*3.1. CFD Simulation*

Coalescence was studied using the Luo coalescence model [27] and the turbulence coalescence model [30]; however, the Luo model over-predicted the results. For example, the coalescence rate was quite high and almost all the smaller-sized droplets were coalesced into large size droplets, and therefore, the concentration of large droplets was high in the scaled-down settler. The results after 20 s are presented in Table 3. The results were obtained at a plane passing through the center of the scaled-down settler at x = 0.

**Table 3.** Results for Luo [27] coalescence model.

From the above results it can be concluded that all the smaller size droplets had coalesced into large size droplets and were not present in the settler after 20 s, which reveals that the coalescence rate was unrealistic. However, even though the coalescence rate might not be accurate, the model shows similar flowing behavior as depicted in the CFD–DEM method below. Thus, it can be concluded that the flow is aligned more towards the center of the settler forming a conical shape. The turbulence model was also used in lieu of the Luo model to obtain a comparison, and the results are presented in Table 4.

**Table 4.** Volume Fraction Contours for 500 μm Droplets at 15, 17, 18, and 20 s.

The volume fraction contours for the small-sized settler, taken at a plane in the center of the settler at x = 0.1 for 500 μm droplets, are presented in Table 4. It can be deduced that coalescence mostly occurred near the top of the slag surface, and as the particles started to settle, they took their own path. Second, the volume fraction was decreasing towards the larger size droplets, which shows that a small number of droplets bigger than 900 μm were present in the settler. Almost all the droplets reached the bottom of the settler within 20 s. In the future, it would be good to focus the study of droplet coalescence on sizes between 500–1000 μm.

The velocity vector profiles for the small settler model with 500 μm droplets are presented in Table 5. The velocity vector profiles confirm the formation of a funnel-shaped flow. After entering the slag layer, the flow channels the droplets towards the center of the settler.

**Table 5.** Velocity Vector Contours for 500 μm Droplets at 15, 17, 18, and 20 s.

The volume fraction contours for the full-sized settler taken at the center plane of the settler (x = 0.5) containing the settler inlet and slag outlet are presented in Table 6. These volume fraction contours reveal that most of the coalescence occurred at the surface of the slag. However, a small number of droplets also coalesced during the descending route because of the turbulence underneath the inlet. This chaotic behavior was created because of the reverse flows caused by vortices and slag movement in the upward direction due to the density difference. This phenomenon is presented in the velocity vector profiles in Table 7.


**Table 6.** Volume fraction contours for 500 μm droplets.

**Table 7.** Velocity Vector Contours for 500 μm Droplets (m/s).

Finally, when we compare the volume fraction contours of the smaller-sized settler presented in Table 4, and the volume fraction contours of the full-size settler presented in Table 6, we can observe a significant difference. This is because in the full-size settler instead of a single funnel-shaped flow, different locally channeled flows are formed, which is exhibited in the profile. The same phenomenon is depicted in the velocity vector profiles in Tables 5 and 7.

The velocity vector profiles of 500 μm droplets are presented at a plane of the settler center (x = 0.5 m). This vector profile exhibits the development of 500 μm droplets and settling behavior. As the matte and slag mixture enters the settler, the matte droplets start settling, and after separation the slag circulates upwards. This creates a turbulent flow and vortices underneath the inlet illustrated by the vector profiles, which also confirm the formation of the local channeling flows aligned to their centers.

Compared to the 900 μm droplets, 1300 μm droplets are present in the settler in fairly low numbers, which is revealed by the number fraction of the different-sized matte droplets plot in Figure 4 and the volume fraction distribution in Figure 5. Figure 5 shows the volume fraction distribution of different-sized droplets present in the settler at different time intervals. Figure 4 also illustrates that a higher number of small droplets are present in the system, which suggests that their coalescence rate is low, and thus, the coalescence rate is low in general. The dominant droplet size is smaller than 300 μm.

**Figure 4.** Number fraction distribution of different-sized droplets inside the settler.

**Figure 5.** Volume fraction distribution curves.

The volume fraction distribution curves presented in Figure 5 show that most of the droplets are between 200 μm to 400 μm. The peak of these curves is usually achieved at around 300 μm. This is also an indication that the transition to large droplets above 400 μm is significantly low.
