Claus Metzner, Patrick Krauss, Ben Fabry. Poresizes in random line networks

Natural Sciences / Physics / Biophysics

Submitted on: Aug 19, 2012, 19:38:50

Description: Many natural fibrous networks with fiber diameters much smaller than the average poresize can be described as three-dimensional (3D) random line networks. We consider here a 'Mikado' model for such systems, consisting of straight line segments of equal length, distributed homogeneously and isotropically in space. First, we derive analytically the probability density distribution $p(r_{no})$ for the 'nearest obstacle distance' $r_{no}$ between a randomly chosen test point within the network pores and its closest neighboring point on a line segment. Second, we show that in the limit where the line segments are much longer than the typical pore size, $p(r_{no})$ becomes a Rayleigh distribution. The single parameter $sigma$ of this Rayleigh distribution represents the most probable nearest obstacle distance and can be expressed in terms of the total line length per unit volume.