The Permeability of a Random Array of Parallel Infinite Cylindrical Rods

Abstract

The permeability of a fibrous material is discussed. The material is assumed to be an assemblage of parallel infinite cylindrical rods fixed at random in space. A statistical formulation developed by Lundgren is applied to the system. When a conditional average is considered, a mean number of the rods in contact with a certain point decreases as the point approaches to a test rod. This particular region is called an intermediate layer. Here the permeability is determined as a function of the radius a, and the volume fraction c, of the rods by taking into account of the layer. Two typical cases, a longitudinal flow past the rods and a transverse one, are considered. The Galerkin method is used to obtain approximate solutions of these flows. We found that the permeability for the transverse flow through random array of rods is smaller than that through spheres for c\gtrsim0.5.