First-order and second-order breakage rate of coarse particles in ball mill grinding

It has been observed by many authors that the breakage rates of coarse particles in a ball mill slow down with increasing grinding time and deviate from the first order. In this paper it is intended to find out whether the breakage rates of coarse particles obey second-order kinetics or not. For this purpose, quartz, limestone, iron ore and a mixture of quartz/limestone (weight ratio of 1:1) were selected as a ball mill feed. The first-order breakage rate was determined for the four particle sizes of quartz, limestone, iron ore and the mixture of quartz/limestone. Results indicating good first-order kinetics were obtained with the fine-sized particles (-1.2+1 mm, -0.6+0.42 mm). However, the coarse-sized particles (-5+4 mm, -3.15+2.5 mm) showed deviations from the first order. These coarse particles were in the abnormal breakage region. The second-order breakage rate was determined for the coarse particles (-5+4 mm, -3.15+2.5 mm). It can be seen that, for both sizes and all the materials, the second-order plot had better fit than the first-order plot. Also, it can be concluded that the second-order kinetics could model the breakage of coarse particles better than the first-order kinetics, and the validity of the second-order breakage rate was increased with increasing particle size. However, it is suggested to examine the validity of the second-order breakage rate kinetics for other materials and particle sizes.