Papers by Olivier Louisnard
Ultrasonics Sonochemistry, 2019
This work investigates the ultrasound propagation within a liquid-solid fluidized bed. The acoust... more 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).
A theoretical formulation is proposed for forced mass transport by pressure gradients in a liquid... more A theoretical formulation is proposed for forced mass transport by pressure gradients in a liquid binary mixture around a spherical bubble undergoing volume oscillations in a sound field. Assuming the impermeability of the bubble wall to both species, diffusion driven by pressure gradients and classical Fick-diffusion must cancel at the bubble wall, so that an oscillatory concentration gradient arises in the vicinity of the bubble. The Péclet number Pe is generally high in typical situations and Fick diffusion cannot restore equilibrium immediately, so that an asymptotic average concentration profile may progressively build up in the liquid over large times. Such a behavior is reminiscent of the so-called rectified diffusion problem, leading to slow growth of gas bubble oscillating in a sound field. A rigorous method formerly proposed by Fyrillas & Szeri (1994) to solve the latter problem is used in this paper to solve the present one. It is based on splitting the problem into a smooth part and an oscillatory part. The smooth part is solved by a multiple scales method and yields the slowly varying average concentration field everywhere in the liquid. The oscillatory part is obtained by matched asymptotic expansions in terms of the small parameter Pe −1/2 : the inner solution is required to satisfy the oscillatory balance between pressure diffusion and Fick diffusion at the bubble wall, while the outer solution is required to be zero. Matching both solutions yields a unique splitting of the problem. The final analytical solution, truncated to leading order, compares successfully to direct numerical simulation of the full convection–diffusion equation. The analytical expressions for both smooth and oscillatory parts are calculated for various sets of bubble parameters: driving pressure, frequency and ambient radius. The smooth problem always yields an average depletion of the heaviest species at the bubble wall, only noticeable for large molecules or nano-particles. For driving pressures sufficiently high to yield inertial oscillations of the bubble, the oscillatory problem predicts a periodic peak excess concentration of the heaviest species at the bubble wall at each collapse, lingering on several tens of time the characteristic duration of the bubble rebound. The two effects may compete for large molecules and practical implications of this segregation phenomenon are proposed for various processes involving acoustic cavitation.
The growth or dissolution of small gas bubbles (R0 < 15 µm) by rectified diffusion in nearly satu... more The growth or dissolution of small gas bubbles (R0 < 15 µm) by rectified diffusion in nearly saturated liquids, subject to low frequencies (20 kHz < f < 100 kHz), high driving acoustic fields (1 bar < p < 5 bar) is investigated theoretically. It is shown that, in such conditions, the rectified diffusion threshold radius merges with the Blake threshold radius, which means that a growing bubble is also an inertially-oscillating bubble. On the assumption that such a bubble keeps its integrity up to the shape instability threshold predicted by single-bubble theory, a numerical estimation, and a fully analytical approximation of its growth-rate are derived. From one hand, the merging of the two thresholds raises the problem of the construction and self-sustainment of acoustic cavitation fields. From the other hand, the lifetime of the growing inertial bubbles calculated within the present theory is found to be much shorter than the time necessary to rectify argon. This allows an alternative interpretation of the absence of single-bubble sonoluminescence (SBSL) emission in multi-bubble fields, without resorting to the conventional picture of shape instabilities caused by the presence of other bubbles.
The acoustic field and the location of cavitation bubble are computed in vials used for freeze-dr... more 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.
In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial ca... more 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.
The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. ... more 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 di↵usion 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 coecient 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.
The steady liquid flow observed under ultrasonic emitters generating acoustic cavitation can be s... more 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 20 kHz 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.
A single bubble oscillating in a levitation cell is acoustically monitored by a piezo-ceramics mi... more 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 to 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.
Physics Procedia, 2010
The effects of operational parameters upon the hydroxyl radical generation of sonochemical reacto... more The effects of operational parameters upon the hydroxyl radical generation of sonochemical reactors are critical to optimize this technology for wastewater treatment purposes. Ultrasonic wave characteristics are usually considered as the main parameter to be taken into account. Nevertheless, it is the interaction of these waves with the liquid medium and the reactor what really affects the process. Therefore, the characterization of sonochemical reactors should be based on the effective pressure distribution in the reactor, which not only includes the wave characteristics but also the propagation and reflection of these ultrasonic oscillations. The pressure field can be characterized using different parameters, such as maximum pressure amplitude or volumetric integration of pressure in the reactor. This study intends to find a correlation between such calculated pressure-distributionrelated parameters and experimental measurements of hydroxyl radicals in the process. Both experiments and calculations are run varying the tip-bottom distance (keeping the rest of parameters constant), creating different reflection effects with the reactor walls and therefore different pressure distributions across the reactor. The hydroxyl radical measurements are performed with salicylic acid dosimetry, applying a specific developed method for biphasic cavitating systems. On the other hand, the pressure distribution was calculated simulating the different configurations with the computational tool COMSOL.
