Analysis of ball mill grinding kinetics for materials with uncommon breakage characteristics

Abstract

Generally, a specific breakage rate function of power-law type and a breakage distribution function that is a weighted sum of two Gaudin-Schumann distributions are adequate for characterizing the breakage properties of materials. In such cases, after a certain period of grinding, a self-similar size distribution regime develops, where the particle size distributions collapse onto a single curve when plotted using particle size scaled by the mean size. The Kapur mean particle size-grinding time relationship is valid in this regime. However, in the case of two samples of dolomite and hematite, the above-mentioned functional form for the breakage distribution function gave a negative value for the fraction reporting to the next finer size interval. After trying several different functional forms, we used a weighted difference of two Gaudin-Schumann distributions instead of the sum. This approach gave good results. It was found that the breakage distribution function curves were concave downwards instead of concave upwards as is generally the case, a relatively small fraction of the broken material reported to the next finer size interval, and the specific breakage rate function was particle size independent. The Kapur mean size-grinding time relationship was valid in the self-similar size distribution regime, and it supported the size independence of the specific breakage rate function. However, the particle size scale factor was not the mean size. It was the mean size squared for dolomite and the mean size cube for hematite. Simulated size distribution data showed that the particle size scale factor varies with the material breakage characteristics.