On the longitudinal permeability of aligned fiber arrays

In this work, we theoretically revisit the longitudinal permeability of aligned fiber arrays from ordered configuration (i.e. rectangular and staggered arrangements) to random pattern, based on a geometrical scaling rule. The scaling model on the basis of the characteristic length and the characteristic ratio quantifies the flow behaviors more accurately than the widely applied Kozeny-Carman equation. The model for actual fiber arrays composed of randomly located fibers is extended from the ordered case, and the randomness of fiber distribution is realized by the Voronoi tessellation method and quantified by a single parameter. The proposed compact and easy-use model is verified by experimental and numerical results throughout the range of fiber volume fractions (FVFs). The structural parameters, including FVF, fiber packing angle, and randomness of fiber distribution are also extensively analyzed.