# Gas-Liquid Mixability Study in a Jet-Stirred Tank for Mineral Flotation
## 3 Results and Discussion
### Influence of Feed Volume on Flow Field
#### 3.1.2 Influence of Feeding Amount on Gas Volume Fraction Distribution  
Figure 8 illustrates the instantaneous distribution of the gas volume fraction in the central ZY plane at various injection velocities. It is evident from the figure that different injection velocities significantly influence the distribution of the gas volume fraction. At lower injection velocity (V = 1 m/s), the overall gas volume fraction remains low, with a relatively uniform distribution and no noticeable localized areas of high gas volume fraction. As the injection velocity increases to V = 5 m/s, the gas volume fraction distribution begins to change slightly, with gradual increases in certain regions, yet maintaining a generally uniform trend across the plane. Figure 7: Liquid phase velocity contours for different feed volumes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Total Feed Volume** & **Amount of Feed per Nozzle** & **Individual Jet Velocity** \\ \hline
1.13 m\({}^{3}\)/h & 0.28 m\({}^{3}\)/h & 1 m/s \\
3.39 m\({}^{3}\)/h & 0.85 m\({}^{3}\)/h & 3 m/s \\
5.64 m\({}^{3}\)/h & 1.41 m\({}^{3}\)/h & 5 m/s \\
7.91 m\({}^{3}\)/h & 1.98 m\({}^{3}\)/h & 7 m/s \\
10.17 m\({}^{3}\)/h & 2.54 m\({}^{3}\)/h & 9 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Setting of velocity inlet boundary conditions. As the injection speed further increases, the rise in the gas volume fraction becomes notably pronounced, and the gas distribution begins shifting towards the center of the reactor body. This phenomenon indicates that higher feed volumes, corresponding to increased injection speeds, not only enhance the generation and dispersion of bubbles but also facilitate their more effective diffusion towards the central region of the tank body. Figure 9 depicts the variation in the gas volume fraction with height under five different inlet velocity conditions, where Figure 8b zooms into the gray area shown in Figure 8a. Each data point in these curves represents the area-weighted average gas volume fraction at the corresponding height level. Observing these curves reveals that increasing the inlet velocity enhances the overall gas volume fraction in the reactor. The slope of each curve indicates the spatial uniformity of the gas volume fraction distribution. At higher inlet velocities, the gap in the gas volume fraction between points within the reactor increases, leading to reduced uniformity in gas volume fraction distribution. To assess the mixing uniformity of the gas volume fraction in the stirred tank, 16 points were strategically selected on the ZY plane at the tank's midpoint, and the gas volume fraction at each point was measured. Variance, a statistical measure, was utilized to evaluate gas-liquid mixing homogeneity, where a larger variance value indicates poorer homogeneity, and a smaller value signifies better mixing. The uniformity of gas volume fraction distribution across this plane was assessed by calculating the variance of the gas volume fraction values at these selected points. The specific locations of these points are illustrated in Figure 10, with coordinates detailed in Table 6. In addition to using variance, to enhance the scientific validity and applicability of the study, the variance was  
Figure 8: The contour of gas volume fraction distribution. Figure 9: Gas volume fraction curve with height for different feed volumes; (**a**) all working conditions; (**b**) local zoom in grey area. also nondimensionalized by combining it with the Reynolds number, a dimensionless parameter. This nondimensionalization facilitates the comparison and verification of results across different scales and conditions, thereby ensuring the broad applicability of the research conclusions. The Reynolds number equation is:  
\[\text{Re}=\frac{\rho\text{UD}}{\mu} \tag{5}\]  
where \(\rho\) is the mixture density, U is the characteristic velocity (e.g., jet velocity), D is the characteristic length (e.g., nozzle diameter), and \(\mu\) is the mixture viscosity.