牛格格， 张世玮， 郭 萍， 苏明旭， 蔡小舒

上海理工大学 能源与动力工程学院， 上海200093

引用格式：

牛格格， 张世玮， 郭萍， 等. 气泡对超声法悬浮液颗粒粒径表征的影响［J］. 中国粉体技术， 2025， 31（6）： 1-13.

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.

DOI：10.13732/j.issn.1008-5548.2025.06.012

收稿日期： 2025-01-11， 修回日期： 2025-03-20， 上线日期： 2025-05-27。

基金项目： 国家自然科学基金项目，编号 ：52376162。

第一作者简介： 牛格格（1999—），女，硕士生，研究方向为超声颗粒测量。E-mail：315140849@qq. com。

通信作者简介： 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。

摘要： 【目的】分析液固两相体系中含有不同粒径、混合比（气泡在混合颗粒体系中所占数量比，下同）的微米级气泡条件下超声衰减及粒径反演结果，评估气泡对固体颗粒超声衰减以及粒径表征的影响。【方法】　在单个固体弹性颗粒和气泡声散射与声吸收理论基础上，建立固体颗粒-气泡混合体系的蒙特卡罗物理模型； 针对单、 多分散状态微米级玻璃珠的水悬浮液体系，数值分析不同粒径和混合比气泡条件的超声衰减问题，探讨其对衰减谱的影响； 研究粒子群算法颗粒粒径反演问题，量化评估气泡存在导致的误差。【结果】　气泡和玻璃珠半径为10 μm、超声频率为1~10 MHz时，混合比为1%的气泡导致的衰减谱均方根误差达到16. 42； 从反演结果看，气泡半径为10 μm、混合比为0. 1%时，玻璃珠颗粒粒径反演相对误差近15%； 半径为60 μm，混合比为0. 1%的气泡，所致反演结果相对误差仅为0. 4%。【结论】　混合比极低（小于1%）的微米级气泡对超声衰减谱及玻璃珠粒径表征会产生明显影响，且受共振散射的影响，气泡尺寸越小，影响越大。

关键词： 超声衰减； 蒙特卡罗方法； 气泡； 颗粒； 粒径反演

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

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