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In this work, novel numerical models were developed and validated to offer new strategies in modelling sonochemical reactors. More specifically, in our original approach the non-linear Louisnard model was coupled with heat and mass transport equations to predict gradients in temperature and species concentration in a sonicated reactor. Additionally, a new operating window was investigated by modelling mixtures of increasing viscosity on both micro- and macroscale sonochemical effects. On the microscale, the effects of increasing viscosity on bubble dynamics were determined by solving the Keller-Miksis equation. Various cavitation threshold definitions were evaluated. The bubble collapse temperature was determined for all investigated mixtures and the energy dissipation of a single bubble was calculated. On the macroscale, different acoustic attenuation models were compared accounting for either linear or non-linear equations. Specifically, viscous losses were implemented in the non-linear Louisnard model, and model predictions were validated against experimental data. The model was able to predict multiple zones of cavitation in the reactor, as observed experimentally, and to estimate the dissipated energy for the different mixtures. Moreover, it was demonstrated that the cavitation-based attenuation dominates the other dissipation phenomena even for the most viscous solutions. The Louisnard model was coupled with heat transport equations, and using this extended version of the model, the temperature profiles were predicted for mixtures of increasing viscosity during sonication. Using a regression formula available in literature, radical production was related to the acoustic pressure field. By including reactions and mass transport in the acoustic model, for the first time in modelling ultrasonic reactors, the full distribution of light in the reactor during sonochemiluminescence (SCL) experiments for water was quantified., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)

This investigation focuses on the influence of geometric factors on cavitational activity within a 20kHz sonoreactor containing water. Three vessels with different shapes were used, and the transducer immersion depth and liquid height were varied, resulting in a total of 126 experiments conducted under constant driving current. For each one, the dissipated power was quantified using calorimetry, while luminol mapping was employed to identify the shape and location of cavitation zones. The raw images of blueish light emission were transformed into false colors and corrected to compensate for refraction by the water-glass and glass-air interfaces. Additionally, all configurations were simulated using a sonoreactor model that incorporates a nonlinear propagation of acoustic waves in cavitating liquids. A systematic visual comparison between luminol maps and color-plots displaying the computed bubble collapse temperature in bubbly regions was conducted. The calorimetric power exhibited a nearly constant yield of approximately 70% across all experiments, thus validating the transducer command strategy. However, the numerical predictions consistently overestimated the electrical and calorimetric powers by a factor of roughly 2, indicating an overestimation of dissipation in the cavitating liquid model. Geometric variations revealed non-monotonic relationships between transducer immersion depth and dissipated power, emphasizing the importance of geometric effects in sonoreactor. Complex features were revealed by luminol maps, exhibiting appearance, disappearance, and merging of different luminol zones. In certain parametric regions, the luminol bright regions are reminiscent of linear eigenmodes of the water/vessel system. In the complementary parametric space, these structures either combine with, or are obliterated by typical elongated axial structures. The latter were found to coincide with an increased calorimetric power, and are conjectured to result from a strong cavitation field beneath the transducer producing acoustic streaming. Similar methods were applied to an additional set of 57 experiments conducted under constant geometry but with varying current, and suggested that the transition to elongated structures occurs above some amplitude threshold. While the model partially reproduced some experimental observations, further refinement is required to accurately account for the intricate acoustic phenomena involved., Competing Interests: Declaration of Competing Interest Olivier Louisnard reports financial support was provided by SinapTec to RAPSODEE center at IMT Mines-Albi. Laurie Barthe reports financial support was provided by SinapTec to the Laboratoire de Génie Chimique. Igor Garcia-Vargas reports a relationship with SinapTec that includes: employment and funding grants. The above-mentioned authors declare that they had full access to all of the data in this study and take complete responsibility for the integrity of the data and the accuracy of the data analysis., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

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., Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Olivier LOUISNARD reports financial support was provided by SinapTec. Laurie BARTHE reports financial support was provided by SinapTec. Igor GARCIA-VARGAS reports a relationship with SinapTec that includes: employment and funding grants., (Copyright © 2022 The Author(s). Published by Elsevier B.V. All rights reserved.)

In this paper we study the generation and behavior of subharmonics in a bubbly liquid confined in an acoustic resonator, through numerical simulations carried out at finite-amplitude acoustic pressure. Several configurations in terms of resonator length and driving frequency are considered here. Our results show that these frequency components, created from a higher-frequency signal at the source (ultrasound), are due to the nonlinearity of the medium at high acoustic-pressure amplitude and to the configuration of the resonator (geometry and boundaries). We also show that they have an amplitude-threshold dependence, which is in concordance with the literature. The response of these subharmonics to different sequences of pressure amplitudes also reveals the hysteretic nature of the bubbly liquid., (Copyright © 2022 The Author(s). Published by Elsevier B.V. All rights reserved.)

