Distribution of fiber intersections in two-dimensional random fiber web cases with a mixture of two fiber lengths

Abstract

The statistical distribution of the number of fiber intersections in a unit area is of great importance in determining the physical and mechanical properties of random fiber webs and the products produced. The distribution of the number of fiber intersections determines the non-uniformity of the basis weight and can be used in designing optimal control strategies relating to such physical properties as strength, elongation, air/water permeability, acoustics and filtering efficiencies of fiber webs and nonwoven fabrics. This paper developed a geometrical and probabilistic model for the number of fiber intersections in two-dimensional random fiber webs, where two distinct fiber lengths are mixed at varying ratios. This work is an extension of a previously derived paper where the model assumed that all fiber lengths are equal. Here, we present a geometrical probabilistic model, theories for deriving expectations and variances of the number of intersections in random fiber webs. The model and statistical parameters are validated through an extensive computer simulation study.