分析了计数法颗粒物质量测量的一般数学模型,结果表明颗粒群总质量能表示成各通道计数值的线性迭加。在此基础上以光散射球形颗粒群质量测量为例,以颗粒物的同质量子集Ni为出发点,依据统计理论推导出计数通道的散射光通量与颗粒群的平均体积之间存在分形关系φ=Lβ,由此得出计数通道平均质量j与计数通道特征参数φ的一般函数关系(φj )≡ρj=ρL-ηφηj ,η为光散射等效截面分形维数,且0<η<3。并将其推广到非球形颗粒的测量之中,由此建立起光散射计数法颗粒群质量测量的完整的数学模型,为实现计数器在线测量颗粒群的质量浓度提供了一种可行途径。

The general mathematics model for aerosol mass measurement by using the counting method is analyzed, and the result indicates that the total mass of aerosol can be expressed as linear addition of counting channels. The light scattering counting method for spherical particles mass measurement was studied as an example. Starting with aerosol mass subset Ni, the fractal relation φ=Lβ between scattering luminous flux of counting channels and aerosol’s average volume can be gained according to statistics. Based on this, the general function (φj )≡ρj=ρL-ηφηj of average mass j and characteristic parameter φ of counting channels can be established, where η is the equivalent section fractal dimension with the range from 0 to 3. In further, all of these were extended to non-spherical particles mass measurement, and then the full mathematics model for aerosol mass measurement founded on light scattering counting method was established. This model provides a feasible way for the counter to measure aerosol mass concentration in real time.