Modeling of three-dimensional pressure fields in sonochemical reactors with an inhomogeneous density distribution of cavitation bubbles. Comparison of theoretical and experimental results

Characterization of the acoustic cavitation in ionic liquids in a horn-type ultrasound reactor

Most ultrasound-based processes root in empirical approaches. Because nearly all advances have been conducted in aqueous systems, there exists a paucity of information on sonoprocessing in other solvents, particularly ionic liquids (ILs). In this work, we modelled an ultrasonic horn-type sonoreactor and investigated the effects of ultrasound power, sonotrode immersion depth, and solvent's thermodynamic properties on acoustic cavitation in nine imidazolium-based and three pyrrolidinium-based ILs. The model accounts for bubbles, acoustic impedance mismatch at interfaces, and treats the ILs as incompressible, Newtonian, and saturated with argon. Following a statistical analysis of the simulation results, we determined that viscosity and ultrasound input power are the most significant variables affecting the intensity of the acoustic pressure field (P), the volume of cavitation zones (V), and the magnitude of the maximum acoustic streaming surface velocity (u). V and u increase with the increase of ultrasound input power and the decrease in viscosity, whereas the magnitude of negative P decreases as ultrasound power and viscosity increase. Probe immersion depth positively correlates with V, but its impact on P and u is insignificant. 1-alkyl-3-methylimidazolium-based ILs yielded the largest V and the fastest acoustic jets - 0.77 cm3 and 24.4 m s-1 for 1-ethyl-3-methylimidazolium chloride at 60 W. 1-methyl-3-(3-sulfopropyl)-imidazolium-based ILs generated the smallest V and lowest u - 0.17 cm3 and 1.7 m s-1 for 1-methyl-3-(3-sulfopropyl)-imidazolium p-toluene sulfonate at 20 W. Sonochemiluminescence experiments validated the model.

Understanding the ultrasound field of high viscosity mixtures: Experimental and numerical investigation of a lab scale batch reactor

In this work, mixtures of increasing viscosity (from 0.9 to ≈720 mPas) are sonicated directly using an ultrasonic horn at 30 kHz to investigate the effect of viscosity on the ultrasound field both from an experimental and numerical point of view. The viscosity of the mixtures is modified by preparing water-polyethylene glycol solutions. The impact of the higher viscosity on the acoustic pressure distribution is studied qualitatively and semi-quantitatively using sonochemiluminescence. The velocity of light scattering particles added in the mixtures is also explored to quantify acoustic streaming effects using Particle Image Velocimetry (PIV). A numerical model is developed that is able to predict cavitationally active zones accounting for both thermoviscous and cavitation based attenuation. The results show that two cavitation zones exist: one directly under the horn tip and one around the part of the horn body that is immersed in the liquid. The erosion patterns on aluminum foil confirm the existence of both zones. The intensity of the cavitationally active zones decreases considerably with increasing viscosity of the solutions. A similar reduction trend is observed for the velocity of the particles contained in the jet directly under the tip of the horn. Less erratic flow patterns relate to the high viscosity mixtures tested. Finally, two numerical models were made combining different boundary conditions related to the ultrasonic horn. Only the model that includes the radial horn movements is able to qualitatively predict well the location of the cavitation zones and the decrease of the zones intensity, for the highest viscosities studied. The current findings should be taken into consideration in the design and modelling phase of horn based sonochemical reactors.

Simulations of a full sonoreactor accounting for cavitation

In spite of the increasing interest in ultrasound processing applications, industrial scale-up remains limited, in particular by the unavailability of predictive computer tools. In this study, using a previously published model of cavitating liquids implementable as a non-linear Helmholtz equation, it is shown that a full sonoreactor can be modelled and simulated. The model includes the full transducer and the vibrations of the vessel walls, using the physics of elastic solids and piezo-electricity. The control-loop used by the generator to set the optimal frequency is also accounted for. Apart from the geometry, the unique input of the model is the current feeding the transducer whereas the dissipated electrical power, transducer complex impedance and working frequency are available as outputs. The model is put to the test against experiments realized in different geometries, varying either the input current or the transducer immersion depth. Despite the overestimation of the power dissipated in the liquid, the evolution of the acoustic load in both cases is reasonably well reproduced by simulation, which partially validates the method used.

