Phase diagrams for sonoluminescing bubbles: A comparison between experiment and theory

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 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.

Critical Analysis of Hydrogen Production by Aqueous Methanol Sonolysis

Recently, several experimental and theoretical studies have demonstrated the feasibility of enhancing the sonochemical production of hydrogen via methanol pyrolysis within acoustic cavitation bubbles (i.e. sonolysis of aqueous methanol solution). This review includes both the experimental and theoretical achievements in the field of hydrogen production by methanol sonolysis. Additionally, the limits of the process's applicability and plausible solutions are highlighted. The impact of different parameters influencing the process performance is discussed. Finally, the effects of methanol concentration on the size distribution of active cavitation bubbles are analyzed.

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.

Estimation of the number density of active cavitation bubbles in a sono-irradiated aqueous solution using a thermodynamic approach

An alternative semi-empirical technique is developed to determine the number density of active cavitation bubbles (N) formed in sonicated solutions. This was achieved by relating the acoustic power supplied to the solution (i.e., determined experimentally) to the released heat by a single bubble. The energy dissipation via heat exchange is obtained by an advanced cavitation model accounting for the liquid compressibility and viscosity, the non-equilibrium condensation/evaporation of water vapor, and heat conduction across the bubble wall and heats of chemical reactions resulting within the bubble at the collapse. A good concordance was observed between our results and those found in the literature. It was found that the number of active bubbles increased proportionally with a rise in ultrasound frequency. Additionally, the increase of acoustic intensity increases the number of active bubbles, whatever the sonicated solution's volume. On the other hand, it was observed that the rise of the irradiated solution volume causes the number of active bubbles to be reduced even when the acoustic power is increased. A decrease in acoustic energy accelerates this negative impact.

A simplified model for the gas-vapor bubble dynamics

This paper presents a full numerical model accounting for the heat transfer and phase-change by combining the modified Keller-Miksis equation with the second order term of compressibility of liquid, partial differential equations (PDEs), and Hertz-Knudsen-Langmuir equation. Then, a simplified model for studying the dynamics of the cavitation bubble or bubble excited by the acoustic waves is proposed. The major contribution is to simplify the full model with PDEs to a set of coupled ordinary differential equations (ODEs). Specifically, two energy PDEs are converted to three ODEs by coupling the boundary conditions. The comparison among the full model and other simplified models is used to validate the accuracy and superiority of the simplified model, from which the application range of the proposed simplified model can be determined.

Merits and Demerits of ODE Modeling of Physicochemical Systems for Numerical Simulations

In comparison with the first-principles calculations mostly using partial differential equations (PDEs), numerical simulations with modeling by ordinary differential equations (ODEs) are sometimes superior in that they are computationally more economical and that important factors are more easily traced. However, a demerit of ODE modeling is the need of model validation through comparison with experimental data or results of the first-principles calculations. In the present review, examples of ODE modeling are reviewed such as sonochemical reactions inside a cavitation bubble, oriented attachment of nanocrystals, dynamic response of flexoelectric polarization, ultrasound-assisted sintering, and dynamics of a gas parcel in a thermoacoustic engine.

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.

Interaction of two bubbles with distortion in an acoustic field

Expression of the secondary Bjerknes force of two bubbles is obtained by considering the distrotion of two bubbles. The secondary Bjerknes forces in different acoustic fields are simulated, and the influence factors are analyzed and discussed. It is shown that the distortion of a bubble has an important influence on the interaction of two bubbles. The strength and even the directions of the secondary Bjerknes force of two bubbles with distortion differ considerably from the predictions of the sherical symmetry theory. The results show that when two bubbles oscillated stably in an acoustic field, the secondary Bjerknes force of two bubbles with distortion is several times more than that of two spherical bubbles in the same condition. The secondary Bjerknes force of two bubble with distortion has more interaction distance than that of two spherical bubbles. The secondary Bjerknes force of two bubbles with distortion depends on the distance of two bubbles, the shape mode of two bubbles, the equilibrium radii of two bubbles and the driving acoustic filed. The nonspherical distortion effects of the secondary Bjerknes has an importance on understanding the structure formation of bubbles and evolution process of bubble group in an acoustic field.

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.

