# X-ray Particle Tracking Velocimetry in an Overflowing Foam
## 2 Materials and Methods
### Tracer Particles  
Custom-tailored tracer particles were designed and prepared for the X-ray particle tracking velocimetry measurements in the overflowing foam. As shown in Figure 4, each tracer particle consisted of a small polymer tetrahedron with four tiny metal beads at its four tips. The two material components had separate functions explained in the following.  
Figure 3: Liquid fraction \(\phi_{l}\) of the foam for the two different SDS concentrations, determined from the electrical conductivity between the left (EP1), middle (EP2), and right electrode pair (EP3), measured in several measurement runs over a measurement time of 10 s each. Liquid fraction data from EP1, EP2, and EP3 in the same measurement run are indicated by the same colour and symbol.  
The tetrahedron made of a polymer material by means of 3D printing was the main structural component. The tetrahedral shape was inspired by the bubble-scale foam structure, namely the four plateau boarders converging in one vertex. Owing to this highly symmetrical shape, the tracers were stuck between the surrounding foam bubbles and, consequently, carried well with the flowing foam. The edge length of the tetrahedron was \((4.0\pm 0.1)\) mm on average (Figure 4a), which is approximately twice the diameter of the largest foam bubbles (Section 2.1, Figure 2). Thus, the polymer tetrahedron distributes the total weight of the tracer particle to the cluster of a few bubbles in the immediate vicinity.  
The four metal beads glued to the four tetrahedral tips served as radiopaque features of the tracer particle. For this purpose, metal beads were utilised that are commonly known as solder balls: made of the binary lead-tin alloy Pb90 Sn10, i.e., with a very high lead content of 90%. Lead as a heavy metal has an accordingly high X-ray attenuation coefficient (\(\mu_{X,Pb90 Sn10}>10\,\mathrm{cm}^{-1}\)) [48], which is approximately three orders of magnitude larger than the coefficient of foam (at 10% liquid fraction: \(\mu_{X,foam}\ll 0.1\,\mathrm{cm}^{-1}\)) in the X-ray photon energy range relevant for the measurements here (Section 2.4, Figure 5). Aiming for a suitable contrast between each individual metal bead and the surrounding liquid foam in the X-ray images, all metal beads had the same nominal size of \(0.5\,\mathrm{mm}\) in diameter.  
For the purpose of adding the tracer particles to the foam flow, small tubes were fitted in the middle section of the foam flow channel. These tubes were placed above the interface between the surfactant solution and the continuously generated foam bubbles but far apart from the region of interest at the horizontal weir, as shown by the X-ray image in Figure 1. A total of three tubes, each with an inner diameter of \(5\,\mathrm{mm}\), could be mounted in through-holes at various positions in the back wall of the flow channel. Using a custom-built linear drive system, the tracer particles were pushed through and out of the tubes, thus into the liquid foam. This was performed remotely controlled, while the foam generation and X-ray image acquisition were already running. Three tracer particles were added in each measurement run; to acquire a relevant amount of X-PTV data, several runs under the same conditions were performed and combined for the data analysis in Section 3.  
Figure 4: Custom-tailored tracer particles: (**a**) based on the CAD concept, small tetrahedra were 3D-printed from polymer material and (**b**) small metal beads were glued to the tips of each tetrahedron. (**c**–**e**) In the X-ray images, only the four metal beads per tetrahedron are visible, (**f**) which can be clearly distinguished from the surrounding liquid foam and from the statistical image noise.