Knowledge of the number of active bubbles in acoustic cavitation field is very important for the prediction of the performance of ultrasonic reactors toward most chemical processes induced by ultrasound. The literature in this field is scarce, probably due to the complicated nature of the phenomena. We introduce here a relatively simple semi-empirical method for predicting the number of active bubbles in an acoustic cavitation field. By coupling the bubble dynamics in an acoustical field with chemical kinetics occurring in the bubble during oscillation, the amount of the radical species OH and HO2 and molecular H2O2 released by a single bubble was estimated. Knowing that the H2O2 measured experimentally during sonication of water comes from the recombination of hydroxyl (OH) and perhydroxyl (HO2) radicals in the liquid phase and assuming that in sonochemistry applications, the cavitation is transient and the bubble fragments at the first collapse, the number of bubbles formed per unit time per unit volume is then easily determined using material balances for H2O2, OH and HO2 in the liquid phase. The effect of ultrasonic frequency on the number of active bubbles was examined. It was shown that increasing ultrasonic frequency leads to a substantial increase in the number of bubbles formed in the reactor.

In this work, the sonochemical degradation of naphthol blue black (NBB), an acidic diazo dye, in water was investigated. The effects of several operating parameters such as initial NBB concentration, acoustic intensity, ultrasonic frequency, nature of the dissolved gas and solution pH on the degradation of the dye were carried out. The obtained results showed that ultrasound completely destroyed NBB (5 mg L(-1)) after 45 min of sonication and most of the chemical oxygen demand was eliminated after 90 min of treatment. It was found that the initial rate of sonolytic degradation increased with increasing the initial NBB concentration. The fitting of the experimental data by a heterogeneous Langmuir-kinetics model showed that NBB degraded mainly at the interfacial region of the bubble by hydroxyl radical (OH) attack. The degradation rate of the dye increased substantially with increasing acoustic intensity in the range of 0.44-3.58 W cm(-2) and decreased with increasing frequency in the range of 585-1140 kHz. The rate of NBB degradation decreased in the order of Ar>air>N2. The significant degradation was achieved in acidic conditions (pH 2) where the initial degradation rate was 1.37 and 1.66 higher than those observed at pH 6 and pH 10, respectively.

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.

In the present work, comprehensive experimental and numerical investigations of the effects of frequency and acoustic intensity on the sonochemical degradation of naphthol blue black (NBB) in water have been carried out. The experiments have been examined at three frequencies (585, 860 and 1140 kHz) and over a wide range of acoustic intensities. The observed experimental results have been discussed using a more realistic approach that combines the single bubble sonochemistry and the number of active bubbles. The single bubble yield has been predicted using a model that combines the bubble dynamics with chemical kinetics consisting of series of chemical reactions (73 reversible reactions) occurring inside an air bubble during the strong collapse. The experimental results showed that the sonochemical degradation rate of NBB increased substantially with increasing acoustic intensity and decreased with increasing ultrasound frequency. The numerical simulations revealed that NBB degraded mainly through the reaction with hydroxyl radical (OH), which is the dominant oxidant detected in the bubble during collapse. The production rate of OH radical inside a single bubble followed the same trend as that of NBB degradation rate. It increased with increasing acoustic intensity and decreased with increasing frequency. The enhancing effect of acoustic intensity toward the degradation of NBB was attributed to the rise of both the individual chemical bubble yield and the number of active bubbles with increasing acoustic intensity. The reducing effect of frequency was attributed to the sharp decrease in the chemical bubble yield with increasing frequency, which would not compensated by the rise of the number of active bubbles with the increase in ultrasound frequency.