## 3 Results and Discussion
### Bed Slanting Angles  
The velocity field in the \(+4D\) separator model was plotted to investigate the effect of bed slanting angles on the separation of PET and PVC plastics (Figure 7). The figure shows that the recirculation zones on the vibrating bed decrease with an increase in slanting angle. The reduction in the recirculation zone causes the majority of the plastic material to accumulate near the leading edge of the vibrating bed, which consequently affects the efficiency of the separation process [26]. The increase in slanting angles also decreases the maximum velocity magnitude of the separator model. These velocity contours suggest that the vibrating bed must not be inclined at larger angles, because the plastic materials may not undergo appropriate separation process, thereby affecting the recycling process [25; 26]. The effect of bed slanting on the separation process was also investigated by computing the velocity magnitude at point 1 in the \(+4D\) separator model (Figure 8a). The graph shows that the velocity magnitude increases with the increase in bed slanting angles. The separator model with the vibrating bed inclined at higher angles results in better ballistic trajectory because of higher kinetic energy. However, higher bed slanting angles reduce the recirculation zones. Therefore, an optimized value of bed slanting angle must be selected to maintain the separation process by achieving effective ballistic trajectory [26; 27]. Shear stress, a linear function of fluid velocity, is helpful in determining friction that is produced against the air ballistic trajectory. Therefore, shear stress should be estimated to completely analyze the effect of bed slanting angles with different duct hole shapes on the \(+4D\) separator model [23; 30]. The maximum shear stress value is obtained when the vibrating bed is at the minimum point (\(\theta\) = 0\({}^{\circ}\)). Increasing the bed slanting angles reduces the mean velocity magnitude of the separator model, which consequently reduces shear stress (Figure 8b). The separation of PET and PVC materials is low at larger bed inclination angles, because more friction will be applied to the airflow. The high friction will thus decrease the kinetic energy of the ballistic trajectory. The triangular duct hole with \(1.5D\) resulted in the highest value of shear stress, which suggests that this duct shape offers greater friction to the airflow during separation process. Higher fluid friction reduces the movement of plastic materials from inlet to the vibrating bed. The intensity of turbulence in the separator model was further investigated by computing the vorticity magnitude with the effect of bed slanting angles and different duct hole shapes on the \(+4D\) separator model (Figure 8c). The vorticity magnitude shows similar patterns as shear stress because of the correlation of these two parameters [31]. Increasing bed slanting angles also decreased the vorticity magnitude in the separator model. The triangular duct hole with \(1.5D\) resulted in the highest value of the vorticity magnitude. Higher bed slanting angles increase the kinetic energy by offering lower fluid friction. However, the recirculation zone on the vibrating bed is reduced at higher bed slanting angles. Therefore, a suitable bed slanting angle must be selected to enhance the separation process without decreasing the recirculation zone on vibrating bed. Figure 7: _Cont._Figure 8: Effect of bed slanting angles (\(\theta\)) on the (**a**) velocity magnitude of +4\(D\) duct hole diameter at point 1, (**b**) shear stress with different duct hole shapes and (**c**) vorticity magnitude with different duct hole shapes at an air inlet velocity of 35 m/s.