Most research on sonoluminescence and sonochemistry has been conducted at acoustic frequencies above ∼20 kHz. Consequently, mathematical models for the dynamics of acoustically-driven bubbles have hardly been examined in the audible frequency spectrum. Here, we develop a new hybrid modelling approach that combines the rigour of the advection–diffusion model whilst retaining the simplicity of a reduced-order boundary layer model to predict phase-change, mass and heat transfer in an inertially collapsing bubble excited by audible sound. Differences in these approaches are explored through a thorough validation against experimental data obtained from ultra-high speed videos of bubble dynamics at 17.8 kHz. Our results indicate that, while the boundary layer model agrees well with the advection–diffusion model at high driving frequencies, there are significant deviations at lower frequencies, where the boundary layer model overpredicts parameters such as bubble size and quantity of trapped vapour while underpredicting others such as temperature and pressure. These deviations at lower frequencies is caused by an inaccurate estimation of the boundary layer thickness originating from the time-scale competition between diffusion and fast bubble wall motion. Our work questions the suitability of existing reduced-order models developed for ultrasonic frequencies when applied to the audible range, reinforcing that further research in the audible range is needed.

中文翻译：

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可听见的声音驱动气泡中的质量和传热


大多数关于声波发光和声化学的研究都是在 ∼20 kHz 以上的声频率下进行的。因此，几乎没有在可听频谱中研究过声学驱动气泡动力学的数学模型。在这里，我们开发了一种新的混合建模方法，该方法结合了平流-扩散模型的严谨性，同时保留了降阶边界层模型的简单性，以预测由可听声音激发的惯性坍缩气泡中的相变、质量和传热。通过对 17.8 kHz 气泡动力学的超高速视频获得的实验数据进行全面验证，探索了这些方法的差异。我们的结果表明，虽然边界层模型在高驱动频率下与平流-扩散模型非常吻合，但在较低频率下存在显着偏差，其中边界层模型高估了气泡大小和捕获蒸汽量等参数，而低估了温度和压力等其他参数。这些较低频率的偏差是由于扩散和快速气泡壁运动之间的时间尺度竞争引起的边界层厚度估计不准确造成的。我们的工作质疑了现有的为超声波频率开发的降阶模型在应用于可听范围时的适用性，从而加强了对可听范围的进一步研究。