A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures

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

Growth by rectified diffusion of strongly acoustically-forced gas bubbles in nearly saturated liquids

The growth or dissolution of small gas bubbles (R0 < 15 μm) by rectified diffusion in nearly satu- rated 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 the- ory 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

Analytical expressions for primary Bjerknes force on inertial cavitation bubbles

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 et al

Crystallization of α-glycine by anti-solvent assisted by ultrasound

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High bubble concentrations produced by ultrasounds in binary mixtures

7th Meeting of the European‐Society‐of‐Sonochemistry, BIARRITZ GUETHARY, FRANCE, MAY 14‐18, 2000International audienceIt 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 mum. 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

Influence of the liquid viscosity on the formation of bubble structures in a 20 kHz field

The cavitation field in a cylindrical vessel bottom-insonified by a 19.7 kHz 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 am- plitude, 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

Axial acoustic field along a solid-liquid fluidized bed under power ultrasound

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)