Simultaneous measurement of particle size distribution and mixing ratio based on Monte Carlo ultrasonic attenuation model

Abstract Mixed particle systems are commonly employed in industrial processes, where the characterization of particle size parameters and mixing ratio can frequently serve as key indicators in process control and production optimization. A Monte Carlo (MC) model was developed to numerically predict and study the ultrasonic attenuation spectrum characteristics in the polymethyl methacrylate (PMMA)-glass aqueous suspension, and together with the particle swarm optimization (PSO) algorithm, to handle the inverse problem in solving the particle size, distribution width, and mixing ratio. The results of the numerical simulations indicate that there exists a linear relationship between the attenuation coefficient and the mixing ratio, with the particle size exerting a significant influence. Furthermore, the multi-parameter simultaneous inversion also yielded calculation deviations of less than 1%, 3%, and 6% for the mixing ratio, characteristic diameter, and distribution width, respectively, in comparison to their given values. Afterward, a series of experiments were conducted to quantify the particle size and mixing ratio through the analysis of ultrasonic spectra. In spherical PMMA-glass aqueous suspensions, the measurement error for the mixing ratio and particle size parameters are found to be less than 7% and 10%, respectively, when compared to the image method and the given values. Nevertheless, the measurement errors are slightly increased in a non-spherical mixed particle system, where the volume median diameter and mixing ratio are still less than 10%. The MC modeling and PSO algorithm offer the potential to characterize particle size and mixing ratio for mixed particle systems in industrial applications.