Spatial variability of void structure in thin stochastic fibrous materials

TL;DR

This paper develops a theoretical framework to analyze the spatial variability of pore structures in stochastic fibrous materials, providing insights into heterogeneity relevant for various fibrous composites.

Contribution

It introduces a theory for the distributions of local process intensity and pore dimensions, linking variance and coefficient of variation to zone size and process intensity.

Findings

Variance of local process intensity is proportional to mean process intensity.

Coefficient of variation of pore area is roughly double that of pore diameter.

Both properties decrease with increasing zone size and process intensity.

Abstract

Theory is presented for the distributions of local process intensity and local average pore dimensions in random fibrous materials. For complete partitioning of the network into contiguous square zones, the variance of local process intensity is shown to be proportional to the mean process intensity and inversely proportional to the zone size. The coefficient of variation of local average pore area is shown to be approximately double that of the local average pore diameter with both properties being inversely proportional to the square root of zone size and mean process intensity. The results have relevance to heterogenous near-planar fibrous materials including paper, nonwoven textiles, nanofibrous composites and electrospun polymer fibre networks.