## 4 Materials and Methods
### Test Water Materials  
Test water was simulated river water, and 100 mg/L kaolinite was dispersed in tap water from the University of Tsukuba. Kaolinite was a Si-based fine mineral particle with an average particle size of about 5 \(\upmu\)m (measured by Laser diffraction particle size analyzer; SALD-3100, Shimadzu Co., Kyoto, Japan). Tap water had a pH of 7.4-7.5 and a water temperature of 20.0-23.0 \({}^{\circ}\)C. Tap, water was degassed in advance by ultrasonic suction deaeration for 10 min to prevent air bubbles from being generated during the rotation test which would interfere with imaging. The room temperature was always kept at 20.0 \({}^{\circ}\)C. The water temperature was 20.0 \({}^{\circ}\)C at the start of the test; due to the heat from an LED light source and the rotational motor, the water temperature gradually increased, reaching a maximum of 23.0 \({}^{\circ}\)C. Although water temperature affects flocculation, we considered that relative comparisons could be made for each condition. The flocculant was poly-aluminum chloride (PACI, 10.0% as Al\({}_{2}\)O\({}_{3}\)), which is commonly used in drinking water treatment in Japan. The advantages of PACI are better flocculation than aluminum sulfate and relatively easy floc formation even at low water temperatures [43]. Disadvantages are lighter flocs weight than iron-based flocculants and a narrow flocculation pH range of 6 to 8. PACI was pre-diluted with ultrapure water and added through the inlet of the outer casing of the Couette device filled with kaolinite suspension to achieve an injection rate \(C_{PACI}\) of 30 to 100 mg/L. The ALT ratio was expressed as:  
\[ALT\ ratio=\frac{C_{PACI}R_{Al}}{C_{K}}. \tag{6}\]  
using the concentration of kaolinite suspension \(C_{K}\) and the aluminum content in the PACI \(R_{Al}\). \(C_{K}\) was fixed and the ALT ratio was adjusted by changing \(C_{PACI}\) with the ALT ratio of 0.03 to 0.10 as the test range. Figure 8 shows the zeta potential measurements (median)of the test water injected with PACI. A preliminary beaker-scale test to determine the flocculant injection rate, called the jar test, was performed to measure the zeta potential of the supernatant water after floc sedimentation. After the flocs were allowed to settle and separate for 1 h, the supernatant water was collected and measured using a zeta potential analyzer (Zeecom; Microtec Co., Ltd., Chiba, Japan). ALT ratios of 0.03-0.10 were within the zeta potential range of \(\pm\)10 mV, where flocculation easily occurs. The ALT ratio of 0.03 had a negative zeta potential and was slightly deficient in flocculant, the ALT ratio of 0.05 had a zeta potential near 0, which was an appropriate condition for near charge neutralization, and the ALT ratio of 0.10 had a positive zeta potential and was considered overdose. After the experiment, the pH was 7.44 at an ALT ratio of 0.03, 7.23 at an ALT ratio of 0.05, and 7.04 at an ALT ratio of 0.10. Conceptualization, M.F.H. and Y.A. ; Methodology, M.F.H., T.M., T.U. and Y.A. ; Validation, M.F.H. and Y.A. ; Formal Analysis, M.F.H. and Y.A. ; Investigation, M.F.H., T.M. and T.U. ; Resources, M.F.H., T.M., T.U. and Y.A. ; Data Curation, M.F.H. ; Writing--Original Draft Preparation, M.F.H. and Y.A. ; Writing--Review and Editing, M.F.H. and Y.A. ; Visualization, M.F.H. and T.U. ; Supervision, Y.A. ; Project Administration, T.I. and Y.A. ; Funding Acquisition, T.I. and Y.A. All authors have read and agreed to the published version of the manuscript. Y.A. had received research grants from the Japan Society for the Promotion of Science [grant numbers 22H00387, 16H06382]. Not applicable. The data that support the findings of the current study are listed within the article. Y.A. had received research grants from the Japan Society for the Promotion of Science [grant numbers 22H00387, 16H06382]. Not applicable. Y.A  
* [PERSON] and [PERSON] (1967) [PERSON]; [PERSON] [PERSON] A study on aluminum floc density-I. _J. Jpn. Water Work. Assoc._**1967**, _397_, 2-10.