An alternative technique for determining the number density of acoustic cavitation bubbles in sonochemical reactors

The present paper introduces a novel semi-empirical technique for the determination of active bubbles' number in sonicated solutions. This method links the chemistry of a single bubble to that taking place over the whole sonochemical reactor (solution). The probe compound is CCl₄, where its eliminated amount within a single bubble (though pyrolysis) is determined via a cavitation model which takes into account the non-equilibrium condensation/evaporation of water vapor and heat exchange across the bubble wall, reactions heats and liquid compressibility and viscosity, all along the bubble oscillation under the temporal perturbation of the ultrasonic wave. The CCl₄ degradation data in aqueous solution (available in literature) are used to determine the number density through dividing the degradation yield of CCl₄ to that predicted by a single bubble model (at the same experimental condition of the aqueous data). The impact of ultrasonic frequency on the number density of bubbles is shown and compared with data from the literature, where a high level of consistency is found.

The hydroxyl radical yields prediction of cavitation bubble clouds during hydrodynamic cavitation process for chitosan degradation

In order to measure the influence of chemical effects in the process of hydrodynamic cavitation (HC) degradation of chitosan, a prediction model for the hydroxyl radical (·OH) yields of cavitation...

A review on pesticide degradation from irrigation water and techno-economic feasibility of treatment technologies

The present study focuses and assures the need for pesticide degradation from various water bodies used for irrigation and the available technologies to treat them effectively. A thorough review of the literature is done on pesticide residues present in various irrigation water sources like rivers, groundwater, river sediments, and soil which signifies the existence of pesticides in the ecosystem. This indicates the severity of water pollution due to various sources around and their adverse effect on the ecosystem. However, several technologies are available to treat these pesticides based on the classification. A Cross comparison between the technologies is done to determine the efficient technology for the treatment of irrigation water.

An inverse method to fast-track the calculation of phase diagrams for sonoluminescing bubbles

A sound driven air bubble can be transformed into an argon bubble emitting light pulses stably. The very foundation to investigate the sonoluminescing bubble is to accurately determine the ambient radius and gas composition in the interior. The conventional approach is to model the air-to-argon transformation process through a large number of bubble dynamics simulations to obtain the physical parameters of the ultimate argon bubble. In this paper, we propose a highly efficient method to pinpoint this information in a phase diagram. The method is based on the diffusive equilibrium for each species inside the bubble and derives the ambient radius and composition inversely. To calculate the former parameter, the bisection algorithm is employed to consecutively narrow down the searching range until the equilibria is approached. Afterward, several cycles of full dynamics simulations are conducted to refine the composition. The method is validated using published experimental data. The calculated ambient radii deviate from the test results by less than 1 μm, which falls within the margin of measurement error. The advantages of this method over the semi-analytical approach reported by Hilgenfeldt et al. [J. Fluid Mech. 365 (1998)] are also discussed. Our study provides a standard procedure to calculate the ambient radius and composition and is beneficial for the numerical simulation of sonoluminescing bubbles.

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).

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 (PA: 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 PA = 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).

Energy balance of high-energy stable acoustic cavitation within dual-frequency sonochemical reactor

The acoustic cavitation bubble as an open energetic system is the seat of conversion of various forms of energy accompanying the bubble oscillation. The energy conversion would explain specific dynamical, thermal and kinetical behaviors. In the present paper, the energy balance related to a stable bubble irradiated by dual-frequency field is simulated numerically and interpreted in accordance with the phenomena occurring inside it. The study particularly focuses on the comparison of the energetic behavior of high-energy stable cavitation with bubbles that are non-active in sonochemistry, submitted to couples of 35, 140, 300 and 515 kHz. The simulation results revealed that pressure forces work is the major energetic input during the bubble oscillation lifetime, while the main energetic loss comes from heat transfer by diffusion and enthalpy loss accompanying water condensation. Besides, high rates of condensation of water molecules and low amounts of accumulated energy inside the bubble volume were identified as the key factors preventing the achievement of the sonochemical activity threshold.

Modeling the thermal behavior of an acoustically driven gas bubble

Numerical simulation of an acoustically driven gas bubble is usually achieved by solving a Rayleigh-Plesset-type equation, in which the time-dependent pressure of the gas inside the bubble needs to be appropriately modeled. This is done in most existing methods by assuming a polytropic relation between the gas pressure and the bubble volume, which sometimes oversimplifies the thermal interaction between the bubble and the ambient liquid. In this paper, a model is developed aiming to perform an accurate and efficient calculation of the pressure variation in the bubble. The approach is different from that in the recent paper by the author and his collaborator which used a combination of an integral and a collocation method to solve the energy equation in the gas [Zhou and Prosperetti (2020). J. Fluid Mech. 901, R3]. The starting point of the proposed method in this paper is the gas continuity equation which is manipulated to lead to three ordinary differential equations. In this way, the thermal behavior of an oscillating gas bubble is captured at a modest coding and computational cost.