Modeling acoustic cavitation with inhomogeneous polydisperse bubble population on a large scale

A model for acoustic cavitation flows able to depict large geometries and time scales is proposed. It is based on the Euler-Lagrange approach incorporating a novel Helmholtz solver with a non-linear acoustic attenuation model. The method is able to depict a polydisperse bubble population, which may vary locally. The model is verified and analyzed in a setup with a large sonotrode. Influences of the initial void fraction and the population type are studied. The results show that the velocity is strongly influenced by these parameters. Furthermore, the largest bubbles determine the highest pressure amplitude reached in the domain, which corresponds to the Blake threshold of these bubbles. Additionally, a validation is performed with a small sonotrode. The model reproduces most of the experimentally observed phenomena. In the experiments, neighboring bubbles are found which move in different directions depending on their size. The numerical results show that the responsible mechanism here is the reversal of the primary Bjerknes force at a certain pressure amplitude.

Multi-frequency sonoreactor characterisation in the frequency domain using a semi-empirical bubbly liquid model

Recently, multi-frequency systems were reported to improve performance in power ultrasound applications. In line with this, digital prototyping of multi-frequency sonoreactors also started gaining interest. However, the conventional method of simulating multi-frequency acoustic pressure fields in the time-domain led to many challenges and limitations. In this study, a multi-frequency sonoreactor was characterised using frequency domain simulations in 2-D. The studied system consists of a hexagonal sonoreactor capable of operating at 28, 40 and 70 kHz. Four frequency combinations were studied: 28-40, 28-70, 40-70 and 28-40-70 kHz. A semi-empirical, modified Commander and Prosperetti model was used to describe the bubbly-liquid effects in the sonoreactor. The root-mean-squared acoustic pressure was compared against experimental validation results using sonochemiluminescence (SCL) images and was noted to show good qualitative agreement with SCL results in terms of antinode predictions. The empirical phase speed calculated from SCL measurements was found to be important to circumvent uncertainties in bubble parameter specifications which reduces error in the simulations. Additionally, simulation results also highlighted the importance of geometry in the context of optimising the standing wave magnitudes for each working frequency due to the effects of constructive and destructive interference.

A strict formulation of a nonlinear Helmholtz equation for the propagation of sound in bubbly liquids. Part II: Application to ultrasonic cavitation

This paper addresses one of the greatest challenges in sonochemistry that has impaired scaling up ultrasonic processes, which is the lack of models capable of predicting the pressure distribution in sonoreactors. This work studies the effect of acoustic pressure on the transmission of sound thought cavitating bubbly liquids by utilizing the nonlinear Helmholtz equation that was demonstrated on the paper part I. The model showed that the wave number and the attenuation can be estimated from the bubble dynamics of inertial bubbles and the local bubble density. The linear model of Commander and Prosperetti is encompassed by the nonlinear model. The model was employed to predict the pressure distribution below an ultrasonic horn tip achieving a relatively close prediction of the experimental data and certainly an accurate qualitative description of the distribution of the pressure field in spite of the simplifications of the model and the assumptions of unknown variables such as the bubble density, bubble distribution and the vessel boundary conditions.

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.

Sludge degradation and microbial community structures analysis in a microbial electrolysis cell-coupled up flow anaerobic blanket reactor with an ultrasound treatment system

This study proposed a sludge degradation system comprised of: (i) an ultrasound treatment (UT) system to disintegrate sludge; (ii) an up flow anaerobic sludge blanket (UASB) reactor to degrade the disintegrated sludge; and (iii) a microbial electrolysis cell (MEC) in replacement of a three-phase UASB separator to deeply degrade the disintegrated sludge. The influence of the ultrasound power, the temperature, and the voltage on the sludge degradation process was discussed. The experimental results showed that the UT unit effectively promoted sludge disintegration, thereby leading to deterioration of the quality of the reactor effluent. The temperature and the voltage parameters were found to be key for the anaerobic degradation (AD) process within this system. The volatile suspended solid concentration in the effluent was maintained at 320–380 mg L⁻¹ (ca. 0.08 times the raw sludge concentration), thereby validating the utilization of MEC as a three-phase separation unit. The total chemical oxygen demand removal was maintained at 61.3% during 5 days of AD upon intermittent exposure of the sludge to the UT unit, thereby showing that the system can effectively degrade solid organic matter. The bacterial community structure of the raw sludge significantly changed, with the high biodiversity of this system increasing the ecological stability. This system can degrade sludge with high efficiency and could be used in further engineering applications.

