Derivation of pacticle size distributions from measurements on plane sections through particle beds. Effect of regularity of particle packing

Abstract

When the size distribution of particles embedded in an opaque, continuous solid phase is required, the general approach is to deduce the distribution from the size distribution of particle cross-sections in a plane cut through the particle bed. When the particles are approximately spherical, this deduction can be performed by making the assumption that the distances from the plane of cut to the particle centers are rectangularly distributed. The validity of this assumption does not, however, appear to have been investigated in previously published work, and in the present contribution the assumption has been considered more closely. The distribution of the distances between the sphere centers and a random plane has been investigated both theoretically and experimentally, starting with regular packings of monosized spheres, and extending the treatment to monosized spheres packed at random and finally to packings of polysized spheres. The distribution of particle center to cutting plane distances will approach a rectangular distribution with increasing sample size even for strictly regular packings. However, for finite samples, the packing regularity may significantly affect the extent to which such a distribution is realized.