# Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow
## 5 Results and Discussion
### Distribution of Particle Number Concentration and Orientation at Outlet
#### 5.2.2 Effect of the Particle Aspect Ratio  
Figure 6 shows the distributions of particle volume concentration on the cross-section at the outlet for different particle aspect ratios. It can be seen that the distributions of particle volume concentration become more uniform with increasing the particle aspect ratio. The reason can be analyzed as follows. The evolution of particle number density  
Figure 4: Distribution of (**a**) particle concentration and (**b**) particle orientation at different axial positions (\(\lambda\) = 8, Re = 20,000, \(L\)/\(D\) = 20). \(\bullet\): \(z\)/\(D\) = 50; \(\bullet\): \(z\)/\(D\) = 100; \(\bullet\): \(z\)/\(D\) = 150; \(\bullet\): \(z\)/\(D\) = 200.  
Figure 5: Distribution of mean particle orientation in different regions on the cross-section at outlet (\(\lambda\) = 8, Re = 20,000, \(L\)/\(D\) = 200). \(\bullet\): region 1; \(\bullet\): 2; \(\bullet\): 3; \(\bullet\): 4; \(\bullet\): 5.  
\(\overline{n}(v)\) as shown in Equations (10) and (11) is determined by the mean shear rate of the fluid, Brownian translational diffusion coefficient \(D_{IB}\) and turbulent diffusion coefficient \(v_{t}\). The existence of particles in the flow has an effect on the turbulent kinetic energy, which increases as the particle aspect ratio increases [16] because the particles with larger aspect ratio can make a stronger momentum transfer with providing a solid link between the adjacent fluid layers. In return, the increase of turbulent kinetic energy can promote particle diffusion. Besides, as shown in Equation (11), the Brownian diffusion coefficient \(D_{IB}\) is proportional to the particle aspect ratio, i.e., the particles are subjected to a larger Brownian diffusion when the aspect ratio is larger. Therefore, the larger the particle aspect ratio is, the stronger the Brownian diffusion and turbulent diffusion are, and the more uniform the distribution of particle volume concentration is.  
Figure 7 shows the distributions of mean particle orientation in region 1 and 5 at outlet for different particle aspect ratios. The particles tended to align with the flow direction, and this preferential orientation is more obvious in the near-wall region and with increasing the particle aspect ratio. The mean probability density function for particle orientation is determined by the Brownian diffusion, turbulent diffusion and mean shear rate of the fluid. Firstly, the Brownian diffusion coefficient was inversely proportional to the particle aspect ratio as shown in Equation (8), so the distribution of mean particle orientation was more non-uniform for the case of a larger aspect ratio. Secondly, the turbulent dispersion coefficient \(\alpha_{\varphi p}=0.7(4\epsilon\rho_{off}/15\mu)^{1/2}\) of angular displacement was proportional to the turbulent dissipation rate \(\varepsilon\), which increased with increasing the particle aspect ratio [16], so the distribution of mean particle orientation was more uniform for the case of a larger aspect ratio. Thirdly, the shear-induced torque exerted on the particle was larger for the case with larger aspect ratio, which caused the particle to spin around the flow direction more effectively. The comprehensive effect of the above factors makes more particles aligned with the flow direction. As shown in Figure 7b, the difference in the distributions of mean particle orientation between the cases with a different aspect ratio was small for the large aspect ratio, which was consistent with the conclusion [26] that the orientation distribution was not sensitive to the aspect ratio for the inertial particles with an aspect ratio larger than 5.