Synthesis of grinding time-size reduction relationships

Several empirical and semi-empirical laws of comminution, which describe the relationships between the cumulative grinding energy input and the degree of size reduction of brittle solids, have been rationally derived in the time-domain in a unified manner, starting with an integro-differential equation of grinding kinetics. The analysis leads to and provides explicit interrelationships between the energy-size reduction laws associated with Kick, Rittinger, Holmes, Bond, Charles and others, and gives useful estimates of their relative merits and validity. It is shown that Holmes' expression is, in fact, a solution to the grinding equation; consequently, this classical law is compatible with the modern theory of comminution based on population balance on particulate species