A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures

TL;DR

This paper develops a reciprocal generalized radiative transfer model for binary mixtures, introducing a new attenuation law and providing a more accurate description of linear transport in stochastic media, improving upon previous Monte Carlo estimates.

Contribution

It derives a reciprocal RGRT framework with a novel attenuation law for binary mixtures, enabling exact homogenization and analytical descriptions of radiative transfer in stochastic media.

Findings

Introduces a new attenuation law for binary mixtures.

Shows previous models reduce to exponential attenuation.

Provides an analytical framework for stochastic media transport.

Abstract

We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional stochastic binary mixtures with Markovian mixing statistics and nonstochastic albedo and phase function. The derivation includes a new attenuation law and related free-path distribution between collisions, which was previously estimated using a Monte Carlo approach. We also show that previous stationary descriptions of binary mixtures with binomial mixing statistics reduce to exponential attenuations and, thus, have an exact homogenization within classical radiative transfer.