The e ect of paper formation and grammageon its pore size distributionC

The pore size distribution in paper, measured by uid 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 occulated networks and so obtain a family of pore size distributions indexed by the degree of occulation 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 non-random papers, when measured by laminar ow. A comparison with data from the literature is provided. Coeecients of variation of free-bre-length and pore radius both increase with occulation but decrease with increasing grammage.