# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 1 Introduction  
Gas bubble flow in liquid metal is encountered in a variety of industrial processes. Examples include liquid metal stirring, purification and continuous casting in metallurgy, liquid metal-based chemical reactors, and more. Controlling the output of these processes is essential and it was proposed that this can be (and in some cases already is) achieved via applied magnetic field (MF) [1; 2; 3; 4; 5; 6; 7; 8]. Single-bubble flow with and without applied MF has been systematically studied using ultrasound Doppler velocimetry (UDV) [9; 10; 11; 12], ultrasound transit time techniques [13; 14], X-ray imaging [14] and numerical simulations [15; 16; 17; 18; 19; 20; 21; 22]. The most important features and physical mechanisms involved in single-bubble flow are presently rather well known [23; 24; 25; 26; 27; 22], but many aspects of bubble collective dynamics, especially in the presence of MF, are not fully understood or have not been studied in-depth [28; 29; 30; 31]. Clearly, this is a problem from the process engineering and optimization perspective, and also from the point of view of computational fluid dynamics (CFD) where it is of interest to improve effective models for bubble flow (Euler-Euler and Lagrangian) [2; 32; 33; 34; 35]. Through recent efforts and the advent of dynamic X-ray and neutron radiography of two-phase liquid metal flow [36; 37; 38; 39; 40; 41; 42], fundamental investigation of bubble chain systems mimicking industrially relevant flow conditions is underway [1; 8; 15; 28; 29; 36; 43; 44; 45; 46]. In bubble chain flow, bubbles are released into a liquid metal system one-by-one with auniform time delay between each, at a certain gas flow rate, and ascend to the free surface of liquid metal. Such systems are usually rectangular vessels filled with gallium [1; 8; 43] or an eutectic gallium-indium-tin alloy [28; 29; 36; 44; 46] where bubbles are introduced via horizontal [8; 43] or vertical [1; 28; 29; 44; 46] nozzles at the bottom of the vessel, or top-submerged vertical [36] nozzles. Bubble chain flow systems are the next logical step from single-bubble flow investigations, since single-bubble flow, while very informative of the bubble wake flow dynamics and characteristic trajectories without and with applied MF, is not representative of the actual flow conditions typical for the above mentioned industrial processes where one has columns and swarms with a high number density of deformable bubbles [47; 48; 49; 50]. Bubble chains are still simple enough to enable experimentation with compact systems [1; 8; 43; 45; 46] and contain computationally manageable numbers of bubbles within the liquid metal volume [8; 15; 43; 45]. Meanwhile, they already exhibit collective dynamics between leading and trailing bubbles [8; 15; 43; 44; 45] and, depending on the system geometry and flow rate, bubble agglomeration, coalescence and breakup can occur [28; 29; 36]. Therefore these systems are a crucial milestone in a transition from studying single-bubble flow to investigations of many-bubble systems that are very close to their actual industrial counterparts. However, despite the _relative simplicity_, dynamics exhibited by bubble chain flow in liquid metal without or with applied MF are still very complex. Depending on the gas flow rate, bubbles produce unstable elongated wake flow regions where periodic vortex detachment occurs and turbulent pulsations are generated--shed vortices and turbulent wakes of leading bubbles strongly affect the trailing bubbles, leading to bubble pair coupling across the ascending chain [8; 15; 43; 45; 51; 52; 53; 54]. There exists a feedback loop involving combined perturbations of bubble shapes and within the bubble chain, surrounding liquid metal flow, and the influence of the free surface at the top of the metal vessels with instabilities and oscillations in the bubble chain shape [8; 15; 43; 45; 54].