Acoustic measurement methods and spatiotemporal distribution patterns of microbubble spectra in water under...

Microbubbles serve as the primary initiators of acoustic cavitation and directly determine the cavitation threshold, intensity, and spatial distribution of cavitation activity. However, measuring microbubble spectra, particularly under high-concentration aeration conditions, remains a major challenge because of the ill-posed nature of acoustic inverse problems and interference from reflected signals. This study develops a comprehensive acoustic theoretical framework and experimental methodology for quantifying microbubble spectra in water, with the specific aim of supporting cavitation control. A fluid continuity equation incorporating microbubble parameters is derived, and the inverse problem of recovering nuclei size distributions from acoustic attenuation and phase velocity data is solved using discretization and Tikhonov regularization. An optimized acoustic measurement system, featuring a transducer-hydrophone configuration and signal timing control, is designed to minimize wall reflections. Experimental validation demonstrates that the measured microbubble spectra follow an exponential distribution and that the proposed method exhibits high repeatability. The temporal evolution and depth-dependent spatial distribution of microbubbles under controlled aeration are systematically investigated. Furthermore, two probabilistic models are proposed to predict the complete microbubbles spectrum from limited experimental data, thereby significantly reducing reliance on broadband acoustic instrumentation. This work provides a practical acoustic diagnostic tool for characterizing cavitation microbubbles in liquid.