A Modified Theory of Fiber Contact in General Fiber Assemblies

Abstract

An earlier idealized theory of fiber contact by Komori and Makishima is modified on the same geometric-probabilistic basis by taking account of steric hindrances be tween fibers. A new characteristic fiber length called the persistent length is introduced to define the basic fiber segments that can be treated as independent statistical elements. The theory predicts that steric hindrance between fibers brings about two opposite effects on fiber contact: on the one hand, it diminishes the chance of contact by restricting the free fiber length on which a new contact may be formed, and on the other hand, it enhances contact by narrowing the free volume in the mass where a fiber can be located without touching the contact parts formed earlier. The total of these two determines the probability of contact, which depends strongly on the per sistent fiber length. The exclusion effect is formulated by a self-consistent mean-field analysis and evaluated explicitly for two idealized fibrous systems (2D and 3D random assemblies).