# Fluid Dynamics in a Continuous Pump-Mixer
## 4 Conclusions  
In this work, a continuously operated DN 300 General Mills designed pump-mixer was investigated in detail considering the pumping behavior and hydrodynamics in a water/paraffin oil system using a shadowgraphic optical probe. The paraffin oil had an around ten times higher viscosity as compared with water. It was found that \(\varphi_{F,\max}\approx 33\) vol.-% is the maximum feed phase ratio in an operation without any external pumps. Quadratic pumping performance curves for the pump-mixer in a General Mills design were estimated at \(N=375\), 400, and 425 rpm with a maximum total flow rate of \(\dot{V}_{tot}\approx 3.3\) L/min at 425 rpm and a maximum head for water of around \(H_{conti}=120\) to 150 mm. The pumping curve of the continuous phase was found to be minimally higher when the feed phase ratio \(\varphi_{F}\) was increased. This is negligible for this setup, but may change with other impeller types. The local holdup in the tank was smaller than the feed phase ratio, which was found by taking volumetric samples of the upper half of the vessel. This is a difference compared with an ideal batch vessel, where local and integral holdups have similar values. It was also found that increasing only the flow rate increases the holdup, which is consistent with the literature [16]. Higher local holdups were measured at high feed phase ratios with a maximum of approximately 22 vol.-%. An image-based shadowgraphic probe with subsequent analysis via a neural network was inserted at three different measurement positions to measure the DSD at the bottom, middle, and outlet of the vessel. While measuring in the middle of the tank was always possible due to local high turbulence as no droplets were attached to the probe, the other positions were limited in that respect. The bottom position near the impeller could be used, except at the highest impeller speed \(N=425\) rpm at feed phase ratios \(\varphi_{F}>20\) vol.-%. The high impeller speed induced a high circular flow in the impeller region, which did not align with the flow direction. The measurement position at the outlet of the vessel was limited to feed phase ratios \(\varphi_{F}<20\) vol.-% since the flow velocity at the outlet weir was comparably low compared to the mixing vessel. At higher feed phase ratios droplets were adsorbed at the probe and hindered an analysis. The volume and number of DSDs were estimated at high resolution and statistically significant numbers with at least 120,000 drops. It was found that the DSD was almost identical at all three measurement positions; therefore, one can assume an axial pumping behavior. It was also observed that the Sauter mean diameter increased with increased feed phase ratio as coalescence tendency increased and larger drops were formed. This was found to be a spontaneous transition for lower impeller speeds (\(N=375\) rpm,  
Figure 13: (**a**) Experimental data and Equation (11) as solid line. (**b**) Parity plot of all experiments versus Equation (11). \(\varphi_{F}\approx 10\) vol.-%) and a more transient evolution for higher impeller speeds (\(N=400\) and 425 rpm). An increase of the flow rate had the same effect because the energy of the impeller was distributed to a larger mass of fluid and decreased the energy dissipation, resulting in larger droplets, which was also found by [PERSON] et al. [6]. For the high-feed-phase ratios of 30 vol.-%, the smallest droplet sizes were found for the middle impeller speed, \(N=400\) rpm. An emulsification at this condition could be repeatedly confirmed by the optical images and the \(q_{0}\) distributions. A Sauter mean diameter correlation of Doulah [25] for batch vessels was modified and utilized to describe a large data set of Sauter mean diameters within a 15% error range. Individual consideration for each impeller speed showed similar trends and as a final result a unified equation covering the complete data set is a more a more applicable approach for technical use.