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

The sonochemical activity and the radial dynamics of a harmonically excited spherical bubble are investigated numerically. A detailed model is employed capable to calculate the chemical production inside the bubble placed in water that is saturated with oxygen. Parameter studies are performed with the control parameters of the pressure amplitude, the forcing frequency and the bubble size. Three different definitions of collapse strengths (extracted from the radius vs.time curves) are examined and compared with the chemical output of various species. A mathematical formula is established to estimate the chemical output as a function of the collapse strength; thus, the chemical activity can be predicted without taking into account the chemical kinetics into the bubble model. The calculations are carried out by an in-house code exploiting the high processing power of professional graphics cards (GPUs). The results shown that chemical activity can be approximated qualitatively from the values of relative expansion. This could be helpful in order to optimise chemical output of sonochemical reactors either from measurement data or simulations as well.

Oxygen-argon acoustic cavitation bubble in a water-methanol mixture: Effects of medium composition on sonochemical activity

The objective of the present numerical study is to examine the sonochemical production within a single acoustic bubble that oscillates in an aqueous methanol solution under an oxygen-argon mixture. The produced molar yield during the strong collapse was analyzed in accordance with the system composition, i.e. the molar fraction of argon and the volume fraction of methanol. The simulation results based on 180 cases demonstrated the reproducibility of pyrolysis and combustion conditions within the bubble volume. Pure water sonolysis resulted in an optimal production at 90% molar of argon, with O, HO^· and HO₂^· as predominant species at low argon concentrations and O, HO^· et H^· at high concentrations. The addition of methanol changed the whole chemical schema evolving inside the bubble that gave rise to specific species such as CH₂OH,CH₃O,CH₂O,HCO,CO₂ and CO. A common optimum appeared at 40% molar of argon for solutions of 20% (v/v) and up of methanol. An absolute maximum was observed at 40% (v/v) of methanol, in spite of argon concentration. In addition, a significant selectivity of products was observed according to the composition of the medium.

A theoretical model to estimate inactivation effects of OH radicals on marine Vibrio sp. in bubble-shock interaction

A theoretical model for estimating inactivation effects on marine Vibrio sp. is developed from the viewpoint of the chemical action of the OH radicals induced by interaction of bubbles with shock waves. It consists of a biological probability model for cell viability and a bubble dynamic model for its collapsing motion due to the shock pressures. The biological probability model is built by defining a sterilized space of the OH radicals. To determine the radius of the sterilized space, the Herring equation is solved in the bubble dynamic model in consideration of the effect of the heat conductivity and mass transportation. Furthermore, the pressure waveform of incident shock wave used in the model is obtained with the pressure measurement. On the other hand, a bio-experiment of marine Vibrio sp. is carried out using a high-voltage power supply in a cylindrical water chamber. Finally, the viability ratio of marine bacteria estimated by the theoretical model is examined under the experimental conditions of this study. In addition, we also discuss the influence of bubble initial size for predicting the inactivation effects.

Mechanical damage induced by the appearance of rectified bubble growth in a viscoelastic medium during boiling histotripsy exposure

In boiling histotripsy, the presence of a boiling vapour bubble and understanding of its dynamic behaviour are crucially important for the initiation of the tissue fractionation process and for the control of the size of a lesion produced. Whilst many in vivo studies have shown the feasibility of using boiling histotripsy in mechanical fractionation of solid tumours, not much is known about the evolution of a boiling vapour bubble in soft tissue induced by boiling histotripsy. The main objective of this present study is therefore to investigate the formation and dynamic behaviour of a boiling vapour bubble which occurs under boiling histotripsy insonation. Numerical and experimental studies on the bubble dynamics induced in optically transparent tissue-mimicking gel phantoms exposed to the field of a 2.0 MHz High Intensity Focused Ultrasound (HIFU) transducer were performed with a high speed camera. The Gilmore-Zener bubble model coupled with the Khokhlov-Zabolotskaya-Kuznetsov and the Bio-heat Transfer equations was used to simulate bubble dynamics driven by boiling histotripsy waveforms (nonlinear-shocked wave excitation) in a viscoelastic medium as functions of surrounding temperature and of tissue elasticity variations. In vivo animal experiments were also conducted to examine cellular structures around a freshly created lesion in the liver resulting from boiling histotripsy. To the best of our knowledge, this is the first study reporting the numerical and experimental evidence of the appearance of rectified bubble growth in a viscoelastic medium. Accounting for tissue phantom elasticity adds a mechanical constraint on vapour bubble growth, which improves the agreement between the simulation and the experimental results. In addition the numerical calculations showed that the asymmetry in a shockwave and water vapour transport can result in rectified bubble growth which could be responsible for HIFU-induced tissue decellularisation. Strain on liver tissue induced by this radial motion can damage liver tissue while preserving blood vessels.

