevertheless, as the power allocation ratio is increased from 1 to 9 at φ = 0 for different frequency differences, the acoustic cavitation exhibits an attenuation trend. When the total acoustic power is evenly distributed, namely β = 1, the largest maximum expansion ratio (i.e. 12.96) was obtained at φ = 0 and f = 5 kHz, which represents a strongest cavitation effect. In addition, for different frequency combinations, the enhancement effect is found under the mixture of low and low frequency, whereas attenuation effect is generated easily by the combination of high and low frequency. Moreover, the effect become more pronounced as the proportion of high frequency component increases.

Extensive investigation of geometric effects in sonoreactors: Analysis by luminol mapping and comparison with numerical predictions

This investigation focuses on the influence of geometric factors on cavitational activity within a 20kHz sonoreactor containing water. Three vessels with different shapes were used, and the transducer immersion depth and liquid height were varied, resulting in a total of 126 experiments conducted under constant driving current. For each one, the dissipated power was quantified using calorimetry, while luminol mapping was employed to identify the shape and location of cavitation zones. The raw images of blueish light emission were transformed into false colors and corrected to compensate for refraction by the water-glass and glass-air interfaces. Additionally, all configurations were simulated using a sonoreactor model that incorporates a nonlinear propagation of acoustic waves in cavitating liquids. A systematic visual comparison between luminol maps and color-plots displaying the computed bubble collapse temperature in bubbly regions was conducted. The calorimetric power exhibited a nearly constant yield of approximately 70% across all experiments, thus validating the transducer command strategy. However, the numerical predictions consistently overestimated the electrical and calorimetric powers by a factor of roughly 2, indicating an overestimation of dissipation in the cavitating liquid model. Geometric variations revealed non-monotonic relationships between transducer immersion depth and dissipated power, emphasizing the importance of geometric effects in sonoreactor. Complex features were revealed by luminol maps, exhibiting appearance, disappearance, and merging of different luminol zones. In certain parametric regions, the luminol bright regions are reminiscent of linear eigenmodes of the water/vessel system. In the complementary parametric space, these structures either combine with, or are obliterated by typical elongated axial structures. The latter were found to coincide with an increased calorimetric power, and are conjectured to result from a strong cavitation field beneath the transducer producing acoustic streaming. Similar methods were applied to an additional set of 57 experiments conducted under constant geometry but with varying current, and suggested that the transition to elongated structures occurs above some amplitude threshold. While the model partially reproduced some experimental observations, further refinement is required to accurately account for the intricate acoustic phenomena involved.

Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles: from the perspective of high-performance GPU programming

A fixed-point iteration technique is presented to handle the implicit nature of the governing equations of nonlinear surface mode oscillations of acoustically excited microbubbles. The model is adopted from the theoretical work of Shaw [1], where the dynamics of the mean bubble radius and the surface modes are bi-directionally coupled via nonlinear terms. The model comprises a set of second-order ordinary differential equations. It extends the classic Keller-Miksis equation and the linearized dynamical equations for each surface mode. Only the implicit parts (containing the second derivatives) are reevaluated during the iteration process. The performance of the technique is tested at various parameter combinations. The majority of the test cases needs only a single reevaluation to achieve 10-9 error. Although the arithmetic operation count is higher than the Gauss elimination, due to its memory-friendly matrix-free nature, it is a viable alternative for high-performance GPU computations of massive parameter studies.

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.

The Reducing Agents in Sonochemical Reactions without Any Additives

It has been experimentally reported that not only oxidation reactions but also reduction reactions occur in aqueous solutions under ultrasound without any additives. According to the numerical simulations of chemical reactions inside an air or argon bubble in water without any additives under ultrasound, reducing agents produced from the bubbles are H, H2, HO2 (which becomes superoxide anion (O2-) in liquid water), NO, and HNO2 (which becomes NO2- in liquid water). In addition, H2O2 sometimes works as a reducing agent. As the reduction potentials of H and H2 (in strongly alkaline solutions for H2) are higher than those of RCHOH radicals, which are usually used to reduce metal ions, H and H2 generated from cavitation bubbles are expected to reduce metal ions to produce metal nanoparticles (in strongly alkaline solutions for H2 to work). It is possible that the superoxide anion (O2-) also plays some role in the sonochemical reduction of some solutes. In strongly alkaline solutions, hydrated electrons (e-aq) formed from H atoms in liquid water may play an important role in the sonochemical reduction of solutes because the reduction potential is extremely high. The influence of ultrasonic frequency on the amount of H atoms produced from a cavitation bubble is also discussed.

