## 2 Material and Methods  
### Experimental Setup: Attritor Mill HD01 and Positron Emission Particle Tracking (PEPT)  
The experimental rig consisted of the laboratory-scale attritor mill HD01 (Union Process, Akron, OH, USA) and the positron emission particle tracking (PEPT) scanner showed in Figure 1a,b. The mill vessel was made of yttria-stabilised zirconia and its capacity was of 1.4 L with a diameter of 90 mm and a height of 164 mm. The impeller shaft was made of stainless steel with a plastic coating which acted as sacrificial layer, whereas the impeller arms were made of yttria-stabilised zirconia with a span of 66 mm. The grinding media used for all the experiments were 5 mm yttria-stabilised zirconia beads with a density of 5950 kg/m\({}^{3}\). Information on the mill dimensions and grinding media are summarised in Table 1. During the experiments, the temperature inside the mill was controlled by circulating water at a constant temperature of 10 \({}^{\circ}\)C through a cooling jacket.  
The operating parameters investigated in this study were: the impeller speed (300 rpm, 450 rpm and 600 rpm; the last being the maximum operating speed of the mill), the bead loading (2.4 kg, 2.7 kg and 3.0 kg) and the bottom clearance (12.7 mm or 1/2 inch, 15.9 mm or 5/8 inch and 19 mm or 3/4 inch where the first and last are the limiting values for the mill used). PEPT measurements should be carried out for a theoretically infinite time [6] to ensure ergodicity of the data and reliable statistical quantification of the three-dimensional flow. However, PEPT experiments are costly and they rely on the radioactive decay of a tracer bead of relatively short half-life which, over time, decreases in activity. Consequently, the experiments were designed to reduce the number and the duration of the tests. The acquisition time of the PEPT measurements was limited to 45 min for the tests at an impeller speed of 300 rpm and it was varied for the tests that used different speed values to maintain constant the number of impeller rotations (approximately 13,500). The full list of the experiments is reported in Table 2. For sake of brevity this paper will discuss in detail the results of the experiments number 4, 5, 6, 9, 10 and 11.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**N** & **Impeller Speed (rpm)** & **Bead Loading (kg)** & **\% Chamber Filling (volumetric)** & **Bottom Clearance (mm)** \\ \hline
1 & 600 & 3.0 & 77 \\
2 & 300 & 3.0 & 77 \\
3 & 300 & 3.0 & 77 \\
4 & 300 & 2.4 & 61 \\
5 & 600 & 2.4 & 61 \\
6 & 600 & 3.0 & 77 \\
7 & 300 & 3.0 & 77 \\
8 & 450 & 2.7 & 69 \\
9 & 300 & 2.4 & 61 \\
10 & 450 & 2.4 & 61 \\
11 & 600 & 2.4 & 61 \\
12 & 300 & 2.7 & 69 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental conditions: impeller speed, bead loading and impeller bottom clearance.  
Figure 1: Experimental rig: **(a)** attritor mill HD1 (Union Process, Akron, OH, USA) with a schematic of the vessel showing the pin positions for the clearance of 12.7 mm (1/2 inch) and **(b)** PEPT scanner (University of Birmingham, Birmingham, UK).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Dimensions (mm)** & **Material** \\ \hline
**Mill chamber** & & \\ Height & 164 & Yttria-stabilised zirconia \\ Diameter & 90 & \\
**Impeller arms** & & \\ Diameter & 66 & Yttria-stabilised zirconia \\
**Grinding media** & & \\ Diameter & 5 & Yttria-stabilised zirconia \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detail of the mill dimensions.