Transport properties of random arrays of freely overlapping cylinders with various orientation distributions

We present dimensionless effective transport coefficients (formation factors) for arrays of cylinders of various orientation distributions, namely, cylinders randomly positioned and oriented with their axes parallel to a line, parallel to a plane, or in the three-dimensional space with no preferred orientation. Both cases of conducting cylinders dispersed in a nonconducting matrix and nonconducting cylinders dispersed in a conducting matrix are considered. The transport coefficients are computed by means of a random walk simulation scheme. A comprehensive survey of past studies on transport properties of random arrays of cylinders is also presented, and our results are compared with the predictions of various analytical approximations or bounds and with experimental data of the literature.