Recent trends in the applications of sonochemical reactors as an advanced oxidation process for the remediation of microbial hazards associated with water and wastewater: A critical review

Water is one of the major sources that spread human diseases through contamination with bacteria and other pathogenic microorganisms. This review focuses on microbial hazards as they are often present in water and wastewater and cause various human diseases. Among the currently used disinfection methods, sonochemical reactors (SCRs) that produce free radicals combined with advanced oxidation processes (AOPs) have received significant attention from the scientific community. Also, this review discussed various types of cavitation reactors, such as acoustic cavitation reactors (ACRs) utilizing ultrasonic energy (UE), which had been widely employed, involving AOPs for treating contaminated waters. Besides ACRs, hydrodynamic cavitation reactors (HCRs) also effectively destroy and deactivate microorganisms to varying degrees. Cavitation is the fundamental phenomenon responsible for initiating many sonochemical reactions in liquids. Bacterial degradation occurs mainly due to the thinning of microbial membranes, local warming, and the generation of free radicals due to cavitation. Over the years, although extensive investigations have focused on the antimicrobial effects of UE (ultrasonic energy), the primary mechanism underlying the cavitation effects in the disinfection process, inactivation of microbes, and chemical reactions involved are still poorly understood. Therefore, studies under different conditions often lead to inconsistent results. This review investigates and compares other mechanisms and performances from greener and environmentally friendly sonochemical techniques to the remediation of microbial hazards associated with water and wastewater. Finally, the energy aspects, challenges, and recommendations for future perspectives have been provided.

Numerical investigation of the translational motion of bubbles: The comparison of capabilities of the time-resolved and the time-averaged methods

In the present study, the accuracies of two different numerical approaches used to model the translational motion of acoustic cavitational bubble in a standing acoustic field are compared. The less accurate but less computational demanding approach is to decouple the equation of translational motion from the radial oscillation, and solve it by calculating the time-averaged forces exerted on the bubble for one acoustic cycle. The second approach is to solve the coupled ordinary differential equations directly, which provides more accurate results with higher computational effort. The investigations are carried out in the parameter space of the driving frequency, pressure amplitude and equilibrium radius. Results showed that both models are capable to reveal stable equilibrium positions; however, in the case of oscillatory solutions, the difference in terms of translational frequency may be more than three fold, and the amplitude of translational motion obtained by the time-averaged method is roughly 1.5 times higher compared to the time-resolved solution at particular sets of parameters. This observation implies that where the transient behaviour is important, the time-resolved approach is the proper choice for reliable results.

Penetration of hydroxyl radicals in the aqueous phase surrounding a cavitation bubble

In the sonochemical degradation of nonvolatile compounds, the free radicals must be delivered into the aqueous solution from the cavitation bubble to initiate reduction-oxidation reactions. The penetration depth in the liquid becomes an important parameter that influences the radical delivery efficiency and eventual treatment performance. However, the transport of radicals in the liquid phase is not well understood yet. In this paper, we focus on the most reactive OH radical and numerically simulate its penetration behavior. This is realized by solving the coupled equations of bubble dynamics, intracavity chemistry, and radical dispersion in the aqueous phase. The results present both the local and global penetration patterns for the OH radicals. By performing simulations over a wide range of acoustic parameters, we find an undesirable phenomenon that the penetration can be adversely suppressed when strengthening the radical production. A mechanistic analysis attributes this to the excessively vigorous recombination reactions associated with high radical concentrations near the bubble interface. In this circumstance, the radicals are massively consumed and converted into molecular species before they can appreciably diffuse away. Our study sheds light on the interplay between radical production inside the bubble and dispersion in the outside liquid. The derived conclusions provide guides for sonochemical applications from a new perspective.

