On Flow through Aligned Fiber Beds and Its Application to Composites Processing

Abstract

In process modeling of continuous fiber composites, matrix flow through aligned fiber beds is traditionally described by Darcy's law, which relates matrix flow rate to matrix pressure gradient, matrix viscosity, and fiber bed permeability. This phenome nological relationship was originally derived for macroscopically isotropic beds of spheri cal or sphere-like particles. Hence it is necessary to establish the conditions under which this relationship may be extended to fiber beds, which are approximately transversely iso tropic. A review of previous work on steady-state Newtonian fluid flow through isotropic porous media is used as a foundation to explore the validity of extending Darcy's law to flow through beds of aligned fibers. Theoretical analyses are compared to experimental results obtained from flow through real fiber beds and ideal beds of regularly spaced cylinders. Functional relationships for flow of generalized Newtonian fluids through iso tropic sphere beds are also reviewed, and their extension to aligned fiber beds is suggested as a first order approximation. The findings are discussed in terms of the usefulness and accuracy of the reviewed and suggested flow rate-pressure drop relationships in process modeling of continuous fiber composites.