Acoustic frequency and optimum sonochemical production at single and multi-bubble scales: A modeling answer to the scaling dilemma

The present work consists of an innovative approach aiming to address the scalability dilemma of the sonochemical activity dependency of acoustic frequency. The study originates from the discordance of observations between the theoretical investigations of the sonochemical activity of the single acoustic cavitation bubble in function of the acoustic frequency, in one hand, and the experimental findings regarding the optimal frequency condition, mainly in terms of pollutant degradation, in the other hand. A single bubble and an up-scaled model of the sonochemical activity are suggested and simulations were conducted based on both of them over the frequencies 20, 200, 300, 360, 443, 500, 600 and 800 kHz under an oxygen atmosphere. The results reveal that the sonochemical production at single bubble scale is monotonously decreasing with the increase of frequency, while all the products demonstrate an absolute optimum of sonochemical production at 200 kHz, except HO^• that attains its maximum molar yield under 300 kHz. Besides, the production of the predominant species, namely HO₂^•, HO^• and O₃, manifests a clear rebound at 500 kHz. All the present results were compared to and confirmed by experimental findings, while the scalability of the concentrations of sonochemically produced species was discussed using a parameter we introduced as "the mass focusing factor".

Perturbation of a radially oscillating single-bubble by a micron-sized object

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.

Part 1: Pressure and temperature profiles around a single bubble

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.

Part 2: Number of ice nuclei generated by a single bubble

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.

New interpretation of the effects of argon-saturating gas toward sonochemical reactions

A number of literature reports showed that argon provides a more sonochemical activity than polyatomic gases because of its higher polytropic ratio; whereas several recent studies showed that polyatomic gases, such as O₂, can compensate the lower bubble temperature by the self decomposition in the bubble. In this work, we show for the first time a numerical interpretation of these controversial reported effects. Computer simulations of chemical reactions inside a collapsing acoustic bubble in water saturated by different gases (Ar, O₂, air and N₂) have been performed for different frequencies (213-1100 kHz). In all cases, OH radical is the main powerful oxidant created in the bubble. Unexpectedly, the order of saturating gases toward the production rate of OH radical was strongly frequency dependent. The rate of production decreases in the order of Ar>O₂>air>N₂ for frequencies above 515 kHz, and Ar starts to lose progressively its first order to the following gases with a gradually decreasing of frequency below 515 kHz up to a final order of O₂>air∼N₂>Ar at 213 kHz. The analysis of chemical kinetic results showed a surprising aspect: in some cases, there exists an optimum bubble temperature during collapse at which the chemical yield is much higher than that of the maximum bubble temperature achieved in the bubble. On the basis of this, we have concluded that the lower sonochemical activity induced by Ar for frequencies below 515 kHz is mainly due to the forte consumption of radicals inside a bubble prior the complete collapse being reached.