This study proposes an ultrasound treatment–up flow anaerobic sludge blanket–microbial electrolysis cell (UT-UASB-MEC) degradation system.

Numerical simulations and electrochemical experiments of the mass transfer of microvias electroforming under ultrasonic agitation

This paper explores the mass transfer mechanism of microvias electroforming under ultrasonic agitation by numerical simulations and electrochemical experiments. Firstly, the velocity distribution of electroforming solution inside the microvias under ultrasound treatment is simulated by COMSOL Multiphysics software. The ultrasonic frequency is that of 120 kHz. The ultrasonic powers are 100 W, 200 W, 300 W and 400 W, respectively. The simulation results indicate that the mean liquid velocity inside the microvias increases with the increasing of acoustic power. In addition, under a certain ultrasonic power, the mean liquid velocity will decrease with increasing the distance between microvias and transducer, the aspect ratio of microvias and the distance between cathode and central position. Secondly, electrochemical experiments are presented to investigate the effect of ultrasonic agitation on the electrode kinetics of microvias electroforming. It is found that ultrasonic treatment decreases the thickness of diffusion layer, increases the limiting diffusion current densities and further enhances the mass transfer of microvias electroforming. Compared with the silent condition, the diffusion layer thicknesses with the acoustic power of 100 W, 200 W, 300 W, 400 W are decreased by 50.0%, 64.1%, 69.3% and 74.5%, respectively. Finally, according to the results above, the 200 × 200 metal micro-column array structures are fabricated by ultrasonic electroforming under the condition of 120 kHz and 200 W. The metal micro-column is 250 μm high and has a diameter of 80 μm. The results show that ultrasonic electroforming can enhance the mass transfer of microvias electroforming, and further solve the problem of porous structure in electroforming layer. This work contributes to expanding the application of ultrasonic agitation in the microvias electroforming.

Ultrasound-assisted emerging technologies for chemical processes

The chemical industry has witnessed many important developments during past decades largely enabled by process intensification techniques. Some of them are already proven at commercial scale (e.g. reactive distillation) while others (e.g. ultrasound-assisted extraction/crystallization/reaction) are on their way to becoming the next-generation technologies. This article focuses on the advances of ultrasound (US)-assisted technologies that could lead in the near future to significant improvements in commercial activities. The aim is to provide an authoritative discussion on US-assisted technologies that are currently emerging from the research environment into the chemical industry, as well as give an overview of the current state-of-the-art applications of US in chemical processing (e.g. enzymatic reactive distillation, crystallization of API). Sufficient information is included to allow the assessment of US-assisted technologies and the challenges for implementation, as well as their potential for commercial applications. © 2017 The Authors. Journal of Chemical Technology & Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Measurement of distribution of broadband noise and sound pressures in sonochemical reactor

Cross-sectional area distribution of broadband noise in a sonochemical reactor was measured to estimate reaction fields. A needle-type hydrophone scanned the sonochemical reactor in horizontal and vertical directions at one-millimeter interval. To show an absolute value of broadband noise, average of broadband sound pressure was defined. The distribution of sound pressures at the fundamental and second harmonic frequencies were also measured. In the case of driving frequency at 130 kHz, sonochemical reaction fields were observed in several ellipse shapes. The reaction fields in upper part of the reactor was high because cavitation bubbles moved upper part due to radiation force. The sound pressure distribution at the fundamental frequency showed existence of standing wave and reaction fields were weak at pressure antinode because cavitation bubbles were repelled by primary Bjerknes force. The sound pressure distribution at the second harmonic frequency indicated that the pattern of bubbles distribution resembled to that of reaction fields closely. In the case at 43 kHz, distributions of reaction fields and sound pressures were complex due to coupled vibration. The reaction fields were relatively weak in areas which had very high sound pressures at the fundamental frequency.

