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

TL;DR

This paper derives an analytical expression for the transport-mean-free path of light in a two-dimensional disordered disk packing, providing insights into photon diffusion in granular media and wet foams.

Contribution

It presents a new analytical formula for the transport-mean-free path considering various physical parameters, enhancing understanding of light transport in disordered media.

Findings

Estimated transport-mean-free paths for glass beads are about half the experimental values.

Transport-mean-free path for air bubbles inversely depends on liquid volume fraction.

The results offer new insights into empirical laws of photon diffusion in wet foams.

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. We present an analytic expression for the transport-mean-free path in terms of the velocity of light in the disks and host medium, radius and packing fraction of the disks, and the intensity reflectance. For the glass beads immersed in the air or water, we estimate transport-mean-free paths about half the experimental ones. For the air bubbles immersed in the water, transport-mean-free paths is an inverse function of liquid volume fraction of the model wet foam. This throws new light on the empirical law of Vera et. al, and promotes more realistic models.