Fundamental Study of Particle Formation, Transport, Deposition and Filtration for Semiconductor Applications A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Dongbin Kwak IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Dr. David Y. H. Pui January 2023 © Dongbin Kwak 2023 i Acknowledgements I would like to express my deepest gratitude to my advisor, Professor David Y. H. Pui for his unconditional support, patience, generosity, and faith throughout my study at the University of Minnesota. He has always encouraged me to challenge myself and given me generous support all the time. If I had not met him, I would not achieve my goal today. I will never forget his countless contribution to my life and my career. I would also like to extend my deepest appreciation to my committee members: Professor David Kittelson, Xiaojia Wang, and Boya Xiong for their valuable comments and suggestions on my research. Thanks for spending your valuable time reviewing my dissertation and offering helpful feedback as well as sincere encouragement. It was really a great honor to get an opportunity to interact with these intelligent people. I’m extremely grateful to Dr. Handol Lee who was my roommate, a good colleague, and especially a great senior. I spent quality time with him by receiving his endless support whenever I need. I would appreciate Dr. Seong Chan Kim's support, especially when I was in the first year of my Ph.D. It was a great help to get the right direction for my research with his abundant experience. I would express my thanks to my former advisor at Hanyang University in Korea, Professor Se-Jin Yook, for his continuous support that made me successfully study at the University of Minnesota. I also would like to thank my previous colleagues: Dr. Jung-Hun Noh, Dr. Won-Geun Kim, and Dr. Jun-Hyung Lim. With their help and direction during my college, I was able to build a solid foundation for my research. It was an invaluable experience that could not be exchanged for anything. ii I am truly grateful to Dr. Jason Wang from Applied Materials for giving me abundant ideas related to particle control in the semiconductor industry as we have had a bi-weekly meeting for five years. Thanks to his contributions, I was able to successfully complete my Ph.D. program. Special thanks to Shu Fan Wu, Jyeshna Rajan, and John Oberman from Applied Materials who helped me to measure sp-ICPMS in San Jose for one month. I would like to send my appreciation to Dr. Chao-Hsin Lin from Boeing. I am grateful for his quality feedback by his extensive experience. With his sponsorship, I was especially given the opportunity to perform the experiment at the top of Europe, known as HFSJG (High Altitude Research Stations Jungfraujoch and Gornergrat) in Switzerland for one month. I would also like to extend my deepest gratitude to Professor Jing Wang, Yibo Zhao from ETH Zurich, and Claudine Frieden from HFSJG for helping me to stay in Switzerland for one month without any difficulties. Many thanks to Dr. Miles Owen from US ARMY Primary Standards Laboratory. It was such a great honor to get valuable feedback as well as continuous sponsorship. I also want to thank Professor George Mulholland who gave detailed feedback. It was a great honor to work together on the US ARMY project. I would like to send my gratitude to Greg Schelske from Entegirs. With his help, I could finish my research when I was not able to finish the experiment at the university. I would like to express my thanks to Keith Gossen from Entegris for his active help when I used the Liquid Particle Counter. I also like to thank Bo Liu from Entegris for his support when I used the wafer surface scanner. iii I would also like to express my deepest gratitude to my current and former colleagues in the Particle Technology Laboratory and Center for Filtration Research: Dr. Seong Chan Kim, Dr. Handol Lee, Dr. Qisheng Ou, Dr. Hoo Young Chung, Dr. Francisco Romay, Dr. Dongbin Kim, Dr. Jing Wang, Dr. Sheng-Chieh Chen, Dr. Da-Ren Chen, Dr. Chang Hyuk Kim, Dr. Christoph Asbach, Dr. Ming Ouyang, Dr. Wilson Poon, Dr. Min Tang, Dr. Yan Ye, Dr. Qingfeng Cao, Dr. Drew Thompson, Dr. Nanying Cao, Dr. Seungkoo Kang, Dr. Chenxing Pei, Dr. Lipeng Su, Dr. Xinjiao Tian, Dr. Qiang Lyu, Weiqi Chen, Md Atiqur Rahman, Hayden Fischer, Tao Song, Jihe Chen. I am grateful to have had a meaningful time with those competent people. I sincerely appreciate your active participation and generous support. During my research, I could always get their sincere advice and delicate feedback. I could expand my viewpoint of the research and be inspired by them every time. Thanks for the financial support from US ARMY, and the Center for Filtration Research (CFR): 3M Corporation, A.O. Smith Company, Applied Materials, Inc., BASF Corporation, Boeing Commercial Airplanes, Corning Co., China Yancheng Environmental Protection Science and Technology City, Cummins Filtration Inc., Donaldson Company, Inc., Entegris, Inc., Ford Motor Company, Freudenberg Filtration Technology, Gore (W. L. Gore & Associates, Inc.), LG Electronics Inc., Mann Hummel, Midea, MSP Corporation, Parker Hannifin, Samsung Electronics Co., Ltd., Shengda Filtration Technology Co., Ltd., Shigematsu Works Co., Ltd., TSI Inc., WatYuan Filtration System Co., Ltd, and the affiliate member National Institute for Occupational Safety and Health (NIOSH). I also gratefully acknowledge the Department of Mechanical Engineering Fellowship, Fred Shapiro International Student Fellowship, Honorary Hanyang Study Abroad Scholarship, and the iv American Filtration and Separation Society Fellowship. Last but not least, my deep and sincere gratitude to my wife, Soojeong, for her emotional support and encouragement. Her deep love and ultimate confidence in me have always been the root of my courage. I am indebted to my parents, sister, and other family members for their trust and love. Without their generous love, unbounded trust, endless patience, and timely encouragement, I would not have been able to successfully complete my Ph.D. v To my wife and parents vi Abstract Nowadays, the major semiconductor manufacturing companies try to fabricate smaller nodes (up to ~2 nm) by using the current start-of-the-art EUV lithography system. As a result, the particle size of interest becomes smaller. Preventing and controlling particle contaminations is essential in the semiconductor manufacturing process to increase semiconductor yield. Examples of these unwanted nanoparticles in the semiconductor industry are airborne molecular contamination (AMC), haze, and deposited nanoparticles. For these reasons, to control and reduce nanoparticle contamination in the semiconductor manufacturing process, particle formation, transport, deposition, and filtration studies should be simultaneously investigated. The objectives of this study were to 1) demonstrate particle formation in a particle-free environment, 2) investigate particle deposition and transport characteristics in commercial gas pipelines, and 3) present a new analytical equation for calculating the pressure drop of nanofiber filter media. In Chapter 2, the detection method for methyl salicylate molecules which is one of the volatile organic samples by using soft X-ray and aerosol measurement techniques was described. The aromatic chemical compounds which have the benzene ring are well detected by the soft X-ray-assisted detection method which converts gas vapors to nanoparticles through the photochemical processes. This chapter reports the characteristics of the formation of the nanoparticles by describing the stage change during the soft X-ray reaction: particle-free mode; nucleation mode; transition mode; accumulation mode; and stable mode. The empirical calibration curves can predict ppbv-level methyl salicylate vapor concentrations by using particle number or volume concentration data obtained from vii the real-time aerosol detection instrument. In Chapter 3, nanoparticle transport through a sharp-bent tube, i.e., elbow connection, was systematically examined by using a particle size ranging from 3 to 50 nm. In the experiments, particle size and flow rate significantly affected the penetration efficiency. To be specific, the smaller particles which had higher diffusion coefficients were more likely deposited on the sharp-bent tube and the higher flow rate reduced the flow- directional nanoparticle residence time resulting in increased penetration efficiency. To explain the experimental penetration efficiency on the sharp-bent tube, characteristics of fluid flow on the sharp-bent tube were studied numerically. The flow field calculations showed that the recirculation pattern occurred at the corner of the sharp-bent tube, and the flow separation and reattachment were observed at the inner wall right after the bending point. Additionally, when compared to a higher Reynolds number, the intensity of the secondary flow was weaker at a lower Reynolds number as well as its center point was located farther from the tube wall. Therefore, the nanoparticle residence time on the sharp- bent tube became longer and a smaller number of particles penetrated the tube at a lower Reynolds number. Based on the experimental data, the penetration efficiency on the sharp- bent tube was predicted by the correlation fitting curve. The relative penetration efficiency on the sharp-bent tube was also obtained by comparing it to the penetration efficiency on the straight tube. The strong diffusion transport rate and weak advection transport rate induced more particle losses due to secondary flow after the bending point, resulting in decreased relative particle efficiency. The characteristics of fluid flow on a sharp-bent tube under various conditions were analyzed in Chapter 4. Numerical simulations for analyzing the particle deposition viii locations and patterns on a sharp-bent tube were conducted by using the modified single- particle tracking analysis based on aerosol mass flow rate. Through the numerical calculation, we showed that after the bending point in a sharp-bent tube, the faster axial velocity occurred near the outer wall, and the boundary layer at a high Reynolds number became thinner. Furthermore, the faster radial velocity near the tube wall was observed at less developed-flow regions at high Reynolds numbers owing to the stronger secondary flow. The nanoparticle deposition locations and patterns were systematically examined from various viewpoints including the cumulative number of deposited particles, local deposition enhancement factor, and particle deposition pattern according to azimuthal angles. We found that most of the nanoparticles were deposited on the outer wall right after the bending point owing to outward-sloping flow. Moreover, the difference in relative deposition efficiency along the azimuthal angles at each section in the sharp-bent tube was reduced as the Reynolds number increased. This is because the nanoparticles near the wall were well mixed due to the strong secondary flow at high Reynolds numbers. The objective of Chapter 5 is to investigate the penetration characteristics of sub- 100 nm nanoparticles on a forked tube (tree-like branching tube) at Reynolds numbers from 370 to 2,000. The modified single-particle tracking analysis based on aerosol mass flow rate was employed for tracking individual particles. The particle deposition efficiency was compared with the experimental results to ensure the accuracy of the numerical analysis method. The flow and deposition characteristics of sub-100 nanoparticles were systematically analyzed by obtaining the contours of particle distribution, particle concentration, and particle ID on various cross-sections in a forked tube. Based on the results, we found non-uniform particle concentration, resulting in creating a particle-free ix zone after passing a bending point. In addition, we suggested the correlation equation for the deposition efficiency on a forked tube at various conditions, which can be simply presented by the Peclet number, and the equation covers the whole tested Reynolds number. Furthermore, the clear differences in deposition behaviors between the forked, straight, and single sharp-bent tubes were presented (dep,FT = 13.75Pe-0.3798). The usage of a correlation equation for a single-bent tube to determine the deposition efficiency in a forked tube (two consecutive elbow connections) overestimated the efficiency due to the non-uniformity of the particle distribution after the particle passes the first elbow. The model presented in this work can be expanded further for more complicated tubing systems and give insight into tracking particle contamination sources in various applications. Nanoparticle resuspension or removal efficiencies on forked tubes with various methods, e.g., pulsed air jet, ultrasonication, and acid dissolution, were evaluated in Chapter 6. We deposited particles on two different surfaces: 200 mm wafers and forked tubes. For depositing particles on 200 mm wafers, PSL particles were deposited by electrophoresis and direct deposition method. On forked tubes, fluorescent and silver nanoparticles were deposited by using the aerosol method, and pulsed air jet, and ultrasonication resuspension or removal efficiency for silver nanoparticles was evaluated. We confirmed that 50 nm silver nanoparticles were hardly resuspended by using the ultrasonication method, and particle removal efficiency is less than 10%. For validating particle deposition efficiency and low particle removal efficiency, we used ultrasonication and particle dissolution by acid extraction method. 40 nm silver nanoparticles were deposited by using the aerosol method. The particle removal efficiency of 40 nm silver nanoparticles is still less than 10%. Based on the series of experimental results for particle x removal efficiency, we confirmed that the small size of silver nanoparticles is hardly resuspended through ultrasonication. In Chapter 7, a semi-empirical correlation curve for predicting nanofiber pressure drop was suggested. By applying the slip effect on the nanofiber surface, the airflows across the nanofiber filter media (0.005 ≤ α ≤ 0.100, and 30 ≤ df ≤ 300 nm) were simulated. We compared and discussed other theoretical models (Brown, 1993; Kuwabara, 1959) and empirical models (Bian et al., 2018; Davies, 1953) with current numerical results and the previous experimental results. xi Table of Contents Acknowledgements ............................................................................................................ i Abstract ............................................................................................................................. vi Table of Contents ............................................................................................................. xi List of Tables .................................................................................................................... xv List of Figures ................................................................................................................ xvii Chapter 1 Introduction ..................................................................................................... 