Bivariate Normal Thickness-Density Structure in Real Near-Planar Stochastic Fiber Networks

We present the analysis of experimental data that supports the recently presented hypothesis that the relationship between local areal density and local thickness in planar stochastic fiber networks may be described by the bivariate normal distribution. Measurements of the local averages of areal density and thickness have been made on experimental fiber networks with differing degrees of structural uniformity. The experimentally determined variance of local density at the 1 mm scale is in excellent agreement with that calculated from the theory. Also, the use of the bivariate normal distribution to describe the relationship between local areal density and local thickness measured in complete sampling schemes is appropriate for both near-random and clumped networks.