Process intensification

Process intensification (PI) is a rapidly growing field of research and industrial development that has already created many innovations in chemical process industry. PI is directed toward substantially smaller, cleaner, more energy-efficient technology. Furthermore, PI aims at safer and sustainable technological developments. Its tools are reduction of the number of devices (integration of several functionalities in one apparatus), improving heat and mass transfer by advanced mixing technologies and shorter diffusion pathways, miniaturization, novel energy techniques, new separation approaches, integrated optimization and control strategies. This review discusses many of the recent developments in PI. Starting from fundamental definitions, microfluidic technology, mixing, modern distillation techniques, membrane separation, continuous chromatography, and application of gravitational, electric, and magnetic fields will be described.

Numerical modelling of ultrasonic waves in a bubbly Newtonian liquid using a high-order acoustic cavitation model

To address difficulties in treating large volumes of liquid metal with ultrasound, a fundamental study of acoustic cavitation in liquid aluminium, expressed in an experimentally validated numerical model, is presented in this paper. To improve the understanding of the cavitation process, a non-linear acoustic model is validated against reference water pressure measurements from acoustic waves produced by an immersed horn. A high-order method is used to discretize the wave equation in both space and time. These discretized equations are coupled to the Rayleigh-Plesset equation using two different time scales to couple the bubble and flow scales, resulting in a stable, fast, and reasonably accurate method for the prediction of acoustic pressures in cavitating liquids. This method is then applied to the context of treatment of liquid aluminium, where it predicts that the most intense cavitation activity is localised below the vibrating horn and estimates the acoustic decay below the sonotrode with reasonable qualitative agreement with experimental data.

A numerical model for the study of the difference frequency generated from nonlinear mixing of standing ultrasonic waves in bubbly liquids

The aim of this paper is the study of the behavior of nonlinear standing ultrasonic waves in bubbly liquids and the generation of the difference frequency by nonlinear mixing of several signals. To this end we present a new numerical model based on the finite-volume method and the finite-difference method. This model solves the differential system formed by the wave equation and a Rayleigh-Plesset equation coupling the acoustic pressure field with the bubble vibrations. We consider a resonator filled with a bubbly liquid excited by an ultrasonic pressure source. The numerical experiments presented here are performed by modifying the source amplitude and frequency, the void fraction in the liquid, as well as the length of the resonator. The results allow us to observe the physical effects due to the presence of the bubbles in the liquid: nonlinearity, dispersion, attenuation. The nonlinear frequency mixing performed in the resonator is also evidenced. The amplitude of the generated difference frequency is studied as a function of the pressure amplitude and for several primary frequencies. Our results suggest that a better response is obtained for primary frequencies situated below the bubble resonance. They show a very high difference-frequency amplitude response for a cavity resonant at one wavelength of the difference frequency in the bubbly medium. This analyze could be useful for some practical applications.

A two-dimensional nonlinear model for the generation of stable cavitation bubbles

Bubbles appear by acoustic cavitation in a liquid when rarefaction pressures attain a specific threshold value in a liquid. Once they are created, the stable cavitation bubbles oscillate nonlinearly and affect the ultrasonic field. Here we present a model developed for the study of bubble generation in a liquid contained in a two-dimensional cavity in which a standing ultrasonic field is established. The model considers dissipation and dispersion due to the bubbles. It also assumes that both the ultrasonic field and the bubble oscillations are nonlinear. The numerical experiments predict where the bubbles are generated from a population of nuclei distributed in the liquid and show how they affect the ultrasonic field.

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.

Influences of non-uniform pressure field outside bubbles on the propagation of acoustic waves in dilute bubbly liquids

Predictions of the propagation of the acoustic waves in bubbly liquids is of great importance for bubble dynamics and related applications (e.g. sonochemistry, sonochemical reactor design, biomedical engineering). In the present paper, an approach for modeling the propagation of the acoustic waves in dilute bubbly liquids is proposed through considering the non-uniform pressure field outside the bubbles. This approach is validated through comparing with available experimental data in the literature. Comparing with the previous models, our approach mainly improves the predictions of the attenuation of acoustic waves in the regions with large kR0 (k is the wave number and R0 is the equilibrium bubble radius). Stability of the oscillating bubbles under acoustic excitation are also quantitatively discussed based on the analytical solution.

