Monodisperse Spheres

Abstract

In this chapter we will evaluate the series representations of the canonical function H _n , derived in the previous chapter, for various assemblies of identical (i.e., monodisperse) spheres of radius R. Such models are not as restrictive as one might initially surmise. For example, one can vary the connectedness of the particle phase (and therefore its percolation threshold) by allowing the spheres to interpenetrate one another in varying degrees. We saw in Chapter 3 that one extreme of this interpenetrable-sphere model is the case of spatially uncorrelated (i.e., Poisson distributed) spheres that we call fully penetrable (or overlapping) spheres. Overlapping spheres, at low sphere densities, are useful models of nonpercolating dispersions (see Figure 3.4). At high densities, overlapping spheres can be used to model consolidated media such as sandstones and sintered materials (Torquato 1986b). Figure 5.1 shows a distribution of identical overlapping disks at a very high density that resembles the sandstone depicted in Figure 1.3.