Energy-size reduction "laws" revisited

Abstract

Criteria for choosing a descriptive measure of the "size" or fineness of comminuted particles are discussed. A new derivation of the energy-size reduction relationship is presented by combining a similarity solution to the integrodifferential equation of grinding with an empirical correlation between breakage rate function and power draft to the mill. This derivation permits an integrated view of the classical grinding laws and the modern approach to grinding kinetics based on particle population balance considerations. In particular, it is shown that: (1) the conventional energy laws are generally not applicable over initial grinding intervals; (2) a sufficient condition for energy laws to hold is that the size distributions of comminuted particles are self-preserving; (3) many common descriptive measures of fineness, for example mean, median, percentiles, specific surface area, are interchangeable; (4) exponent α in the power law for the breakage rate function is related to exponent n in the energy-size reduction law by n=α +1; and (5) depending on the nature of the breakage rate function, it is possible to derive more general energy-size relationships which encompass the laws of Kick, Bond and Rittinger.