1 1.1 Background .............................................................................................................. 1 1.1.1 Particle contamination ......................................................................................... 2 1.1.2 Particle formation ................................................................................................ 3 1.1.3 Particle transport and deposition ......................................................................... 5 1.1.4 Particle filtration .................................................................................................. 6 1.2 Research objectives .................................................................................................. 8 1.3 Dissertation outline .................................................................................................. 9 Chapter 2 Nanoparticle formation from Volatile Organic Compounds (VOCs) by the Soft X-ray irradiation ..................................................................................................... 10 2.1 Introduction ........................................................................................................... 10 2.2 Experimental methodology ................................................................................... 15 2.3 Results and discussion ........................................................................................... 19 2.4 Conclusion .............................................................................................................. 38 Chapter 3 Experimental study of nanoparticle transport and penetration efficiency on a sharp-bent tube (elbow connection) ...................................................................... 41 xii 3.1 Introduction ........................................................................................................... 41 3.2 Theory ..................................................................................................................... 46 3.3 Experimental method ............................................................................................ 50 3.4 Numerical method ................................................................................................. 55 3.5 Results and discussion ........................................................................................... 57 3.5.1 Effect of Schmidt number ................................................................................. 57 3.5.2 Effect of Reynolds number and comparison between straight and sharp-bent tubes ........................................................................................................................... 61 3.5.3 Velocity profile and secondary flow .................................................................. 64 3.5.4 Empirical correlation of penetration efficiency on a sharp-bent tube ............... 68 3.6 Conclusions............................................................................................................. 71 Chapter 4 Numerical investigation of nanoparticle deposition location and pattern on a sharp-bent tube wall ............................................................................................... 74 4.1 Introduction ........................................................................................................... 74 4.2 Numerical method ................................................................................................. 78 4.2.1 Computational domain ...................................................................................... 78 4.2.2 Numerical approach .......................................................................................... 79 4.2.3 Particle transport modeling ............................................................................... 81 4.2.4 Particle injection model ..................................................................................... 85 4.3 Experimental method ............................................................................................ 89 4.4 Result and discussion............................................................................................. 92 4.4.1 Velocity magnitude and streamline in the midplane of a sharp-bent tube......... 92 4.4.2 Axial velocity at the cross-section of a sharp-bent tube .................................... 95 4.4.3 Secondary flow in the cross-section of a sharp-bent tube ................................. 97 4.4.4 Deposition efficiency according to particle size ............................................. 101 4.4.5 Deposition location and pattern....................................................................... 104 4.5 Conclusions............................................................................................................ 110 xiii Chapter 5 Numerical study of nanoparticle penetration characteristics in forked tubes using tracking particle identification ................................................................. 113 5.1 Introduction .......................................................................................................... 113 5.2 Method ................................................................................................................... 117 5.2.1 Numerical method ............................................................................................117 5.2.2 Experimental method ...................................................................................... 126 5.3 Results and discussion ......................................................................................... 128 5.3.1 Nanoparticle deposition efficiency .................................................................. 128 5.3.2 Flow characteristics ......................................................................................... 134 5.3.3 Particle concentration and ID .......................................................................... 138 5.3.4 Effect of Peclet number ................................................................................... 153 5.3.5 Comparison of deposition efficiency between different tube geometries ....... 155 5.4 Conclusion ............................................................................................................ 160 Chapter 6 Nanoparticle resuspension or removal on forked tubes using the pulsed air jet, ultrasonication, and acid dissolution method ................................................. 163 6.1 Introduction ......................................................................................................... 163 6.2 Particle deposition and resuspension or removal on 200 mm wafers ............. 168 6.2.1 Deposition by Electrophoresis ........................................................................ 168 6.2.2 Direct deposition method ................................................................................ 173 6.2.3 PSL 1.6 µm resuspension or removal by a pulsed air jet ................................ 174 6.3 Nanoparticle deposition on forked tubes ........................................................... 184 6.3.1 Fluorescent nanoparticle ................................................................................. 184 6.3.2 Silver nanoparticle........................................................................................... 189 6.4 Nanoparticle resuspension or removal on forked tubes ................................... 192 6.4.1 Clean air transport ........................................................................................... 192 6.4.2 Pulsed air jet experiment ................................................................................. 193 6.4.3 Ultrasonication ................................................................................................ 195 6.4.4 Ultrasonication and dissolution by acid extraction ......................................... 198 xiv 6.5 Conclusion ............................................................................................................ 210 Chapter 7 Semi-empirical equation for determining the nanofiber pressure drop by considering the slip effect .............................................................................................. 211 7.1 Introduction .......................................................................................................... 211 7.2 Fibrous filter pressure drops .............................................................................. 215 7.3 Numerical simulation .......................................................................................... 222 7.3.1 Computational domain and cases .................................................................... 222 7.3.2 Flow field calculation ...................................................................................... 223 7.4 Results and discussion ......................................................................................... 226 7.5 Conclusion ............................................................................................................ 233 Chapter 8 Summary and Future works ...................................................................... 234 8.1 Summary and conclusion .................................................................................... 234 8.2 Future works ........................................................................................................ 237 Bibliography .................................................................................................................. 238 Appendix ........................................................................................................................ 281 xv List of Tables Table 2.1 Summary of statistical results for total number concentration of MeSNPs. .... 34 Table 2.2 Summary of statistical results for total volume concentration of MeSNPs. ..... 35 Table 2.3 Summary of sensor time constant (τ), and sensor response time (5τ) of the total number and volume concertation of MeSNPs. The sensor time constant (τ) is the sensor output to reach 63.2 % of its correlated data. Sensor response time (5τ) is the time for the sensor output to reach 99.3 % of its correlated data. ........................................................ 38 Table 3.1 Diffusion coefficient and Schmidt number with different particle sizes. ......... 59 Table 4.1 Comparison of Brownian diffusion effect and thermophoretic diffusion effect at different particle sizes. .................................................................................................... 104 Table 5.1 Schmidt number with different particle sizes. ................................................ 129 Table 5.2 Experimentally obtained particle penetration and deposition. ....................... 130 Table 6.1 The tested particle size of each different location (#1~#9) and applied voltage (Vd) of the experiment are in Figure 6.3e. ....................................................................... 172 Table 6.2 Experiment result of fluorescent nanoparticle deposition on a forked gas line experiment. Volume mode size was measured by SMPS. The measured value was determined by fluorescence signal. The calculated concentration was determined by using a correlation Equation (6.15). Deposition efficiency was calculated by comparing fluorescein nanoparticles concentration obtained in forked gas lines (CFT) and filters (Cfilter) solution data by using Equation (6.16). The averaged experimentally measured deposition results by using fluorescent nanoparticles were approximately 13.2%. ......................... 189 Table 6.3 The experiment result of resuspension after the pulsed air jet experiment. The two-stage of tube furnace system instead of the single-stage of tube furnace was employed for generating spherical 50 nm AgNPs, as shown in Figure 6.14a at the University of Minnesota (UMN). Pulsed air jet cleaning was performed as illustrated in Figure 6.17 at Applied Materials (AMAT). The estimated deposited nanoparticles were calculated by Equation (6.17). .............................................................................................................. 195 Table 6.4 Experiment result of resuspension by high power ultrasonication (U/S or WRS). It should be noticed that the total flow rate of the forked tube was set to 1.0 L/min (Re = 310) and the two-stage of tube furnace system instead of the single-stage of tube furnace xvi was employed for generating spherical 50 nm AgNPs as shown in Figure 6.14a. Internal surface high-power ultrasonication was performed as illustrated in Figure 6.18a at Applied Materials. The 1st U/S and 2nd U/S were performed on a plastic rack (Figure 6.18b) and a metal rack (Figure 6.18c), respectively. The estimated deposited nanoparticles were calculated as 5.62% by Equation (6.17).......................................................................... 198 Table 6.5 Cleaning process of each forked tube and evaluated cleanliness of forked tubes before particle deposition experiment. ............................................................................ 201 Table 6.6 AgNPs deposition results (Step 1 in Figure 6.20). ......................................... 202 Table 6.7 The resuspension results (Step 2 in Figure 6.20) of AgNPs in the internal surface of forked tubes by 200 W/in2 high power ultrasonication (1200 W and 78 kHz) which is depicted in Figure 6.18a. Forked tubes were filled with 7.5 mL of deionized water and sonicated twice for 15 minutes. ...................................................................................... 203 Table 6.8 Sample preparation for the remaining AgNPs in the internal surface of gas lines by acid extraction with 3 wt.% HNO3 (For Step 3 in Figure 6.20). ................................ 204 Table 6.9 Measured mass concentration of dissolved AgNPs solution extracted from each forked tube (Step 3 in Figure 6.20). The converted number of particles was calculated by the calibration curve, as shown in Figure 6.19 and Equation (6.20). Note: AgNPs were not deposited on the #20 forked tube. ................................................................................... 204 Table 6.10 Summary of 40 nm AgNPs deposition, resuspension, and dissolution results. The experimental deposition efficiency (ηdep,FT,MS), particle resuspension or removal efficiency (PREMS) was based on MS analysis, and particle resuspension or removal efficiency (PREcor) was based on correlation DE results. Particle DEs of estimated deposited particles based on correlation results and numerical results are 5.51%, and 2.67%, respectively. .................................................................................................................... 206 xvii List of Figures Figure 1.1 Typical particle defects scenario schematic in integrated circuits (ICs) (Martin Knotter and Wali, 2010). (e-: electron, S: source, D: drain, g: Gate) ................................. 3 Figure 1.2 Particle formation, transport, deposition, and filtration in the semiconductor manufacturing process. ....................................................................................................... 