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

Authors
Journal
Journal of Quantitative Spectroscopy and Radiative Transfer
0022-4073
Publisher
Elsevier
Volume
133
Identifiers
DOI: 10.1016/j.jqsrt.2013.10.001
Keywords
  • Beer–Lambert–Bouguer Law
  • Poisson Process
  • Optical Depth
  • Stochastic Media
  • Non-Exponential Transmission Laws
Disciplines
  • Computer Science
  • Mathematics
  • Physics

Abstract

Abstract 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.

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