Solutions of the Batch Grinding Equation Leading to Rosin-Rammler Distributions

Application of the Charles and Bond Laws to batch grinding can be deduced as a special case of solution of the first-order batch grinding equation. With additional limitations on the feed size distribution, this special case also gives Rosin-Rammler distributions of constant slope, with the 36.79% retained point a simple function of time. In general, the assumptions concerning the breakage parameters S and B which are necessary to get Charles' and Bond's laws, are not valid except as a crude approximation. With less restrictive assumptions, it is still possible to get approximate Rosin-Rammler distributions, but the slopes change with time of grinding, and the 36.79% retained point is a more complicated function of time. An alternative form to Charles' law is suggested, which accomplishes the same result and has the same errors, but avoids the use of energy of grinding and deals with specific rate of grinding.