# X-ray Particle Tracking Velocimetry in an Overflowing Foam
## 4 Discussion
### X-PTV Compared with PEPT  
X-ray particle tracking velocimetry (X-PTV) competes with positron emission particle tracking (PEPT), as both measurement techniques employ tracer particles and make use of X-rays or gamma rays for flow visualisation in laboratory-scale experiments with optically opaque fluids such as liquid foam and froth. PEPT offers the outstanding advantage that very different particles can be prepared as radioactive-labelled tracers, for example small tracer particles in the size range typical for froth flotation in mineral processing [24], composite particles with a coating as surface functionalisation [25; 28], or directly activated mineral particles [26]. In the case of PEPT tracer particles made from haematite or quartz, having a size of approximately 0.1 mm in diameter, the estimated weight-to-area is smaller than 10 N m\({}^{-2}\) and, therefore, lower than that of the X-PTV tracer particles used here (Section 4.1, Table 2). Because of the inherent measurement principle of positron emission tomography (PET) scanners, the spatial resolution in PEPT measurements is typically in the order of 1 mm, and the total number of tracer particles in the measurement volume is limited to a very few. Usually, only one or two tracer particles should be in the region of interest at the same time in order to detect and distinguish them from each other. Using tracer particles with sufficiently different activities, up to three of them have been tracked at once [27]. X-PTV is based on particle tracking algorithms established for optical measurements. Compared to PET scanners for PEPT measurements, X-ray imaging instruments are in wide use in different fields, such as medicine, material science, and engineering, thus more easily available and accessible. For X-PTV measurements in liquid foam and froth, custom-tailored tracer particles are required. Progressing from our first prototypes of fully metallic tracer particles [42], here we used composite particles consisting of a small polymer tetrahedron with tiny metal beads at its tips. The tetrahedral base body is characterised by a high symmetry and, therefore, does not have a distinct preferential direction to stick to the bubble-scale foam structure. The metal beads serving as radiopaque features have the same diameter and distance from each other, which facilitates the image processing and makes the data analysis more robust, thus reducing random measurement uncertainties. Compared to PEPT measurements, X-PTV is able to provide a higher spatial resolution but needs larger and heavier tracer particles. In the X-PTV measurements presented here, the effective spatial resolution was 0.1 mm to 0.2 mm, which is between the image pixel size of approximately 0.05 mm and the metal bead diameter of 0.5 mm. However, because of the measurement principle of transmission imaging, this spatial resolution is achieved only in measuring planes perpendicular to the X-ray beam direction. Along the beam direction, the position of the tracer particles has to be estimated from the projected size of the metal beads in the X-ray images, yielding a similar spatial resolution in this direction as commonly reported for PEPT measurements. Depending on the foam properties and flow conditions, the total mass of the composite tracer particles has to be considered. X-PTV with these tracers may come to its limit in unstable foam at high liquid fraction, i.e., if the yield stress of the foam is lower than the weight-to-area ratio of a tracer particle. At high flow velocities, the tracer particles may be affected by their inertia and not able to follow the streamlines of the foam flow very well. Similar to PEPT measurements, the total number of X-PTV tracer particles in the measurement volume is limited in order to detect and distinguish them without having overlapping projections of the metal beads in the X-ray images.