## 5 Conclusions  
Positron emission particle tracking (PEPT) was used to investigate the grinding media dynamics in a laboratory-scale attritor mill in absence of powder. The media motion was studied as a function of typical operating parameters: impeller speed, impeller clearance and bead fill level. The PEPT experiments showed that the impeller speed had the strongest influence on the velocity field. An increase of this parameter led toward a development of the upper and lower recirculation loops which are expected to improve the distribution of the material to be ground inside the mill. The impeller clearance was found to affect the size of the region of very low velocity located below the impeller bottom pin. When the impeller clearance was set at the maximum value of 19 mm high tracer occupancy was observed at the bottom of the attritor. This suggests that the increase in clearance favoured the tight packing of the beads which consequently reduced the exchange of beads between this part of the equipment and the rest of the pot. The PEPT experiments also showed that the bead loading had only a minor effect on the beads motion. The increase of the beads weight from 2.4 kg to 3.0 kg did not modify either the maximum velocity or the size of the area of high velocity, but increased the machine power consumption. Among the presented data two PEPT experiments were selected and compared to a Discrete Element Method model of the attritor under the same conditions. A novel methodology, based on the calculation of the probability density function of the bead velocity in three regions of the attritor, was used for the selection of the static friction coefficient. Based on this methodology, for the correct representation of the global beads motion inside the mill the understanding of the motion in sub-regions of the equipment is required. Even after the optimisation of the static friction coefficient to the value of 0.50 differences with the measured velocity were still present. However, after the time and spatial average of the data, the agreement between DEM simulations and PEPT measurements was excellent from both a qualitative and quantitative point of view as remarked by the velocity maps and the profile of velocities along the vessel height. This highlights the capability of the DEM to model complex systems which involves grinding media flow as well as the possibility, once the model is validated, to extract meaningful information on the collision energy spectra of the mill. Despite the overall very good comparison, for a small portion of the vessel, near the wall, the simulations overpredicted by about 10% the beads velocity. This minor discrepancy can be attributed to either deficiencies of the PEPT measurements or to an over simplified validation procedure. An improvement of the current validation strategy can be certainly achieved by adjusting at the same time the static friction coefficient, the Young's modulus and the coefficient of restitution, but a substantial increase of the computational effort will be necessary. This validated DEM-model will be used for future work to establish relationships between the milling conditions and the material properties after milling. In this framework, the DEM model will support the development of more robust methodologies for the transfer of product formulations to either different milling equipment or at different scales.  
D.D., J.V., A.I., A.A., E.H.S., M.M.; methodology, D.D.; software, D.D., J.V., A.I., A.A., E.H.S., M.M.; formal analysis, D.D.; investigation, D.D.; data curation, D.D.; writing--original draft preparation, D.D., J.V., A.I., A.A., E.H.S., M.M.; writing--review and editing, M.M.; project administration, M.M.; funding acquisition.  
[PERSON] is currently an Engineering Doctorate (EngD) post-graduate student with the University of Birmingham, UK. [PERSON] acknowledges the support and funding from the Engineering & Physical Sciences Research Council (EPSRC) UK, grant number EP/L015153/1, and Johnson Matthey PLC.  
The authors declare no conflict of interest.