## 3 Results and Discussion
### Trajectory of Side-by-Side Particles of Different Densities
The particle-particle collision that has been reported in the settling of two identical particles in shear thinning liquids [20, 28] was not observed in our experiments as a result of the different sedimentation velocities caused by the different densities. The heavier particle's settling velocity is larger than the lighter one; thus the lighter particle is only attracted to the CRV. Interestingly, after a certain distance following the heavy particle's wake, the light particle would rebound from the CRV and the horizontal distance between the particles increases gradually. Since the PAAm solution is a shearing thinning viscoelastic fluid, the fluid will deform under stress due to the particle motion and partial recovery to the undeformedstate once the stress disappears [7]. Inspired by this, the negative wake behind the settling particles was successfully captured in our experiments, as shown in Figure 6. The negative wake probably induced the downstream fluid and the particle to move upwards. Therefore, the combined effect of the shear-thinning property of the PAAm solution and the negative wake could be responsible for the type (i) path of the light particle. Figure 12: Cont. In the cases of type (ii), after a time period of vertical settling of the two particles, the light particle was attracted by CRV, which is similar to the early attractive stage of type (i). The trajectories of the two particles obtained from type (ii) also exhibit a similarity to the work in which the particles tended to attract [28]. In this previous study [28], two identical stainless steel particles were released side by side; however, the two particles gradually converge until they touch each other, and then settle (one up and one down) at the same velocity. In our experiments, the density difference always causes the heavy particle to settle ahead of the light one without collision when the two particles were released side by side. Although obvious tendency of the light particle to approach the heavy one can be seen in the test section, the rebounding stage in the type (i) is not observed in type (ii), which is probably caused by our limited field of the view of the camera. In the cases of type (iii), the light particle first slightly shifted away from its original position in the horizontal direction, and then returned to this initial position. A similar repulsive effect had been reported in the settling of two side-by-side particles of identical densities when the initial separation distance was larger than a critical value [26; 28]. Figure 12: The settling process of two side-by-side particles at different initial separation distance under binocular vision; (**a1**) \(x\)-\(z\) plane, Left particle: ZrO\({}_{2}\), right particle: Stainless steel; (**a2**) \(y\)-\(z\) plane, Particle: ZrO\({}_{2}\), Stainless steel; (**b1**) \(x\)-\(z\) plane; Left particle: Si\({}_{3}\)N\({}_{4}\); right particle: ZrO\({}_{2}\); (**b2**) \(y\)-\(z\) plane, Particle: Si\({}_{3}\)N\({}_{4}\), ZrO\({}_{2}\); (**c1**) \(x\)-\(z\) plane; Left particle: Si\({}_{3}\)N\({}_{4}\); right particle: Stainless steel; (**c2**) \(y\)-\(z\) plane, Particle: Si\({}_{3}\)N\({}_{4}\), Stainless steel. Figure 13: Typical settling trajectories of two particle settling side by side, with an example for each type. According to a previous deduction [28], the particle-particle repulsion can be attributed to the fluid inertia. This is a different phenomenon from the settling behaviors of two identical particles in different non-Newtonian fluids [20]. As explained above, the particle-particle attraction is mainly caused by the effects of the shear-thinning viscoelasticity properties of the fluid, hence, the first normal stress difference of the PAAm solution and the lower pressure of the CRV can drive the light particle back to its original lateral-position.