Effects of spatial correlations in particulate media on dependent scattering and radiative transport

Abstract

Radiative transport in particulate media is a ubiquitous problem with energy, manufacturing, and catalysis applications. Despite the limited applicability of the theory of independent scattering, it continues to be widely applied to model radiative transport in an ensemble of large particles. While scale factors that correct for dependent scattering effects have been obtained as a function of the solid volume fraction, its dependencies on the spatial distributions of the particles have not been investigated. Herein, we examine the influences of the three-dimensional spatial distributions and the solid volume fraction of particles on radiative transport, and quantify the resulting deviations from the independent scattering assumption. Packed beds with Poisson, random, ordered and clustered spatial distributions of particles, and varying solid volume fractions (0.05–0.5) are computationally generated. Spatial correlations of particles are statistically quantified using an index of cluster sampling. Monte Carlo ray tracing simulations are preformed to obtain radiative transmittance, path-length distribution, angular distribution of the transmitted rays, and the scattering phase function. Results reveal that the radiative transmittance and the extinction coefficient are strongly influenced by the spatial distributions of the particles, in addition to the solid volume fraction. For the first time, we have developed a generalized correlation that predicts scale factors as a function of the index of cluster sampling, which is dictated by the spatial distributions and the solid volume fractions of the particles. Ordered beds with perfectly negative correlations in the spatial positions of the particles exhibit a more discrete interaction of radiation with the ensemble as compared to the other spatial distributions. This aspect leads to increased directionality of transmitted radiation and anisotropy in the scattering phase function for large solid volume fractions.