# Experimental Investigation in Drag Coefficient of Cubes
## 2 Experimental Facility and Procedure
The percentages of glycerine used to define the specific mixtures were determined by volume. The kinematic viscosity of every mixture was measured by a DVS+ spindle viscometer (manufactured by Brookfield, New York, NY, USA; as shown in Figure 1b) under the temperature encountered during the experiment. The accuracy of the viscometer was guaranteed within \(\pm\)1% of the full-scale range of the spindle/speed combination in use, and it had been calibrated using viscosity standard fluids. The specific gravity of the fluid was measured by a float-type hydrometer. The temperature and specific gravity were measured regularly during the experiment to ensure that the properties of the fluid have not been changed. The mixture of water and glycerine was stirred by a large mixer for at least 10 min to obtain a uniform solution. The fluid was loaded into the tube and kept static for 24 h before the experiment to allow small air bubbles to escape. As a result, the thermal equilibrium can be reached. During this period, the top end of the fall tube was sealed by a plastic membrane to minimize the evaporation losses in the case of glycerol solutions. Figure 1: Experimental setup. (**a**) Experimental measurement system. (**b**) Brookfield DVS+ spindle viscometer. There were two types of cubes used in this investigation. One is the uniform cube which is made by a single material, such as aluminum, brass, steel, and PVC with the density of 2750 kg/m\({}^{3}\), 8300 kg/m\({}^{3}\), 7730 kg/m\({}^{3}\), and 1380 kg/m\({}^{3}\), respectively. The uniform cubes have three geometry types with the side length of 10 \(\pm\) 0.3 mm, 16 \(\pm\) 0.3 mm and 20 \(\pm\) 0.3 mm. The other cubes were spliced into two parts which were made by different materials, as shown in Figure 2. The barycenter of the spliced cube is far away from its geometric center, which can keep the orientation angle constant during the settlement. As a result, a moment of force is formed to suppress the secondary motion of the spliced cube and the drag coefficient with a fixed orientation angle is obtained through the free settling experiment. The information on the geometry features and the material of the spliced cubes are listed in Table 2. All the cubes had smooth surfaces, and surface roughness effects were negligible for the studied Reynolds number range. In order to ensure that the cubes achieve rapid stabilization of their orientation angles during the settling process, the cubes with different configurations have different initial released angles. The initial released angle of uniform cubes and spliced cubes with \(h/a\) = 0.5 are 0\({}^{\circ}\)\(\pm\) 1\({}^{\circ}\). The spliced cubes with \(h/a\) = 0.67 and 1.0 are settled in an initial released angle of 20\({}^{\circ}\)\(\pm\) 1\({}^{\circ}\) and 45\({}^{\circ}\)\(\pm\) 1\({}^{\circ}\), respectively. The same particle was subjected to the sedimentation experiment under the same conditions for three repetitions to reduce random errors. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No** & \(a\) **(mm)** & \(b\) **(mm)** & \(c\) **(mm)** & \(h/a\) & **Material A** & **Material B** & \begin{tabular}{c} **Particle Density** \\ **(kg/m\({}^{3}\))** \\ \end{tabular}