# X-ray Particle Tracking Velocimetry in an Overflowing Foam
## 1 Introduction  
Particle tracking velocimetry (PTV) is a well-established optical method to measure velocities of individual objects along their motion paths [1]. In fluid dynamics research, these objects are usually small solid particles that are suspended and neutrally buoyant in an optically transparent fluid flow. By tracking individual particles over time, the fluid velocity field can be reconstructed. State-of-the-art PTV measurement arrangements make use of fluorescent particles illuminated by laser light. Two-dimensional measurements require a laser sheet, i.e., a thin quasi-2D illumination plane, whereas three-dimensional PTV measures particle motions in a truly 3D observation volume. Taking also the time component into account, time-resolved 3D-PTV is usually referred to as 4D-PTV [2]. Besides PTV, other optical methods employing particles dispersed in the fluid flow include, for example, laser Doppler velocimetry [3], particle image velocimetry [4], particle shadow velocimetry [5], or combinations of them [6]. However, these standard methods are not applicable for flow measurement in a liquid foam or froth, at least not in three-dimensional flow configurations. Optical observation is only commonly used for measurements at the free surface or close to a transparent wall. In contrast, the foam volume underneath the surface near foam bubbles is not accessible for optical measurements using visible light. The opacity of liquid foam is due to its complex three-dimensional structure: the liquid phase constitutes a continuous network of interconnected films between the gas bubbles, and the curved gas-liquid interfaces reflect visible light to a great extent. Froth refers to a gas-liquid two-phase mixture that is additionally laden with small solid particles. At high solid fraction, the dispersed particles contribute significantly to the opacity of the froth. This is particularly the case in industrial applications, such as flotation de-inking during waste paper recycling [7] or froth flotation in mineral processing [8]: hydrophobic particles selectively attach to gas bubbles in flotation cells, forming a particle-laden froth phase on the top of the pulp. In this way, solid particles [9] and liquid [10; 11] are transported with the overflowing froth and out of the flotation cell for further processing. In flotation plants for mineral processing, the overflowing froth employed for collecting, transporting, and recovering the valuable mineral particles is typically monitored only by optical observation, which is therefore limited to the the free surface of the froth phase. Beyond optical measurements through transparent walls in quasi-two-dimensional configurations [12; 13], ultrasound measurements gave insights into the bulk flow field in foam [14] and the local liquid fraction distribution [15; 16]. Moreover, laboratory-scale investigations make use of imaging measurements with different kinds of radiation. This includes X-rays, neutrons, or positrons and gamma rays, which can pass through many liquid and solid materials that are opaque to visible light. Positron emission particle tracking (PEPT) [17; 18] was used for mapping the movement of particles in flotation froth [19], including the attachment of particles to bubbles in the pulp and their detachment in the froth [20], for both hydrophobic and hydrophilic particles [21]. For the purpose of visual verification, PEPT was combined with optical imaging [22; 23]. Various experimental studies focusing on the tracer particles showcased that PEPT works out with fine tracer particles down to 50 um in diameter [24], larger tracers having either hydrophilic or hydrophobic surface coatings [25], and directly activated mineral particles [26]. With respect to the measurement principle, PEPT is limited to a very few tracer particles in order to distinguish between them [27], thus requiring repetitive measurements of the tracer motions in steady flow conditions [28].