On the Geometry of the Particle Free Sifting Threshold

The propagation of fine particles through the interstices in a bed of static large particles due to gravity is known as free sifting. It is governed by the geometrical trapping threshold, R_t = 6.464, defined as the ratio of the large bed spherical particle diameter to the diameter of the largest fine particle that can pass through the throat between three touching bed particles. However, R_t is idealized for uniform rigid particles. In practice, the free sifting threshold depends on the deformation of the bed particles (or overlap in simulations) and the size distribution of the bed particles. Simple geometric arguments show that the size ratio necessary for fine particles to pass through a bed of large particles can increase well beyond R_t for particle overlap of just a few percent and bed particle distributions with particle size variations of only 10-20%. Simulations for common conditions and materials demonstrate how fine particle trapping can occur even for situations where the fine particle to bed particle diameter ratio is well above R_t = 6.464.