The contribution of out-of-plane pore dimensions to the pore size distribution of paper and stochastic fibrous materials

Theory is presented for the distribution of the narrowest dimension of voids encountered in a path through a stochastic fibre network from one side of its plane to the other. Using expressions from the literature we show that the mean out-of-plane pore dimension is always less than half the mean in-plane dimension such that out-of-plane pore dimensions have a controlling influence on the measured pore size distribution. An approximate model is derived which predicts that the overall mean pore dimension of a network of fibres with given dimensions is inversely proportional to its areal density and proportional to a simple function of porosity. Good agreement is demonstrated between this model and experimental data. Regression analysis suggests that out-of-plane pore dimensions account for more than 70% of the measured pore size distribution.