Relying on the fact that both of chemical and physical impacts of sonication are in strong relation to the number of acoustic cavities, the present paper introduces an innovative technique for the estimation of the number of active bubbles using the degradation of nonvolatile pollutants in the bulk liquid as a probe. The internal (gas pages) and external (liquid) bubble sonochemistry were simulated to track the radicals generation and use for nonvolatile pollutants degradation (in the liquid phase). To this end, COPASI® chemical kinetics software has been used for optimizing the acoustic bubble number density by linking the instantaneous bubble gas reaction (described by a bubble dynamic model accounting for the radical dissolution mechanism) and the aqueous free radicals degradation kinetics [i.e. concentration vs. time] of several nonvolatile organics (phenol, 4-chlorophenol, dyes…). Based on this strategy, the number density of active bubbles was determined for different operating circumstances (i.e. acoustic intensity, frequency, liquid temperature and saturation gas type). The performance of our method was evaluated by comparing our findings to those available in the literature, where an excellent agreement was established. Our technique showed that the number density monotonously goes up with increasing ultrasound frequency from 200 to 1140kHz, regardless of the experimental conditions used in this investigation. The opposite behavior has been obtained with the increase of the liquid temperature and acoustic intensity. Additionally, it has been noticed that the variation in the number of cavities with respect to the nature of saturating gas is frequency-dependent. At a frequency of 200kHz, the number of bubbles is in the order: O2>Ar>air. However, over this frequency (>200kHz), the number of acoustic bubbles is in the order: O2>air>Ar. On the other hand, it has been shown that below a frequency of ~860kHz, the variation of void fraction (ε) is synchronized with change in number density (N); nevertheless, over this value (>860kHz), these two parameters (N, ε) are no longer closely connected. As a result, in this case (>860kHz), the evaluation of number density from the total volume fraction of bubbles could not be directly performed without more information regarding the bubbles population, (e.g. size distribution, bubble-bubble interactions, bubbles deformation…etc.). Finally, the current proposed technique is flexible and can determine the number density of active bubbles for a wide range of operating conditions and circumstances.
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