Mm. Tomadakis et Sv. Sotirchos, EFFECTIVE DIFFUSIVITIES AND CONDUCTIVITIES OF RANDOM DISPERSIONS OF NONOVERLAPPING AND PARTIALLY OVERLAPPING UNIDIRECTIONAL FIBERS, The Journal of chemical physics, 99(12), 1993, pp. 9820-9827
Computer simulation results are presented for the effective bulk trans
ition, and Knudsen diffusion coefficients in structures consisting of
parallel nonoverlapping (impenetrable) or partially overlapping (penet
rable) fibers. The numerical procedure is based on a discrete step-by-
step random walk mechanism used to determine the mean square displacem
ent of molecules traveling in the interior of the porous medium. The c
omputed transition regime diffusivities are compared with the predicti
ons of the reciprocal additivity effective diffusivity expression. The
bulk diffusivity results are also expressed as formation factors desc
ribing other transport properties (e.g., thermal and electrical conduc
tivity, magnetic permeability, and dielectric constant) of the fibrous
structures or in general of the corresponding arrays of cylinders (ei
ther nonconducting or infinitely conducting with respect to the matrix
phase). The formation factors of nonoverlapping cylinders are compare
d with variational bounds and analytical and numerical results of the
literature.