Bubble dynamics in boiling histotripsy

Boiling histotripsy is a non-invasive, cavitation-based ultrasonic technique which uses a number of millisecond pulses to mechanically fractionate tissue. Though a number of studies have demonstrated the efficacy of boiling histotripsy for fractionation of solid tumours, treatment monitoring by cavitation measurement is not well studied because of the limited understanding of the dynamics of bubbles induced by boiling histotripsy. The main objectives of this work are to (a) extract qualitative and quantitative features of bubbles excited by shockwaves and (b) distinguish between the different types of cavitation activity for either a thermally or a mechanically induced lesion in the liver. A numerical bubble model based on the Gilmore equation accounting for heat and mass transfer (gas and water vapour) was developed to investigate the dynamics of a single bubble in tissue exposed to different High Intensity Focused Ultrasound fields as a function of temperature variation in the fluid. Furthermore, ex vivo liver experiments were performed with a passive cavitation detection system to obtain acoustic emissions. The numerical simulations showed that the asymmetry in a shockwave and water vapour transport are the key parameters which lead the bubble to undergo rectified growth at a boiling temperature of 100°C. The onset of rectified radial bubble motion manifested itself as (a) an increase in the radiated pressure and (b) the sudden appearance of higher order multiple harmonics in the corresponding spectrogram. Examining the frequency spectra produced by the thermal ablation and the boiling histotripsy exposures, it was observed that higher order multiple harmonics as well as higher levels of broadband emissions occurred during the boiling histotripsy insonation. These unique features in the emitted acoustic signals were consistent with the experimental measurements. These features can, therefore, be used to monitor (a) the different types of acoustic cavitation activity for either a thermal ablation or a mechanical fractionation process and (b) the onset of the formation of a boiling bubble at the focus in the course of HIFU exposure.

Ultrasonic waveform upshot on mass variation within single cavitation bubble: Investigation of physical and chemical transformations

The mechanical disturbance created by an ultrasonic wave travelling through a liquid medium induces the formation of cavitation that oscillates due to rarefaction and compression of the wave. The duration and the magnitude of the pressure applied by the ultrasonic wave at each instant would generate a specific impact on the variation of the bubble radius, the temperature, the pressure and the mass inside it. In this paper, a numerical study is conducted to simulate four waveforms (sinusoidal, square, triangular and sawtooth) travelling an aqueous media saturated with oxygen with an amplitude of 1.5 and 2 atm and a frequency of 200, 300 and 500 kHz. The purpose is to highlight the mass evolution within acoustic cavitation bubble during one cycle due to physical transformations and sonochemical effect. The obtained results demonstrated that square signal enhances temperature and pressure growth inside the bubble, as well as mass transfer by evaporation and condensation. This leads to an improvement of produced quantities of free radicals but also to a selectivity of O as a major product in the detriment of HO₂ and OH. These trends are less and less observed when passing to sinusoidal, triangular and square signal.

Computational study of state equation effect on single acoustic cavitation bubble's phenomenon

Many models have been established to study the evolution of the bubble dynamics and chemical kinetics within a single acoustic cavitation bubble during its oscillation. The content of the bubble is a gas medium that generates the evolution of a chemical mechanism governed by the internal bubble conditions. These gases are described by a state equation, linking the pressure to the volume, temperature and species amounts, and influencing simultaneously the dynamical, the thermal and the mass variation in the cavitation bubble. The choice of the state equation to apply has then a non-neglected effect on the obtained results. In this paper, a comparative study was conducted through two numerical models based on the same assumptions and the same scheme of chemical reactions, except that the first one uses the ideal gas equation to describe the state of the species, while the second one uses the Van der Waals equation. It was found that though the dynamic of the bubble is not widely affected, the pressure and temperature range are significantly increased when passing from an ideal gas model to a real one. The amounts of chemical products are consequently raised to approximately the double. This observation was more significant for temperature and pressure at low frequency and high acoustic amplitude, while it is noticed that passing from ideal gas based approach to the Van der Waals one increases the free radicals amount mainly under high frequencies. When taking the results of the second model as reference, the relative difference between both results reaches about 60% for maximum attained temperature and 100% for both pressure and free radicals production.

