Diffusive transport of light in a Kelvin foam

Although diffusing-wave spectroscopy has already been successfully applied to study dynamic properties of foams, we still lack a clear understanding of the diffusive transport of photons in foams. In this paper, we present a thorough study of photon diffusion in the Kelvin structure as an example for a three-dimensional model foam. We consider the photons' random walk as they are reflected or transmitted by the liquid films according to the rules of ray optics. For constant reflectance and special one- and two-dimensional photon paths, we are able to calculate diffusion constants analytically. Extensive numerical simulations reveal a remarkable similarity with our previous two-dimensional investigations. To implement a more realistic model, we use thin-film reflectances. The simulated diffusion constants exhibit oscillations for varying film thickness d which vanish when disorder is introduced in d. Absolute values and the behavior at small d agree with measurements in very dry foams providing a strong argument for the importance of liquid films in the diffusive photon transport. An analytical theory with a minimum of input parameters reproduces the numerical results.