## 2 Experimental Method  
The experimental setup was mainly composed of a transparent tank, a particle releasing system and a shadowgraph setup, as shown in Figure 1. The tank is an open acrylic container with a height of 1000 mm with a squared cross-section with a 500-mm width, and is filled with polyacrylamide solution. The two side-by-side particles arranged horizontally can be released simultaneously with a specified distance as required by the particle releasing system, which uses an ejector to generate the vacuum pressure in the two particle pipettes. We used two high-speed cameras (FASTCAM Mini UX, Photron, Yonezawa, Japan), two LED arrays and a computer linked to the cameras to facilitate high-speed shadowgraph binocular-imaging. Thus, the particle trajectories can be tracked on both x-z and y-z planes through this binocular imaging system. Meanwhile, we used the particle image velocimetry (PIV) system to investigate the flow field in the wake of the particle (Figure 2). The PIV system includes a high-speed camera (FASTCAM Mini UX, Photron, Yonezawa, Japan), a continuum laser (SN: CL007, Beijing SMIHY Technology Co. Ltd., Beijing, China), a computer linked to the camera and the fluorescent tracer particles (W-TG1, Beijing HSKT Technology Co. Ltd., Beijing, China). Three types of spherical particles (with less than a 0.25 um diameter variation and spherical error and 0.02 um of the surface roughness) were used in our experiments (Table 1), and 0.5 wt% polyacrylamide (PAAm, supplied by Shanghai Macklin Biochemical Co., Shanghai, China) solution was used. The density of PAAm solution is 1005 kg/m\({}^{3}\), which is very close to that of water. The rheological properties of the PAAm solution were examined at 20 \({}^{\circ}\)C by a rheometer (MCR 702 Multidrive, Anton Paar Co., Graz, Austria). Figure 3 show the rheological curves of the shear stress \(\tau\) to the shear rate \(\gamma\) with steady state in the PAAm solution and pure water, where the slope of the curves represents the fluid viscosity \(\eta\). Figure 4 shows the rheological curves of the fluid viscosity \(\eta\) to the shear rate \(\gamma\) in the PAAm solution and pure water. It can be seen that the shear stress \(\tau\) and shear rate \(\gamma\) of pure water have a linear relationship, while PAAm solution exhibits a very high viscosity value at a low shear rate \(\gamma\). With the increase of the shear rate \(\gamma\), the viscosity of PAAm solution decreases and becomes stable. This indicates that the PAAm solution has a strong shear thinning property [31]. Figure 1: Schematic of the experimental setup for two side-by-side particles settling. In order to verify whether the PAAm solution has viscoelasticity, the frequency sweep response was performed through the MCR rheometer at a shear strain = 1%. The data (Figure 5) indicate that the storage modulus G\({}^{\prime}\) and loss modulus G\({}^{\prime\prime}\) increased with the increasing frequency, which indicates the yield behavior of the test solution. This demonstrates that the PAAm solution in this study is a viscoelastic fluid by [PERSON] et al. (2020). Apart from this, the negative wake (the instantaneous profile) was confirmed by our results using PIV (Figure 6). In the previous work, the negative wake was considered a large strain phenomenon associated with viscoelasticity ([PERSON] et al., 2020; [PERSON] et al., 2020) and the reason for this formation was proven to derive from the shear and extensional motion of the particle wake in the viscoelastic fluid. Under the complex shear and extensional motion, the viscoelastic fluid exhibits rapid elastic recoil, similar to an elastic thread, which seems to be the cause of the negative wake ([PERSON] et al., 2020; [PERSON] et al., 2020). Thus, it can be concluded that the PAAm solution in this study is a viscoelastic fluid.