NIU Gege， ZHANG Shiwei， GUO Ping， SU Mingxu， CAI Xiaoshu

School of Energy and Power Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China

Abstract

Objective　When ultrasonic waves propagate through a liquid-solid suspension containing gas bubbles， significant acoustic scattering occurs at the gas-liquid interface due to the large acoustic impedance contrast， resulting in excess acoustic attenuation.This introduces errors in characterizing the particle size of solid particles based on the acoustic attenuation spectral analysis. The ultrasonic attenuation and inversion results are analyzed in a liquid-solid two-phase system by changing particle size and mixingratio of micrometer bubbles， evaluating their influence on acoustic attenuation and the accuracy of particle size characterization for solid particles.

Methods　The acoustic scattering and absorption characteristics of solid elastic particles and bubbles were compared and analyzed， with a focus on the resonance scattering properties of bubbles. Based on the theory of acoustic scattering and absorption  in single solid elastic particles and bubbles， a Monte Carlo model for the solid particle-bubble hybrid system was developed.Numerical analysis was conducted on the ultrasonic attenuation of bubbles with different sizes and mixing ratios in monodisperse and polydisperse aqueous suspensions of micron-sized glass beads to evaluate their effect on the acoustic attenuation spectra.Furthermore， by comparing the accuracy of particle size inversion using the differential evolution algorithm， genetic algorithm，and particle swarm optimization algorithm， the particle swarm algorithm was selected to investigate the deviation in particle size inversion caused by the presence of bubbles.

Results and Discussion　As the bubble mixing ratio increased， the decay curve of the mixed particle system gradually shifted upward， with the root mean square error of the mixed particle system reaching up to 16. 42. According to the particle size inversion results， in a monodisperse system where the bubbles and glass bead radius were 60 μm， the error was about 0. 4% at a mixing ratio of 0. 1%， around 1% at 0. 3%， and about 6% at 1%. In the polydisperse system， a higher bubble mixing ratio led to an increase in the inverted particle size and a broader distribution width. For the ultrasonic frequency range of 1~10 MHz， micronsized bubbles（ >10 μm） were located at the right side of the resonance scattering region. As the bubble size and ultrasonic frequency decreased（ gradually approaching the resonance scattering region）， the effect of bubbles on acoustic attenuation and particle size characterization of solid particles became more significant. When the radius of both bubble and glass bead was 60 μm，the inversion error remained around 0. 4% at a 0. 1% mixing ratio. However， for bubbles with a 30 μm radius， the error increased to about 2% at the same mixing ratio. At a radius of 10 μm， bubbles with a 0. 1% mixing ratio caused an inversion error of nearly 15%.

Conclusion　This study establishes a Monte Carlo model for a gas-liquid-solid three-phase mixed particle system and evaluates

the effect of micro-bubbles on acoustic attenuation spectra and particle size characterization. The findings indicate that as the bubble mixing ratio increases， the errors in ultrasound attenuation and particle size characterization also increase. Moreover，resonance scattering significantly amplifies the errors when the bubble sizes approach the resonance scattering region. These results provide a theoretical basis for evaluating and mitigating bubble interference in particle measurement experiments.

Keywords： ultrasound attenuation； Monte Carlo method； bubbles； particle； size inversion

Get Citation: NIU Gege， ZHANG Shiwei， GUO Ping， et al. Effect of bubbles on characterization of particle size in suspensions using ultrasound［J］. China Powder Science and Technology， 2025， 31（6）： 1−13.

Received: 2025-01-11 .Revised: 2024-03-20 ,Online: 2025-05-29

Funding Project: 国家自然科学基金项目，编号 ：52376162。

First Author: 牛格格（1999—），女，硕士生，研究方向为超声颗粒测量。E-mail：315140849@qq. com。

Corresponding Author: 苏明旭（1973—），男，教授，博士，博士生导师，研究方向为颗粒与两相流测量。E-mail：sumx@usst. edu. cn。

DOI：10.13732/j.issn.1008-5548.2025.06.012

CLC No: TB551              Type Code: A

Serial No:1008-5548（2025）06-0001-13