Abstract: The measurement of particulate matter covers a wide range of aeras and is of great importance for the development of society and the progress of science and technology. The light extinction method is one of the particle measurement methods, which is simple in principle, easy to measure, and can be applied to the measurement of particles in three phases: gas-liquid-solid. The traditional light extinction model is applicable to a single particle system, in which the extinction particle size measurement model is typically constructed based on Mie scattering theory and Lambert-Beer Law. However, the light extinction phenomena of mixed particles are more complex. Factors such as particle size, refractive index, mixing ratio, and particle size distribution affect the light extinction characteristics, making the traditional model inadequate. A mixed extinction model had been developed by weighting the extinction cross-section in terms of the mixing ratio. This model aimed to investigate the extinction characteristics of mixed particles, categorized as monodisperse and polydisperse, while analyzing the effects of particle size, refractive index, mixing ratio, and distribution parameters on the extinction spectra. Furthermore, a measurement system for extinction spectra was established, and a series of experiments were conducted using properly prepared suspensions of silica and polystyrene particles with mixing ratios of 0.25, 0.5, and 0.75. The experimental spectra were then inverted using an improved differential evolutionary algorithm. The results showed that the calculations using the mixed extinction method were in better agreement with the experimental extinction spectra, with root mean square errors within 0.08. Afterwards, simultaneous multi-parameter inversion of the polydisperse mixed particle system under different mixing ratios had been achieved. The absolute values of maximal inversion errors for particle sizes and mixing ratios were 7.44% and 7.48%, respectively, which were smaller than those obtained under the monodisperse hypothesis. The distribution parameters also reflect the characteristics of the experimental samples with narrow particle size distribution.

Key words: mixed particle system, Lambert-Beer law, extinction spectrum, mixing ratio, inversion

摘要： 在单一颗粒系中，消光光谱法颗粒粒径测量模型通常基于Mie散射理论和朗伯-比尔定律(Lambert-Beer Law)构建。但由多种颗粒物构成的混合颗粒系消光特性更为复杂，颗粒粒径及分布、折射率、颗粒配比均会影响消光谱，传统模型不再适用。本工作将消光截面按混合比等效，构建了一种混合颗粒消光模型。对于多种混合颗粒系进行消光谱数值计算，将混合颗粒系分为单分散和多分散两种情况，分别探讨了颗粒粒径、折射率、混合比及分布参数对消光光谱影响规律。研究了混合颗粒系粒径、分布参数和混合比多参数同步反演问题，搭建消光谱测量系统并配置混合比为0.25, 0.5及0.75的二氧化硅和聚苯乙烯混合颗粒悬浮液进行实验，采用改进差分进化算法对实验谱进行反演。结果表明，混合消光模型预测与实验消光谱吻合，均方根误差小于0.08；实现了在不同混合比条件下多分散混合颗粒系的多参数同步反演，粒径和混合比的最大反演误差绝对值分别为7.44%和7.48%，均小于单分散假定时混合颗粒系参数反演误差绝对值，分布参数结果较好地反映了实验样品颗粒粒径分布较窄的特点。

关键词: 混合颗粒系, 朗伯-比尔定律, 消光谱, 混合比, 反演