## 2 Results and Discussion
### Floc Images and Structual Change  
Figure 1a-f shows images taken for test conditions at varying ALT ratios, from 0.03 to 0.05 and 0.10, and at rotational speeds of 120 rpm and 160 rpm. For each test condition, images were taken 4, 30, 60, 80, 120, 180, 300, 420, 540, and 600 s after the test had commenced. Figure 1 includes original RGB images converted to 16-bit to easily confirm the progress of floc aggregation with the naked eye. For image analysis, the original RGB image was converted to 8-bit. In Figure 1, the original images of 1024 pixel squares were cropped to 512 pixel squares including the ROI (region of interest) for easy comparison of each condition. This was a characteristic of background illumination: kaolinite did not transmit light and therefore appeared black, while the gel portion, which was insoluble aluminum hydroxide, was transparent and did not appear in the image. Therefore, as shown in a previous report [36], when the floc density was small, the kaolinite in the floc was dispersed and appeared to be light gray in color, while when the floc density was high the kaolinite was concentrated and appeared to be dark black. The brightness of the flocs afforded a qualitative understanding of the density transition of flocs. As the rotation continued, indistinct flocs with light gray contours began to form. Gradually, the flocs grew, and multiple large bulky flocs were observed to be present. After the flocs reached their maximum diameter, further continued rotation caused the bulky flocs to disappear. There were two types of flocs: those that destroyed and refined, and those that incorporated the surrounding micro flocs and underwent a dense structural change (rearrangement). At the time of the disappearance of the former bulky flocs, the flocs had become smaller in size due to separate breakup of the flocs. In the latter case, shear forces caused erosive breaking of the floc surface, and fine fragments were incorporated into other flocs and densified.  
Figure 1: _Cont_.  
Figure 1: Photographed images of flocs in six tests in which the flocculation conditions are changed to two different rotation speeds and three different ALT ratios: (**a**) 120 rpm, ALT ratio 0.03, (**b**) 120 rpm, ALT ratio 0.001, (**c**) 120 rpm, ALT ratio 0.002, (**d**) 120 rpm, ALT ratio 0.003, (**d**) 120 rpm, ALT ratio 0.004, (**e**) 120 rpm, ALT ratio 0.005, (**f**) 12  
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. The horizontal bar in the bottom left corner of each image is a 2 mm scale bar. Figure 1 includes RGB original images converted to 16-bit for confirmation by the naked eye. For image analysis, the original RGB images were converted to 8-bit according to the specifications of the analysis software.  
Figure 2a,b shows the logarithmic relationship between \(D_{90}\) and \(GT\) values, i.e., the result of image analysis. The \(GT\) value on the horizontal axis is the product of the agitation strength (shear rate) \(G\) value and the elapsed time. \(D_{90}\) increased following a power-law relationship with \(GT\), and then decreased after a certain point around 13,000 \(GT\) value. This trend was also observed in other test conditions. The floc growth stage and the breakup and rearrangement stage were clearly separated by a certain \(GT\) value.  
Figure 2: Log–log plots of \(D_{90}\) vs. \(GT\) values, (**a**) 120 rpm and (**b**) 160 rpm conditions. \(D_{90}\) increases as a power of the \(GT\) value in the growth stage and tends to decrease after a certain \(GT\) value. \(D_{90}\) decreases by a power in the breakup and rearrangement stage.