8 Figure 2.1 Experimental setup for detecting methyl salicylate vapors using the soft X- ray and the scanning mobility particle sizer. ..................................................................... 17 Figure 2.2 Effect of flow rate through soft X-ray chamber: (a) total volume concentration of generated MeS nanoparticles; (b) particle mode size of generated MeS nanoparticles. ........................................................................................................................................... 20 Figure 2.3 Total particle concentration and particle size distribution performed with MeS 201 ppbv under soft X-ray: (a) total particle volume concentration; (b) particle volume size distribution (nm3/cm3); (c) total particle number concentration; (d) particle number size distribution (#/cm3). Dashed lines represent a line separating the stage to explain the change of particle formation over time. The x-axis in (a), and (c) is the particle concentration, and the x-axis in (b), and (d) is the particle diameter with a lognormal scale. The y-axis indicates time. The particle volume and number size distributions are represented as colors in (b), and (d). .............................................................................................................................. 22 Figure 2.4 MeSNPs volume size distribution evolution performed with MeS 201 ppbv under soft X-ray. Mono-modal particle distribution continues to move towards the larger particle size and then changes to the bi-modal particle distribution MeSNPs particle formation and growth. ....................................................................................................... 24 Figure 2.5 Example experimental results of particle volume distribution performed with different MeS vapor concentrations for three hours with particle diameter on the log x-axis, time on the y-axis, and the particle volume size distribution via colors: (a) 22.5 ppbv; (b) 35.7 ppbv; (c) 63.9 ppbv; (d) 142 ppbv; (e) 201 ppbv; (f) 439 ppbv. ............................... 26 Figure 2.6 Averaged particle (a) number and (b) volume size distribution of example experimental results during 1~3 hours. ............................................................................. 28 Figure 2.7 Log-log regression of (a) total volume concentration, and (b) total number concentration as a function of MeS vapor concentration. ................................................. 31 xviii Figure 2.8 Variation of the soft X-ray MeS detection system for the total volume and number concentration on successive exposure to different MeS vapors (46.4-302 ppbv). Solid red and blue lines represent the total volume concentration and the total number concentration, respectively. The lines parallel to the x-axis are the total number and volume concentration predicted by Equations (2.6), and (2.7), respectively. The y-axis on the above and below figures has a lognormal and linear scale, respectively. ON or OFF represent whether the soft X-ray reaction is turned on or off. .......................................................... 37 Figure 3.1 Experimental schematic for measuring penetration efficiency of nanoparticles on a sharp-bent tube. ......................................................................................................... 51 Figure 3.2 Particle size distribution after classifying AgNPs aerosol flow by using a Nano- DMA. ................................................................................................................................ 51 Figure 3.3 Geometry of test-section of a sharp-bent tube. ............................................... 55 Figure 3.4 Numerically calculated velocity comparison between experimental results and numerical results of a smooth-bent tube: (a) velocity magnitude contour, (b) velocity profile at cross-section of 30o point and (c) velocity profile at cross-section of 60o point. ........................................................................................................................................... 56 Figure 3.5 Results of mesh independent test of a sharp-bent tube: (a) velocity magnitude contour results and (b) axial velocity results after a sharp-bent tube from 1 mm. ........... 57 Figure 3.6 Effect of Schmidt number on penetration efficiency with different Reynolds numbers: (a) Re = 200, (b) Re = 300, (c) Re = 500, (d) Re = 700, (e) Re = 1000 and (f) Re = 1500. .............................................................................................................................. 60 Figure 3.7 Effect of Reynolds number on penetration efficiency with different Schmidt numbers: (a) Sc = 25.46, (b) Sc = 70.37, (c) Sc = 137.27, (d) Sc = 278.12, (e) Sc = 618.14 and (f) Sc = 1085.31. ........................................................................................................ 63 Figure 3.8 Velocity magnitude and streamline in the midplane of a sharp-bent tube: (a) low Reynolds number (Re = 200) and (b) high Reynolds number (Re = 1000). .............. 65 Figure 3.9 Radial velocity and secondary flow streamline after a sharp-bent tube from 1 mm: (a) low Reynolds number (Re = 200) and (b) high Reynolds number (Re = 1000). 67 Figure 3.10 Penetration efficiency comparison of a straight tube and a sharp-bent tube and correlation results as a function of Peclet number. Symbols represent the experimentally obtained penetration efficiency for a sharp-bent tube. ...................................................... 69 xix Figure 3.11 Penetration efficiency comparison of a straight tube and a sharp-bent tube and correlation curve fitting curve as a function of Peclet number. Symbols represent the experimentally obtained penetration efficiency for a sharp-bent tube. ............................. 71 Figure 4.1 Schematic of the calculation domain and descriptions on a sharp-bent tube. 79 Figure 4.2 Evaluation of coagulation effect during penetrating the sharp-bent tube: (Left) Calculated normalized averaged particle size (=dp,avg(t)/dp,i=1); (Right) Calculated normalized particle concentration (=Cnum,i=1(t)/Cnum,i=1(t=0)). ......................................... 85 Figure 4.3 Algorithm for determining particle injection positions based on the aerosol mass flow rate. ........................................................................................................................... 88 Figure 4.4 Distribution of 0.1 million particles at the injection plane based on aerosol mass flow rate. ........................................................................................................................... 89 Figure 4.5 Schematic of the experimental setup for measuring nanoparticle deposition efficiency of nanoparticles on a sharp-bent tube. ............................................................. 91 Figure 4.6 Velocity magnitude and streamline in a sharp-bent tube at y = 0 surface (xz plane) for different Reynolds numbers: (a) Re = 100; (b) Re = 300; (c) Re = 500; (d) Re = 1,000. ............................................................................................................................... 94 Figure 4.7 Normalized velocity magnitude along the radial position in a smooth-bent tube obtained by the present numerical simulation (red line) and experimental work done by Enayet et al. (blue rectangle) under two different Reynolds number conditions (Enayet et al., 1982). .......................................................................................................................... 95 Figure 4.8 Axial velocity on a sharp-bent tube at various cross-sections (Ain-Aout, Bin-Bout, Cin-Cout, Din-Dout, Ein-Eout, and Fin-Fout) for different Reynolds numbers: (a) Re=100; (b) Re=300; (c) Re= 500; (d) Re=1,000. .............................................................................. 97 Figure 4.9 Radial velocity and secondary flow on a sharp-bent tube at various cross- sections (Ain-Aout, Bin-Bout, Cin-Cout, Din-Dout, Ein-Eout, and Fin-Fout,) for different Reynolds number: (a) Re=100; (b) Re=300; (c) Re= 500; (d) Re=1,000. ........................ 98 Figure 4.10 Secondary flow boundary layer thickness at Bin-Bout (surface at x = z), and Cin- Cout (surface at z = -1 mm) with various Reynolds numbers (Re = 100, 300, 500, and 1,000). ......................................................................................................................................... 100 Figure 4.11 Nanoparticle deposition efficiency on a sharp-bent tube for different Reynolds numbers: (a) Re = 500; (b) Re = 1,000; (c) Re = 1,500. ............................................... 102 xx Figure 4.12 Cumulative number of deposited particles on a sharp-bent tube according to the position at the x- and z-coordinate for different Reynolds numbers and different particle sizes: (a) dp = 1 nm; (b) dp = 3 nm; (c) dp = 5 nm; (d) dp = 10 nm. ............................... 106 Figure 4.13 Local deposition enhancement factor (LDEF) on a sharp-bent tube at each section for various Reynolds numbers and particle sizes. ............................................. 108 Figure 4.14 Particle deposition pattern right after the bending point, obtained by calculating relative deposition efficiency at various locations and particle sizes for different Reynolds numbers: (a) Re=100; (b) Re=300; (c) Re= 500; (d) Re=1,000. .....................110 Figure 5.1 Geometry of forked tube: (a) photo of a forked tube; (b) computational domain of forked tube; (c) schematic view of elbow connection (left) and union tee (right). .....118 Figure 5.2 Results of the grid-independent study. For considering the enhanced wall treatment, the dimensionless distance from the tube wall (y+) was set to one and the grid size of the first cell near the tube wall was selected as 34 m with a growth factor of 1.2 until the next fifth cell. All results from grid independent study showed that there is no significant difference. But, at first union tee, the symmetry of the flow velocity contour is slightly broken until Mesh 2 (1.61 million). From Mesh 3 (2.19 million), the velocity contour started not to be distorted. For getting more accurate results of particle penetration, the number of grids was chosen as 5.1 million. .............................................................. 121 Figure 5.3 Particle injection positions based on aerosol mass flow rate: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. ............................... 125 Figure 5.4 Experimental setup for measuring nanoparticle deposition efficiency on forked tubes. ............................................................................................................................... 127 Figure 5.5 Comparison of nanoparticle penetration efficiency on a forked tube at each outlet between numerical and experimental results: (a) Re=500; (b) Re=1000; (c) Re=2000. Lines represent the numerically calculated penetration efficiency on forked tubes. Symbols with error bars represent the experimentally obtained penetration efficiency on forked tubes. ......................................................................................................................................... 133 Figure 5.6 Comparison between numerical and experimental results for nanoparticle deposition efficiency in forked tubes: (a) Re = 500; (b) Re = 1000; (c) Re = 2000. Solid lines and open circular symbols with error bars represent the numerical and experimental deposition efficiency in a forked tube, respectively. ....................................................... 134 xxi Figure 5.7 Effects of union tee on flow streamlines and vortex cores: (left) Re = 370; (right) Re = 2000. Green regions represent the vortex cores with Q* = 0.1; grey lines represent the streamlines uniformly released from the union tee inlet; red lines represent the streamlines released from the surface with Q* = 0.8. ......................................................................... 136 Figure 5.8 Effects of elbow connection on flow streamlines and vortex cores: (left) Re = 370; (right) Re = 2000. Green regions represent the vortex cores with Q* = 0.1; grey lines represent the streamlines uniformly released from the elbow connection inlet; red lines represent the streamlines released from the surface with Q* = 0.8. ................................ 137 Figure 5.9 Particle penetration characteristics before first union tee with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. ................................................................................................................. 139 Figure 5.10 Particle penetration characteristics after first union tee with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. The red dotted line in (a) marks the particle-free zone. ........................ 141 Figure 5.11 Particle penetration characteristics before first elbow connection with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. ......................................................................................... 143 Figure 5.12 Particle penetration characteristics after first elbow connection for various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. ....................................................................................... 144 Figure 5.13 Particle penetration characteristics before second union tee with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. ......................................................................................... 145 Figure 5.14 Individual particle trajectory results of dp = 100 nm at first elbow connection. The initial position represents the particle position before passing through the first elbow connection (Figure 5.11). The position after passing the elbow connection represents the particle position after passing through the first elbow connection (Figure 5.12). Here, we can categorize the three different groups of particles: (Group 1) initial particle position near the tube wall (pale yellow), (Group 2) initial particle position with tube centerline (pale orange), and (Group 3) initial particle position between Group 1 and Group 2 (pale green). The arrow direction indicates the particle movement trend. ........................................... 146 xxii Figure 5.15 Particle penetration characteristics after second union tee with various particle sizes and Reynolds numbers: top diagrams (a, b, c) represent particles toward the outer outlet in Figure 5.1b; bottom diagrams (d, e, f) represent particles toward the inner outlet in Figure 5.1b; (a, d) particle distribution; (b, e) normalized particle concentration; (c, f) particle ID. ..................................................................................................................... 148 Figure 5.16 Particle penetration characteristics before second elbow connection with various particle sizes and Reynolds numbers: top diagrams (a, b, c) represent particles toward the outer outlet in Figure 5.1b; bottom diagrams (d, e, f) represent particles toward the inner outlet in Figure 5.1b; (a, d) particle distribution; (b, e) normalized particle concentration; (c, f) particle ID. ...................................................................................... 