The energy-size reduction relationships in comminution of solids

Abstract

Starting with the integro-differential equation of grinding kinetics, a new derivation of the Charles energy-size reduction relationship is presented. The procedure entails matching the moments of particle-size distribution from the grinding equation with those computed from the empirical Gaudin-Schuhmann size distribution equation. The analysis is extended to the Rosin-Rammler size distribution function, and an analogous energy-size reduction expression is obtained. It is shown that functionally both the Gaudin-Schumann and Rosin-Rammler distributions conform to the similarity solution to the integro-differential equation of grinding kinetics, moreover, this similarity solution provides a general energy-size reduction relationship of which the Charles equation is a specialized case.