Numerical investigation of the effect of dual frequency sonication on stable bubble dynamics

Tetracycline degradation by dual-frequency ultrasound combined with peroxymonosulfate

Tetracycline has received a great deal of interest for the harmful effects of substance abuse on ecosystems and humanity. The effects of different processes on the degradation of tetracycline were compared, with dual-frequency ultrasound (DFUS) in combination with peroxymonosulfate (PMS) being the most effective for the tetracycline degradation. Free radical scavenging experiments showed that O2∙-,SO4∙- and •OH were the main reactive radicals in the degradation of tetracycline. According to the major intermediates of tetracycline degradation identified, three possible degradation pathways were proposed, which are of significance for translational studies of tetracycline degradation. Notably, these intermediates were found to be significantly less toxicity. The number of active bubbles in the degradation vessel was calculated using a semi-empirical formula, and a higher value of 1.44 × 108 L-1s-1 of bubbles was obtained when using dual-frequency ultrasound at 20 kHz (210 W/L) and 80 kHz (85.4 W/L). Therefore, compared to 20 kHz, although the yield of strong oxidizing substances from individual active bubbles decreased slightly, a significant increment of the number of active bubbles still resulted in a higher synergistic effect, and the combination of DFUS and PMS should be effective in promoting the generation of reactive free radicals and mass transfer processes within the degradation vessel, which provides a method for efficient removal of tetracycline from wastewater.

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.

Sonochemical reactor characterization in the presence of cylindrical and conical reflectors

Ultrasonic systems must be able to produce an acoustic field with the highest possible energy concentration in sonochemical reactors to accomplish maximum efficacy in the sonolytic degradation of water contaminants. In the present study, the impact of cylindrical and conical stainless-steel reflectors placed on the liquid surface on the sonochemical oxidation activity of ultrasonication reactors was investigated. The amount of effective acoustic power transferred to the ultrasonicated medium without and with reflectors was measured by calorimetric characterization of the sono-reactors at diverse ultrasonication frequencies in the interval of 300-800 kHz and different electrical powers in the range of 40-120 W. Iodide dosimetry without and with reflectors at diverse ultrasonication conditions (300-800 kHz and 40-120 W) and various aqueous solution volumes in the range of 300-500 mL was used to assess the sonochemical oxidation activity, i.e., the generation of oxidative species (mainly hydroxyl radicals). Sonochemiluminescence (SCL) imaging was used to study the active acoustic cavitation bubbles distribution in the sono-reactors without and with reflectors. Significant impacts of the position and shape of the reflectors on the active acoustic cavitation bubble distribution and the sonochemical oxidation activity were observed due to remarkable modifications of the ultrasonic field by directing and focusing of the ultrasonic waves. A significant augmentation in the triiodide formation rate was obtained in the presence of the conical reflector, especially at 630 kHz and 120 W (60.5% improvement), while iodide oxidation was quenched in the presence of the cylindrical reflector at all ultrasonication frequencies and powers. The SCL images show a noteworthy modification in the ultrasonic field and the acoustic cavitation bubble population when reflectors were used. The sonochemical oxidation activity was improved by the conical reflector when placed in the Fresnel zone (near field region).

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.

Enhancing cavitation dynamics and its mechanical effects with dual-frequency ultrasound

Objective. Acoustic cavitation and its mechanical effects (e.g. stress and strain) play a primary role in ultrasound applications. Introducing encapsulated microbubbles as cavitation nuclei and utilizing dual-frequency ultrasound excitation are highly effective approaches to reduce cavitation thresholds and enhance cavitation effects. However, the cavitation dynamics of encapsulated microbubbles and the resultant stress/strain in viscoelastic tissues under dual-frequency excitation are poorly understood, especially for the enhancement effects caused by a dual-frequency approach. The goal of this study was to numerically investigate the dynamics of a lipid-coated microbubble and the spatiotemporal distributions of the stress and strain under dual-frequency excitation. Approach. The Gilmore–Zener bubble model was coupled with a shell model for the nonlinear changes of both shell elasticity and viscosity to accurately simulate the cavitation dynamics of lipid-coated microbubbles in viscoelastic tissues. Then, the spatiotemporal evolutions of the cavitation-induced stress and strain in the surrounding tissues were characterized quantitatively. Finally, the influences of some paramount parameters were examined to optimize the outcomes. Main results. We demonstrated that the cavitation dynamics and associated stress/strain were prominently enhanced by a dual-frequency excitation, highlighting positive correlations between the maximum bubble expansion and the maximum stress/strain. Moreover, the results showed that the dual-frequency ultrasound with smaller differences in its frequencies and pressure amplitudes could enhance the bubble oscillations and stress/strain more efficiently, whereas the phase difference manifested small influences under these conditions. Additionally, the dual-frequency approach seemed to show a stronger enhancement effect with the shell/tissue viscoelasticity increasing to a certain extent. Significance. This study might contribute to optimizing the dual-frequency operation in terms of cavitation dynamics and its mechanical effects for high-efficient ultrasound applications.