149 Figure 5.17 Particle penetration characteristics after second elbow connection with various particle sizes and Reynolds numbers: top diagrams (a, b, c) represent particles toward the outer outlet in Figure 1b; bottom diagrams (d, e, f) represent particles toward the inner outlet in Figure 1b; (a, d) particle distribution; (b, e) normalized particle concentration; (c, f) particle ID. ................................................................................................................... 151 Figure 5.18 Ratio of particles divided by second union tee and effect of particle initial location at the inlet of the forked tube with various particle sizes and Reynolds numbers. Particle ID number in the x-axis indicates the middle of a group of particle ID numbers, e.g., 2500 represents the particle ID from 1 to 5000, and 17500 represents the particle ID from 15001 to 20000. The contour of the inserted quadrant is a visualization of the resulting ratios. A and B outlets represent the outer and inner outlets, respectively. The darker the color, the more particles progress toward the outer outlet (A outlet) direction. ............. 153 Figure 5.19 Nanoparticle deposition efficiency on a forked tube as a function of Peclet number............................................................................................................................. 155 Figure 5.20 Nanoparticle deposition efficiencies for straight tube, sharp-bent tube (elbow connection), two consecutive sharp-bent tubes (2×sharp-bent tube), and forked tube as a function of Peclet number. .............................................................................................. 158 Figure 5.21 Penetration efficiency of different particle locations at the inlet of the forked tube with various particle sizes (dp = 3, 10, and 100 nm) and Reynolds number (Re = 370, 1000, and 2000). Section number 1 is the inlet of the forked tube (Figure 5.3); Section number 2 is the inlet of the first union tee (Figure 5.9); Section number 3 is the outlet of xxiii the first union tee (Figure 5.10); Section number 4 is the inlet of the first elbow connection (Figure 5.11); Section number 5 is the outlet of the first elbow connection (Figure 5.12); Section number 6 is the inlet of the second union tee (Figure 5.13); Section number 7 is the outlet of the second union tee (Figure 5.15); Section number 8 is the inlet of the second elbow connection (Figure 5.16); Section number 9 is the outlet of the second elbow connection (Figure 5.17). The blue solid line with a circle symbol represents the particle ID number from 1 to 5000; The light blue dashed line with a triangular symbol represents the particle ID number from 5001 to 10000; The orange dash-dotted line represents the particle ID number from 10001 to 15000; The red dash-dot-dotted line represented the particle ID number from 15001 to 20000. ...................................................................... 159 Figure 0.1 Geometry of forked tube (Dtube = 4.572 mm, A1 = 40.4 mm, A2 = 67.2 mm, A3 = 90.7 mm, B1 = 46.2 mm, and B2 = 23.5 mm). ............................................................. 167 Figure 6.2 Experiment setup for PSL nanoparticle deposition on 200 mm wafers by controlling electrophoresis. ............................................................................................. 170 Figure 6.3 PSL nanoparticle deposition results which are determined by the wafer surface scanner: (a) 102 nm raw data of 200 mm wafer full scanning result; (b) magnified wafer scanning results in controlled spot size; (c) particle deposition results in different size bin channel; (d) 102nm particle count of each size bin channel; (e) PSL 300, 600, 900 nm deposition results. ........................................................................................................... 171 Figure 6.4 (a) Examples of magnified images of Figure 6.3 and PSL 300 nm nanoparticle deposition results which are determined by the wafer surface scanner, (b) 90-degree bend tube at the aerosol deposition chamber inlet. .................................................................. 173 Figure 6.5 Experiment setup for 1.6 µm PSL particles to be directly deposited on 200 mm wafers. ............................................................................................................................. 174 Figure 6.6 (a) Particle removal force by air jet; (b) particle adhesion force; (c) free body diagram; (d) particle resuspension mechanisms: sliding, rolling, and lifting. ................ 178 Figure 6.7 Computational domain for numerically investigating impinging air jet. ..... 179 Figure 6.8 Numerically calculated velocity field of impinging air jet and validation results of friction velocity with various model and experimental results................................... 181 Figure 6.9 Particle resuspension experiment setup by using pulsed air jet: (a) experiment setup schematic; (b) a photo of experiment setup; mechanisms: (c) nozzle with a diameter xxiv of 2.38 mm. ..................................................................................................................... 182 Figure 6.10 Particle resuspension experiment before and after pulsed air jet result: (a) particle scatter diagram before pulsed air jet; (b) particle scatter diagram after pulsed air jet; (c) contour diagram before pulsed air jet; (d) contour diagram after pulsed air jet. . 183 Figure 6.11 (a) Schematic of fluorometer working mechanism. (b) Fluorescein sodium salt emission and excitation wavelength and fluorometer light excitation and emission filter wavelength. NB and SC refer to narrow band, and sharp-cut, respectively (Kwak et al., 2021a). ............................................................................................................................ 185 Figure 6.12 Comparison between fluorescence signal measured by fluorometer and fluorescent tracer concentration. The red solid line indicates the fitting curve results (Kwak et al., 2021a). ................................................................................................................... 186 Figure 6.13 (a) Fluorescent nanoparticle deposition on a forked gas line experiment setup; (b) fluorescent nanoparticle size distribution measured by SMPS; (c) fluorescent nanoparticle collecting method for upstream concentration. .......................................... 187 Figure 6.14 (a) Experiment setup for obtaining the large size of silver nanoparticle and comparing CPC and sp-ICPMS; (b) description of silver nanoparticle collecting method for measuring sp-ICPMS and SEM image of ENM and collected spherical silver nanoparticles; (c) Intercomparison results between CPC and sp-ICPMS. ..................... 191 Figure 6.15 Experiment setup for resuspension during clean air transport: (a) clean air test; (b) experiment set-up for silver nanoparticles resuspension test. ................................... 192 Figure 6.16 Experiment results of resuspension during clean air transport: (a) real-time cumulative particle number results; (b) Comparison of each experiment results between clean air test, baseline test, 1-hour resuspension test, and 9-hour resuspension test. ..... 193 Figure 6.17 Experiment setup for particle resuspension by using a pulsed air jet. ........ 194 Figure 6.18 Internal surface high-power ultrasonication for silver nanoparticle resuspension: (a) a photo of immersed forked tubes in high power ultrasonic bath with capped with red plastic caps; (b) a photo of the first high-power ultrasonic plastic rack to hold forked tubes; (c) a photo of the second high power ultrasonic plastic rack to hold forked tubes. .................................................................................................................... 196 Figure 6.19 40 nm silver nanoparticles calibration results for acid extraction performed by Applied Materials. For 3 wt.% HNO3. ............................................................................ 199 xxv Figure 6.20 Experiment procedures for evaluating particle deposition rate by aerosol method, particle resuspension rate by high power ultrasonication, and dissolution rate by acid extraction. ................................................................................................................ 200 Figure 6.21 Particle resuspension results (Step 2 in Figure 6.20) of AgNPs in the internal surface of forked tubes by 200 W/in2 high power ultrasonication (1200 W and 78 kHz). Forked tubes were filled with 7.5 mL of deionized water and sonicated twice for 15 minutes. The raw data of these results were shown in Table 6.7. .................................................. 203 Figure 6.22 Particle dissolution results (Step 3 in Figure 6.20) of AgNPs in the internal surface of forked tubes by 3 wt.% HNO3. Each dissolution method were described in Table 6.8. The converted number of particles was calculated by the calibration curve, as shown in Figure 6.19 and Equation (6.20). The raw data of these results were shown in Table 6.9. ......................................................................................................................................... 205 Figure 6.23 Estimated number of removed particles was evaluated by (1) ultrasonication and (2) the sum of ultrasonication and acid extraction methods. ................................... 207 Figure 6.24 Comparison of particle deposition efficiency on forked tubes of each different evaluation method. .......................................................................................................... 208 Figure 6.25 Particle removal or resuspension efficiency (PRE) is based on the different particle deposition efficiency by ultrasonication. ........................................................... 209 Figure 7.1 Characteristics of the airflow through filter fibers according to Knudsen number (Bian et al., 2018; Xia et al., 2018; Zhao et al., 2016). ................................................... 214 Figure 7.2 Reciprocal of dimensionless permeability as a function of solidity with various experimental data, Kuwabara’s model, and Davis’s model. ........................................... 218 Figure 7.3 Reciprocal of dimensionless permeability as a function of solidity with various experimental data, Davis’s model, and Brown’s model (30, 300, and 3000 nm). .......... 220 Figure 7.4 Reciprocal of dimensionless permeability as a function of solidity with various experimental data, Davis’s model, and Bian’s empirical model (30, 300, and 3000 nm). ......................................................................................................................................... 222 Figure 7.5 (a) Schematic of boundary conditions ; (b) Velocity field for airflow through nanofiber filter media. ..................................................................................................... 225 Figure 7.6 (a) Numerically calculated reciprocal of dimensionless permeability (fNum (α, df)) as a function of fiber diameters with various solidities; (b) Comparison factor (ξ), i.e., xxvi fNum (α, df) / fDavis (α), as a function of Knudsen number with various solidities. ........... 227 Figure 7.7 Reciprocal of dimensionless permeability as a function of solidity with various experimental data, and the present numerical calculation results (0.005 ≤ α ≤ 0.100, and 30 ≤ df ≤ 300 nm). ................................................................................................................ 228 Figure 7.8 Reciprocal of dimensionless permeability as a function of solidity with var ious experimental data, Davies model, and the present model (30, 300, and 3000 nm). ......................................................................................................................................... 230 Figure 7.9 Comparison between each different model: (a) Davies model; (b) Brown model; (c) Bian model; (d) Present model. The x-axis is the experimentally or numerically determined reciprocal of dimensionless permeability. The y-axis is the reciprocal of dimensionless permeability by using (a) Equation (7.8), (b) Equation (7.10), (c) Equation (7.12), and (d) Equation (7.18). ...................................................................................... 232 1 Chapter 1 Introduction 1.1 Background Due to the extraordinary size-dependent physicochemical properties of nanomaterials, engineered nanomaterials have been widely applied in various fields including semiconductors (Jiang et al., 2019; Morales and Lieber, 1998; Saha et al., 2018; Wang et al., 2017), energy (Ma and Zou, 2018; Peng et al., 2018; Sheikholeslami et al., 2018; Watanabe et al., 2018), filtration (Kang et al., 2019; Kim et al., 2017; Lee et al., 2018, 2017b) and health (Jakobsson et al., 2016; Lapresta-Fernández et al., 2012; Lee et al., 2015; Shi et al., 2004; Ye et al., 2022). Although these engineered nanomaterials are beneficial to the development of nanotechnology, additional concerns have been raised that unwanted nanoparticles which are unintentionally released into the environment during the process of manufacturing, usage, and disposal may have adverse direct or indirect effects on living organisms including humans (Kaegi et al., 2008; Lapresta-Fernández et al., 2012; Schmid and Stoeger, 2016; Shi et al., 2004). Moreover, preventing and controlling particle contaminations is essential in the semiconductor manufacturing process to increase 2 semiconductor yield. Examples of these unwanted nanoparticles in the semiconductor industry are airborne molecular contamination (AMC), haze, and deposited nanoparticles. Also, manufacturing equipment like chemical vapor chambers and epitaxial growth reactors can generate lots of nanoparticles (D. Kim et al., 2016; Kim et al., 2018; Lee et al., 2021). Therefore, great efforts have been made to maintain a particle-free environment (such as cleanrooms) using high-efficiency particulate air (HEPA) filters and ultra-low particulate air (ULPA) filters in the semiconductor manufacturing process (Donovan, 1990; C. Kim et al., 2016b; S. C. Kim et al., 2020, 2006). 