Applicability of Beer's law in particulate system from random to regular arrangement: A numerical evaluation

Abstract

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.