## 4 Materials and Methods  
### Couette Device and Photographic Equipment  
Flocs had complex structures and were brittle and easily broken. To quantify the floc in the water, an imaging method was chosen, but some ingenuity was required to capture the sides of the rotating cylinder. To visualize the floc in the water, a preliminary test was first conducted with ceiling lighting, and a luminance distribution was observed in the vertical direction of a cylinder filled with test water. Since this vertical luminance distribution was fallacious because of erroneous capture of the particle size and shape of the floc, we decided to use background illumination [38]. There were some problems with imaging caused by the background illumination. For example, extremely small particles or abundant particles could not be detected, errors occurred in particle size determination due to their distribution in the depth direction, and the 3D shape, including the depth direction, could not be grasped. In addition, if there were multiple flocs within the depth of focus of the imaging sensor, they tended to appear as one floc when they were close together. Conversely, if the particles were sparsely clustered, even if they belonged to a single floc, they were erroneously counted as multiple particles as a result of the brightness threshold setting for analyses [39; 40]. Despite these problems, particle measurement techniques using imaging with background illumination were well suited to the measurement of rapidly growing flocs. This is because flocs flow in water, grow from a few micrometers to several millimeters, and change their structure. Rotation tests to capture changes over time in the floc structure were performed using the Couette device, a double-cylinder device with a rotating outer cylinder placed horizontally and a high-speed camera (FASTCAM Mini AX50; Photron Ltd., Tokyo, Japan). Figure 7 shows the configuration of the test equipment. The Couette device was placed horizontally and a high-speed camera was fixed in front of it; LED flat lighting was placed behind it across the double cylinder. The Couette device was placed horizontally to avoid the effects of gravity settling. The Couette device and camera were covered with a blackout curtain to avoid the influence of ambient light. The gap between the inner and outer cylinders of the Couette device was filled with test water. The inner diameter of the outer cylinder was 11.5 cm, the outer diameter of the inner cylinder was 9 cm, and the gap was 1.25 cm. The length of the cylinder was 26 cm, and the volume of the gap was approximately 1 L. To stabilize the flow generated in the gap, the inner cylinder was fixed and only the outer cylinder was able to rotate. The Couette device had a motor for the rotation of the outer cylinder, and the speed could be adjusted from 1 rpm to 267 rpm by a speed controller (BXM series; Oriental Motor Co., Ltd., Tokyo, Japan). During the rotation, a constant upward shear force \(\tau\) N/m\({}^{2}\) was generated in the gap, as viewed from the camera side, by [PERSON]'s viscosity law, \(\tau\):  
\[\tau=\mu\frac{U}{h}. \tag{2}\]  
where \(\mu\) represents the viscosity of water, \(U\) represents the velocity of movement of the wall surface, and \(h\) represents the distance from the wall surface. When the outer cylinder was rotated at 120 rpm and 160 rpm in this test, a constant shearing force of 0.058 N/m\({}^{2}\) and 0.077 N/m\({}^{2}\), respectively, was generated in the gap. Both the inner and outer cylinders were made of transparent acrylic, and the floc aggregation in the gap was photographed from the outside of the device by a high-speed camera. The target was a particle near the vertical center of the double cylinder, in the middle of the gap between the inner and outer cylinders.