1.1.1 Particle contamination State-of-the-art fabrication facilities such as semiconductors manufacturing plants have required stringent standards to control particulate and gaseous contaminants in cleanrooms to improve product yield since the deposited nanoparticles on masks or wafers can cause defects in semiconductor chips (Hoefflinger, 2012; Hu et al., 2017; Kim et al., 2015, 2018; D. Kim et al., 2016; Kwak et al., 2018b; Yook et al., 2008). Microprocessor manufacturing in the semiconductor industry consists of several manufacturing process steps. The manufacturing process steps which can be sensitive to particle contamination can be generally categorized as shown in Figure 1.1 (Martin Knotter and Wali, 2010). One of the most prevalent defects scenarios in integrated circuits (ICs) is Particles in trenches or holes as shown in Figure 1.1a. The deposited particles between the two metal layers disrupt the conductivity and cause defects in ICs. The simple transistor schematic diagram is described in Figure 1.1b. If particles were deposited on the gate area, it causes poor 3 transistor performance. Figure 1.1c shows a ghost pattern in the final product even though deposited particles are resuspended or removed. Compared to particles in the mask case, particles inhibit the etching process on a patterned wafer, resulting in a short circuit. Figure 1.1 Typical particle defects scenario schematic in integrated circuits (ICs) (Martin Knotter and Wali, 2010). (e-: electron, S: source, D: drain, g: Gate) 1.1.2 Particle formation To maintain a particle-free environment inside the semiconductor manufacturing facilities, outdoor air is purified by a series of aerosol filtration systems using high- efficiency particulate air (HEPA) filters and ultra-low particulate air (ULPA) filters (a) Particles in trench (b) In-film particles Clean Dirty (c) Particles as mask (d) Patterning deviations Clean Dirty Insulator Particle Conductor Semiconductor e- e- +++ G S D G S D+++ e- Short Block Block Block 4 (Donovan, 1990; C. Kim et al., 2016b; S. C. Kim et al., 2020, 2006). However, the problem of contamination at the molecular level, known as AMCs (Airborne Molecular Contaminations), arises from gaseous pollutants, outgassing from construction materials, outgassing from particulate matter (PM2.5 or PM10), or solvents (wet chemicals) in particle- free cleanrooms during the semiconductor manufacturing process (Billet et al., 2007; Dallas et al., 2002; C. Kim et al., 2016b; Kim et al., 2019, 2015). According to Semiconductor Equipment and Materials International, AMCs can be categorized into acid, base, condensable, and dopant (Donovan, 2001; Kim et al., 2015; Semiconductor equipment and materials international (SEMI), 1996). Despite the ultra-low concentration (e.g., part per billion (10−9) or part per trillion (10−12)) of volatile and condensable AMCs, it can cause particle and haze contaminations on wafers or photomasks when AMCs are exposed to shorter wavelength light sources such as deep ultraviolet (DUV) laser (e.g., 248 nm krypton-fluoride (KrF) excimer laser, 193 nm argon-fluoride (ArF) excimer laser), or 13.5 nm extreme ultraviolet (EUV) laser (Chuang and Chang, 2013; Daly, 2015; Den et al., 2006; Gordon et al., 2005; Ito and Okazaki, 2000; C. Kim et al., 2020; Kim et al., 2015; Lobert et al., 2018, 2010, 2009; Otto, 2015; Pic et al., 2010; Weineck et al., 2010). By using the current start-of-the-art EUV lithography system, which is developed by ASML, Intel, Samsung Electronics, and TSMC try to fabricate smaller nodes (up to ~2 nm). Smaller transistors operate faster and require less power. For example, the optimized 3nm process obtains 45% reduced power usage, 23% improved performance, and 16% smaller surface area compared to the 5nm process (SamsungNewsroom, 2022). Therefore, it is very important to understand the gas-to-particle conversion process under the energy of the soft X-ray, which is similar to EUV wavelengths to prevent AMCs in the semiconductor 5 manufacturing process, resulting in minimizing the defects on chips. 1.1.3 Particle transport and deposition The loss of manufactured nanoparticles during the manufacturing process should be reduced for obtaining a high yield of production. Meanwhile, gas-based nanofluids are considered a potential candidate for improving the heat transfer performance in gas-cooled nuclear power plants (Williams, 2015) as well as solar energy collectors (de Risi et al., 2013; Potenza et al., 2017). Moreover, the enhancement of heat transfer performance in liquid-based nanofluids has been reported by various researchers (Cai et al., 2020; Haridas et al., 2015; Hashimoto et al., 2020; Rajput and Srivastava, 2016; Srinivas Rao and Srivastava, 2014). However, deterioration of heat transfer performance occurs when nanoparticles settle and form a layer on the surface, resulting in reduced heat transfer efficiency (Das et al., 2006), similar to fouling in heat exchangers (Wang et al., 2019; Zhang et al., 2019) or heat sinks (Oguntala et al., 2018; Sarafraz et al., 2017). On the other hand, technological advances in the semiconductor industry have led to reduced minimum pitch size and increased wafer size (Hu et al., 2016; Kwak et al., 2018b; Lallart et al., 2018). As a result, the size of particles that causes semiconductor failure has decreased, and thus controlling particle contamination attracts great attention (Cho et al., 2019; D. Kim et al., 2016; Sato et al., 2003; Woo et al., 2018). One example of particle contamination that may occur during a semiconductor process is when deposited particles in a pipeline are resuspended and cause secondary deposition/contamination on the wafers (C. Kim et al., 2016a; Kim et al., 2015; Ziskind, 2006). The interaction of several effects on nanoparticles 6 and fluid flow, including Brownian diffusion, drag force, and secondary flow, determines the nanoparticle transport characteristics such as deposition on tubular walls or in branched regions (Kwak et al., 2020; Shi et al., 2004). Transport systems for these applications are generally composed of complicated tubing systems with several branched structures or inlets/outlets to improve the process efficiency (Ho et al., 2020; Lyu et al., 2020; Patil et al., 2020; Shi et al., 2004; Shui et al., 2018) and with consisting of bent tubes and finite elbow tubes for effective utilization of limited space. Therefore, it is imperative to carefully investigate fluid flow characteristics, particle deposition, and penetration during nanoparticle transport to improve production yields and quality in various applications. Many researchers have studied nanoparticle deposition or penetration in a straight tube (Gormley and Kennedy, 1975; Ingham, 1991, 1984; Martonen et al., 1996). Nanoparticle transport on a straight tube can be easily predicted owing to its simple geometry; however, their analytical solution is not suitable in many realistic applications that consist of curved pipe systems or branched structures in which a secondary flow effect appears, resulting in complex particle motion (Kwak et al., 2020; Olin and Dal Maso, 2020; Wang et al., 2002; Yook and Pui, 2006; Zhao et al., 2020). 1.1.4 Particle filtration PM1.0, PM2.5, and PM10 indicate particulate matter (PM) less than 1.0, 2.5, and 10 μm, respectively. U.S. Environmental Protection Agency (USEPA) established the first standard for PM2.5 due to concern over the health effects of fine particles in the ambient environment (Pui et al., 2014). To remove the large size of particles like PM2.5, and PM10, 7 with large inertia, an inertial particle separator, e.g. cyclone separator, zigzag separator, and impactor, can be employed (Cheon et al., 2017; M.-W. Kim et al., 2021; Kim et al., 2013; Lim et al., 2021; Noh et al., 2020; Park et al., 2015). However, nano-sized particles like ultrafine particles (particulate matter less than 0.1 μm) or PM1.0 with low inertia are difficult to remove by using inertial particle separator systems. Therefore, the filter media are widely used for removing ultrafine particles or PM1.0 due to the effective removal of PM (Kang et al., 2019; S. C. Kim et al., 2020). In addition to this, under the current COVID- 19 pandemic situation, the importance of respirators using filter media has been proven for preventing SARS-CoV-2 virus transmission (Ou et al., 2020; Pei et al., 2020). To prevent particle contamination in the semiconductor manufacturing process, first of all, it is necessary to remove not only the air introduced from the external environment but also the particles generated indoors. The surest way to remove particles is to use HEPA or ULPA filters. However, air filter media needs to be denser as well as thicker to enhance particle collection efficiencies on filter media, which leads to large differential pressure between the upstream and downstream of the filter media, thus resulting in increased operating costs (S. C. Kim et al., 2020). Nanofiber filter media which consists of nanometer-scale fiber has been introduced and studied for reducing the pressure drop across the filter media, (i.e. reducing the operating cost) as well as increasing particle collection efficiencies (Choi et al., 2017; Leung et al., 2009). However, predicting the pressure drop of nanofiber media which causes slip flow effect on nano-sized fiber has not been yet established. Therefore, the new model should be developed to calculate the pressure drop easily and analytically across nanofiber filter media. 8 1.2 Research objectives As shown in Figure 1.2, to control and reduce particle contamination in the semiconductor manufacturing process, particle formation, transport, deposition, and filtration studies should be simultaneously investigated. The objectives of this study were to 1) demonstrate particle formation in a particle-free environment, 2) investigate particle deposition and transport characteristics in commercial gas pipelines, and 3) present a new analytical equation for calculating the pressure drop of nanofiber filter media. Figure 1.2 Particle formation, transport, deposition, and filtration in the semiconductor manufacturing process. Particle Formation Particle Transport Particle Deposition + (T c o ld ) − (T h o t ) Ground (+) Particle Gravity Air flow (Particle direction) Drag Electrostatic Thermophoretic + Diffusion Particle Filtration VOCs Nucleation Accumulation Particle-free (Gas vapor) Particle formation 9 1.3 Dissertation outline This dissertation is organized in the following order. In Chapter 1, a brief review of the research backgrounds and objectives is described. For the rest of the dissertation, each chapter contains a separate manuscript that has been published, is under review, or is in preparation. In Chapter 2, the formation of nanoparticles of volatile organic compounds in a particle-free environment by soft X-ray irradiation is described. The volatile organic compound used in this study is Methyl Salicylate. The studies described in this chapter were financially supported by US ARMY. In Chapters 3-5, nanoparticle deposition and penetration characteristics on gas pipelines are described. To be specific, nanoparticle penetration efficiency on a sharp-bent tube (elbow connection) was systematically measured through the experiment. The correlation curve for predicting the nanoparticle penetration or deposition efficiencies is reported in Chapter 3. In Chapter 4, nanoparticle deposition location and pattern on a sharp-bent tube and numerical analysis method are discussed. In Chapter 5, nanoparticle penetration characteristics in a forked tube are presented. Nanoparticle penetration efficiencies on different tube structures, e.g., straight tube, sharp-bent tube (elbow connection), and forked tube, are compared. In Chapter 6, nanoparticle resuspension or removal efficiencies of pulsed air jet and ultrasonication are discussed. In Chapter 7, a semi-empirical correlation for determining the pressure drop of linear nanofiber is suggested. 10 Chapter 2 Nanoparticle formation from Volatile Organic Compounds (VOCs) by the Soft X-ray irradiation 2.1 Introduction Due to the technological innovation in nanotechnology and the demands of the market, the integration density of devices on a silicon chip has dramatically increased for over five decades, following Moore’s law which is the historical trend prediction that the number of transistors on an integrated circuit will approximately double every two years. The performance of semiconductors has significantly improved through the use of advanced photolithography techniques which transfer smaller patterns from a mask to a silicon wafer (Ito and Okazaki, 2000). Outdoor air is purified by a series of aerosol filtration systems using high- efficiency particulate air (HEPA) filters and ultra-low particulate air (ULPA) filters (Donovan, 1990; C. Kim et al., 2016b; S. C. Kim et al., 2020, 2006) to keep a particle-free environment inside the semiconductor manufacturing facilities. However, the problem of contamination at the molecular level, known as AMCs (Airborne Molecular 11 Contaminations), arises from gaseous pollutants, outgassing from construction materials, outgassing from particulate matter (PM2.5 or PM10), or solvents (wet chemicals) in particle- free cleanrooms during the semiconductor manufacturing process (Billet et al., 2007; Dallas et al., 2002; C. Kim et al., 2016b; Kim et al., 2019, 2015). When AMCs are exposed to shorter wavelength light sources such as deep ultraviolet (DUV) laser (e.g., 248 nm krypton-fluoride (KrF) excimer laser, 193 nm argon-fluoride (ArF) excimer laser), or 13.5 nm extreme ultraviolet (EUV) laser, AMCs can form particle or haze contaminations on wafers or wafers, despite the ultra-low concentration (e.g., part per billion (10−9) or part per trillion (10−12)) of volatile and condensable AMCs (Chuang and Chang, 2013; Daly, 2015; Den et al., 2006; Gordon et al., 2005; Ito and Okazaki, 2000; C. Kim et al., 2020; Kim et al., 2015; Lobert et al., 2018, 2010, 2009; Otto, 2015; Pic et al., 2010; Weineck et al., 2010). Nowadays, the major semiconductor manufacturing companies (including Intel Corporation, Samsung Electronics Co., Ltd., and Taiwan Semiconductor Manufacturing Company) try to fabricate smaller nodes (up to ~2 nm) by using the current start-of-the-art EUV lithography system, which is developed by ASML. This is because smaller transistors operate faster and require less power. For example, the Optimized 3nm process obtains 45% reduced power usage, 23% improved performance, and 16% smaller surface area compared to the 5nm process (SamsungNewsroom, 2022). Therefore, it is very important to understand the gas-to-particle conversion process under the energy of the soft X-ray, which is similar to EUV wavelengths to prevent AMCs in the semiconductor manufacturing process, resulting in minimizing the defects on chips. In addition to semiconductor applications, gas-to-particle conversion principles can be applied in real-time volatile organic compounds (VOCs) detection technology (C. 12 Kim et al., 2020; Kim et al., 2019, 2015). For example, Chemical warfare agents (CWAs) were developed and used during World War I (1914-18), resulting in tens of thousands of deaths and casualties (Stockholm International Peace Research Institute (SIPRI), 1971; Szinicz, 2005). Agent Orange was utilized in the Vietnam War (1962-1971) for defoliating forests, but, later, caused adverse health effects on the population (Pitschmann, 2014), Sulphur mustard was employed in the Iran-Iraq war (1980-1988), resulting in more than 100,000 people to be poisoned (Gupta, 2009; Mangerich and Esser, 2014). Even though the Chemical Weapons Convention, which aims to remove weapons of mass destruction, was ratified in 1997, rockets containing the chemical agent Sarin were used to kill thousands of people during the Syrian Civilian War (2013) (Dolgin, 2013). Because the CWAs did not target only military forces but also killed civilians who were not equipped for protecting themselves, the impact of the CWAs during the war was extremely terrible. However, detecting and removing the CWAs were very difficult during the war. Therefore, it is necessary to develop the CWAs detection method for protecting an unspecified number of the general public as well as the military