FLOW THROUGH MIXED FIBROUS POROUS MATERIALS

Creeping flow through a composite porous material composed of two fiber types has been analyzed for the situation in which the radii of the two fiber populations are highly dissimilar. The composite material has been idealized as a porous matrix that is composed of fine fibers (permeability K(f)), into which cylindrical inclusions (radius a(c)) have been embedded, and flow through the resulting system has been modeled by the Debye-Brinkman equation. Two different methods of accounting for the random geometry of a real porous material have been considered: a unit cell approach and replacement of the coarse fibers by a periodic fiber lattice. Model results are in good agreement with each other and reduce in the appropriate limit to well-accepted models for flow in single-component fibrous materials. Plots of net composite permeability as a function of fiber diameter and packing density are presented. In the parameter ranges of interest, viscous effects at the coarse fiber surfaces lead to a signficantly lower overall permeability than that predicted by a simple application of Darcy's law.