On the link between particle size and deviations from the Beer-Lambert-Bouguer law for direct transmission

- We observe deviations from classical Beer-Lambert-Bouguer behavior in correlated random media.
- We have demonstrated that absorber size is a spatial scale relevant to BLB law deviations.
- We have argued that BLB deviations that neglect consideration of particle size are bound to fail.

Ballistic photon models of radiative transfer in discrete absorbing random media have demonstrated deviations from the Beer-Lambert-Bouguer law of exponential attenuation. A number of theoretical constructs to quantify the deviation from the Beer-Lambert-Bouguer law have appeared in the literature, several of which rely principally on a statistical measure related to the statistics of the absorber spatial positions alone. Here, we utilize a simple computational model to explore the interplay between the geometric size of the absorbing obstacles and the statistics governing the placement of the absorbers in the volume. We find that a description of the volume that depends on particle size and the spatial statistics of absorbers is not sufficient to fully characterize deviations from the Beer-Lambert-Bouguer law. Implications for future further theoretical and computational explorations of the problem are explored.