On the variability of the Kozeny constant for saturated flow across unidirectional disordered fiber arrays

Flow in porous media is frequently analysed as a potential flow problem, in which the local flux is related to the local potential gradient through Darcy's law. The relevant constant is the permeability, which is a property of the porous medium. If the latter is described in terms of the Carman-Kozeny equation, morphological parameters of the medium are "hidden" (or, incorporated) in the Kozeny constant (kc), which should not be a function of porosity. Experiments seeking to determine the value of the Kozeny constant in fibrous systems have resulted in values that, for systems of same porosity, show a significant scatter. The objective of this study is to computationally study flow across many unidirectional fiber arrays and, in the process, explain the wide scatter in (kc) values observed experimentally. This task is made possible by a parallel implementation of the Boundary Element Method. A large number of simulations are carried out in model systems generated by a Monte Carlo procedure, in which porosity (Φ=0.45, 0.5, 0.6, 0.7 and 0.8) and the allowable minimum inter-fiber distance (d min =0.1 1.0R) are variable. The raw permeability data are converted to the corresponding Kozeny constant values; the results indicate a substantial scatter of the predicted (kc) values at each porosity level. This shows conclusively that the microstructure of fiber beds is at the heart of the observed variations in experimentally-determined values of (kc).