Effects of operating parameters on bubble collapse temperature and sonochemical product yields in dual‑frequency...

This work presents a single‑bubble model for dual‑frequency acoustic cavitation in an O₂ environment. Dual-frequency acoustic cavitation generates extremely high temperatures in liquids, thereby driving complex sonochemical reactions. However, a direct quantitative link between operating parameters and sonochemical product yields has not been fully established. In this study, we systematically quantify the relationships between the maximum bubble temperature (T_max) and a range of key operating parameters, including acoustic field settings (power allocation ratio, phase difference, frequency combination, and excitation amplitude) and initial bubble conditions (initial water vapor mole fraction and initial bubble radius). Using T_max as an intermediate variable, we then establish quantitative correlations between these parameters and the yields of chemical products (total chemical species, H₂, H₂O₂, and OH). Numerical simulations are performed for multiple dual-frequency combinations (20 + 40, 20 + 140, 20 + 200, 40 + 140, 40 + 200, and 140 + 200 kHz) while systematically varying each parameter. The results reveal that the sensitivity of T_max to the power allocation ratio and phase difference is strongest under low-frequency combinations and weakens under high total acoustic pressure amplitude. A "high-frequency-dominant region" is identified, in which the specific low-frequency value no longer affects T_max. The initial water vapor mole fraction exerts a noticeable modulating effect on T_max at low acoustic pressures, but this effect is progressively suppressed as the excitation amplitude increases, except for certain frequency combinations at higher acoustic pressures. T_max (approximately 3000-10190 K) determines the product yields, which follow distinct patterns. The overall trend of sonochemical yields as a function of T_max remains consistent across different initial bubble radii, although the specific transition temperatures for each product vary with the initial radius; the initial radius of 2 μm is chosen as a representative case for the subsequent detailed analysis. H₂ exhibits a three-stage pattern: "low plateau, sharp jump, slow saturation", with a threshold temperature of 5818 K and the sharp increase occurring between 5818 K and 7260 K; H₂O₂ shows a unimodal distribution with a peak at 6210 K; OH displays a multi-peak oscillation pattern with a peak at 6354 K. At 7237 K, the growth rate of the total yield of chemical species decelerates, marking a transition from reaction control to dissipation control. Based on these findings, we propose model-dependent optimal temperature windows for target products: approximately 7260 K for H₂, 6210 K for H₂O₂, and 6354 K for OH, with the understanding that these values are derived from the present single-bubble model under an O₂ atmosphere and serve as theoretical references rather than universal experimental guidelines. This study provides a theoretical basis for optimizing operating parameters to understand the selectivity of dual-frequency ultrasonic cavitation technology in the context of green hydrogen production and pollutant degradation.