Spontaneous interparticle percolation

Abstract

A study is made of the spontaneous percolation occurring when particles fall under gravity through a fixed bed of larger particles. A variety of different circumstances arise in practical applications in for example powder mixing but there are two limiting cases which are still both important. The first is when small particles cascade almost elastically through an ensemble of layer particles. It is shown that the percolation velocity is proportional to (1 – α ) 1/4 , where α is the coefficient of restitution.The diffusion tensor is calculated from which Péclet numbers are derived. These results are compared with computer experiments with reasonable agreement. The second case is of almost inelastic interactions when the percolating particle slithers and drops into the next encounter in the fixed bed. The distributions of landing angles (the angles which the percolating particles make on the spherical obstacle on landing) and the Péclet numbers are deduced and differ substantially from random models. It is shown that there is low radial diffusion and the Péclet number is high.