# Fluid Dynamics in a Continuous Pump-Mixer
## 1 Introduction  
Pump-mixer-settlers are frequently used in metal extraction processes for the production or recovery of metals from ores or environments such as copper, manganese, and cobalt (e.g., PUREX plutonium uranium recovery by reactive extraction). These apparatuses are a special version of conventional mixer-settlers including not only mixing and dispersing, but also the pumping of the liquids. To achieve this, the impeller is used in combination with a suction orifice to pump the fluid between the mixer-settlers in a cascade, thus reducing the need for pumps. In addition, the system is rather robust against suspended solid particles as no pump impeller is involved in the fluid transport. While pumps tend to fail under the abrasion of solids, stirred vessels are comparatively tolerant in respect to solids. The shear forces in conventional pumps are much higher than in stirred vessels, causing higher entrainment of small, dispersed phase droplets, which is another advantage of this setup. The concept of the pump-mixer was first reported 1939 in a US patent [1] and is nowadays in industrial use as more advanced designs [2], such as the General Mills or the Davy-Powergas designs. Although the pump-mixer concept has obvious advantages and is industrially used, there is little basis for two-phase or three-phase (with solid particles) design and layout of these apparatuses. Since 2000, pump-mixers have been the subject of increased research, where the majority of publications are related to exclusively simulative studies or single-phase experiments. Only a few recent publications reveal more sophisticated data, such as DSD. To the best of our knowledge, no studies exist thatconsider both the pumping behavior and internal variables, such as the flow pattern or the DSD. Models or correlations that predict droplet size in the apparatus are rare and do not account for the necessary pumping behavior. In the following, a short overview of publications related to pump-mixers is provided. In 2004, [PERSON] et al. [3] published an approach to predict the pumping and power characteristics of a General Mills pump-mixer in single-phase operation using a neural network. In the following years, the research group conducted many studies using Computational Fluid Dynamics (CFD), focusing on the flow field at different impeller types and geometry [4; 5]. In addition, different suction orifice geometries were investigated, using a draft-tube to suck the liquids in the General Mills and the Davy-Powergas design. In a later work, [PERSON] et al. published a correlation for the DSD and the local holdup [6] in two-phase pump-mixers. [PERSON] et al. started with the head characteristics of different impellers and impeller heights in 2008 [7] and published two-phase experiments and CFD modeling. Their measurement setup was similar to the one reported by [PERSON] et al. [6] and their focus was on detailed phenomena between the flow pattern in the tank and its respective DSD [8; 9]. In 2010, [PERSON] et al. published their CFD results on pump-mixers in General Mills design using a square vessel [10]. In 2012, another paper was published that focused mainly on the simulative study of different geometric design parameters considering the energy dissipation in the vessel based on particle image velocimetry (PIV) data [11]. [PERSON] et al. published, in 2019, measurements in a square-tank pump mixer and investigated droplet breakage [12] and the influence of dispersed phase viscosity [13]. In their experiments, the dispersed phase was pumped into the vessel instead of sucking it with the impeller. In 2021, they published a CFD approach with a coupled population balance model (PBM) in highly diluted dispersions [14]. [PERSON] et al. also published a study in a square-tank continuous pump-mixer with CFD combined with PBM relying on flow field PIV measurements [15]. They correlated their data but only investigated a flow rate of 3 L/min, which was controlled by a peristaltic pump [16].