forces. Gas chromatography-mass spectrometry (GC-MS) has been widely utilized to analyze VOCs for several decades (Black et al., 1994; Kientz, 1998). GC is frequently used as a separation technique, which conjuncts with various ionization methods using flame, photo, and thermal desorption. The composition of the compounds separated from the chemical agent containing samples through GC is determined by MS. Gas chromatography-tandem MS (GC-MS/MS) is also used to enhance the detection capability (Canosa et al., 2007b, 2007a). Despite several benefits of GC-MS or GC-MS/MS, these methods require a chemical derivatization step to make samples suitable for GC analysis, 13 which makes it time-consuming, and labor-intensive (Ao et al., 2017; Chen et al., 2018; Špánik and Machyňáková, 2018). Furthermore, the expensive instrumentation and complexity of the analysis procedure prevent the use of GC-MS or GC-MS/MS from real- time measuring CWAs on battlefields or public places (Fang and Ramasamy, 2015; Park et al., 2019). Because of the hazardous properties of the CWAs, analyzing and investigating CWAs is highly dangerous. For these reasons, CWAs simulants which are chemical analogs with similar physicochemical properties have been employed to investigate the CWAs (Lafuente et al., 2020). Even though each simulant can only mimic certain aspects of the reactivity of the specific agent as well as the results obtained by using the simulants are not directly related to the target chemical agent, using the simulant makes it easier to isolate the variables that affect the agent chemistry and safer to investigate the properties of the CWAs. Sulfur mustard was particularly the most dangerous chemical agent, triggering more casualties than the total casualties of all other CWAs (Black, 2016). Methyl salicylate (MeS) is considered one of the sulfur mustard simulants and is classified as a volatile organic compound (VOC) with a benzene ring. Fang et al. (Fang et al., 2016) developed a bi-enzyme-modified electrode sensor for detecting MeS through three steps: hydrolyzation using potassium hydroxide to form salicylate and methanol, production of hydrogen peroxide, and electron transfer from the electrode to hydrogen peroxide. Park et al. (Park et al., 2019) developed a surface-enhanced Raman spectroscopy (SERS) substrate with silver nanoparticles for the determination of MeS. However, these works (Fang et al., 2016; Park et al., 2019) are not suitable for real-time detection or monitoring of the amount of MeS in the air, because it is necessary to dissolve MeS in water and analyze samples in the 14 liquid phase, and too many procedures are needed for analysis by field technicians. The gas-to-particle conversion is often observed in the formation of secondary organic aerosols (SOAs) from hydrocarbon mixtures (HCs), sulfur oxides (SOx), and nitrogen oxides (NOx) in the atmosphere (Hildebrandt et al., 2009; C. Kim et al., 2016a; Kulmala et al., 2004; Maskey et al., 2016; Zheng et al., 2014). For example, Fritz Went (Went, 1960) reported that organic vapors in the air can condense to submicroscopic particles when a strong beam of light, e.g. UV, passes through the air. In this study, we developed the detection method for MeS molecules in the air by using soft X-ray (in which energy per photon is bigger than UV) and aerosol measurement techniques. The aromatic chemical compounds which have the benzene ring are well detected by the soft X-ray- assisted detection method which converts gas vapors to nanoparticles through the photochemical processes (C. Kim et al., 2016b). As discussed by Seinfeld and Pandis, the primary step of the photochemical reaction of MeS may be written as (Seinfeld et al., 1998): MeS + hν →MeS* where MeS* is an electronically excited state of the molecule. The excited molecule MeS* may subsequently react: Dissociation MeS* → B1 + B2 Direct Reaction MeS* + B → C1 + C2 Collisional deactivation MeS* + M → MeS + M Ionization MeS* → MeS+ + e 15 The direct reaction may lead to the formation of a molecule with a high enough concentration and a low enough equilibrium vapor pressure that particles are formed by homogeneous nucleation. It is also possible that multiple condensable reactions could be formed, polymerization-type reactions could occur or ion-induced nucleation could occur from the reaction sequence given above. The specific mechanism is not currently known for MeS. In this chapter, by mimicking the gas-to-particle conversion process using the soft X-ray, which wavelength is similar to EUV wavelengths, the number and volume concentration of MeS was determined. To our best knowledge, there is no study related to quantifying CWAs simulants in the air through converting gas-to-particles and aerosol instruments. Furthermore, we expect that this study could be also applied in bio- engineering fields since MeS has been considered a suitable biomarker for signaling pathogenic injections and infestation (Fang et al., 2016; Park et al., 2019). 2.2 Experimental methodology Figure 2.1 shows the experimental setup for detecting methyl salicylate vapors using a soft X-ray and scanning mobility particle sizer. The compressed air was dehumidified and purified through calcium sulfate (DH, CaSO4), granular activated carbon (GAC), and a high-efficiency particulate air filter (HEPA). The purified air carried MeS vapors released from a permeation tube device (Methyl Salicylate, CAS no. 119-36-8, PD- 3160-CR, VICI Metronics Inc., WA, USA) which had a permeation rate of 3000 ng/min 16 (PRref) at 70 oC (Tref), and temperature of the permeation tube device was controlled by a temperature controller (Dynacalibrator, Model 150, VICI Metronics Inc., WA, USA) as 50 oC or 70 oC with an accuracy of ± 0.01oC. The flow rate through the permeation tube device (Qp) was fixed as 0.4 L/min, and the dilution flow rate (Qd) was controlled as 2.0 ~ 10.0 L/min for adjusting MeS vapor concentration ([MeS]). The permeation rate (PR) was determined as follows (Susaya et al., 2012, 2011). log 𝑃𝑅 = log 𝑃𝑅𝑟𝑒𝑓 + 𝛼(𝑇 − 𝑇𝑟𝑒𝑓), (2.1) where PR is the permeation rate in ng/min, α is the temperature coefficient with the value of 0.03 for high-emission tubes, and T is the temperature of the permeation tube device. The subscript of ref represents the reference. The MeS vapor concentration ([MeS]) was calculated as follows. [MeS] = 𝑃𝑅 ∙𝐾 𝑄 , (2.2) where [MeS]vapor is the gas standard concentration in ppmv (parts-per-million by volume, 10-6), PR is the permeation rate in ng/min, K is the molar constant with a value of 0.161 L/g for MeS, and Q is the total flow rates in cm3/min, i.e., Q=Qp+Qd. The concentration range of MeS studied here is from about 20 ppbv to 400 ppbv. 17 Figure 2.1 Experimental setup for detecting methyl salicylate vapors using the soft X- ray and the scanning mobility particle sizer. The diluted MeS vapor concentration was introduced to a soft X-ray chamber. The introduced flow rates into the soft X-ray chamber were controlled as 0.5 ~ 2.0 L/min. The overflowed flow was discharged into the air which was purified by activated carbon filters (ACF, Model 8800-12-000, Parker Balston, MA, USA). The soft X-ray chamber was fabricated in the form of a cylinder with a diameter of 127 mm, and a height of 203 mm. In the soft X-ray chamber, a 10 keV soft X-ray ionizer (Model SXN-10F, SUNJE, Busan, Republic of Korea) with a power controller (Model SXC-10, SUNJE, Busan, Republic of Korea) was employed for assisting gas-to-particle conversion through the photochemical processes. The generated nanoparticle size distribution was measured by a scanning mobility 18 particle sizer (SMPS) consisting of a nano-differential mobility analyzer (Nano-DMA, Model 3085, TSI, MN, USA), an electrostatic classifier (Model 3080, TSI, MN, USA), and an ultrafine condensation particle counter (UCPC, Model 3776, TSI, MN, USA). The aerosol flow rate and sheath air flow rate through the Nano-DMA were automatically controlled by the electrostatic classifier and set to be 0.3, and 3.0 L/min, respectively. The applied voltage to the Nano-DMA ranges from 10.7 to 9933.1 V, and the corresponding nanoparticle size is 4.53 to 165.5 nm. The scanning, retracing, and purging times for the SMPS measurements were set to 104, 6, and 10 sec, respectively. Because most of the generated nanoparticles are sub-100 nm, the nanoparticle concentration was corrected by considering particle loss due to diffusion based on the analytical solution of nanoparticle penetration efficiency obtained by Gormley and Kennedy (Gormley and Kennedy, 1975). It is worthwhile to mention that the whole system should be carefully controlled. If one of the components in the system is contaminated by other chemicals, e.g. super glue or cutting oil, this component was placed in an oven at 150°C over 72 hours to prevent outgassing. In addition, Kim et al reported that the soft X-ray assisted detection method also can detect some alcohols and aromatic components (C. Kim et al., 2016b). However, it should be noted that it is not reported whether other interferants like terpenes, or the many unsaturated molecules, are detected by the soft X-ray assisted detection method. Here, the authors would like to mention that the results might be highly affected by the presence of interferant gases, resulting in providing false-positive readings. For example, in a preliminary experiment that was carried out immediately after a few days of fabricating the soft X-ray chamber, we found that lots of nanoparticles were generated when the soft X- ray was turned on, even though no MeS was added, and only clean air was introduced. This 19 was probably because the cutting oil that was used when fabricating the chamber remained in the chamber. Moreover, even when compressed air was supplied by recycling the pipe used in other experiments, we also confirmed that lots of nanoparticles were generated when we turned on the soft X-ray. 2.3 Results and discussion To investigate the effect of reaction time through the soft X-ray chamber, the flow rates through the soft X-ray chamber were changed to 0.5, 1.0, 1.4, and 1.8 L/min, as shown in Figure 2.2. We obtained MeS vapor concentration as 201 ppbv (parts-per-billion by volume, 10-9) by controlling the temperature of the MeS permeation tube device as 50 oC, and the additional flow rate as 2.0 L/min. In general, when the flow rates through the soft X-ray chamber increase, the reaction time inside the soft X-ray chamber is reduced because the bulk residence time of MeS vapors inside the chamber decreases. It should be noticed that the investigation of volume concentration is more reasonable rather than one of number concentration, especially varying the reaction time, because the soft X-ray photochemical process is a mass-based conversion process (C. Kim et al., 2016b; Kim et al., 2015). As shown in Figure 2.2a, the volume concentrations of MeS nanoparticles (MeSNPs) linearly decrease with the increased flow rates through the soft X-ray chamber. Furthermore, particle mode size, i.e., the highest peak seen in particle size distribution, decreases when the reaction time increases, as depicted in Figure 2.2b. These results imply that it is important to choose the appropriate flow rates through the soft X-ray chamber depending on MeS vapor concentrations. In this study, the flow rates through the soft X-ray chamber 20 were fixed at 0.5 L/min, for detecting the ppbv-level of MeS vapor concentrations. Figure 2.2 Effect of flow rate through soft X-ray chamber: (a) total volume concentration of generated MeS nanoparticles; (b) particle mode size of generated MeS nanoparticles. 21 The particle volume size distribution was measured as time changed by using the SMPS, to investigate the conversion MeS vapor-to-particle phenomena inside the soft X- ray chamber. Before starting the particle volume size distribution measurement, a fixed MeS vapor concentration was injected into the soft X-ray chamber without turning on the soft X-rays for a sufficient time to obtain a steady result. After 4 minutes of particle volume size distribution measurement, the soft X-ray was turned on Figure 2.3 represents the total particle concentration and particle size distribution performed with MeS 201 ppbv under a soft X-ray. We divide the particle formation stage as (0) particle-free mode, (1) nucleation mode, (1)+(2) transition mode with nucleation and surface growth, (2) accumulation mode with surface growth and possibly coagulation, and (3) stable mode which is separated by dashed lines, as shown in Figure 2.3. There will also be evaporation of smaller particles by evaporation from the Kelvin effect. 22 Figure 2.3 Total particle concentration and particle size distribution performed with MeS 201 ppbv under soft X-ray: (a) total particle volume concentration; (b) particle volume size distribution (nm3/cm3); (c) total particle number concentration; (d) particle number size distribution (#/cm3). Dashed lines represent a line separating the stage to explain the change of particle formation over time. The x-axis in (a), and (c) is the particle concentration, and the x-axis in (b), and (d) is the particle diameter with a lognormal scale. The y-axis indicates time. The particle volume and number size distributions are represented as colors in (b), and (d). 23 To simplify and analyze the particle formation phenomena, a concept of a general dynamic equation (GDE) was introduced as follows (Prakash et al., 2003). 𝐽 = 𝑑𝑁 𝑑𝑡 | 𝑁𝑢𝑐𝑙 + 𝑑𝑁 𝑑𝑡 | 𝐴𝑐𝑐𝑢 , (2.3) where J is the nucleation rate, N is the particle concentration, and t is time. The subscript of Nucl, and Accu represent the nucleation and accumulation, respectively. At (0) particle- free mode, there is no particle formation because the soft X-ray is turned off. At (1) nucleation mode (~0.1h), MeS vapor begins to react with the soft X-ray producing a range of molecular species from which the particles start to be formed. Most generated MeSNPs are in sub-10nm at the very early stage of nucleation mode, and the nucleation rate increases rapidly, as shown in Figures 2.3c, and 2.3d. At (1)+(2) transition mode with nucleation and surface growth (~0.2h), even though the total number concentration starts to decrease, the total volume concentration keeps increasing. This could result from the evaporation of the smallest MeSNPs or from the coagulation of the smallest MeSNPs with the largest. Therefore, the particle mode size keeps increasing over time, as shown in Figures 2.3b, and 2.3d. At (2) accumulation mode with surface growth and possibly coagulation (~0.3h), the nucleation rate is almost unchanged, the particle mode size keeps increasing as illustrated in Figure 2.3b. This phenomenon is a very similar trend which is a so-called ‘banana’ reported by Ye et al.’s work (Ye et al., 2019). Mono-modal particle distribution continues to move towards the larger particle size and then changes instantaneously to the bi-modal particle distribution at the end of accumulation mode (~0.5h), as shown in Figure 2.4. The particle population balance is then stabilized and introduced into (3) stable mode (~0.6h). 