# Fluid Dynamics in a Continuous Pump-Mixer
## 2 Materials and Methods
### Pump-Mixer Geometry  
The object of investigation was a fully-baffled cylindrical pump-mixer based on a General Mills design schematically shown in Figure 2. The mixer has an inner diameter of \(T=300\) mm and a total height of \(H_{0}=390\) mm. With the overflow weir, the liquid height in operation was constant at \(H=360\) mm, providing a \(H/T=1.2\) ratio. This is slightly diverging from the literature [23; 24] with \(H/T=1\). The tank is equipped with a 6-blade Rushton turbine impeller with a diameter \(D=T/3=100\) mm mounted on a 26 mm shaft driven by a stirring unit (Heidolph instruments & Co. KG, RZR 2052 control, Schwabach, Germany). The impeller disc was 75 mm in diameter and 2 mm thick. The impeller blades are equally spaced and have a width of 25 mm, a height of 20 mm, and a thickness of 2 mm. The lower edge of the impeller is 1 mm above the suction orifice and therefore has an off-bottom clearance \(C=T/36=10\) mm (measured from the suction orifice to the impeller disc).  
Figure 1: Scheme of the DN300 pump-mixer-settler.  
The suction orifice has a diameter of \(T_{S}=T/4=75\) mm and a thickness of 4 mm. The suction chamber beneath the orifice has a diameter of \(T_{SC}=200\) mm and a suction chamber height of \(H_{sc}=55\) mm. The tank has 4 equal-spaced baffles (4 \(\times\) 90\({}^{\circ}\)) each with a width of \(B=T/10=30\) mm and a thickness of 8 mm while also covering the full height \(H_{0}\) of the tank. The baffles were simply clamped against the wall; hence, they were not sealed against the wall completely. It can still be assumed that there is no flow behind the baffles.  
Three Optical Multimode Online Probes (OMOP) [30] were used to investigate the droplet size distribution (\(MP_{1-3}\)) at different positions and the local holdup was measured in the upper half of the vessel (\(MP_{H}\)) as depicted in Figure 3.  
An endoscopic optical probe is inserted from outside at \(MP_{1}\) and was also used in previous works [22; 29; 31; 32] and is described elsewhere [33]. The positions \(MP_{2}\) and \(MP_{3}\) are based on a two-sided design by [PERSON] [30] needing a measurement flange. The measurement position \(MP_{2}\) is a symmetric DN50 measurement flange with a \(\O 22\) mm optical probe. Hence, the overflow weir is necessary to ensure the outlet tube is filled with liquid. Position \(MP_{3}\) is an eccentric measurement flange with a \(\O 38\) mm optical probe. The probe in \(MP_{3}\) can be rotated at an angle of 12\({}^{\circ}\) (see Figure 3, left) for a better alignment with the assumed flow direction generated by the Rushton turbine. All measurement positions are equipped with a Basler acA 1300-60 gm camera and a 1\(\times\) telecentric lens, providing an image size of 1024 \(\times\) 1024 pixels (5.4 mm \(\times\) 5.4 mm). All measurement positions were adjusted at a depth of the measurement gap of 2 mm between the camera and LED light source of the probe. Additionally, the local holdup was measured at  
Figure 3: Measurement positions \(MP_{1-3}\) in the DN300 General Mills pump-mixer.  
Figure 2: Geometry of the DN300 pump-mixer in accordance with the General Mills design.  
by taking samples of 25 mL into a graduated cylinder. The dimensions of the measuring positions mentioned in Figure 3 are listed in Table 1.