The effects of the polydispersity of the characteristic diffusion leng
th of the pore space of fibrous media on the effective diffusion coeff
icients of gases are studied by investigating the problem of gaseous d
iffusion in the Knudsen, transition, and bulk regimes in square arrays
of filament bundles, of cylindrical cross section consisting of unidi
rectional, freely overlapping cylindrical filaments. Effective diffusi
on coefficients are computed using a stochastic simulation method base
d on the computation of the mean square displacement of a large number
of molecules (random walkers) diffusing in the pore space. The depend
ence of effective diffusivity on filament to bundle radius ratio, intr
abundle porosity, interbundle porosity, and Knudsen number is investig
ated in detail. The computed diffusivities are compared to the predict
ions of analytical or semianalytical formulas based on expressions der
ived in the literature for two-phase media or bidisperse pore structur
es.