University of South Carolina
Columbia, South Carolina, U. S. A.
The flow transverse to unidirectional square arrays of multi-fiber bundles (tows) is investigated computationally using the boundary integral method. In the systems studied, each bundle consists of a number (up to a few hundred) of individual fibers, arranged in uniform square or hexagonal packing inside the perimeter of the tow. The employed unit cells are therefore characterized by two porosities: an inter-tow porosity, which is determined by the macroscopic spatial distribution of the tows and an intra-tow porosity, which is determined by the distance between the fibers inside each tow. The analysis is based on numerical solution of the Stokes equations in the entire space occupied by the fluid and thus, no artificial separation of the flow in the inter-tow region from that in the intra-tow space influences our results. Numerical calculations reveal the details of the flow at the tow-fluid interface and also indicate that the effective permeability of assemblies of such porous tows depends (strongly) on the intra- tow porosity only at low values, typically below 40%, of the inter-tow voidage. At higher values of the latter, the effect of the intra-tow porosity is negligible and the tow behaves effectively as an impermeable entity even at intra-tow porosities as high as 57%. For the range of the inter-tow porosities considered, the deviation of the effective permeability of the porous-tow system from that of a system consisting of impermeable tows can be successfully described in terms of polynomials of the effective voidage (c), which is a measure of the deviation of the intra-tow porosity from maximum packing. Results of experimental measurement of fluid velocities in the inter-fiber space, obtained using the technique of magnetic resonance imaging, are also presented and compared to model predictions.