High energy milling in a planetary ball mill: Discrete element and population balance modelling

As the world reserves of high quality ores are getting depleted at a rate higher than ever, the liberation of valuable minerals from low grade ores is becoming more and more relevant and imperative. But, liberation of minerals from low grade ores requires grinding of ore to extremely fine sizes. High energy milling in a planetary ball mill is one such option where one can produce particles in the nano-meter range. Although planetary mill is employed extensively for ultrafine grinding, dynamics of grinding inside the mill is not fully understood because of the dependency of grinding kinetics on many interconnected phenomena like collisions between media, particles and wall, time dependent rheology, adsorption and desorption of dispersant, abrasion of media, agglomeration of particles, etc. It was well articulated in literature that media motion and number of media collisions have strong effect on grinding kinetics and final product size distribution. Simulations were carried out using the discrete element method (DEM) to compare the performance of a planetary mill with a ball mill, with and without lifters, in terms of impact energy and number of collisions and it was found that number of collisions is considerably high in the planetary mill. The high number of collisions might be the reason for production of ultrafine particles in the planetary mill. We have also fitted a population balance model (PBM) to experimental data from a laboratory scale planetary mill for prediction of particle size distribution. Unlike previous models, we have incorporated functional forms for the selection function and the breakage distribution function so that the number of parameters in the PBM is just five. The predicted product particle size distributions at different grinding times are in reasonably good agreement with experimental data.