Minerals Beneficiation - The Statistical Theory of Primary Breakage Distributions for Brittle Materials

An equation is derived describing fragment size for single fracture of brittle solids. It contains the equations of earlier workers as special or approximate cases and, in addition, is capable of describing coarse distributions in which a few large particles are produced on fracture. The equation can be fitted well to single fracture experiments where over-breakage is avoided. In 1956 Broadbent and callcottl described a method of analyzing the unit operation of grinding, applicable to homogeneous breakage of brittle materials. In essence, the grinding process was split into two parts: 1) the fractional amount of a given size which is selected for grinding per unit time, 2) the size-weight distribution of the fragments produced by breakage of this certain size (primary breakage distribution function). The theory was formulated using matrix algebra. They attempted an experimental verification of the theory using an assumed primary breakage distribution but the results were not very satisfactory. Austin and Gardner2 showed that this assumed distribution was widely different from experimental values and that it led to the poor agreement of predicted size-weight distributions with experiment found by Broadbent and Callcott. In addition, Austin and Gardner2,3,4 reformulated the original approach in terms of differential equations of grinding and demonstrated that the approach led to a very satisfactory description of the grinding process, providing that the descriptive parameters were measured experimentally. Recent work5 has substantiated these findings and the distribution functions of several materials ground under different conditions in different mills have been determined experimentally. The fraction underweight versus size used by