Synchrotron radiation X-ray imaging of cavitation bubbles in Al-Cu alloy melt

Cavitation bubbles in Al-10 wt.%Cu melt has been investigated by adopting synchrotron radiation X-ray imaging technology. In-situ observation reveals that most of bubbles concentrate within an intense cavitation zone nearby the radiation face. The measured near-maximum bubble radii obey a similar truncated Gaussian distribution as in water but increase by nearly the magnitude of one order due to higher ultrasonic intensity applied in aluminum melt.

Simulation of the spatial distribution of the acoustic pressure in sonochemical reactors with numerical methods: a review

Numerical methods for the calculation of the acoustic field inside sonoreactors have rapidly emerged in the last 15 years. This paper summarizes some of the most important works on this topic presented in the past, along with the diverse numerical works that have been published since then, reviewing the state of the art from a qualitative point of view. In this sense, we illustrate and discuss some of the models recently developed by the scientific community to deal with some of the complex events that take place in a sonochemical reactor such as the vibration of the reactor walls and the nonlinear phenomena inherent to the presence of ultrasonic cavitation. In addition, we point out some of the upcoming challenges that must be addressed in order to develop a reliable tool for the proper designing of efficient sonoreactors and the scale-up of sonochemical processes.

An Euler-Lagrange method considering bubble radial dynamics for modeling sonochemical reactors

Unsteady numerical computations are performed to investigate the flow field, wave propagation and the structure of bubbles in sonochemical reactors. The turbulent flow field is simulated using a two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The distribution of the acoustic pressure is solved based on the Helmholtz equation using a finite volume method (FVM). The radial dynamics of a single bubble are considered by applying the Keller-Miksis equation to consider the compressibility of the liquid to the first order of acoustical Mach number. To investigate the structure of bubbles, a one-way coupling Euler-Lagrange approach is used to simulate the bulk medium and the bubbles as the dispersed phase. Drag, gravity, buoyancy, added mass, volume change and first Bjerknes forces are considered and their orders of magnitude are compared. To verify the implemented numerical algorithms, results for one- and two-dimensional simplified test cases are compared with analytical solutions. The results show good agreement with experimental results for the relationship between the acoustic pressure amplitude and the volume fraction of the bubbles. The two-dimensional axi-symmetric results are in good agreement with experimentally observed structure of bubbles close to sonotrode.

Investigation of design parameters in ultrasound reactors with confined channels

This paper presents a three-dimensional numercial simulation of sonochemical degradation upon cavitational activity. The model relates the simulation of the acoustic pressure distribution to the sonochemical reaction rate. As a case study, the thermal degradation of carbon tetrachloride during sonication is studied in a tubular milliscale reactor. The model is used to optimize the reactor diameter, ultrasound frequency and power dissipated to the ultrasound transducers. The results indicate that multiple transducers at a moderate power level are more efficient than one transducer with high power level. Furthermore, the average cavity volume fraction is proposed as a reaction independent parameter to estimate the optimal reactor design. Within the results obtained in this paper, it appears possible to optimise reactor design based on this parameter.

Dynamic features of a laser-induced cavitation bubble near a solid boundary

This paper deals with detailed features of bubble dynamics near a solid boundary. The cavitation bubble was created by using a Q-switched Nd: YAG laser pulse and observed using a high-speed camera (up to 100,000 frames per second). A hydrophone system was employed to monitor the acoustic signals generated by the transient pressure impulses and estimate the bubble oscillation periods. Experimental observations were carried out for bubbles with various maximum expanded radius Rmax (between 1.0mm and 1.6mm) and stand-off distances, ds (defined as the distance between the solid boundary and the bubble center at inception) of 0.4≤γ≤3.0, and γ=ds/Rmax. The existence of a solid boundary created asymmetry in the flow field and forced the bubble to collapse non-spherically, which finally brought forth the jet impact phenomenon. The dimensionless first and second oscillation periods were dependent on γ. A series of expansion and collapse of the bubble with cascading loss of energy were observed after the bubble had been generated. This study revealed that most bubbles lost about two-thirds of the total energy from the first maximum expansion to the second maximum expansion.

