Diffusive transport of light in three-dimensional disordered Voronoi structures

TL;DR

This study models light diffusion in dry foams using 3D Voronoi tessellations, revealing that film properties mainly influence light transport, with minimal impact from foam disorder, aligning well with experimental data.

Contribution

It demonstrates that foam disorder has little effect on light transport, emphasizing the role of liquid films, and provides theoretical estimates consistent with experiments.

Findings

Transport-mean-free path is insensitive to foam disorder.

Liquid films significantly influence light diffusion.

Theoretical values match experimental measurements.

Abstract

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: a constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for transport-mean-free path fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in {dry} foams.