The effect of paper formation and grammage on its pore size distribution

The pore size distribution in paper, measured by fluid permeation perpendicular to the plane of the sheet, is known to be approximately lognormal with standard deviation proportional to the mean. Also, this corresponds quite well to the polygonal size distribution arising from a random array of lines in a plane, which may be approximated using the negative exponential distribution for inter-crossing distances in random networks. We use the gamma distribution to generalize to the distribution of inter-crossing distances in flocculated networks and so obtain a family of pore size distributions indexed by the degree of flocculation in the network. This new analytic work helps understand the hitherto-unexplained observation that the standard deviation of pore size increases with the mean for manifestly nonrandom papers, when measured by laminar flow. A comparison with data from the literature is provided. Coefficients of variation of free-fibre-length and pore radius both increase with flocculation but decrease with increasing grammage.