Numerical simulations of three-dimensional nonlinear acoustic waves in bubbly liquids

This paper presents three-dimensional simulations of nonlinear propagation of ultrasonic waves through bubbly liquids, which represent the continuity of our previous works included in the numerical tool SNOW-BL. The behavior of three-dimensional nonlinear acoustic waves in bubbly liquids is analyzed by means of numerical predictions. Nonlinearity, attenuation, and dispersion due to the presence of bubbles in the liquid are taken into account. The numerical solution to the differential problem is obtained by means of a finite-difference scheme. The simulations we present here consider a homogeneous distribution of bubbles in the liquid. Results compare high and low-amplitude waves to detect the nonlinear effects of the bubbles. Results are shown for radiation and enclosure problems.

Numerical simulation of liquid velocity distribution in a sonochemical reactor

Ultrasonically induced flow is an important phenomenon observed in a sonochemical reactor. It controls the mass transport of sonochemical reaction and enhances the reaction performance. In the present paper, the liquid velocity distribution of ultrasonically induced flow in the sonochemical reactor with a transducer at frequency of 490 kHz has been numerically simulated. From the comparison of simulation results and experimental data, the ultrasonic absorption coefficient in the sonochemical reactor has been evaluated. To simulate the liquid velocity near the liquid surface above the transducer, which is the main sonochemical reaction area, it is necessary to include the acoustic fountain shape into the computational domain. The simulation results indicate that the liquid velocity increases with acoustic power. The variation of liquid height also influences the behavior of liquid velocity distribution and the mean velocity above the transducer centre becomes a maximum when the liquid height is 0.4m. The liquid velocity decreases with increasing the transducer plate radius at the same ultrasonic power.

Acoustic cavitation mechanism: a nonlinear model

During acoustic cavitation process, bubbles appear when acoustic pressure reaches a threshold value in the liquid. The ultrasonic field is then submitted to the action of the bubbles. In this paper we develop a model to analyze the cavitation phenomenon in one-dimensional standing waves, based on the nonlinear code SNOW-BL. Bubbles are produced where the minimum rarefaction pressure peak exceeds the cavitation threshold. We show that cavitation bubbles appear at high amplitude and drastically affect (dissipation, dispersion, and nonlinearity) the ultrasonic field. This paper constitutes the first work that associates the nonlinear ultrasonic field to a bubble generation process.

A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.

Nonlinear ultrasonic standing waves: two-dimensional simulations in bubbly liquids

We present the results of numerical predictions for analyzing the behavior of nonlinear ultrasonic standing waves in two-dimensional cavities filled with bubbly liquids. The model we solve accounts for nonlinearity, dissipation, and dispersion of the two-dimensional media due to the bubbles. The numerical simulations are based on a finite-difference scheme. They consider the bubbles evenly distributed in the liquid. Results are shown for high-amplitude signals. They make it possible to observe how the linear modes turn into multi-frequency nonlinear fields.

Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.

Single-transducer dual-frequency ultrasound generation to enhance acoustic cavitation

Dual- or multiple-frequency ultrasound stimulation is capable of effectively enhancing the acoustic cavitation effect over single-frequency ultrasound. Potential application of this sonoreactor design has been widely proposed such as on sonoluminescence, sonochemistry enhancement, and transdermal drug release enhancement. All currently available sonoreactor designs employed multiple piezoelectric transducers for generating single-frequency ultrasonic waves separately and then these waves were mixed and interfered in solutions. The purpose of this research is to propose a novel design of generating dual-frequency ultrasonic waves with single piezoelectric elements, thereby enhancing acoustic cavitation. Macroscopic bubbles were detected optically, and they were quantified at either a single-frequency or for different frequency combinations for determining their efficiency for enhancing acoustic cavitation. Visible bubbles were optically detected and hydrogen peroxide was measured to quantify acoustic cavitation. Test water samples with different gas concentrations and different power levels were used to determine the efficacy of enhancing acoustic cavitation of this design. The spectrum obtained from the backscattered signals was also recorded and examined to confirm the occurrence of stable cavitation. The results confirmed that single-element dual-frequency ultrasound stimulation can enhance acoustic cavitation. Under certain testing conditions, the generation of bubbles can be enhanced up to a level of five times higher than the generation of bubbles in single-frequency stimulation, and can increase the hydrogen peroxide production up to an increase of one fold. This design may serve as a useful alternative for future sonoreactor design owing to its simplicity to produce dual- or multiple-frequency ultrasound.