Crystallization of α-glycine by addition of an anti-solvent (ethanol) assisted by ultrasound is studied. The experiments of crystallization are conducted at 303.15 K in a solution of 150 ml with continuous agitation by a magnetic rod. Ultrasound is then applied at powers ranging from 8 to 41 W thanks to an ultrasonic horn at 20 kHz. The supersaturation ratio (S) is followed throughout all the experiment. At the end of the experiment, the suspension is filtered, the solid is washed with ethanol and dried at 333.15 K. The resulting crystals are characterized by their final size distributions measured by laser granulometry, their morphologies observed by scanning electronic microscope (SEM) and their crystalline structures by differential scanning calorimetry (DSC). The influence of ultrasonic power (continuous 13, 28 and 40 W or pulsed modes), measured by calorimetry method, is studied for different addition rates (0.05 to 0.36 g of ethanol/min). Ultrasound permits to reduce the metastable zone width and to decrease the size of crystals due to an increase of the nucleation rate. The rate of de-supersaturation is higher in presence of ultrasound, inducing a higher nucleation rate, a higher growth rate or both. At 40 W, the decrease of supersaturation is faster, and the crystallization is finished in 40 min instead of 80 min (at 13 and 28 W) or 120 min without ultrasound. The use of pulsed ultrasound (50 on/50 off) is interesting from an economic point of view because similar results are obtained: comparable size distributions and resembling concentration profiles., (Copyright © 2019 Elsevier B.V. All rights reserved.)

This work investigates the ultrasound propagation within a liquid-solid fluidized bed. The acoustic mapping of the reactor is achieved by means of a hydrophone. A spectral analysis is carried out on the measured signals to quantify the cavitation activity. The effects of several parameters on the spectral power distribution is appraised - including emitted ultrasound power, liquid superficial velocity and solid hold-up. Results show that increasing US power promotes a higher energy transfer from the driving frequency toward the broad-band noise - which is the signature of transient cavitation - and yields a stronger acoustic shielding. The presence of a flow opposite to the acoustic streaming may affect the sonoreactor behavior by sweeping the cavitation bubbles away from the ultrasonic horn. Finally the presence of millimeter sized particles significantly increases wave attenuation, presumably due to viscous losses on the one hand, and through the contribution of their surface defects to bubble nucleation on the other hand. Moreover, the influence of the solid hold-up appears to depend upon the particle material (glass or polyamide)., (Copyright © 2019 Elsevier B.V. All rights reserved.)

The steady liquid flow observed under ultrasonic emitters generating acoustic cavitation can be successfully predicted by a standard turbulent flow calculation. The flow is driven by the classical averaged volumetric force density calculated from the acoustic field, but the inertial term in Navier-Stokes equations must be kept, and a turbulent solution must be sought. The acoustic field must be computed with a realistic model, properly accounting for dissipation by the cavitation bubbles [Louisnard, Ultrason. Sonochem., 19, (2012) 56-65]. Comparison with 20kHz experiments, involving the combination of acoustic streaming and a perpendicular forced flow in a duct, shows reasonably good agreement. Moreover, the persistence of the cavitation effects on the wall facing the emitter, in spite of the deflection of the streaming jet, is correctly reproduced by the model. It is also shown that predictions based either on linear acoustics with the correct turbulent solution, or with Louisnard's model with Eckart-Nyborg's theory yields unrealistic results., (Copyright © 2016 Elsevier B.V. All rights reserved.)

A single bubble oscillating in a levitation cell is acoustically monitored by a piezo-ceramics microphone glued on the cell external wall. The correlation of the filtered signal recorded over distant cycles on one hand, and its harmonic content on the other hand, are shown to carry rich information on the bubble stability and existence. For example, the harmonic content of the signal is shown to increase drastically once air is fully dissociated in the bubble, and the resulting pure argon bubble enters into the upper branch of the sonoluminescence regime. As a consequence, the bubble disappearance can be unambiguously detected by a net drop in the harmonic content. On the other hand, we perturb a stable sonoluminescing bubble by approaching a micron-sized fiber. The bubble remains unperturbed until the fiber tip is approached within a critical distance, below which the bubble becomes unstable and disappears. This distance can be easily measured by image treatment, and is shown to scale roughly with 3-4 times the bubble maximal radius. The bubble disappearance is well detected by the drop of the microphone harmonic content, but several thousands of periods after the bubble actually disappeared. The delay is attributed to the slow extinction of higher modes of the levitation cell, excited by the bubble oscillation. The acoustic detection method should however allow the early detection and imaging of non-predictable perturbations of the bubble by foreign micron-sized objects, such as crystals or droplets., (Copyright © 2016 Elsevier B.V. All rights reserved.)

