Modelling of comminution processes in Spex Mixer/Mill

It is well known that mathematical models which simulate comminution processes represent a useful tool in several fields of academic and industrial research, with particular emphasis on nano-material and pharmaceutical production. In the present work a mathematical model which is able to quantitatively describe comminution processes in a ball milling system (i.e., Spex-Mixer/Mill) has been developed. The proposed approach takes into account three different contributions: dynamics of the vial, dynamics of spheres motion and simulation of the comminution process. The vial dynamics has been modelled by taking advantage of an appropriate roto-translation matrix. Model results have been successfully compared with literature experimental data. The spheres motion within the Spex Mixer/Mill has been simulated using a 3D dynamic model based on classical mechanics as well as the so-called discrete element method, which is widely adopted to quantitatively describe multi-body collision behaviour. In particular, existing models of impact with dissipation as well as the classical Hertz impact theory have been taken into account. This part of the global model allows one to obtain, for different operating conditions, the impact specific energy and impact velocity as a function of time. The latter ones represent input parameters for the simulation of comminution processes that is performed through suitable population balances, where different breakage functions as well as appropriate breakage probabilities have been considered. Model results are reported in terms of granulometric distribution of powders within the mixer-mill as a function of time, minimal grain size obtainable and time needed to complete the comminution process for various operating conditions (i.e., mill frequency and charge ratio).