Comminution of single particles in a rigidly-mounted roll mill part 2: Product size distribution and energy utilization

Abstract

Product size distributions are invariably self similar when particles are comminuted singly under compression in a rigidly-mounted roll mill. This is a consequence of the geometrically similar crack patterns formed on a progressively finer scale with increasing input of energy. Rumpfs similarity law of fracture mechanics formulated in terms of surface area is modified by making use of the self-preserving nature of the size spectra into an energy-reduction ratio relationship in terms of median size. This relationship, which is far more convenient for analysis of the experimental data, provides a measure of the inherent grindability of the material or of its energy utilization capacity. The energy investment equation derived in Part 1 is coupled with the energy utilization equation presented here for an integrated formulation of the role of particle size, compression ratio and energy expended on energy utilized and size reduction achieved when single particles are comminuted. Conditions are established under which comminuted size distributions become a unique function of the product of particle size and specific energy input and breakage distribution functions are normalizable with respect to the parent size. These results are in agreement with previous data in the literature on single-particle breakage.