Diffusive transport of light in a two-dimensional disordered packing of disks: Analytical approach to transport mean free path

Abstract

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant r . We present an analytic expression for the transport mean free path l;{*} in terms of the velocity of light in the disks and host medium, radius R and packing fraction of the disks, and the intensity reflectance. For glass beads immersed in air or water, we estimate transport mean free paths about half the experimental ones. For air bubbles immersed in water, l;{*}R is a linear function of 1epsilon , where epsilon is the liquid volume fraction of the model wet foam. This throws light on the empirical law of Vera [Appl. Opt. 40, 4210 (2001)] and promotes more realistic models.