FEM simulation of a sono-reactor accounting for vibrations of the boundaries

The chemical effects of acoustic cavitation are obtained in sono-reactors built-up from a vessel and an ultrasonic source. In this paper, simulations of an existing sono-reactor are carried out, using a linear acoustics model, accounting for the vibrations of the solid walls. The available frequency range of the generator (19-21 kHz) is systematically scanned. Global quantities are plotted as a function of frequency in order to obtain response curves, exhibiting several resonance peaks. In absence of the precise knowledge of the bubbles size distribution and spatial location, the attenuation coefficient of the wave is taken as a variable, but spatially uniform parameter, and its influence is studied. The concepts of acoustic energy, intensity, active power, and source impedance are recalled, along with the general balance equation for acoustic energy, which is used as a convergence check of the simulations. It is shown that the interface between the liquid and the solid walls cannot be correctly represented by the simple approximations of either infinitely soft, or infinitely hard boundaries. Moreover, the liquid-solid coupling allows the cooling jacket to receive a noticeable part of the input power, although it is not in direct contact with the sonotrode. It may therefore undergo cavitation and this feature opens the perspective to design sono-reactors which avoid direct contact between the working liquid and the sonotrode. Besides, the possibility to shift the main pressure antinode far from the sonotrode area by exciting a resonance of the system is examined.

Sonochemical degradation of PAH in aqueous solution. Part I: monocomponent PAH solution

The sonolysis of selected monocomponent PAH aqueous solution is studied at 20 and 506 kHz in the microg l(-1) range. The highest activity observed at 506 kHz, compared to 20 kHz, is tentatively explained by examination of the physical characteristics of bubbles (size and life-time) as well as by the calculation of the number of bubble at both frequency (5 x 10(3)bubbles l(-1) at 20 kHz and 4.5 x 10(9)bubbles l(-1) at 506 kHz). It is demonstrated that the main mechanism of sonodegradation is the pyrolysis of PAHs in the heart of the cavitation bubbles, and that a possible PAH oxidation by means of HO degrees appears as a minor way, since gaseous byproducts such as CO, CO2, C2H2 and CH4 have been detected. Correlations have been found by examination of kinetic variations in terms of the physical-chemical properties of PAHs. The rate constants of PAH degradation increase when the water solubility, the vapour pressure and the Henry's law constant increase.

Determination of the receiving range of sound field measurements in cavitating media

Sound field measurements are widely used for the quantitative description of cavitation processes. For practical purposes it is important to know how local a sound field measurement information is, and therefore a technique is presented which allows the determination of the receiving range of such a measurement. The sound field is detected by two calibrated, similar hydrophones, mounted face to face in the cavitation cloud. The distance between the hydrophones is varied and the correlation between the two time-dependent signals is analyzed in the frequency domain defining a local parameter. The dependence of this parameter on the distance between the hydrophones describes the receiving range of a sound field measurement by means of a characteristic distance. The technique was applied to two different cavitation applications, and effective distances in the range 1-3mm were obtained. It is shown that the spatial resolution of a sound field measurement in a cavitation field is determined by the hydrophone size and does not depend on the cavitation conditions if at least a medium cavitation activity is provided.