Production and dispersion of free radicals from transient cavitation Bubbles: An integrated numerical scheme and applications

As an advanced oxidation process with a wide range of applications, sonochemistry relies on acoustic cavitation to induce free radicals for degrading chemical contaminants. The complete process includes two critical steps: the radical production inside the cavitation bubble, and the ensuing dispersion of these radicals into the bulk solution. To grasp the physicochemical details in this process, we developed an integrated numerical scheme with the ability to quantitatively describe the radical production-dispersion behavior. It employs coupled simulations of bubble dynamics, intracavity chemical reactions, and diffusion-reaction-dominated mass transport in aqueous solutions. Applying this method to the typical case of argon and oxygen bubbles, the production mechanism for the main radicals is revealed. Moreover, the temporal-spatial distribution of the radicals in the liquid phase is presented. The results demonstrate that the enhanced radical production observed in oxygen bubbles can be traced to the initiation reaction O2 + H2O → OH+HO2, which requires relatively low activation energy. In the outside liquid region, the dispersion of radicals is limited by robust recombination reactions. The simulated penetration depth of OH is around 0.2 μm and agrees with reported experimental measurements. The proposed numerical approach can be employed to better capture the radical activity and is instrumental in optimizing the engineering application of sonochemistry.

Production of O Radicals from Cavitation Bubbles under Ultrasound

In the present review, the production of O radicals (oxygen atoms) in acoustic cavitation is focused. According to numerical simulations of chemical reactions inside a bubble using an ODE model which has been validated through studies of single-bubble sonochemistry, not only OH radicals but also appreciable amounts of O radicals are generated inside a heated bubble at the violent collapse by thermal dissociation of water vapor and oxygen molecules. The main oxidant created inside an air bubble is O radicals when the bubble temperature is above about 6500 K for a gaseous bubble. However, the concentration and lifetime of O radicals in the liquid water around the cavitation bubbles are unknown at present. Whether O radicals play some role in sonochemical reactions in the liquid phase, which are usually thought to be dominated by OH radicals and H2O2, should be studied in the future.

Fundamentals, biomedical applications and future potential of micro-scale cavitation-a review

Thanks to the developments in the area of microfluidics, the cavitation-on-a-chip concept enabled researchers to control and closely monitor the cavitation phenomenon in micro-scale. In contrast to conventional scale, where cavitation bubbles are hard to be steered and manipulated, lab-on-a-chip devices provide suitable platforms to conduct smart experiments and design reliable devices to carefully harness the collapse energy of cavitation bubbles in different bio-related and industrial applications. However, bubble behavior deviates to some extent when confined to micro-scale geometries in comparison to macro-scale. Therefore, fundamentals of micro-scale cavitation deserve in-depth investigations. In this review, first we discussed the physics and fundamentals of cavitation induced by tension-based as well as energy deposition-based methods within microfluidic devices and discussed the similarities and differences in micro and macro-scale cavitation. We then covered and discussed recent developments in bio-related applications of micro-scale cavitation chips. Lastly, current challenges and future research directions towards the implementation of micro-scale cavitation phenomenon to emerging applications are presented.

Dataset of exponential growth rate values corresponding non-spherical bubble oscillations under dual-frequency acoustic irradiation

The dataset described in this paper is related to the paper [1], in which the exponential growth rate values of a spherically oscillating gas bubble modelled by the Keller–Miksis equation are recorded. As the bubble is excited by dual-frequency, the employed parameters are the pressure amplitudes and frequencies corresponding to the first and second harmonic components, respectively, the phase shift between harmonic components, and the equilibrium bubble radius. At each parameter combinations the exponential growth rate values corresponding to mode 2 up to mode 6, and the maximum bubble radius are stored. The huge amount of numerical data are generated that are stored in a public repository [2]. The present paper describes the generated data, the applied numerical model and the implementation details of the program code used to generate the data on graphics processing units (GPUs).

