Light propagation in moderately dense particle systems: a reexamination of the Kubelka-Munk theory.

A numerical method (NM) is developed to characterize radiative transfer in a moderately dense particle population, i.e., a suspension of concentration of <1-10% by volume. It assumes that the particles scatter in accord with the Mie equations, that the propagation of light over short distances is in accord with the exponential transmission law, and that the light flows in many (thirty-six) directions. For representative systems, predictions of the Kubelka-Munk theory (KMT) are compared with those of the NM; partial agreement is found. While this theory can be a useful tool, radiative transport in representative samples is found not to obey strictly either the assumptions for writing the basic differential equations of the KMT or those for solving them. The movement of diffuse light through an attenuating system is found to often collimate it, not to make it more diffuse as expected. This effect causes errors in absolute KMT predictions. New transport equations, like Schuster's, with four parameters instead of two are written and solved to obtain some new KMT equations. Their predictions are compared with those of the NM.