Particle & Particle Systems Characterization, 2007
This paper discusses the effects of ultrasound on the production of particles by precipitation an... more This paper discusses the effects of ultrasound on the production of particles by precipitation and crystallization. Examples are given from the formation of crystals of BaSO 4 , K 2 SO 4 , TiO 2 and sucrose. It is shown that ultrasound reduces the induction time, narrows the width of the metastable zone and leads to the production of more, finer, and more uniform crystals in some cases. The reasons for these effects of ultrasound on the nucleation of crystals are discussed and a possible mechanism is presented.
Chemical Engineering Journal, 2002
A study of cooling crystallisation of a potassium sulphate solution in a batch reactor is describ... more A study of cooling crystallisation of a potassium sulphate solution in a batch reactor is described in this paper. The effect of ultrasound on primary nucleation was investigated by measures of induction time and metastable zone width of unseeded solutions. The appearance of crystals is detected by conductivity measurements.
Ultrasonics Sonochemistry, 2016
ABSTRACT
The rapid collapse of inertial cavitation bubbles are known to produce huge temperatures owing to... more The rapid collapse of inertial cavitation bubbles are known to produce huge temperatures owing to the nearly adiabatic compression of the incondensible gas. The main collapse is followed by an expansion and several rebounds. The classical simplified model of bubble dynamics accounting for heat and water transport between the liquid and the bubble predicts that the post-collapses expansions are not isothermal, and freeze the bubble center down to several tenth of °C below zero. The water vapour trapped in the bubble would therefore be driven in conditions where ice crystals could nucleate. This opens the way to a possible new mechanism for ice sonocrystallization, which is discussed. 1. Modelling bubble oscillations When driven by a large amplitude sound field, gas bubbles undergo a large expansion followed by a rapid collapse. During the expansion, water evaporates into the bubble almost isothermally, whereas along the collapse, water and heat remain trapped in the bubble, since the...
bubble dynamics for a single, stable, cavitation bubble. J. Acoustic. Soc. Am., 91(6), 3166-3183.... more bubble dynamics for a single, stable, cavitation bubble. J. Acoustic. Soc. Am., 91(6), 3166-3183. Afin de comprendre les mécanismes mis en jeu en présence d'ultrasons, des études présentant des gouttelettes ou des particules au voisinage d'une bulle unique de cavitation sont essentielles. La présence ou l'apparition de tel objet à proximité de la bulle de cavitation peuvent la perturber et modifier la périodicité de ses oscillations. Cette perte de périodicité peut être détectée par l'écoute de l'émission acoustique de la bulle avec un microphone. Grâce à une corrélation croisée en temps réel entre deux cycles acoustique de la bulle, on est capable de différencier ses régimes d'oscillation. • La méthode mise au point pour analyser les traces du coefficient de corrélation permet de caractériser les régimes d'oscillation d'une bulle unique de cavitation acoustique. • À l'aide de cette méthode, nous sommes capables de détecter la présence d'un co...
: Amplitude profiles of the total vial wall displacement, non-dimensionalized by the driving disp... more : Amplitude profiles of the total vial wall displacement, non-dimensionalized by the driving displacement U 0 , along the external part of the vial boundary (sketched on the left), in the conditions of . The X-axis represents the curvilinear abscissa along the vial boundary, starting from 0 at the bottom on-axis point, and ending on the top of the neck. The circle markers on the curves match the ones on the vial sketch. The liquid height is 7 mm, f = 35890 Hz, and from top to bottom, driving amplitude U 0 = 0.005, 0.02, 0.05, 0.08, 0.1, 0.2, 0.5, 1 µm. It is seen that at low amplitudes, the wall displacement can reach several tens of U 0 . This is because in absence of cavitation, the coupled solid-liquid system develops a pure standing wave with the corresponding amplification (note that there is no other dissipation mechanism than cavitation in the model, such as for example damping terms in solid parts). As cavitation develops, more energy is dissipated and the standing wave amplification disappears.
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Papers by Olivier Louisnard