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We study photon diffusion in a two-dimensional random packing of monodispersedisks as a simple model of granular media and wet foams. We assume that theintensity reflectance of disks is a constant. We present an analytic expressionfor the transport-mean-free path in terms of the velocity of light in the disksand host medium, radius and packing fraction of the disks, and the intensityreflectance. For the glass beads immersed in the air or water, we estimatetransport-mean-free paths about half the experimental ones. For the air bubblesimmersed in the water, transport-mean-free paths is an inverse function ofliquid volume fraction of the model wet foam. This throws new light on theempirical law of Vera et. al, and promotes more realistic models.

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