# Penetration Efficiency and Concentration Distribution of Nanoparticles in a Hollow Tapered Cylinder
###### Abstract
Therefore, the particle penetration and concentration profile of the hollow tapered cylinder are important to the particulate measurement. On the other hand, the nanoparticle penetration efficiency of the hollow tapered cylinder with the conical column affects the intrinsic charging efficiency and the performance of the needle charger. The intrinsic efficiency of needle chargers can be increased by increasing the number and charging rate of nanoparticles within the needle charger [19; 24; 25]. [PERSON] et al. [19] evaluated a corona-based cylindrical ionizer with the conical column for the charging efficiency, and results showed that smaller particles have higher diffusion loss than larger particles, resulting in a lower nanoparticle penetration. While the methods for increasing particle penetration by increasing the flow rate are well known, a quantitative analysis of the improvement of the nanoparticle penetration has not been fully reported in the literature. Furthermore, the effect of adding the conical column on the particle penetration and the outlet concentration profile is also lacking. In the previous study [26], the nanoparticle deposition was investigated by simulating the flow field and the particle trajectory within a needle charger. The results showed that most of the particles inside the needle charger without applied voltage were attached to the outer wall instead of the electrode wall. One of the achievements in the previous study is to solve the movement of nanoparticles while considering the corrected Stokes drag force and Brownian force, and to provide a comparison of the two forces for nanoparticles, so as to understand the underlying physics more easily. However, it is important to see if the conical column has an effect on the concentration distribution when the nanoparticles move toward the outlet of the hollow tapered cylinder. Therefore, this study solves the nanoparticle concentrations by modeling the nanoparticle diffusion inside the hollow tapered cylinder with or without the conical column, which differs remarkably from previous research. The aim of this study is to evaluate the effect of the presence or absence of the conical column within the hollow tapered cylinder on the nanoparticle penetration efficiency and the concentration distribution. In this paper, we investigated the nanoparticle concentration distribution of the hollow tapered cylinder with or without the conical column by using the flow field and convective diffusion methods, which constitutes a novelty of the present work. The penetration efficiencies of nanoparticles in the hollow tapered cylinder were then evaluated numerically under different flow rates and the results are discussed comprehensively. The outlet concentration profiles of the cross sections for a range of particle sizes were also calculated by using the axisymmetric computational model. In the presence of the conical column, the model was validated for the nanoparticle penetration efficiency of the hollow tapered cylinder. The Brownian diffusion and convection of nanoparticles in the hollow tapered cylinder with or without the conical column has not been described in the works earlier to our knowledge. It very well may be trusted that the investigation of the nanoparticle concentration distributions and penetration efficiencies of the hollow tapered cylinder is useful for the robust assessment, attribution, and quantification of nanoparticles produced by various activities.