This paper deals with the inertial cavitation of a single gas bubble in a liquid submitted to an ultrasonic wave. The aim was to calculate accurately the pressure and temperature at the bubble wall and in the liquid adjacent to the wall just before and just after the collapse. Two different approaches were proposed for modeling the heat transfer between the ambient liquid and the gas: the simplified approach (A) with liquid acting as perfect heat sink, the rigorous approach (B) with liquid acting as a normal heat conducting medium. The time profiles of the bubble radius, gas temperature, interface temperature and pressure corresponding to the above models were compared and important differences were observed excepted for the bubble size. The exact pressure and temperature distributions in the liquid corresponding to the second model (B) were also presented. These profiles are necessary for the prediction of any physical phenomena occurring around the cavitation bubble, with possible applications to sono-crystallization., (Copyright © 2015 Elsevier B.V. All rights reserved.)

In the preceding paper (part 1), the pressure and temperature fields close to a bubble undergoing inertial acoustic cavitation were presented. It was shown that extremely high liquid water pressures but quite moderate temperatures were attained near the bubble wall just after the collapse providing the necessary conditions for ice nucleation. In this paper (part 2), the nucleation rate and the nuclei number generated by a single collapsing bubble were determined. The calculations were performed for different driving acoustic pressures, liquid ambient temperatures and bubble initial radius. An optimal acoustic pressure range and a nucleation temperature threshold as function of bubble radius were determined. The capability of moderate power ultrasound to trigger ice nucleation at low undercooling level and for a wide distribution of bubble sizes has thus been assessed on the theoretical ground., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The acoustic field and the location of cavitation bubble are computed in vials used for freeze-drying, insonified from the bottom by a vibrating plate. The calculations rely on a nonlinear model of sound propagation in a cavitating liquid [Louisnard, Ultrason. Sonochem., 19, (2012) 56-65]. Both the vibration amplitude and the liquid level in the vial are parametrically varied. For low liquid levels, a threshold amplitude is required to form a cavitation zone at the bottom of the vial. For increasing vibration amplitudes, the bubble field slightly thickens but remains at the vial bottom, and the acoustic field saturates, which cannot be captured by linear acoustics. On the other hand, increasing the liquid level may promote the formation of a secondary bubble structure near the glass wall, a few centimeters below the free liquid surface. These predictions suggest that rather complex acoustic fields and bubble structures can arise even in such small volumes. As the acoustic and bubble fields govern ice nucleation during the freezing step, the final crystal's size distribution in the frozen product may crucially depend on the liquid level in the vial., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The cavitation field in a cylindrical vessel bottom-insonified by a 19.7kHz large area transducer is studied experimentally. By adding controlled amounts of Poly-Ethylene Glycol (PEG) to water, the viscosity of the liquid is varied between one- and nine-fold the viscosity of pure water. For each liquid, and for various displacement amplitudes of the transducer, the liquid is imaged by a high-speed camera and the acoustic field is measured along the symmetry axis. For low driving amplitudes, only a spherical cap bubble structure appears on the transducer, growing with amplitude, and the axial acoustic pressure field displays a standing-wave shape. Above some threshold amplitude of the transducer, a flare-like structure starts to build up, involving bubbles strongly expelled from the transducer surface, and the axial pressure profile becomes almost monotonic. Increasing more the driving amplitude, the structure extends in height, and the pressure profile remains monotonic but decreases its global amplitude. This behavior is similar for all the water-PEG mixtures used, but the threshold for structure formation increases with the viscosity of the liquid. The images of the bubble structures are interpreted and correlated to the measured acoustic pressure profiles. The appearance of traveling waves near the transducer, produced by the strong energy dissipated by inertial bubbles, is conjectured to be a key mechanism accompanying the sudden appearance of the flare-like structure., (Copyright © 2014 Elsevier B.V. All rights reserved.)

