Radiative Transfer in Two-Phase Dispersed Materials

This chapter presents the treatment of radiative transfer in two-phase dispersed media in the framework of radiative transfer theory. With this aim, two modeling approaches, under the geometric optic hypothesis, are described and then compared. The first one is the traditional treatment of dispersed media as continuous and homogeneous systems, referred to here as the Homogeneous Phase Approach (HPA). The radiation propagation is characterized by effective radiative properties and modeled by the conventional Radiative Transfer Equation (RTE). The second approach is based on a separate treatment of radiative transfer in the continuous and dispersed phases, referred as the Multi-Phase Approach (MPA). In this approach, each constituting phase has its own effective radiative properties and temperatures. For each approach, the methods for predicting the radiative properties are reviewed. The radiative transfers through typical two-phase dispersed media, such as glass containing bubbles, packed bed of opaque spheres, and packed-bed of semitransparent spheres, are analyzed. The results of transmittances and reflectances from these predictive approaches are compared with available experimental data or Monte Carlo (MC) simulation.

Through this contribution, it is shown that the HPA is satisfactory for analyzing radiative transfer in two-phase dispersed media provided that the effective radiative properties are correctly predicted. For practical purpose, it is recommended to use first the well-known independent scattering theory when dispersed contents (or scatterers) are largely spaced or when their volume fraction is small. An example of these media is the glass containing bubbles studied herein. Then, the correlated scattering theory proposed by Brewster or Singh and Kaviany is the simplest model when the continuous phase is non-absorbing and the dispersed phase is constituted of opaque spheres. Finally, the ray-tracing (RT) based method can be used for arbitrary dispersed materials fulfilling the geometric optic regime.

Concerning the MPA, it is generally a suitable approach, as exemplified with glass containing bubbles and packed bed of opaque particles. It is however inaccurate for a few cases for which the scattering pattern presents strong peaks (known as rainbow peaks) due to the correlation between the rays incident on a scatterer and those transmitted through it after undergoing several internal reflections. This problem may occur only when (1) the continuum is less refracting than the scatterers; (2) the scatterers are weakly absorbing; and (3) the scatterer boundaries are specular and regular in shape. It is, for example, the case with a packed-bed of semitransparent specularly reflecting spheres.