  Experiments by Gittings, Bandyopadhyay, and Durian [Europhys. Lett.\
\textbf{65}, 414 (2004)] demonstrate that light possesses a higher probability
to propagate in the liquid phase of a foam due to total reflection. The authors
term this observation photon channelling which we investigate in this article
theoretically. We first derive a central relation in the work of Gitting {\em
et al.} without any free parameters. It links the photon's path-length fraction
$f$ in the liquid phase to the liquid fraction $\epsilon$. We then construct
two-dimensional Voronoi foams, replace the cell edges by channels to represent
the liquid films and simulate photon paths according to the laws of ray optics
using transmission and reflection coefficients from Fresnel's formulas. In an
exact honeycomb foam, the photons show superdiffusive behavior. It becomes
diffusive as soon as disorder is introduced into the foams. The dependence of
the diffusion constant on channel width and refractive index is explained by a
one-dimensional random-walk model. It contains a photon channelling state that
is crucial for the understanding of the numerical results. At the end, we
shortly comment on the observation that photon channelling only occurs in a
finite range of $\epsilon$.
