## 2 Material and Methods
### Positron Emission Particle Tracking (PEPT)  
Positron emission particle tracking (University of Birmingham, Birmingham, UK) is a non-intrusive technique that can be used to track the location of a radioactively-labelled particle moving inside a bulk of material in process equipment. The particle used as tracer must have the same physical characteristics (e.g. density, size, shape, roughness) as the other particles in the bulk in order to be representative of the granular material dynamics and, therefore, guarantee the fidelity of the PEPT data [35]. The technique relies on the beta decay of a tracer particle resulting in the emission of positrons. The subsequent annihilation of each positron with an electron will release energy in the form of two gamma rays back-to back at 180\({}^{\circ}\), measured by the pair of PEPT detectors showed in Figure 1 For more details on the technique the reader is referred to [8; 36; 37; 38]. The accuracy of the PEPT measurements is system dependent with the main source of errors arising from: the velocity of the tracer particle (tracers moving fast may have moved a significant distance during the acquisition window), the tracer activity (tracer activity decreases over time leading to a decrease of the number of detections per time) and the thickness of material standing between the tracer and the detectors (the intensity of the gamma-rays is attenuated or scattered) [36; 37; 39]. In this work, the maximum tracer velocity was always below 2.1 m/s and tracers with high activity were used in the experiments to guarantee a high rate of data acquisition. A 5 mm yttria-stabilised zirconia media ball was used as tracer particle, labelled by direct activation using the MC40 Cyclotron (University of Birmingham, Birmingham, UK) by means of a 33 MeV 3 He beam. Fluorine-18 was used as radioisotope with a half-life of 109 min. Data Processing: Tracer Location Reconstruction  
Just a few events (photon pairs) are in theory necessary to locate the tracer particle position, but not all the gamma rays detected give a valid tracer location, as a proportion will be electron scattered during passage through the granular material under investigation and the material of the equipment (container walls, impeller shaft, impeller arms). These scattered gamma rays are so called \"corrupted events\" and are discarded to leave predominantly \"valid events\" by means of an iterative algorithm developed at Positron Imaging Centre of the University of Birmingham (UK). In determining the tracer location, the algorithm takes a fixed number of consecutive photon pairs, each represented by a line-of-response (LOR), which describes the apparent paths of the two photons from the annihilation event. The centroid of this cluster of lines is determined and those lines furthest away are removed and the centroid recalculated. The procedure is repeated iteratively until a fraction, \(f\), of the initial number of events remains; the tracer location is taken as the centroid of the remaining lines, time-stamped with the average time of these lines. _The number of events per slice_ and _the fraction of event \(f\)_ are the two inputs of the algorithm; these are not known a priori, and optimum values will depend on the tracer velocity, the amount of scattering material present and the tracer activity [36]. These two parameters should not be arbitrarily selected because they are inversely proportional to the accuracy of the tracer location for a fixed spatial resolution of the camera [37]. In the current work optimum values were obtained by minimisation of the location error as proposed by [40]. According to this method, a _number of events per slice_ equal to 100 and a _fraction of events_ equal to 0.2 was determined and then used to process the entire set of PEPT data. Using the described reconstruction method, the X, Y, Z locations over time were obtained from the raw PEPT data.