The importance of chemical mechanisms in sonochemical modelling

A state-of-the-art chemical mechanism is introduced to properly describe chemical processes inside a harmonically excited spherical bubble placed in water and saturated with oxygen. The model uses up-to-date Arrhenius-constants, collision efficiency factors and takes into account the pressure-dependency of the reactions. Duplicated reactions are also applied, and the backward reactions rates are calculated via suitable thermodynamic equilibrium conditions. Our proposed reaction mechanism is compared to three other chemical models that are widely applied in sonochemistry and lack most of the aforementioned modelling issues. In the governing equations, only the reaction mechanisms are compared, all other parts of the models are identical. The chemical yields obtained by the different modelling techniques are taken at the maximum expansion of the bubble. A brief parameter study is made with different pressure amplitudes and driving frequencies at two equilibrium bubble sizes. The results show that due to the deficiencies of the former reaction mechanisms employed in the sonochemical literature, several orders of magnitude differences of the chemical yields can be observed. In addition, the trends along a control parameter can also have dissimilar characteristics that might lead to false optimal operating conditions. Consequently, an up-to-date and accurate chemical model is crucial to make qualitatively and quantitatively correct conclusions in sonochemistry.

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.

GPU accelerated numerical investigation of the spherical stability of an acoustic cavitation bubble excited by dual-frequency

The spherical stability of an acoustic cavitation bubble under dual-frequency excitation is investigated numerically. The radial dynamics is described by the Keller-Miksis equation, which is a second-order ordinary differential equation. The surface dynamics is modelled by a set of linear ordinary differential equation according to Hao and Prosperetti (1999), which takes into account the effect of vorticity by boundary layer approximation. Due to the large amount of investigated parameter combinations, the numerical computations were carried out on graphics processing units. The results showed that for bubble size between R_E=2μm and 4μm, the combination of a low and a high frequency, and the combination of two close but not equal frequencies are important to prevent the bubble losing its shape stability, while reaching the chemical threshold (R_max/R_E=3) (Kalmár et al., 2020). The phase shift between harmonic components of dual-frequency excitation has no effect on the shape stability.

Estimation of chemical and physical effects of cavitation by analysis of cavitating single bubble dynamics

Cavitation events create extreme conditions in a localized 'bubble collapse' region, leading to the formation of hydroxyl radicals, shockwaves and microscopic high-speed jets, which are useful for many chemical and physical transformation processes. Single bubble dynamics equations have been used previously to investigate the chemical and physical effects of cavitation. In the present study, the state of the art of the single bubble dynamics equations was reviewed and certain noteworthy modifications were implemented. Simulations reaffirmed previously reported collapse temperatures of the order ~5,000 K and collapse pressures well over ~1,000 bar under varying operating conditions. The chemical effects were assessed in terms of the hydroxyl radical generation rate (OHG), calculated by applying the minimization of the Gibb's Free Energy method using simulated collapse conditions. OHG values as high as 1x1012OH molecules per collapse event were found under certain operating conditions. A new equation was proposed to assess the physical effects, in terms of the impact pressure of the water jet - termed as the jet hammer pressure (JHP), formed due to the asymmetrical collapse of a bubble near a wall. The predicted JHP were found to be within a range of ~100 to 1000 bar under varying operating conditions. Important issues such as the onset of cavitation and chaotic solutions, for a cavitating single bubble dynamics were discussed. The Blake threshold pressure was found to be a sufficient criterion to capture the onset of cavitation. The impact of key operating parameters on the chemical and physical effects of cavitation were investigated exhaustively through simulations, over the parameter ranges relevant to acoustic and hydrodynamic cavitation processes. Presented methodology and results will be useful for optimisation and further investigations of a broad range of acoustic and hydrodynamic cavitation-based applications.

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.

GPU accelerated study of a dual-frequency driven single bubble in a 6-dimensional parameter space: The active cavitation threshold

The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (R_max-R_E)/R_E, where R_E is the equilibrium size of the bubble and R_max is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for (R_max-R_E)/R_E=2, the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3μm, the best option is to use just a single frequency of a low value in the giant response region. For medium sized bubbles, between 3μm and 6μm, the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6μm, the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to (R_max-R_E)/R_E=3, the optimal choice is always single frequency driving with the lowest value (20kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the dual-frequency driving (different frequency values) has no effect on the threshold.