Particle concentration measurement is crucial in chemical, biomedical, and environmental fields. Concentration can be determined through ultrasonic attenuation analysis. However, the complex acoustic behavior and energy dissipation mechanisms in liquid–solid two-phase suspensions have not been fully elucidated, limiting detection accuracy and application. This work analyzed ultrasonic attenuation mechanisms in low-concentration, small-particle suspensions, including Rayleigh scattering, viscous dissipation, and thermal conduction. An integrated acoustic–thermal–flow multiphysics model was developed to quantify the relationship between particle concentration and these attenuation mechanisms. An ultrasonic phased array acquired echoes from 10 μm SiO2 particle suspensions via the ultrasonic backwall echo method. Signals were decomposed using the Sym4 wavelet, denoised with SURE Shrink (optimal threshold λ∗), and their envelopes were extracted via the Hilbert transform, which were then segmented using time windows. The echo peaks were identified with a second-derivative extremum detection algorithm. A linear scanning approach was adopted at angles of 5°, 7°, and 9° to balance directivity, coverage, and signal-to-noise ratio. At each angle, concentration inversion exhibited a relative deviation (RD) within ±26%, root mean square error (RMSE) 0.0024, and mean absolute percentage error (MAPE) 17%, collectively validating the robustness of the proposed Integrated Model. Multi-angle data fusion was implemented to optimize global particle concentration inversion, successfully confining RD to ±20.65%, reducing RMSE to 0.00145 and MAPE to 10.39%, demonstrating that multi-angle data fusion mitigated the primary error sources in single-angle measurements. The findings provide a theoretical foundation and methodological framework for high-precision ultrasonic detection of particle concentration.
Li et al. (Sun,) studied this question.