Beer's law is the foundation of the classic radiative transfer theory. Recently, many studies have pointed out the existence of non-Beerian transport behavior in spatially correlated and statistically non-homogeneous and anisotropic particulate systems. However, there still lacks a comprehensive quantitative evalution of the applicability of Beer's law in particulate medium from random to regular arrangement. In this work, a numerical approach is proposed to quantitatively analyze and determine the applicability of Beer's law in particulate systems from regular arrangement to random arrangement. A simple approach for characterizing structural randomness of particulate system is presented. The results show that the non-Beerian behaviors exist in statistically isotropic and homogeneous particulate media. The structural randomness has a significant influence on the transmission distribution and hence the applicability of Beer's law in particulate systems. Quantitative dependent relation of validity of Beer's law on structural randomness in particulate system is obtained. Both particle spacing and structural randomness have significant impact on the applicability of Beer's law. This work is helpful for the understanding of non-Beerian radiative transfer in particulate media and guiding related engineering applications of radiative transfer theory.

比尔定律是经典辐射传输理论的基础。最近，许多研究指出在空间相关和统计上非均匀和各向异性的颗粒系统中存在非比尔输运行为。然而，目前还缺乏对比尔定律在颗粒介质中从随机排列到规则排列的适用性的全面定量评价。在这项工作中，提出了一种数值方法来定量分析和确定比尔定律在从规则排列到随机排列的颗粒系统中的适用性。提出了一种表征颗粒系统结构随机性的简单方法。结果表明，非比尔行为存在于统计各向同性和均质颗粒介质中。结构随机性对传输分布有显着影响，因此对比尔定律在颗粒系统中的适用性有显着影响。得到了比尔定律有效性对颗粒体系结构随机性的定量依赖关系。粒子间距和结构随机性都对比尔定律的适用性有显着影响。这项工作有助于理解颗粒介质中的非比尔辐射传递，并指导辐射传递理论的相关工程应用。粒子间距和结构随机性都对比尔定律的适用性有显着影响。这项工作有助于理解颗粒介质中的非比尔辐射传递，并指导辐射传递理论的相关工程应用。粒子间距和结构随机性都对比尔定律的适用性有显着影响。这项工作有助于理解颗粒介质中的非比尔辐射传递，并指导辐射传递理论的相关工程应用。