A new pressure formulation for gas-compressibility dampening in bubble dynamics models

We formulated a pressure equation for bubbles performing nonlinear radial oscillations under ultrasonic high pressure amplitudes. The proposed equation corrects the gas pressure at the gas-liquid interface on inertial bubbles. This pressure formulation, expressed in terms of gas-Mach number, accounts for dampening due to gas compressibility during the violent collapse of cavitation bubbles and during subsequent rebounds. We refer to this as inhomogeneous pressure, where the gas pressure at the gas-liquid interface can differ to the pressure at the centre of the bubble, in contrast to homogenous pressure formulations that consider that pressure inside the bubble is spatially uniform from the wall to the centre. The pressure correction was applied to two bubble dynamic models: the incompressible Rayleigh-Plesset equation and the compressible Keller and Miksis equation. This improved the predictions of the nonlinear radial motion of the bubble vs time obtained with both models. Those simulations were also compared with other bubble dynamics models that account for liquid and gas compressibility effects. It was found that our corrected models are in closer agreement with experimental data than alternative models. It was concluded that the Rayleigh-Plesset family of equations improve accuracy by using our proposed pressure correction.

Mechanistic analysis of ultrasound assisted enzymatic desulfurization of liquid fuels using horseradish peroxidase

This study has attempted to gain physical insight into ultrasound-assisted enzymatic desulfurization using system comprising horseradish peroxidase enzyme and dibenzothiophene (DBT). Desulfurization pathway (comprising DBT-sulfoxide and DBT-sulfone as intermediates and 4-methoxy benzoic acid as final product) has been established with GC-MS analysis. Intrinsic fluorescence and circular dichroism spectra of ultrasound-treated enzyme reveal conformational changes in secondary structure (reduction in α-helix and β-conformations and increase in random coil content) leading to enhancement in activity. Concurrent analysis of desulfurization profiles, Arrhenius and thermodynamic parameters, and simulations of cavitation bubble dynamics reveal that strong micro-convection generated by sonication enhances enzyme activity and desulfurization kinetics. Parallel oxidation of DBT by radicals generated from transient cavitation gives further boost to desulfurization kinetics. However, random motion of enzyme molecules induced by shock waves reduces frequency factor and limits the ultrasonic enhancement of enzymatic desulfurization.

New interpretation of the effects of argon-saturating gas toward sonochemical reactions

A number of literature reports showed that argon provides a more sonochemical activity than polyatomic gases because of its higher polytropic ratio; whereas several recent studies showed that polyatomic gases, such as O₂, can compensate the lower bubble temperature by the self decomposition in the bubble. In this work, we show for the first time a numerical interpretation of these controversial reported effects. Computer simulations of chemical reactions inside a collapsing acoustic bubble in water saturated by different gases (Ar, O₂, air and N₂) have been performed for different frequencies (213-1100 kHz). In all cases, OH radical is the main powerful oxidant created in the bubble. Unexpectedly, the order of saturating gases toward the production rate of OH radical was strongly frequency dependent. The rate of production decreases in the order of Ar>O₂>air>N₂ for frequencies above 515 kHz, and Ar starts to lose progressively its first order to the following gases with a gradually decreasing of frequency below 515 kHz up to a final order of O₂>air∼N₂>Ar at 213 kHz. The analysis of chemical kinetic results showed a surprising aspect: in some cases, there exists an optimum bubble temperature during collapse at which the chemical yield is much higher than that of the maximum bubble temperature achieved in the bubble. On the basis of this, we have concluded that the lower sonochemical activity induced by Ar for frequencies below 515 kHz is mainly due to the forte consumption of radicals inside a bubble prior the complete collapse being reached.

A method for predicting the number of active bubbles in sonochemical reactors

Knowledge of the number of active bubbles in acoustic cavitation field is very important for the prediction of the performance of ultrasonic reactors toward most chemical processes induced by ultrasound. The literature in this field is scarce, probably due to the complicated nature of the phenomena. We introduce here a relatively simple semi-empirical method for predicting the number of active bubbles in an acoustic cavitation field. By coupling the bubble dynamics in an acoustical field with chemical kinetics occurring in the bubble during oscillation, the amount of the radical species OH and HO2 and molecular H2O2 released by a single bubble was estimated. Knowing that the H2O2 measured experimentally during sonication of water comes from the recombination of hydroxyl (OH) and perhydroxyl (HO2) radicals in the liquid phase and assuming that in sonochemistry applications, the cavitation is transient and the bubble fragments at the first collapse, the number of bubbles formed per unit time per unit volume is then easily determined using material balances for H2O2, OH and HO2 in the liquid phase. The effect of ultrasonic frequency on the number of active bubbles was examined. It was shown that increasing ultrasonic frequency leads to a substantial increase in the number of bubbles formed in the reactor.

