# Fluid Dynamics in a Continuous Pump-Mixer
## 2 Materials and Methods
### Experimental Procedure  
The apparatus was filled with the water/Na\({}_{2}\)SO\({}_{4}\) solution in the feed tank B1 and the paraffin oil in feed tank B2. The impeller was used to fill the apparatus until the whole mixer-settler was filled and paraffin oil flowed into the compensating tank B3 in Figure 1. Afterwards, the impeller was shut off and the feed tanks were refilled to the overflow level of B3 to ensure the apparatus was completely filled. Then, the impeller was set to the desired impeller speed \(N\) and the ratio control was set to the desired phase feed ratio \(\varphi_{F}\) (using valve V1). All combinations of the impeller speeds \(N=375\), 400 and 425 rpm and feed phase ratios \(\varphi_{F}=10\) to 30 vol.-% in 5 vol.-% steps were investigated. The parameter set for \(N=400\) rpm was measured a second time using only measurement position \(MP_{1}\) to ensure reproducibility of the DSD. The ratio was determined by the flow rates measured at the two FC's, where \(\dot{V}_{c}\) is the flow rate of the continuous phase and \(\dot{V}_{d}\) the one of the disperse phase, respectively the total flow rate \(\dot{V}_{tot}\). After 1 h the apparatus was at a steady state, which was confirmed by constant liquid heights in the feed tanks and the settler and constant flow rates over at least 4 min. After the steady state was ensured, the flow rates were measured via the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measurement Position** & **Measurement Height** & **in mm** & **Measurement Radius** & **in mm** \\ \hline \(MP_{1}\) & \(H_{1}\) & 195.0 & \(r_{1}\) & 75.0 \\ \(MP_{2}\) & \(H_{2}\) & 332.5 & \(r_{2}\) & 290.0 \\ \(MP_{3}\) & \(H_{3}\) & 59.0 & \(r_{3}\) & 115.0 \\ \(MP_{H}\) & \(H_{4}\) & 240.0 & \(r_{4}\) & 75.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the measurement positions measured from the top edge of the suction orifice to the middle of the measurement position. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Substance** & **Density \(\rho\) in kg/m3** & \
\begin{tabular}{c} **Kinematic Viscosity \(\
u\)** \\ in mm2/s \\ \end{tabular} & \begin{tabular}{c} **Interfacial Surface** \\ **Tension \(\sigma_{d,c}^{sat}\) in mN/m** \\ \end{tabular} \\ \hline \
\begin{tabular}{c} Wer + Na\({}_{2}\)SO\({}_{4}\) \\ (50 mmol/L) \\ Paraffin oil FC 2006 \\ \end{tabular} & 1000 & 1.0 & - \\
\begin{tabular}{c} Paraffin oil FC 2006 \\ \end{tabular} & 825 & 13.1 & 37 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical properties of the chemicals. two FC's, the liquid heights \(H_{conti}\) and \(H_{disp}\) (see Figure 1) in the feed tanks were measured manually to determine the head, and the DSD was measured at the measurement positions \(MP_{1}\) to \(MP_{3}\). At each measurement position, 1500 pictures were captured at 10 fps and an exposure time of 10 \(\upmu\)s. After all measurements were finished, the local holdup \(\Phi\) was measured at the position \(MP_{H}\) by taking a 25 mL sample of dispersion through a tube into a graduated cylinder. This negligible sampling amount did not influence the overall process (25 mL << 28 L). The local holdup, \(\Phi\), was measured by determining the heights of the continuous phase, \(h_{c}\), and disperse phase, \(h_{d}\), in the measuring cylinder of the settled sample using Equation (6):  
\[\Phi=\frac{h_{d}}{h_{d}+h_{c}} \tag{6}\]  
The liquid heights \(H_{conti}\) and \(H_{disp}\), which determine the head, increased and the flow rate decreased when equal amounts of liquid from each phase were removed from the apparatus. This procedure was repeated until the heads were so high that the impeller could not maintain a flow rate (\(\dot{V}_{c}=\dot{V}_{d}=0\) L/min). At this limiting point, only the liquid heights and no DSD were measured. This was performed for every impeller speed (\(N=375\), 400, and 425 rpm) and each feed phase ratio (\(\varphi_{F}=10\), 15, 20, 25, and 30 vol.-%).