A mean-field formalism that addresses spatial non-uniformities in fibre networks was combined with the cylindrical cell model to calculate the diffusion constant for a spherical tracer. Deviations from randomness in the fibre distribution were described by an operational distribution over volume fractions that was parametrized by mean values for the pore radii and void space chord lengths. Weight factors for elements with different radii in the cell model were assigned in a manner that enforces agreement with the distribution over pore sizes predicted by the present treatment of heterogeneous networks. Illustrative calculations suggested that the tracer diffusion constant was quite sensitive to non-uniformities in the network; particularly for tracer particles having radii that were large compared to the fibre diameter.

Tracer Diffusion in Fibre Networks: the Impact of Spatial Fluctuations in the Fibre Distribution. A.P.Chatterjee: Journal of Physics - Condensed Matter, 2011, 23[37], 375103