## 3 Results and Discussion
### Effect of the Media Loading Evaluated from PEPT Experiments
For this reason, instead of evaluating the probability density function of the bead velocity for the entire mill, it would be more meaningful to evaluate it for three regions of the equipment which influence directly the grinding media flow. These three regions, illustrated in Figure 13, are: 1) the region above the top impeller pin, 2) the middle region where all the impeller pins are located and 3) the region beneath the impeller base. Figure 13 also shows the velocity histogram for the entire attritor mill as well as for the top, middle and bottom regions calculated using the PEPT data. The plot highlights that the velocity histogram calculated for the entire mill can be seen as the sum of three velocity histograms. Figure 12: PEPT normalised tracer occupancy plot for two bead loading: 2.4 kg and 3.0 kg of media. Test case using the clearance of 19 mm and the impeller speed of 600 rpm. The division of the attritor mill in sub-regions helped both the understanding of the grinding media dynamics and the assessment of the best friction coefficient. The histograms of velocity in the three regions were remarkably dissimilar because of the different mechanisms driving the media motion. In the bottom region, the bead motion was expected to be constrained by the high packing and as consequence of that the beads moved at low velocity. In the middle region, the impeller pins drove the bead motion through continuous collisions, ensuring a wide range of velocity. In the top region, the beads were not directly in contact with the impeller and, hence, the average velocity was substantially lower compared to the middle region. Figure 14 compares the probability density functions of the velocity magnitude for PEPT experiments and DEM simulations as a function of the friction coefficient for two impeller speeds. For the PEPT, the probability density functions of the velocity were calculated using the entire dataset before the azimuthal averaging, whereas for the DEM simulations the last ten consecutive time steps were used. For both the impeller speeds, the DEM simulations were able to qualitatively match the trends for the probability density function of the velocity derived from PEPT measurements by modifying the static friction coefficient. The friction coefficients of 0.35 and 0.50 led to similar velocity distributions, whereas the lowest friction coefficient equal to 0.15 significantly overestimated the velocity compared to the PEPT data for all the three considered regions. The effect of the friction coefficient on the velocity distribution was greater for the top and middle regions than for the bottom region presumably because of the different conditions of stress within the attritor. In fact, both in the top and the middle regions the grinding media are characterised by moderate bulk density and high shear rate, leading to a fluid-like behaviour of the grinding media [49]. At the bottom region the grinding media are instead characterised by high bulk density and low shear rates and, hence, the grinding media shows a solid-like bulk behaviour [49]. Although generally good prediction was ensured by the static friction coefficient of 0.50, there were some differences in the velocity probability density functions of the DEM simulations and PEPT data. At both the impeller speeds, the DEM slightly overpredicted the velocity within the three regions. As previously observed by [34] in a study of the particle motion within a paddle mixer, the differences between PEPT measurements and DEM simulations are likely to arise from the way the two techniques calculate the bead velocity; PEPT tracks a single bead for long time, while DEM uses the velocity of the entire bead-population over a limited number of simulation time steps.