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being estimated directly from the fully nonlinear radial dynamics. The use of this model in a mono-dimensional configuration has shown that the attenuation near the vibrating emitter was much higher than predictions obtained from linear theory, and that this strong attenuation creates a large traveling wave contribution, even for closed domain where standing waves are normally expected. In this paper, we show that, owing to the appearance of traveling waves, the primary Bjerknes force near the emitter becomes very large and tends to expel the bubbles up to a stagnation point. Two-dimensional axi-symmetric computations of the acoustic field created by a large area immersed sonotrode are also performed, and the paths of the bubbles in the resulting Bjerknes force field are sketched. Cone bubble structures are recovered and compare reasonably well to reported experimental results. The underlying mechanisms yielding such structures is examined, and it is found that the conical structure is generic and results from the appearance a sound velocity gradient along the transducer area. Finally, a more complex system, similar to an ultrasonic bath, in which the sound field results from the flexural vibrations of a thin plate, is also simulated. The calculated bubble paths reveal the appearance of other commonly observed structures in such configurations, such as streamers and flare structures., (Copyright © 2011 Elsevier B.V. All rights reserved.)

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., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Power ultrasound is known to enhance crystals nucleation, and nucleation times can be reduced by one up to three orders of magnitude for several organic or inorganic crystals. The precise physics involved in this phenomenon still remains unclear, and various mechanisms involving the action of inertial cavitation bubbles have been proposed. In this paper, two of these mechanisms, pressure and segregation effects, are examined. The first one concerns the variations of supersaturation induced by the high pressures appearing in the neighbourhood of a collapsing bubble, and the second one results from the modification of clusters distribution in the vicinity of bubble. Crystallisation experiments were performed on zinc sulphate heptahydrate ZnSO(4)·7H(2)O, which has been chosen for its pressure-independent solubility, so that pressure variations have no effect on supersaturation. As observed in past studies on other species, induction times were found lower under insonification than under silent conditions at low supersaturations, which casts some doubts on a pure pressure effect. The interfacial energy between the solid and the solution was estimated from induction times obtained in silent conditions, and, using classical nucleation theory, the steady-state distribution of the clusters was calculated. Segregation theory was then applied to calculate the over-concentrations of n-sized clusters at the end of the collapse of a 4 μm bubble driven at 20 kHz by different acoustic pressures. The over-concentration of clusters close to the critical size near a collapsing bubble was found to reach more than one order of magnitude, which may favour the direct attachment process between such clusters, and enhance the global nucleation kinetics., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Sonochemistry is a technique that offers promise for pollutant degradation, but earlier studies on various chlorinated substrates do not give a definitive view of the effectiveness of this methodology. We now report a thorough study of ultrasonic operational variables upon perchloroethylene (PCE) degradation in water (variables include ultrasonic frequency, power and system geometry as well as substrate concentration) and we attempt to close the mass balance where feasible. We obtained fractional conversions of >97% showing very effective loss of pollutant starting material, and give mechanistic proposals for the reaction pathway based on cavitational phenomena inducing pyrolytic and free radical processes. We note major products of Cl(-) and CO(2)/CO, and also trichloroethylene (TCE) and dichloroethylene (DCE) at ppm concentrations as reported earlier. The formation at very low (ppb) concentration of small halocompounds (CHCl(3), CCl(4)) and also of higher-mass species, such as pentachloropropene, hexachloroethane, is noteworthy. But of particular importance in our work is the discovery of significant quantities of chloroacetate derivatives at ppm concentrations. Although these compounds have been described as by-products with other techniques such as radiolysis or photochemistry, this is the first time that these products have been identified in the sonochemical treatment of PCE; this allows a much more effective account of the mass balance and may explain earlier inconsistencies. This reaction system is now better identified, but a corollary is that, because these haloacetates are themselves species of some toxicity, the use of ultrasound here may not sufficiently diminish wastewater toxicity., (Copyright © 2010 Elsevier B.V. All rights reserved.)

A preliminary study of the 20 kHz sonoelectrochemical degradation of perchloroethylene in aqueous sodium sulfate has been carried out using controlled current density degradation sonoelectrolyses in batch mode. An important improvement in the viability of the sonochemical process is achieved when the electrochemistry is implemented, but the improvement of the electrochemical treatment is lower when the 20 kHz ultrasound field is simultaneously used. A fractional conversion of 100% and degradation efficiency around 55% are obtained independently of the ultrasound power used. The current efficiency is also enhanced compared to the electrochemical treatment and a higher speciation is also detected; the main volatile compounds produced in the electrochemical and sonochemical treatment, trichloroethylene and dichloroethylene, are not only totally degraded, but also at shorter times than in the sonochemical or electrochemical treatments., (Copyright © 2010 Elsevier B.V. All rights reserved.)