Sensitivity of free radicals production in acoustically driven bubble to the ultrasonic frequency and nature of dissolved gases

Central events of ultrasonic action are the bubbles of cavitation that can be considered as powered microreactors within which high-energy chemistry occurs. This work presents the results of a comprehensive numerical assessment of frequency and saturating gases effects on single bubble sonochemistry. Computer simulations of chemical reactions occurring inside a bubble oscillating in liquid water irradiated by an ultrasonic wave have been performed for a wide range of ultrasonic frequencies (213-1100kHz) under different saturating gases (O2, air, N2 and H2). For O2 and H2 bubbles, reactions mechanism consisting in 25 reversible chemical reactions were proposed for studying the internal bubble-chemistry whereas 73 reversible reactions were taken into account for air and N2 bubbles. The numerical simulations have indicated that radicals such as OH, H, HO2 and O are created in the bubble during the strong collapse. In all cases, hydroxyl radical (OH) is the main oxidant created in the bubble. The production rate of the oxidants decreases as the driving ultrasonic frequency increases. The production rate of OH radical followed the order O2>air>N2>H2 and the order becomes more remarkable at higher ultrasonic frequencies. The effect of ultrasonic frequency on single bubble sonochemistry was attributed to its significant impact on the cavitation process whereas the effects of gases were attributed to the nature of the chemistry produced in the bubble at the strong collapse. It was concluded that, in addition to the gas solubility, the nature of the internal bubble chemistry is another parameter of a paramount importance that controls the overall sonochemical activity in aqueous solutions.

Radical production inside an acoustically driven microbubble

The chemical production of radicals inside acoustically driven bubbles is determined by the local temperature inside the bubbles and by their composition at collapse. By means of a previously validated ordinary differential equations (ODE) model [L. Stricker, A. Prosperetti, D. Lohse, Validation of an approximate model for the thermal behavior in acoustically driven bubbles, J. Acoust. Soc. Am. 130 (5) (2011) 3243-3251], based on boundary layer assumption for mass and heat transport, we study the influence of different parameters on the radical production. We perform different simulations by changing the driving frequency and pressure, the temperature of the surrounding liquid and the composition of the gas inside the bubbles. In agreement with the experimental conditions of new generation sonochemical reactors, where the bubbles undergo transient cavitation oscillations [D. F. Rivas, L. Stricker, A. Zijlstra, H. Gardeniers, D. Lohse, A. Prosperetti, Ultrasound artificially nucleated bubbles and their sonochemical radical production, Ultrason. Sonochem. 20 (1) (2013) 510-524], we mainly concentrate on the initial chemical transient and we suggest optimal working ranges for technological applications. The importance of the chemical composition at collapse is reflected in the model, including the role of entrapped water vapor. We in particular study the exothermal reactions taking place in H2 and O2 mixtures. At the exact stoichiometric mixture 2:1 the highest internal bubble temperatures are achieved.

Interacting bubble clouds and their sonochemical production

An acoustically driven air pocket trapped in a pit etched on a surface can emit a bubble cluster. When several pits are present, the resulting bubble clusters interact in a nontrivial way. Fernández Rivas et al. [Angew. Chem. Int. Ed. 49, 9699-9701 (2010)] observed three different behaviors at increasing driving power: clusters close to their "mother" pits, clusters attracting each other but still well separated, and merging clusters. The last is highly undesirable for technological purposes as it is associated with a reduction of the radical production and an enhancement of the erosion of the reactor walls. In this paper, the conditions for merging to occur are quantified in the case of two clusters, as a function of the following control parameters: driving pressure, distance between the two pits, cluster radius, and number of bubbles within each cluster. The underlying mechanism, governed by the secondary Bjerknes forces, is strongly influenced by the nonlinearity of the bubble oscillations and not directly by the number of nucleated bubbles. The Bjerknes forces are found to dampen the bubble oscillations, thus reducing the radical production. Therefore, the increased number of bubbles at high power could be the key to understanding the experimental observation that, above a certain power threshold, any further increase of the driving does not improve the sonochemical efficiency.