24 Figure 2.4 MeSNPs volume size distribution evolution performed with MeS 201 ppbv under soft X-ray. Mono-modal particle distribution continues to move towards the larger particle size and then changes to the bi-modal particle distribution MeSNPs particle formation and growth. The temperature of the permeation tube device and the dilution flow rates were adjusted to investigate the change of particle formation according to the various MeS vapor concentrations by using Equations (2.1), and (2.2). Figure 2.5 illustrates example experimental results of particle volume distribution performed with six different MeS vapor concentrations, i.e., 22.5, 35.7, 63.9, 142, 201, and 439 ppbv, for three hours with particle diameter on the log x-axis, time on the y-axis, and the particle volume size distribution via colors. The particle formation pattern from MeS vapor under the soft X- 25 ray shows a similar pattern regardless of the MeS vapor concentrations. However, since the time to reach the stable mode in each case was slightly different, the calibration curve and averaged particle size distribution was analyzed using one hour of data after measurement. 26 Figure 2.5 Example experimental results of particle volume distribution performed with different MeS vapor concentrations for three hours with particle diameter on the log x-axis, time on the y-axis, and the particle volume size distribution via colors: (a) 22.5 ppbv; (b) 35.7 ppbv; (c) 63.9 ppbv; (d) 142 ppbv; (e) 201 ppbv; (f) 439 ppbv. 27 The averaged particle volume size distributions of six different MeS vapor concentrations, i.e., 22.5, 35.7, 63.9, 142, 201, and 439 ppbv, are illustrated in Figure 2.6b. The particle volume size distribution data provides that the particle mode size and overall particle concentration also increase as MeS vapor concentration increases. This suggests that the more the amount of MeS vapor molecules, the higher the rate at which particles are nucleated as well as accumulated via surface growth and coagulation. However, it should be noticed that the variation of overall particle concentration shows a more obvious difference than the variation of particle mode size, especially at a low ppbv level. Therefore, the total concentration of converted to MeSNPs from MeS vapor under the soft X-ray reaction gives information on MeS vapor concentrations. 28 Figure 2.6 Averaged particle (a) number and (b) volume size distribution of example experimental results during 1~3 hours. a b 29 The variation of the total number and volume concentration of generated MeSNPs under the soft X-ray according to the various MeS vapor concentrations is shown in Figure 2.7a, and Figure 2.7b. When MeS vapor concentration increased, both of total number and volume concentration of generated MeSNPs under the soft X-ray reaction also increases, as shown in Figure 2.7a, and Figure 2.7b. The nucleation rate (J) can be estimated by determining the ratio of measured particle number concentration (Np) to the nucleation time (∆t) as follows (Iland et al., 2004; Zhang et al., 2004): 𝐽 = 𝑁𝑝 ∆𝑡 . (2.4) The empirical relationship between the nucleation rate and saturation ratio was suggested as follows (Easter and Peters, 1994; Munir et al., 2013): 𝐽 = 𝐶𝑎𝑆 𝐶𝑏 , (2.5) where Ca and Cb are correlation coefficients, and S is the saturation ratio, i.e., S=Pi/Ps∝[MeS]. At the stable mode, if each measurement datum of the soft X-ray reaction time and intensity is constant, we can simply assume that the nucleation rate is proportional to particle number concentration, i.e., J∝Np. Furthermore, because the variation of particle mode size does not show a significant difference compared to the variation of particle concentration, as shown in Figure 2.6, the relation between nucleation rate and particle volume concentration can be simplified as J∝Vp. Therefore, the empirical correlation for total number or volume concentration can be expressed as follows: log(𝑁𝑝,𝑐𝑜𝑟) =𝐶1,𝑁 log([MeS]) + 𝐶2,𝑁, (2.6) 30 and log(𝑉𝑝,𝑐𝑜𝑟) =𝐶1,𝑉 log([MeS]) + 𝐶2,𝑉. (2.7) The experimentally obtained total number or volume concentration data shows a good agreement with the correlated results. The correlation constants of C1,N, C2,N, C1,V and C2,V are determined as 0.7803, 3.416, 1.494, and 6.065, respectively. The coefficient of determination (R2) of Equation (2.6), and Equation (2.7) are 0.91, and 0.92, respectively. Furthermore, all experimentally obtained total number or volume concentrations are placed in a single curve, one can predict the MeS vapor concentrations using the correlation suggested in this study. 31 Figure 2.7 Log-log regression of (a) total volume concentration, and (b) total number concentration as a function of MeS vapor concentration. 32 The uncertainty in the measurement was carried out. Each day 61 measurements were made of the volume concentration over two hours (one measurement every two minutes). The MeS detection system was assumed to be stabilized over one hour before making the measurements, as shown in Figure 2.5. A known MeS vapor concentration was produced using the permeation tube device by controlling the temperature of the permeation tube device and total flow rates. This same procedure was performed on two other days to assess the day-to-day variability. In addition, measurements were carried out at two other concentrations with three different concentrations, i.e., 46.4, 81.9, and 201 ppbv. The statistical model for the measurements is 𝑁𝑝,𝑖𝑗 = 𝜇 + 𝛼𝑖 + 𝜖𝑖𝑗, (2.8) where i (1-3) denotes the day, and j (1-61) denotes the repeats within one day. The αi is assumed to be distributed as independent Gaussian random variables with mean zero, and variance (σα2), and the εij are also independent Gaussian with mean zero, and variance (σε2). We wish to estimate the true mean value of the MeSNPs number (μ) and give an uncertainty of this estimation. We estimate μ as 𝑁𝑝̅̅̅̅ , the average of the three-day means: 𝑁𝑝̅̅̅̅ = 1 3 ∑ 𝑁𝑝,𝑖̅̅ ̅̅ ̅ 3 𝑖=1 , (2.9) where 𝑁𝑝,𝑖̅̅ ̅̅ ̅ = 1 61 ∑ 𝑁𝑝,𝑖𝑗̅̅ ̅̅ ̅̅ 61 𝑗=1 . (2.10) The standard deviation of the average is determined by: 33 𝜎𝑎𝑣𝑔(𝑁𝑝̅̅̅̅ ) = √ ∑ (𝑁𝑝,𝑖̅̅ ̅̅ ̅̅ −𝑁𝑝̅̅ ̅̅ ) 23 𝑖=1 3∙2 , (2.11) the 95% uncertainty interval, u(95%), based on the Student t-test distribution with two degrees of freedom is calculated as follows: 𝑢(95%) = 𝑁𝑝̅̅̅̅ ± 𝑡(0.975,2)𝜎(𝑁𝑝̅̅̅̅ ), (2.12) the value of the Student t parameter is 4.3 based on the two degrees of freedom. For large values of the degrees of freedom, this value approaches 2.0. The fractional 95% confidence interval for the average value for the number concentration ranges from ±0.20 for 201 ppbv of MeS vapor concentration to ±0.91 for 46.4 ppbv of MeS vapor concentration, as shown in Table 2.1. This approach accounts for day-to-day variability. If one neglects the day-to-day variation and obtains the following expression for the standard deviation of the mean denoted by the subscript 1 as follows: 𝜎1(𝑁𝑝̅̅̅̅ ) = √ ∑ ∑ (𝑁𝑝,𝑖𝑗−𝑁𝑝̅̅ ̅̅ ) 261 𝑗=1 3 𝑖=1 183∙182 , (2.13) the magnitude of the confidence interval using Equation (2.12), which neglects day-to-day variability, is less than one-tenth of the value including the day-to-day variability. This implies that the day-to-day variability is dominant, so the standard deviation obtained by Equation (2.11) provides a better estimation. The last item in Table 2.1 is the reduced standard deviation of the MeSNPs number rather than that of the average value of the MeSNPs number and calculated as follows: 34 𝜎𝑒𝑎𝑐ℎ(𝑁𝑝̅̅̅̅ ) = √ ∑ ∑ (𝑁𝑝,𝑖𝑗−𝑁𝑝̅̅ ̅̅ ) 261 𝑗=1 3 𝑖=1 182 , (2.14) the confidence interval in this case as shown in the last entry of Table 2.1 is lower compared to the value obtained by Equation (2.11). This suggests that day-to-day variation, as well as within-day variations, occurs. There may also be time-dependent drift caused by unknown factors such as the different chemical compositions of the compressed air. The 95% confidence interval is at least a factor of two times larger for 46.4 ppbv of MeS vapor concentration compared to 81.9, and 201 ppbv of MeS vapor concentration. Table 2.1 Summary of statistical results for total number concentration of MeSNPs. [MeS], ppbv 46.4 81.9 201 𝑁𝑝,1̅̅ ̅̅ ̅, #/cm 3 4.80 × 10 4 7.07 × 10 4 1.68 × 10 5 𝑁𝑝,2̅̅ ̅̅ ̅, #/cm 3 3.77 × 10 4 6.27 × 10 4 1.81 × 10 5 𝑁𝑝,3̅̅ ̅̅ ̅, #/cm 3 5.80 × 10 4 7.68 × 10 4 1.83 × 10 5 𝑁𝑝̅̅̅̅ , #/cm 3 4.79 × 10 4 7.01 × 10 4 1.77 × 10 5 𝜎𝑎𝑣𝑔(𝑁𝑝̅̅̅̅ )/𝑁𝑝̅̅̅̅ , - 0.212 0.101 0.047 95% conf. int./𝑁𝑝̅̅̅̅ , - ±0.911 ±0.434 ±0.200 𝜎1(𝑁𝑝̅̅̅̅ )/𝑁𝑝̅̅̅̅ , - 0.027 0.012 0.007 95% conf. int./𝑁𝑝̅̅̅̅ , - ±0.054 ±0.025 ±0.014 𝜎𝑒𝑎𝑐ℎ(𝑁𝑝̅̅̅̅ )/𝑁𝑝̅̅̅̅ , - 0.363 0.168 0.093 95% conf. int./𝑁𝑝̅̅̅̅ , - ±0.726 ±0.335 ±0.186 35 The volume concentration data obtained by the SMPS were also analyzed with the same type of statistical model. The results are given in Table 2.2. The 95% confidence interval of volume concentration is at least a factor of four times larger for 46.4 ppbv of MeS vapor concentration compared to 81.9, and 201 ppbv of MeS vapor concentration. It is noteworthy that the value of the mean volume concentration for day 1 is at least a factor of three times larger compared to the other days. It appears that this value may be an outlier. This one outlier may increase the 95% confidence interval by a factor of 2 to 3. The increased confidence interval for the volume concentration is similar to that for the number concentration for the two higher concentrations, i.e., 81.9, and 201 ppbv, and is a factor of two higher for the lowest concentration, i.e., 46.4 ppbv. Two possible causes of this effect are a change in the size distribution of MeSNPs at the lower concentration without affecting the number concentration, or non-spherical morphologies of MeSNPs. Table 2.2 Summary of statistical results for total volume concentration of MeSNPs. [MeS], ppbv 46.4 81.9 201 𝑉𝑝,1̅̅ ̅̅ ̅, #/cm 3 1.29 × 10 9 5.60 × 10 8 3.89 × 10 9 𝑉𝑝,2̅̅ ̅̅ ̅, #/cm 3 2.07 × 10 8 4.55 × 10 8 3.24 × 10 9 𝑉𝑝,3̅̅ ̅̅ ̅, #/cm 3 3.75 × 10 8 6.86 × 10 8 3.40 × 10 9 𝑉?̅?, #/cm 3 6.23 × 10 8 5.67 × 10 8 3.51 × 10 9 𝜎𝑎𝑣𝑔(𝑉?̅?)/𝑉?̅?, - 0.538 0.118 0.056 95% conf. int./𝑉?̅?, - ±2.314 ±0.506 ±0.240 𝜎1(𝑉?̅?)/𝑉?̅?, - 0.058 0.015 0.008 95% conf. int./𝑉?̅?, - ±0.117 ±0.030 ±0.017 𝜎𝑒𝑎𝑐ℎ(𝑉?̅?)/𝑉?̅?, - 0.788 0.205 0.111 95% conf. int./𝑉?̅?, - ±1.576 ±0.410 ±0.223 36 The soft X-ray system was run with exposure to four different MeS vapor concentrations by adjusting for 22 hours with the soft X-ray on, and off, to see whether the detection system can measure the sustainable and reproducible data for a long time of period. Figure 2.8 shows the real-time evolution of the change in the total number and volume concentration of generated MeSNPs while the soft X-ray MeS detection system is exposed to varying MeS vapor concentrations from 46.4 to 302 ppbv. The lines parallel to the x-axis in Figure 2.8 are the total number and volume concentration predicted by the empirical correlation results (Equations (2.6), and (2.7)). It should be noticed that the y- axis on the above and below figures in Figure 2.8 has a lognormal, and linear scale, respectively. It has been observed that ppbv-level of MeS vapor concentrations are well predicted by using the soft X-ray detection system. 37 Figure 2.8 Variation of the soft X-ray MeS detection system for the total volume and number concentration on successive exposure to different MeS vapors (46.4-302 ppbv). Solid red and blue lines represent the total volume concentration and the total number concentration, respectively. The lines parallel to the x-axis are the total number and volume concentration predicted by Equations (2.6), and (2.7), respectively. The y-axis on the above and below figures has a lognormal and linear scale, respectively. ON or OFF represent whether the soft X-ray reaction is turned on or off. To determine how quickly the total number or volume concentration reaches the steady state through the soft X-ray detection method, we compared the sensor time constant (τ), and sensor response time (5τ). The time constant for an increasing system is usually defined as the rise time to reach 63.2%, i.e., 1-1/e, of its steady-state response. Because we have already obtained the calibration curve for ppbv-level MeS vapor concentrations at stable mode (Equations (2.6), and (2.7)), the value of steady-state response is assumed to be the same value of correlated results. Sensor time constant, and sensor response time of total number and volume concentration measurements are presented in Table 2.3. Sensor 38 time constant, and sensor response time decreases with the decrease of MeS vapor concentrations. Furthermore, both the sensor time constant and sensor response time of total number concentration is two times shorter than those of total volume concentration. This is due to the fact that the particle formation of MeSNPs has a series of stage changes during the soft X-ray reaction as described in Figure 2.3. Table 2.3 Summary of sensor time constant (τ), and sensor response time (5τ) of the total number and volume concertation of MeSNPs. The sensor time constant (τ) is the sensor output to reach 63.2 % of its correlated data. Sensor response time (5τ) is the time for the sensor output to reach 99.3 % of its correlated data. [MeS], ppbv 46.4 81.9 201 302 Number concentration τ, s 441 290 162 144 5τ, s 512 318 186 159 Volume concentration τ, s 828 492 420 308 5τ, s 1047 558 595 574 2.4 Conclusion By mimicking the gas-to-particle conversion process using the soft X-ray in the semiconductor EUV lithography process, we demonstrated that VOC formed nanoparticles in a particle-free environment. To the best of our knowledge, this study is the first report on using the soft X-ray detection system for estimating MeS vapor concentration which is one of VOCs. The present study reports the characteristics of the MeSNPs formation by 39 describing the stage change during the soft X-ray reaction, the empirical calibration curves which can predict ppbv-level MeS vapor concentrations by using particle number or volume concentration data obtained from the aerosol instrument, e.g., SMPS, and the statistical and response time analysis. The results of particle size distribution over time show differences between each particle growth stage. Each stage including particle-free, nucleation, transition mode with nucleation and surface growth, accumulation mode with surface growth and possibly coagulation, and stable mode is described by comparing each term of a general dynamic equation. When a soft X-ray starts to assist the conversion of MeS vapor to particle, a high concentration of small MeSNPs is generated. As small MeSNPs concentrations reached a certain level, the size of MeSNPs tends to grow and then become stabilized (steady state). Based on the experimental data obtained at various MeS vapor concentrations at ppbv-level, the empirical correlation fitting curves were obtained for estimating the MeS vapor concentrations from the aerosol concentration. The R2 value for the volume concentration measurements was slightly larger (0.92) than for the number concentration measurements (0.91). The statistical analysis finds that the dominant uncertainty in the mean value of the nanoparticle concentration arises from the day-to-day variability. The reduced 95 % confidence intervals for the two higher concentrations for both the volume concentration and number concentration of the nanoparticle are in the range of 0.2 to 0.5. The volume concentration measured at 46.4 ppbv of MeS vapor concentration on day 1 appears to be an outlier; however, the number concentration for the same MeS vapor concentration is not 40 an outlier. It is also found that the 95% confidence interval for the total number or volume concentration for a fixed MeS vapor concentration based on all measurements is close to the value for the confidence interval for the day-averaged total number or volume concentration data. In addition, the sensor response time of number concentration provides a shorter response time. These statistical analyses and sensor response time imply that total number concentration data gives slightly more reliable results for predicting MeS vapor concentration by using the soft X-ray detection system. Therefore, using both number and volume concentration data is highly recommended when measuring VOC concentration or characterizing the gas-to-particle conversion phenomena by using a soft X-ray-assisted SMPS system. The soft X-ray detection method can be further investigated or developed for detecting other ppbv-level aromatic compounds (e.g., benzene, toluene, or xylene) and monitoring AMC or VOC levels in semiconductor manufacturing facilities. Furthermore, it is worthwhile to mention that research on how the soft X-ray assisted detection method responds in a situation in which various chemicals and MeS are mixed, rather than in a situation where only MeS exists, must also need to be conducted for application in the real outdoor environment. 