Stochastic radiative transfer in a finite plane with anisotropic scattering in a binary Markovian mixture

The time-independent linear transport problem in a stochastic finite-plane medium with linear anisotropic scattering is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The Pomraning-Eddington approach is used to obtain an explicit solution to the problem in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution for the problem under consideration. In the case of isotropic scattering, explicit analytic results for reflectivity and transmissivity, which show a good agreement with Monte Carlo benchmark results, are given. Results for reflectivity and transmissivity in the case of linear anisotropic scattering are also given.