The sonoelectrochemical treatment of aqueous solutions of trichloroacetic acid (TCAA) has been scaled-up from the voltammetric analysis to pre-pilot stage. The degradation in absence of ultrasound field has yield to a poor performance which has been improved in presence of ultrasound. The sonovoltametry study has provided the range of potentials and/or current densities to be used with the lowest current efficiency penalty. Sonoelectrolyses at batch scale (carried out with a horn-transducer 24 kHz positioned at about 3 cm from the surface of the electrode) achieved little improvement in the degradation. However, when a specifically designed sonoelectrochemical reactor (not optimized) was used during the scale-up, the presence of ultrasound field provided better results (fractional conversion 97%, degradation efficiency 26%, selectivity 0.92 and current efficiency 8%) at lower ultrasonic intensities and volumetric flow., (Copyright 2009 Elsevier B.V. All rights reserved.)

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.

The primary Bjerknes force is responsible for the quick translational motion of radially oscillating bubbles in a sound field. The problem is classical in the case of small-amplitude oscillations, for which an analytical expression of the force can be easily obtained, and predicts attraction of sub-resonant bubbles by pressure antinodes. But for high-amplitude sound fields the bubbles undergo large-amplitude nonlinear oscillations, so that no analytical expression for the force is available in this case. The bubble dynamics is approximated on physical grounds, following the method of Hilgenfeldt [J. Fluid Mech. 365, 171 (1998)], but carefully accounting for surface tension. The analytical expression of the maximum radius of the bubble is recovered, the time of maximum expansion is noticeably refined, and an estimation of the collapse time is found. An analytical expression for the time-varying bubble volume is deduced, and the Bjerknes force is obtained in closed form. The result is valid for any shape of the sound field, including purely standing or purely traveling waves, and is ready to use in a theoretical model of bubble cloud evolution. In addition, the well-known sign inversion of the Bjerknes force for large standing waves is recovered and the inversion threshold in the parameter space is obtained analytically. The results are in good agreement with numerical simulations and allow a quantitative assessment of the effects of physical parameters. It is found that either reduction of the surface tension or increase in the static pressure should produce a widening of the bubble-free region near high-amplitude pressure antinodes.

Pressure diffusion is a mass diffusion process forced by pressure gradients. It has the ability to segregate two species of a mixture, driving the densest species toward high pressure zones, but requires very large pressure gradients to become noticeable. An inertial cavitation bubble develops large pressure gradients in its vicinity, especially as the bubble rebounds at the end of its collapse, and it is therefore expected that a liquid mixture surrounding such a bubble would become segregated. Theory developed in an earlier paper shows that this is indeed the case for sufficiently large molecules or nano-particles. The main theoretical results are recalled and a possible implication of this segregation phenomenon on the well-known cavitation-enhanced crystals nucleation is proposed.

The growth or dissolution of small gas bubbles (R0<15 microm) by rectified diffusion in nearly saturated liquids, subject to low frequencies (20 kHz

It was discovered that simultaneous insonification and air blowing of different aqueous binary solutions such as water/sodium-dodecyl-sulphate (SDS), water/methanol or water/potassium-sulphate yields a very concentrated bubble cloud invading the whole vessel in a few seconds. After the end of insonification, this cloudiness remained in the solution for about 1 min. The phenomenon was investigated by computer-treatment of solution pictures recorded every second after the end of insonification. Turbidity appeared to increase with ultrasound power, and also with SDS concentration. During the disappearance of the cloud, a turbidity front appeared rising and spreading upward. This front was studied in the characteristic plane and interpreted as a spatial segregation of different bubble sizes rising with different terminal velocities. The bubble sizes involved were estimated to about 10 microns. Adsorption of surface active species are invoked to explain the cloud formation and its abnormally slow disappearance, but the occurrence of the phenomenon for potassium-sulphate salt remains unexplained.

The influence of ultrasound power on the C-alkylation of phenylacetonitrile by ethyl bromide was studied under solid-liquid phase transfer catalysis in the presence of potassium hydroxide and tetrabutylammonium hydrogenosulfate. Experimental results are reported on the influence of the ultrasonic power on the yields. The optimum efficiency of ultrasounds is determined and the way in which ultrasound power may affect the yields is discussed.