Numbers of Fiber-to-Fiber Contacts in General Fiber Assemblies

Abstract

General formulas are derived for the estimation of the number of fiber-to-fiber contacts in fiber assemblies with arbitrary distributions of orientation and fiber length. The average number of contacts per unit volume of an assembly ñ_v is given by

where

In this equation fi is the density function of orientation, D is the diameter of the cross section of the fiber, L_v is the total length of fiber per unit volume, and θ, φ, and θ', φ' are respective polar angles characterizing the orientation of two fibers to be brought into contact each other. The application of this general result is shown to lead to the same results in the special cases considered by van Wyk, and Kallmes and Corte.