Modeling a class of stochastic porous media

Abstract

This note extends E. H. Lloyd's model of pore structure in random fibre networks to a large class of stochastic fibre networks containing the random model as a special case. The key to the generalization is the substitution of a family of gamma distributions for the negative exponential family used for intercrossing distances on fibres. This allows closed expressions to be obtained for the variance and mean of the equivalent pore size distributions in a planar array of line elements representing fibres. The analytical details have been made available in a Mathematica notebook, via the World Wide Web. The result has application in modeling the forming of nonwoven textiles and paper from fibre suspensions, and in modeling their void structures and transmission of fluids.