Micro-scale modeling of axial flow through unidirectional disordered fiber arrays

The objective of this study is to develop a model for the axial hydraulic permeability (K∥) of fibrous media, taking explicit account of the underlying microstructure and its variability. In this numerical study, a unidirectional fiber array is represented by a unit cell consisting of ∼600 randomly placed fiber cross-sections. Stokes flow through such a unidirectional fiber array in the axial direction is modeled by a two-dimensional Stokes equation and solved using a parallel implementation of the boundary element method. A large number of simulations in such geometries have been carried out. The results indicate that (K∥) increases as the underlying microstructure progresses from a uniform distribution to a non-uniform one. To explain this relation between (K∥) and microstructure, a microstructural parameter, namely the mean nearest inter-fiber spacing, is proposed to characterize the heterogeneity of the fiber distribution. Following this, an empirical model correlating the axial permeability and the mean nearest inter-fiber spacing is presented.