The grinding models developed previously are concerned with size reduction only. Although they have proven to be useful in the simulation and design of grinding mills, they do not provide information on liberation which is the main objective of most comminution operations. In the present investigation, a population balance model describing the combined processes of size reduction and mineral liberation has been developed for batch grinding operation. The model parameters include conventional breakage rate and breakage distribution functions, along with a new parameter i.e., liberation function that is used to describe changes in particle composition. These parameters have been determined experimentally by examining mill products under optical microscope using a SEM-IPS image analyzer. The areal assays, obtained from the image analysis of monosized particle mounts, have been found to correspond quite closely to the actual chemical assays. It has been found that the method used to prepare particle mounts is critical in achieving accuracy.

In the present work, it has been shown that the breakage characteristics of component minerals can be determined by examining the mill feeds and products using an image analyzer. The model parameter analysis has shown that while the breakage rate functions are sensitive to the grinding environment, breakage distribution functions are independent of it. Furthermore, the breakage distribution functions have been found to be normalizable with feed size, thus reducing the number of parameters that must be estimated. The study has also shown that both the breakage rate and the liberation function suggest a preferential breakage of sphalerite over dolomite gangue.

The model has been validated by simulating the batch grinding of a sphalerite ore from ASARCO's Young Mine in eastern Tennessee. The model can predict the product size distributions for the total ore and its components, including gangue, sphalerite, and composite particles. An excellent agreement between the model predictions and the experimental results has been observed for both monosized and multisized feed materials. The model is capable of handling multiple classes of composite particles for a binary ore; however, the model has been verified against experimental results by considering only two composite classes. The method of determining liberation functions has also been discussed. The liberation function has been found to be useful for analyzing the liberation mechanisms of composite particles.