Numerical simulation of chemical reactions inside an isolated spherical bubble of oxygen has been performed for various ambient bubble radii at different frequencies and acoustic amplitudes to study the effects of these two parameters on the range of ambient radius for an active bubble in sonochemical reactions. The employed model combines the dynamic of bubble collapse with the chemical kinetics of single cavitation bubble. Results from this model were compared with some experimental results presented in the literature and good apparent trends between them were observed. The numerical calculations of this study showed that there always exists an optimal ambient bubble radius at which the production of oxidizing species at the end of the bubble collapse attained their upper limit. It was shown that the range of ambient radius for an active bubble increased with increasing acoustic amplitude and decreased with increasing ultrasound frequency. The optimal ambient radius decreased with increasing frequency. Analysis of curves showing optimal ambient radius versus acoustic amplitude for different ultrasonic frequencies indicated that for 200 and 300kHz, the optimal ambient radius increased linearly with increasing acoustic amplitude up to 3atm. However, slight minima of optimal radius were observed for the curves obtained at 500 and 1000kHz.
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.
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