Morphological effects on the transverse permeability of arrays of aligned fibers

The effect of micro-structure on the effective transverse permeability (K) of unidirectional arrays of cylindrical fibers is investigated computationally using the Boundary Element Method (BEM). By converting the original problem into an integral equation on the boundaries of the domain of interest, the BEM allows the straightforward discretization of complex, multi-connected domains with a fraction of the effort required by domain methods. The equations of Stokes flow are solved in cells containing up to 36 individual fibers located either in uniform arrays (square and hexagonal) or in random locations and the effective permeability is calculated from the corresponding pressure drop and flow rate. Random placement of particles results in the generation of individual microstructures whose permeability shows a scatter around a mean value. This scatter increases significantly as the porosity (phi) of the cell is reduced. Statistical averages are compared to analytical and numerical predictions for the permeability of a perfect square array. It is found that a fully random structure exhibits a permeability slightly higher than a perfect square array for very high porosity values (phi > 0.8), with this trend disappearing for phi less than or equal to 0.8 and tile averages coinciding with the result of the perfect square array. Additionally, the effect of random perturbations in the location and size of fibers around mean values corresponding to perfect square packing of mono-sized fibers is investigated. It is found that such variations have little effect on K at the high-porosity end (phi > 0.8), but they result in a noticeable increase in the effective permeability (as compared to a perfect square array) at the limit of low porosity (phi < 0.5).