A statistical thermodynamic approach to sonochemical reactions

The calculation of the equilibrium constants K of the sonolysis reactions of CO2 into CO and O atom, the recombination of O atoms into O2 and the formation of H2O starting with H and O atoms, has been studied by means of statistical thermodynamic. The constants have been calculated at 300 kHz versus the pressure and the temperature according to the extreme conditions expected in a cavitation bubble, e.g. in the range from ambient temperature to 15200 K and from ambient pressure to 300 bar. The decomposition of CO2 appears to be thermodynamically favored at 15200 K and 1 bar with a constant K1=1.52 x 10(6), whereas the formation of O2 is not expected to occur (K2=1.8 x10(-8) maximum value at 15200 K and 300 bar) in comparison to the formation of water (K3=3.4 x 10(47) at 298 K and 300 bar). The most thermodynamic favorable location of each reactions is then proposed, the surrounding shell region for the thermic decomposition of CO2 and the wall of the cavitation bubble for the formation of water. Starting from a work of Henglein on the sonolysis of CO2 in water at 300 kHz, the experimental amount of CO formed (7.2 x 10(20)molecules L(-1)) is compared to the theoretical CO amount (1.4 x 10(27)molecules L(-1)) which can be produced by the sonolysis of the same starting amount CO2. With the help of the literature data, the number of cavitation bubble has been evaluated to 6.2 x 10(15) bubbles L(-1) at 300 kHz, in 15 min. This means that about 1 bubble on 1900000 is efficient for undergoing the sonolysis of CO2.

On the interaction between ultrasound waves and bubble clouds in mono- and dual-frequency sonoreactors

Since the last decades, extensive work have been done on the numerical modeling of mono-frequency sonoreactors, we here consider the modeling of dual-frequency sonoreactors. We first present the basic features of the CAMUS code (CAvitating Medium under UltraSound), for mono-frequency excitation. Computation at low, medium and high frequency are presented. Extension of the numerical tool CAMUS is also presented: Caflisch equations are modified to take into account the dual-frequency excitation of the sound. We consider 28-56, 28-100 and 28-200 kHz sonoreactors. Fields of cavitation bubble emergence are quite different from the ones under mono-frequency. Study of spatio-temporal dynamics of cavitation bubbles in a 28-56 kHz sonoreactor is also considered. Taking into account the pressure field induced by the dual-frequency wave propagation, we compute the Bjerknes force applied on the cavitation bubble that is responsible for the bubble migration. A two phase flow approach allows to compute the bubble migration.

Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results

The propagation of ultrasound through a liquid induces the growth of inceptions and germs into bubbles. In a low frequency reactor, fragmentary transient bubbles emerge due to the acoustic driving. They violently collapse in one cycle and fragment into many smaller bubbles than in turn cavitate. This violent collapse is responsible for the mechanical effects of ultrasounds effects. The latter bubbles gather in a ball-shaped cloud and migrate to pressure antinodes. During their migration, their nonexplosive collapses mainly contribute to activate chemical reactions by producing OH. radicals. Mathematical modelling is performed as a new approach to predict the bubbles field. Through numerical simulation, we determinate emergence sites of mechanically active cavitation bubbles. Calculus are compared with aluminium foil degradation. The modelling of bubble migration allow us to have an insight on the privileged sites of the chemical reactions. Validation of the modelling is made through direct comparison with chemiluminescence photo. All experiments and computations are made in a 28.2 kHz sonoreactor.

Numerical simulation of cavitation bubble dynamics induced by ultrasound waves in a high frequency reactor

The use of high frequency ultrasound in chemical systems is of major interest to optimize chemical procedures. Characterization of an open air 477 kHz ultrasound reactor shows that, because of the collapse of transient cavitation bubbles and pulsation of stable cavitation bubbles, chemical reactions are enhanced. Numerical modelling is undertaken to determine the spatio-temporal evolution of cavitation bubbles. The calculus of the emergence of cavitation bubbles due to the acoustic driving (by taking into account interactions between the sound field and bubbles' distribution) gives a cartography of bubbles' emergence within the reactor. Computation of their motion induced by the pressure gradients occurring in the reactor show that they migrate to the pressure nodes. Computed bubbles levitation sites gives a cartography of the chemical activity of ultrasound. Modelling of stable cavitation bubbles' motion induced by the motion of the liquid gives some insight on degassing phenomena.

Numerical modeling of high-power ultrasonic systems: current status and future trends

Numerical models of high power ultrasonic systems are usually based on finite element or boundary element methods. The basic physical models are linear and rely upon the theory of elasticity, the constitutive law of piezoelectricity and the theory of linear acoustics. They are only valid at low drive level. Some recent developments include nonlinearities of the transduction mechanism and of the propagation medium. In this paper, standard and advanced numerical models are discussed and illustrated by several application examples of high power ultrasonics.