AN IMPROVED SELF-CONSISTENT METHOD FOR ESTIMATING THE PERMEABILITY OF A FIBER ASSEMBLY

This paper presents an improved self-consistent method for estimating the permeability of an aligned flber assembly, in both longitudinal and transverse directions. In this method an insertion is assumed to include open space surrounded by densely packed fibers. This improvement allows us to describe effectively the permeability of dense structures containing distributed voids. As used in self-consistent methods, the insertion is placed into a homogeneous medium with an unknown permeability. Stokes flow and Darcy flow are then considered, respectively, at different regions. Boundary and interface conditions as well as two consistency conditions, including the total amount of the flow and the dissipation energy, are applied accordingly. The permeability is solved from these considerations. This improved permeability model captures the flow characteristics of a fiber bundle. in the longitudinal flow case, the openings within a bundle due to disturbance dominate the flow path. In the transverse flow case, the gaps between neighboring fibers govern the flow resistance. The derived expression for the transverse permeability contains two variables, the averaged fiber volume fraction and the maximum packing efficiency, which adequately describe the status of a fiber bundle. These two variables can also be measured experimentally. The predictions agree with available data reported. The result for the longitudinal flow shows not only the influence of these two parameters, but also the very strong effect of the openings within the bundle on the permeability. This explains the significant differences between the data of idealized packings, such as square and hexagonal packing, and those measured from real fiber bundles. The comparison also provides an estimation of the average opening sizes within a fiber bundle as a function of fiber volume fraction. Numerical simulation results of previous studies are also used to verify this approach.