# Penetration Efficiency and Concentration Distribution of Nanoparticles in a Hollow Tapered Cylinder
###### Abstract  
Knowing particle penetration efficiencies and concentration distributions in an inlet channel of a sampling device is beneficial for the robust assessment, attribution and quantification of nanoparticles produced by various activities. The aim of this research is to evaluate the effect of the presence or absence of a conical column inside a hollow tapered cylinder on the nanoparticle penetration efficiency and its outlet concentration profile for different flow rates. The particle penetration characteristics of various sizes from 3 nm to 20 nm were numerically investigated by using the flow field and convection diffusion equations within the hollow tapered cylinder. Firstly, the proposed model of the nanoparticle penetration efficiency for the hollow tapered cylinder with the conical column is validated with the experimental data in the literature. Then, the results indicate that the concentration at the outlet of the hollow tapered cylinder with the conical column exhibits annular profiles for 3 nm and 5 nm nanoparticles at a flow rate of 2.0 L/min, which is found to avoid centralizing the particles in the exit area. In addition, the penetration efficiency of nanoparticles can be improved by increasing flow rates or removing the conical column inside the hollow tapered cylinder. Finally, the ring-shaped concentration profile of the 10 nm nanoparticles at the outlet of the hollow conical cylinder with the conical column becomes more obvious as the flow rate decreases. This study interprets and quantitatively decides the nanoparticle penetration efficiency and its exit concentration profile for the hollow tapered cylinder with or without the conical column. Therefore, the results can provide some useful design references for the transport of nanoparticles in the hollow tapered cylinder. s 2022 202  
particles within a specific area of the collection plate is important for the ideal grid position of the image generation [10; 11]. Therefore, the calculation of the particle concentration profile at the exit and the avoidance of high concentrations at the center location are well worth exploring. In addition, the penetration efficiency of the particles at the inlet channel of the sampling device also greatly affects the measurement error. Transport studies of nanoparticles have been extensively utilized for various applications involving the transportation phenomenon in different geometries, the conduction properties in fluids, and the assistance in obtaining efficient energy during heat transfer [12; 13; 14; 15]. In many tube flow studies, theoretical models and empirical equations of Brownian diffusion were used to compare and predict the penetration efficiency of nanoparticles [16; 17]. In contrast to the numerous studies of the tube flow, the Brownian diffusion of nanoparticles in the hollow tapered cylinder with the conical column was rarely reported in the literature. However, there are many applications of the nanoparticle measurement for the hollow tapered cylinder, including the sampler inlets and the needle chargers [18; 19; 20]. [PERSON] et al. [21] determined how many particles were produced through coughing, deep breathing, and singing events compared to natural breathing events by using a hollow tapered funnel to collect the particles and passed through a circular conduit to a particle measuring instrument. Respiratory events such as coughing, speaking, and breathing had been shown to produce measurable aerosol concentrations [22; 23]. Due to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), social activities and many economic activities have been significantly affected. Based on strict prevention of airborne transmission, proper particulate sampling is important to assist in the identification of the particle sources [20; 21]. The particle penetration efficiencies and concentration distributions at the entrance in front of the particle detection instrument affect the measurement results.