A novel and simplified model of radiant fields in strongly forward scattering media: Shadow area model

Abstract

Computing radiative fields in scattering media can be quite challenging due to the integro-differential nature of the radiative transfer equation. Several simplifications to this equation are suggested such as Beer’s law, two-flux model (TFM) or six-flux model (SFM). Assumptions and final equations can differ depending on the field. For example, aerosol optics is often studied in length scales relevant to atmospheric sciences to study air pollution or cloud formation. The assumptions and approach adopted in aerosol sciences is different than the approach adopted in the field of photochemistry. In this work, we investigate the solution of radiative fields in aerosol photoreactors where there is a strong forward scattering. We are applying the equations used to compute radiative transfer equation in photocatalytic reactors to aerosol photoreactors with some adjustments. In addition, we suggest a novel approach to the solution of radiative transfer equation based on the shadow areas of the droplets. We showed that intersection areas of randomly distributed disks could be predicted by Poisson distribution. Then, shadow area model (SAM) was developed by a photon balance. Probability of forward and back scattering from several droplet diameters ranging between 5 to 300 µm were found by a ray tracing model in COMSOL Multiphysics. SAM is able to predict absorption and transmission with a similar accuracy to TFM and SFM. However, equations developed for SAM are simpler than TFM or SFM. Therefore, SAM provides an easier grasp of the physical phenomena.