Tracer diffusion in fibre networks: the impact of spatial fluctuations in the fibre distribution.

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