Ultrasound artificially nucleated bubbles and their sonochemical radical production

We describe the ejection of bubbles from air-filled pits micromachined on a silicon surface when exposed to ultrasound at a frequency of approximately 200 kHz. As the pressure amplitude is increased the bubbles ejected from the micropits tend to be larger and they interact in complex ways. With more than one pit, there is a threshold pressure beyond which the bubbles follow a trajectory parallel to the substrate surface and converge at the center point of the pit array. We have determined the size distribution of bubbles ejected from one, two and three pits, for three different pressure amplitudes and correlated them with sonochemical OH· radical production. Experimental evidence of shock wave emission from the bubble clusters, deformed bubble shapes and jetting events that might lead to surface erosion are presented. We describe numerical simulations of sonochemical conversion using the empirical bubble size distributions, and compare the calculated values with experimental results.

Mechanistic investigation of the sonochemical synthesis of zinc ferrite

In this investigation, an attempt has been made to establish the physical mechanism of sonochemical synthesis of zinc ferrite with concurrent analysis of experimental results and simulations of cavitation bubble dynamics. Experiments have been conducted with mechanical stirring as well as under ultrasound irradiation with variation of pH and the static pressure of the reaction medium. Results of this study reveal that physical effects produced by transient cavitation bubbles play a crucial role in the chemical synthesis. Generation of high amplitude shock waves by transient cavitation bubbles manifest their effect through in situ micro-calcination of metal oxide particles (which are generated through thermal hydrolysis of metal acetates) due to energetic collisions between them. Micro-calcination of oxide particles can also occur in the thin liquid shell surrounding bubble interface, which gets heated up during transient collapse of bubbles. The sonochemical effect of production of OH radicals and H(2)O(2), in itself, is not able to yield ferrite. Moreover, as the in situ micro-calcination involves very small number of particles or even individual particles (as in intra-particle collisions), the agglomeration between resulting ferrite particles is negligible (as compared to external calcination in convention route), leading to ferrite particles of smaller size (6 nm).

Plasma core at the center of a sonoluminescing bubble

Considering high temperature and pressure during single bubble sonoluminescence collapse, a hot plasma core is generated at the center of the bubble. In this paper a statistical mechanics approach is used to calculate the core pressure and temperature. A hydrochemical model alongside a plasma core is used to study the bubble dynamics in two host liquids of water and sulfuric acid 85 wt % containing Ar atoms. Calculation shows that the extreme pressure and temperature in the plasma core are mainly due to the interaction of the ionized Ar atoms and electrons, which is one step forward to sonofusion. The thermal bremsstrahlung mechanism of radiation is used to analyze the emitted optical energy per flash of the bubble core.

Bubble dynamics and sonoluminescence from helium or xenon in mercury and water

Numerical simulations of bubble pulsation and sonoluminescence (SL) have been performed for helium or xenon bubbles in mercury and water under the experimental conditions of Futakawa et al. [M. Futakawa, T. Naoe, and M. Kawai, in Nonlinear Acoustics-Fundamentals and Applications: 18th International Symposium on Nonlinear Acoustics (ISNA 18), AIP Conf. Proc. No. 1022, edited by B. O. Enflo, C. M. Hedberg, and L. Kari (AIP, New York, 2008), p. 197]. The results of the numerical simulations have revealed that the bubble expansion is much larger in water than in mercury mainly because the density of water is one order of magnitude smaller than that of mercury. The SL intensity is higher in water than that in mercury although the maximum bubble temperature is lower. This is caused by the much larger amount of vapor inside a bubble as the saturated vapor pressure of water is four orders of magnitude larger than that of mercury at room temperature. The SL intensity from xenon is much larger than that from helium due both to lower ionization potential and higher bubble temperature due to lower thermal conductivity. The instantaneous SL power may be as large as 200 W from xenon in water. The maximum temperature inside a xenon bubble in mercury may be as high as about 80 000 K. It is suggested that the maximum pressure in mercury due to shock waves emitted from bubbles increases as the SL intensity increases, although they are not simply correlated in water because the amount of water vapor trapped inside a bubble influences the SL intensity in a complex way.

