# Study on the Flow Velocity of Safe and Energy-Saving Transportation of Light-Particle Slurry
## 4 Analysis and Discussion of Results
### Effect of Solid-Phase Content and Particle Size on Critical Flow Velocity  
A numerical simulation of the flow of light particle slurry (solid phase is polyethylene particles) in a horizontal circular pipe with pipe diameters D = 28 mm and 17 mm; particle diameters d = 0.3 mm, 0.4 mm, and 0.5 mm; and solid-phase content C\({}_{\rm v}\) = 5 vol%, 10 vol%, 15 vol%, and 20 vol% is carried out. The critical flow velocity for each condition is obtained using the concentration distribution method and the results are organized in Figure 14. It can be found that the critical flow velocity increases with the increase in solid-phase content under the simulated conditions. This is because the increase in solid-phase content of the light particle slurry inhibits the turbulence intensity, weakens the support of the carrier fluid on the solid-phase particles, and requires an increase in the flow velocity to maintain a certain degree of turbulence intensity [32]. At the same time, the increase in solid-phase content makes the viscosity of the light particle slurry increase, and the solid-phase particles are more tightly bonded to each other; moreover, due to the existence of the difference in the densities between the two phases, a tendency to upward movement occurs, and a larger flow velocity is required in order to maintain the state of the suspended bed, therefore, the critical flow velocity will also be increased. This is in agreement with the conclusion obtained by [PERSON] [15].  
Figure 14: Variation of critical flow velocity with solid-phase content and particle size: (**a**) D = 28 mm; (**b**) D = 17 mm.  
Figure 13: Variation of pressure drop with flow velocity: (**a**) d = 0.3 mm; (**b**) d = 0.4 mm.  
It can also be observed in Figure 14 that the critical flow velocity increases with the increase in the solid-phase particle size under the simulated conditions. This is because, on the one hand, solid-phase particles with larger particle sizes are subjected to larger buoyancy and inertia forces, and larger flow velocities are required to suppress these two forces. On the other hand, however, the larger the solid-phase particles are, the larger the area of action of drag force exerted on the particles, and the drag force required to keep them in motion increases, therefore, larger flow velocities are required to make the light-particle slurry exhibit a suspended-bed flow. This is more consistent with the conclusions of [PERSON] [21], but he believes that the increase in additive concentration during ice production leads to a decrease in the density difference between the solid-liquid two-phase, which also affects the determination of the critical flow velocity. However, in this paper, the selection of polyethylene particles as the solid phase does not have the time-dependent behavior of ice-crystalline particles, does not occur in the ice-crystalline particles of melting and agglomeration, and is able to always maintain a constant particle size, while the density of slurry is unchanged, which allows for a more accurate determination of critical flow velocity [33]. It is also found that the critical flow velocities of the three particle sizes are close to each other when the solid-phase content is 5 vol%, as shown in Figure 12a, which are 0.34 m/s, 0.36 m/s, and 0.39 m/s, respectively. This is due to the fact that when the solid-phase content is lower, the solid-phase particles are more dispersed in the pipeline, and the denseness of the solid-phase particles is more in play, which makes the effect of the size of the solid-phase particles on the critical flow velocity weaker.