Radiative transfer equation and direct simulation prediction of reflection and absorption by particle deposits

• Hemispherical reflectance and absorptance of particle deposits are calculated.
• The exact superposition solution, and the scalar radiative transport model, are used.
• Exact and RT predictions converge for small particle volume fractions.
• Large volume fractions lead to significant differences in exact and RT reflectance.

Two methods for computing the normal incidence absorptance and hemispherical reflectance from plane parallel layers of wavelength–sized spherical particles are presented. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a system of randomly–positioned spherical particles excited by an incident plane wave. The second method is based upon the scalar radiative transport equation (RTE) applied to a plane parallel medium. Comparisons are made using five values of particle refractive index, sphere size parameters ranging from 1 to 4, and particle volume concentrations ranging from 0.05 to 0.4. The results indicate that the multiple sphere T matrix method (MSTM) and RTE predictions of hemispherical reflectance and absorptance converge when particle volume fraction becomes small. At higher volume fractions the RTE can yield results for hemispherical reflectance that, depending on the particle size and refractive index, significantly depart from the exact predictions. On the other hand, RTE and MSTM predictions of absorptance have a much closer agreement which is largely independent of the sphere optical properties and volume concentration.