The emissivity of spherical carbon particles is calculated in both the infrared and visible regions of the spectrum. The scattering and absorption cross sections for individual particles are obtained from the Mie theory of scattering. A suitable dispersion equation is derived which represents the optical properties of carbon at flame temperatures. An expression is obtained for the radiation intensity emitted by a large number of dispersed particles which includes all higher order scattering processes. From these results the emissivity of carbon particles in flames is calculated for particle radii in the range from 50 to 800 A and for 109 to 1015 particles cm-2. In addition the emissivity is obtained for several different particle size distributions which are representative of actual flames. A quantitative explanation is given for the occurrence of the intensity maximum at shorter wavelengths than corresponds to the blackbody maximum at the same temperature.
V. ROBERT STULL and GILBERT N. PLASS, "Emissivity of Dispersed Carbon Particles," J. Opt. Soc. Am. 50, 121-125 (1960)