## 2 Results and Discussion
### Compactification of Floc Structure  
Figure 6 shows the relationship between \(D_{90}\) and the \(G\) values for each of the ALT ratio for the breakup and rearrangement stage, \(GT\) = 13,000. At an ALT ratio of 0.03, the power was \(-0.70\) and \(D_{90}\) decreased relative to the \(G\) value, indicating breakup; at an ALT ratio of 0.05, the power was very small (\(-0.091\)) and \(D_{90}\) was maintained. Lastly, at an ALT ratio of 0.10, the power was \(-0.66\), indicating breakup as in the case of an ALT ratio of 0.03. This result indicates that, under conditions away from charge neutralization, the flocs are more likely to break with respect to the \(G\) value, whether the ALT ratio causes overdose or shortage. The unbalanced charge on the floc surfaces suggests that the flocs are slippery and more likely to fracture rather than bond. Under optimum ALT ratio conditions, \(D_{90}\) was found to maintain its size relative to the \(G\) value, with densification occurring without a pronounced breakup. In the flow field, the flocs are densified and stabilized by incorporating small fragments under alternating compressive and tensile stresses. This phenomenon results in the formation of flocs with high intensity against high shear forces. As is evident from the  
Figure 5: Relative frequency and temporal variation of circularity. (**a**) 120 rpm, ALT ratio 0.03, (**b**) 120 rpm, ALT ratio 0.05, (**c**) 120 rpm, ALT ratio 0.10, (**d**) 160 rpm, ALT ratio 0.03, (**e**) 160 rpm, ALT ratio 0.05, and (**f**) 160 rpm, ALT ratio 0.10. In (**b**,**e**), the approach to the circular shape was clear. results in Figure 5e, the circularity approaches 1 with time. The floc under this condition transforms structurally into a compact, dense, circular floc, with breakup and rearrangement occurring. In this report, we observed changes in floc structure occur under laminar flow conditions while maintaining the same \(G\) values. As shown in this test results, the ALT ratio and \(G\) value affect the growth and breakup rate of flocs. The ALT ratio has a significant effect on the growth rate, and the structure of the flocs changed with the ALT ratio in the breakup/rearrangement stage. For the same ALT ratio, the higher the \(G\) value, the greater the growth rate. Therefore, the ALT ratio has a significant effect on the growth and breakup of the flocs. Furthermore, under the optimum ALT ratio conditions, floc breakup is not significant even with an increasing \(G\) value, and a compact structural change to high-density spherical particles was observed. The phenomenon of floc densification is clearly caused by the gelation behavior of the aluminum hydroxide gel. We postulate that the gel structure produced by insoluble aluminum hydroxide adsorbs and densifies the small fragments, and that erosion breakup forms even denser and more spherical flocs. This phenomenon was more pronounced under high-shear conditions (160 rpm). By comparing Figure 1d 600 s, Figure 1e 600 s, and Figure 1f 600 s, it is possible to observe that there are more fragments and smaller flocs in the shortage and overdosage ALT ratio conditions (Figure 1d 600 s, Figure 1f 600 s). Only Figure 1e 600 s, the optimum ALT ratio, has fewer fine fragments. Fragmentation due to the high density and compacting of the floc results from breakup. During the growth stage, fracturing occurs simultaneously with floc growth. Separate breakups predominate, resulting in relatively large clumps of flocs. These flocs, again, contribute to floc growth and form bulky flocs. In the fracture and rearrangement stage, erosion breakup is predominant, and small fragments are generated. The flocs incorporate these fragments and become denser and more compact. High-density, spherical flocs have a high solid-liquid separation rate and improve water treatment efficiency. In this study, tests were conducted in a high-shear field to evaluate the structural changes in the floc, although confirmation is needed in a low-shear field as well.