Temperature and intensity of sonoluminescence radiation in sulfuric acid

The spectral radiation of sonoluminescence (SL) from sulfuric acid doped with various Xe concentrations has been studied in a hydrochemical simulation, including radiation effects of both continuum and line emissions. The simulation considers the same temperature for both continuum and line parts of the SL spectrum and gives results in agreement with the experiment. Also, it can properly show period-doubling dynamics for a 50 torr bubble. For most of the allowable driving pressures, it is shown that both the temperature and the intensity of SL for a 4 torr bubble are greater than those of a 50 torr bubble. However, for the range of pressures near the maximum driving conditions of the 50 torr bubble, the SL intensity of this bubble can be up to three orders of magnitude greater than the 4 torr bubble. This case, which is in agreement with the experiment, is obtained when the light-emitting region of the 50 torr bubble is about three orders of magnitude greater than the 4 torr bubble.

Ambient temperature effect on single-bubble sonoluminescence in different concentrations of sulfuric acid solutions

The effect of ambient temperature on the parameters of the single-bubble sonoluminescence in sulfuric acid (SA) diluted in water is studied. Using a hydrochemical model, three dominant instabilities of shape, Bjerknes, and diffusion are considered. The phase diagrams of the bubble in the (R0 - Pa) space are presented, and the parametric dependence of the light intensity is discussed. In contrast to water, the calculated thermal-bremsstrahlung mechanism of light emission at the fixed degassing condition of high SA concentrations shows that, with increasing the temperature of aqueous SA solutions, the light intensity increases. However, at diluted SA solutions similar to water, the light intensity decreases with increasing the ambient temperature. For 50 wt % SA, it was observed that the emitted light was almost temperature independent. Furthermore, it is found that, at the fixed temperatures of 20 °C, 10 °C, and 0 °C, the aqueous solutions of 65 wt %, 50 wt %, and 45 wt % SA, respectively, have the maximum light emission.

Bubble dynamics in a standing sound field: the bubble habitat

Bubble dynamics is investigated numerically with special emphasis on the static pressure and the positional stability of the bubble in a standing sound field. The bubble habitat, made up of not dissolving, positionally and spherically stable bubbles, is calculated in the parameter space of the bubble radius at rest and sound pressure amplitude for different sound field frequencies, static pressures, and gas concentrations of the liquid. The bubble habitat grows with static pressure and shrinks with sound field frequency. The range of diffusionally stable bubble oscillations, found at positive slopes of the habitat-diffusion border, can be increased substantially with static pressure.

Validation of an approximate model for the thermal behavior in acoustically driven bubbles

The chemical production of radicals inside acoustically driven bubbles is determined by the local temperature inside the bubbles. Therefore, modeling of chemical reaction rates in bubbles requires an accurate evaluation of the temperature field and the heat exchange with the liquid. The aim of the present work is to compare a detailed partial differential equation model in which the temperature field is spatially resolved with an ordinary differential equation model in which the bubble contents are assumed to have a uniform average temperature and the heat exchanges are modeled by means of a boundary layer approximation. The two models show good agreement in the range of pressure amplitudes in which the bubble is spherically stable.

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.

Effects of fluid viscosity on a moving sonoluminescing bubble

Based on the quasi-adiabatic model, the parameters of the bubble interior for a moving single bubble sonoluminescence in water, adiponitrile, and N-methylformamide are calculated for various fluid viscosities. By using a complete form of the hydrodynamic force, the bubble trajectory is calculated for a moving single bubble sonoluminescence (m-SBSL). It is found that as the fluid viscosity increases, the unique circular path changes to an ellipsoidal and then linear form and along this incrementally increase of viscosity the light intensity increases. By using the Bremsstrahlung model to describe the bubble radiation, gradual increase of the viscosity results in brighter emissions. It is found that in fluids with higher viscosity the light intensity decreases as time passes.

Liquid compressibility effects during the collapse of a single cavitating bubble

The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied. While it is known that compressibility damps the amplitude of bubble rebounds, the extent to which this effect is accurately captured by weakly compressible versions of the Rayleigh-Plesset equation is unclear. To clarify this issue, partial differential equations governing conservation of mass, momentum, and energy are numerically solved both inside the bubble and in the surrounding compressible liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured. Results obtained with Rayleigh-Plesset type equations accounting for compressibility effects, proposed by Keller and Miksis [J. Acoust. Soc. Am. 68, 628-633 (1980)], Gilmore, and Tomita and Shima [Bull. JSME 20, 1453-1460 (1977)], are compared with those resulting from the full model. For strong collapses, the solution of the latter reveals that an important part of the energy concentrated during the collapse is used to generate an outgoing pressure wave. For the examples considered in this research, peak pressures are larger than those predicted by Rayleigh-Plesset type equations, whereas the amplitudes of the rebounds are smaller.