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.

Effects of flat sweep frequency and pulsed ultrasound on the activity, conformation and microstructure of mushroom polyphenol oxidase

The effects of thermal processing (TP) and flat sweep frequency and pulsed ultrasound (FSFPU) treatment with different frequency modes on the activity, conformation and physicochemical properties of mushroom polyphenol oxidase (PPO) were investigated. The results showed that the relative enzymatic activity of PPO gradually decreased with increasing temperature and duration, and thermosonication decreased the PPO activity to a greater extent compared with thermal processing. FSFPU treatment with dual-frequency of 22/40 kHz mode showed the most significant effect. Circular dichroism (CD) showed that the content of α-helix and β-turn dropped, while that of β-sheet and random coil raised after FSFPU treatment. The intensity of endogenous fluorescence decreased, indicating that PPO protein unfolded and the tertiary structure was destroyed. The amount of free sulfhydryl, protein aggregation index, and turbidity all rose. Moreover, FSFPU treatment led to the aggregation of protein from the analysis of atomic force microscope (AFM). Conclusively, FSFPU can be used as an effective method to inhibit the activity of endogenous enzymes in food.

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.

Numerical Characterization of Acoustic Cavitation Bubbles with Respect to the Bubble Size Distribution at Equilibrium

In addition to bubble number density, bubble size distribution is an important population parameter governing the activity of acoustic cavitation bubbles. In the present paper, an iterative numerical method for equilibrium size distribution is proposed and combined to a model for bubble counting, in order to approach the number density within a population of acoustic cavitation bubbles of inhomogeneous sizing, hence the sonochemical activity of the inhomogeneous population based on discretization into homogenous groups. The composition of the inhomogeneous population is analyzed based on cavitation dynamics and shape stability at 300 kHz and 0.761 W/cm2 within the ambient radii interval ranging from 1 to 5 µm. Unstable oscillation is observed starting from a radius of 2.5 µm. Results are presented in terms of number probability, number density, and volume probability within the population of acoustic cavitation bubbles. The most probable group having an equilibrium radius of 3 µm demonstrated a probability in terms of number density of 27%. In terms of contribution to the void, the sub-population of 4 µm plays a major role with a fraction of 24%. Comparisons are also performed with the homogenous population case both in terms of number density of bubbles and sonochemical production of HO•,HO2•, and H• under an oxygen atmosphere.

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.

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.

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.

Numerical study on dual-frequency ultrasonic enhancing cavitation effect based on bubble dynamic evolution

Ultrasonic cavitation is a physical dynamic phenomenon of bubbles inflation, compression, and collapse in liquid. A dual-frequency ultrasonic cavitation dynamics model is established in this paper to investigate dynamic evolution of bubble under single and dual frequency ultrasonic modes. The variation of bubble radius, pressure, energy, temperature, and number of water vapor molecules inside the bubble in single and dual frequency ultrasonic modes are analyzed, respectively. The results show the oscillation of cavitation bubbles is more unstable and easier to collapse in dual-frequency ultrasound field than those in single-frequency ultrasound field. With the increase of the ultrasonic frequency, cavitation effect is weakened due to the shortage of oscillation period. Under the same ultrasonic power, the maximums of bubble radius, pressure, and water vapor molecules number inside the bubble in the dual-frequency mode are larger than those in the single-frequency mode. Under the ultrasonic excited by 50 kHz + 70 kHz, the maximum bubble radius and pressure can reach 36.061 μm and 2285.9 MPa, respectively, which are much larger than 18.183 μm, 730.61 MPa at 50 kHz and 14.576 μm, 332.25 MPa at 70 kHz. The calculation results of three different frequency combinations (30 kHz + 50 kHz, 40 kHz + 60 kHz and 50 kHz + 70 kHz) indicate dual-frequency ultrasound can significantly enhance the cavitation effect.

Void fraction, number density of acoustic cavitation bubbles, and acoustic frequency: A numerical investigation

The present paper consists of a numerical study attempting to characterize the bubble population within a sonochemical reactor through modeling and simulating the number density of bubbles and the void fraction. In a first step, both previous parameters were estimated under 1.52 bar and various acoustic frequencies ranging from 20 to 1000 kHz in function of normalized time. The results showed that the average number density of bubbles, varying within the interval 2.810⁴-1.4 × 10¹² bubbles dm^-3, follows a clear monotonous evolving trend as the frequency increases, while the average void fraction, comprised between 9.05 × 10^-5 and 1.95 × 10^-4, demonstrates no dependency of acoustic conditions. In a second step, an energy analysis was performed at microscopic and macroscopic scales, which led the authors to figure out that the evolution of the number density of bubbles in function of acoustic frequency is mainly governed by the energy required to maintain oscillating the single cavitation bubble.