# X-ray Particle Tracking Velocimetry in an Overflowing Foam
## 1 Introduction
Positron emission tomography (PET), i.e., without radioactive-labelled tracer particles but with radioactive liquid, was demonstrated for measuring the liquid fraction in an overflowing foam [29]. Transmission imaging with neutrons is particularly suitable for imaging the bubble-scale froth structure [30] and mapping the liquid fraction distribution in foam [31]. This is mainly because neutrons are strongly moderated by hydrogen, resulting in a high effective neutron attenuation coefficient of the liquid phase, which is usually an aqueous surfactant solution. Neutron radiography is also suitable for particle tracking in froth [32], especially with gadolinium-based particles, as this rare-earth metal has an outstanding high neutron attenuation coefficient. However, the tracking of individual particles is challenging because of the low contrast-to-noise ratio for small particle sizes imaged at high frame rate [33], which requires sophisticated image processing tools [34]. Using X-rays instead of neutrons, time-resolved tomographic imaging gave insights into the process of foaming in an aqueous solution [35; 36] as well as in a liquid metal [37]. Further, fast X-ray micro-tomography was applied to resolve the three-dimensional liquid foam flow around a sphere [38] and through a cylindrical hopper [39]. Particle tracking measurements in X-ray image sequences require tracer particles that are opaque for X-rays. To this end, radiopaque composite particles are manufactured, in which one component or coating is a heavy metal with a high X-ray attenuation efficient, such as bismuth [40] or tungsten [41]. In combination with the much larger volume of a low-density material, e.g., polymer foam or hollow spheres, the desired effective density of the composite particle can be tailored to match with the density of the fluid. For our previous experimental study on X-ray particle tracking velocimetry (X-PTV) in liquid foam flow [42], we prepared different types of tracer particles from steel and with three-dimensional shapes by selective laser melting. We demonstrated that the 3D-printed tracers with a foam-inspired shape stick to the bubble-scale foam structure and, thus, are able to follow the streamlines of the foam flow very well. They can be used as measurement tools in stable foam with less than approximately 5% liquid fraction, but they are slightly too heavy for X-PTV measurements in unstable foam at a higher liquid fraction. In this work, aiming to reduce measurement uncertainties in X-PTV measurements in foam and froth flows with up to approximately a 10% liquid fraction, we have prepared composite tracer particles and standardised their shape, size, and mass. For testing purposes, we used these tracer particles in a laboratory-scale foam flow experiment, which was inspired by a froth flotation cell, and investigated the flow behaviour of an aqueous foam at a weir. Simultaneously with the X-ray imaging measurement, the liquid fraction of the overflowing foam was monitored by means of electric conductivity measurements using electrode pairs. Focusing on the velocity field at the weir, where the liquid is recovered from the foam, we researched how the tracer velocity depends on the vertical position above the weir crest, i.e., underneath the free surface of the overflowing foam.