41 Chapter 3 Experimental study of nanoparticle transport and penetration efficiency on a sharp-bent tube (elbow connection) 3.1 Introduction Due to the special attention to nanotechnology, nanomaterials have been widely used in various fields including semiconductors (Jiang et al., 2019; Morales and Lieber, 1998; Saha et al., 2018; Wang et al., 2017), energy (Ma and Zou, 2018; Peng et al., 2018; Sheikholeslami et al., 2018; Watanabe et al., 2018), filtration (Kang et al., 2019; Kim et al., 2017; Lee et al., 2018, 2017b) and health (Jakobsson et al., 2016; Lee et al., 2015; Shi et al., 2004). Specifically, lots of studies have been conducted to synthesize and manufacture nanoparticles such as ultrafine liquid atomization (Mezhericher et al., 2018), flame synthesis (Strobel et al., 2006; Wegner and Pratsinis, 2004), laser ablation (Morales and Lieber, 1998; Streubel et al., 2016), microwave-assisted techniques (Blanco-Andujar et al., 2015; Ranjan et al., 2016), and chemical vapor deposition (D. S. Choi et al., 2016; Rezaei et al., 2014). To increase the acquisition rate of the produced nanoparticles, the loss of nanoparticles during particle transport should be minimized. 42 Even though these nanoparticles are beneficial to the development of nanotechnology, unwanted nanoparticles, which are harmful to the human respiratory system (Schmid and Stoeger, 2016; Shi et al., 2004) and cause contamination problems in the semiconductor manufacturing process (Hu et al., 2017; Kim et al., 2015, 2018; D. Kim et al., 2016; Kwak et al., 2018b), should be monitored and controlled. Examples of these unwanted nanoparticles in the semiconductor industry are airborne molecular contamination (AMC), haze, and deposited nanoparticles on the pipeline. Deposited nanoparticles are unwanted because they can be resuspended and re-deposited on the semiconductor chips (C. Kim et al., 2016a; Kim et al., 2015; Kwak et al., 2018b). Therefore, it is essential to accurately examine the fluid flow and deposition during nanoparticle transport so as to enhance manufacturing yields. To quantify and evaluate the particle transport characteristics, the penetration and deposition efficiencies are introduced. They are effective, direct, and understandable parameters to estimate nanoparticle loss during particle transport. The deposition efficiency is defined as the ratio of the number of deposited particles on the tube wall to the number of introduced particles at an inlet. Similarly, the penetration efficiency is measured by comparing the number of particles at the inlet and the outlet. Therefore, the summation of the penetration and deposition efficiency is considered unity. Various research on nanoparticle deposition and penetration on tubes have been performed. The analytical solution for predicting the nanoparticle penetration efficiency on the straight cylindrical tube was suggested by Gormley and Kennedy (under the parabolic velocity inlet condition), Ingham, and Martonen et al. (both under the uniform velocity inlet condition) (Gormley and Kennedy, 1975; Ingham, 1991; Martonen et al., 1996). Shi et al. compared the findings 43 of these analytical solutions and the numerical results. In the present study, since the fully developed flow was assumed, Gormley and Kennedy’s analytical model was employed as a reference model (Shi et al., 2004). Most transport systems, however, usually contain bent tubes or finite elbows which are necessary and ubiquitous components in tubing systems as well as straight tubes due to the complexity of the transport system. Over the past several years, lots of studies on the deposition and penetration efficiency in curved pipes have been carried out (McFarland et al., 1997; Peters and Leith, 2004a; Pui et al., 1987; Sippola and Nazaroff, 2005; Sun et al., 2013, 2011; Sun and Lu, 2013; Tsai and Pui, 1990; Wilson et al., 2011). Pui et al. suggested a correlation fitting curve of deposition efficiency as a function of Stokes number, i.e., Stk = (pVdp2Cc)/(9Dtube), for the particle size of dp = 2.5-10 μm; after measuring deposition and penetration efficiency on a 90o smooth-bent pipe and employing micro-sized liquid particles in which uranine was dissolved by comparing the total mass of uranine on the bending section and on outlet filter section (Pui et al., 1987). Tsai and Pui performed the numerical analysis for calculating micro-sized particle deposition efficiency on a 90° smooth-bent tube with different velocity inlet profile conditions (Tsai and Pui, 1990). McFarland et al. presented a correlation fitting curve of penetration efficiency based on experimental and numerical results as a function of Stokes number, bend angle, and curvature ratio and compared Pui et al’s correlation fitting results (Pui et al., 1987) (McFarland et al., 1997). Peters and Leith developed a method to measure particle deposition in curved industrial ducts for dp = 5-150 μm and found that particle deposition efficiency increased from approximately 35% to 95% in the particle size range from 15 44 to 100 μm (Peters and Leith, 2004a). Sippola and Nazaroff obtained particle deposition efficiency on connectors and 90o bent tubes and compared the particle enhancement factor at the ceiling, side wall, and floor position by using monodisperse fluorescent particles for dp = 1-16 μm (Sippola and Nazaroff, 2005). Wilson et al. experimentally and numerically investigated the effect of Reynolds number on particle deposition efficiency and corrected the numerical calculation at low Stokes number through an analytical method considering the eddy frequency scale for dp = 1-11 μm (Wilson et al., 2011). Sun et al. conducted research on particle deposition on 90° smooth-bent tubes in the view of particle deposition velocity for dp = 1-16 μm (Sun et al., 2011) and dp = 0.7-100 μm (Sun et al., 2013; Sun and Lu, 2013). However, the previous studies have mainly focused on the micro-sized particles by only considering the inertial impaction deposition on curved pipes; these studies were not applicable to nanoparticles with small inertia. Recently, particle penetration efficiency on nanoparticles has been studied on bent tubes and coils (Ghaffarpasand et al., 2012; Lee and Gieseke, 1994; Lin et al., 2015; Sato et al., 2003; Wang et al., 2002; Yook and Pui, 2006). Sato et al. studied the particle transport to determine the particle deposition efficiency and suggested the equation for finding Stk50 (Stokes number at 50% deposition efficiency) as a function of Dean number, i.e., De = Re(2R/Dtube)-0.5 and curvature ratio through comparing the Tsai and Pui’s work (Tsai and Pui, 1990) for dp = 180-630 nm (Sato et al., 2003). Wang et al. conducted the experiment to measure the particle penetration efficiency of nanoparticles on 90° smooth-bent tubes and sharp-bent tubes with particle sizes ranging from 5 to 15 nm (Wang et al., 2002). Ghaffarpasand et al. measured the particle penetration efficiency of tungsten oxide and ammonium nitrate particles ranging from 3 to 17 nm on a 90° smooth-bent tube and 45 represented the results as a function of Stokes number (Ghaffarpasand et al., 2012). However, they (Ghaffarpasand et al., 2012; Wang et al., 2002) did not present any formula for predicting the particle penetration efficiency and did not provide the fluid flow analysis which was essential to explain the degree of particle deposition or penetration efficiency. In addition, even though Stokes number is one of the most important parameters to find the particle deposition by inertial impaction on the tube, Stokes number of nanoparticles is usually too low to consider the inertial impaction on tubes (Ghaffarpasand et al., 2012; Lee and Gieseke, 1994; Lin et al., 2015); thus other dimensionless parameters which could represent the diffusion effect instead of inertia effect should be required (Lin et al., 2015). Other than the abovementioned studies on the 90° bent tube, Yook and Pui (for dp = 3-50 nm) (Yook and Pui, 2006) and Lin et al. (for dp = 8-550 nm) (Lin et al., 2015) measured the penetration efficiency on smooth-bent coil or 180° smooth-bent tube. The results from the introduced studies and their applications prove that particle deposition and penetration behaviors are active and vibrant research fields; however, still, there has been a lack of research related to the penetration efficiency of nanoparticles on a bent tube compared to one of the micro-sized particles. Moreover, the exact explanations for the observed deposition phenomena on bent tubes are still unknown. To our best knowledge, there is no study to suggest the empirical correlation relationship to determine the nanoparticle penetration efficiency on a sharp-bent tube, i.e., elbow connection, as a function of the Peclet number. Therefore, the objectives of the present study are to give an intuition of nanoparticle transport on a sharp-bent tube by analyzing the fluid flow, showing the diverse experimental results, and suggesting the empirical correlation curve fitting to directly estimate the particle penetration or loss on a sharp-bent tube. 46 3.2 Theory The particle losses in a tube during sampling and transporting aerosol occur due to the deposition of particles by gravitational sedimentation, inertial impaction, thermophoresis, electrophoresis, and Brownian diffusion (Friedlander, 2000; Hinds, 1982; Lee et al., 2012; Lee and Yook, 2015). During the nanoparticle transport, temperature difference and electric field inside tubes can be easily controlled or removed by adjusting operation conditions, e.g., installing the heat exchanger, water bath, and conductive material pipeline. Furthermore, nanoparticle depositions by gravitational sedimentation and inertial impaction are usually negligible because of the very small Stokes number (Stk) of the nanoparticles (Ghaffarpasand et al., 2012; Lin et al., 2015). Therefore, the most dominant deposition mechanism of small nanoparticles is Brownian diffusion, which is the random motion of nanoparticles resulting from collisions by fluid molecules. The Brownian motion is characterized by the diffusion coefficient (D) as follows: 𝐷 = 𝑘𝑏𝑇𝐵 (3.1) where kb is the Boltzmann constant of 1.3807×10-23 J/K, T is the temperature, here 296.15 K, and B is the dynamic mobility defined as: 𝐵 = 𝐶𝑐 3𝜋𝜇𝑑𝑝 (3.2) where µ is the gas dynamic viscosity of 1.8325×10-5 kg/ms, dp is the particle diameter and Cc is the slip correction factor obtained from the correlation as a function of Knudsen number suggested by Kim et al. as follows (Kim et al., 2005): 47 𝐶𝑐 = 1 + Kn(1.165 + 0.483 exp (− 0.997 Kn )), (3.3) where Kn is Knudsen number, i.e., 2/dp and the mean free path () is assumed as 67.3 nm at a standard pressure of 101.3 kPa and a standard temperature of 23oC. The slip correction factor obtained from Equation (3.3) is validated for Knudsen number from 0.5 to 83. Because the tested nanoparticle size range is from 3 to 50 nm which corresponding Knudsen number range is from 2.69 to 44.9, Equation (3.3) can be employed. In this study, we compared the penetration efficiencies of nanoparticles on straight and sharp-bent tubes. Gormley and Kennedy obtained the analytical solution for predicting the nanoparticle penetration efficiency on a straight cylindrical tube under a fully developed flow (Gormley and Kennedy, 1975). They considered uniformly distributed particles across the cross-section of the tube and the diffusional particle loss on the tube. The nanoparticle penetration efficiency on the straight tube (G-K,ST) was given as: 𝜂𝐺−𝐾,𝑆𝑇(𝜁) = { 1 − 2.56𝜁2/3 + 1.2𝜁 + 0.177𝜁4/3 0.819𝑒−3.657𝜁 + 0.097𝑒−22.3𝜁 + 0.032𝑒−57𝜁 𝑓𝑜𝑟 𝜁 < 0.02 𝑓𝑜𝑟 𝜁 ≥ 0.02 (3.4) where  is the dimensionless parameter estimated by the ratio of the flow-directional residence time (tx) to the radial-directional residence time (tr), i.e.,  = tx/2tr. The flow- directional residence time is determined by the ratio of a tube length (L) to bulk mean velocity (V), i.e., tx = L/V, and the radial-directional residence time is obtained from the root-mean-square displacement, i.e., xrms = (2Dtr)1/2 (Hinds, 1982; Yook and Ahn, 2009). Therefore, the dimensionless parameter () can be defined as follows: 48 𝜁 = 𝑡𝑥 2𝑡𝑟 = 𝐿/𝑉 2(𝑥𝑟𝑚𝑠 2 /2𝐷) . (3.5) For a particle at the center of the cross-section of the tube to deposit on the tube wall, the root-mean-square displacement (xrms) should be similar to the tube radius, i.e., xrms  Dtube/2 (Yook et al., 2010; Yook and Ahn, 2009). Therefore, Equation (3.5) can be modified to Equation (3.6) as a function of flow rate through the tube (Q) and diffusion coefficient as follows: 𝜁 ≈ 𝐿/𝑉 (𝐷𝑡𝑢𝑏𝑒/2)2/𝐷 = 𝜋𝐷𝐿 𝑄 . (3.6) As shown in Equations (3.4) and (3.6), the penetration efficiency on a straight tube can be characterized by the flow rate and diffusion coefficient, which is related to particle size. The physical phenomena of particle transport can be described by the general convection- diffusion equation (Atreya, 2016) as follows: 𝜕𝐶 𝜕𝑡 = ∇ ∙ (𝐷∇𝐶) − ∇ ∙ (𝒗𝐶) + 𝑆. (3.7) Here, C is the particle concentration, v is the velocity vector and S is the source. If the flow field is the steady state and incompressible, the diffusion coefficient is constant, and there are no sources or sinks, the equation can be simplified as follows (Atreya, 2016): 𝒗 ∙ ∇𝐶 = 𝐷∇2𝐶. (3.8) The left-hand side term in Equation (3.8) describes the advection, and the right-hand side term stands for diffusion. Therefore, we employed the dimensionless parameters of Reynolds number (Re), Schmidt number (Sc), and Peclet number (Pe) to characterize the 49 deposition behaviors of nanoparticles through tubes. Reynolds and Schmidt numbers are defined, respectively, as: Re = 𝜌𝑉𝐷𝑡𝑢𝑏𝑒 𝜇 , (3.9) and Sc = 𝜇/𝜌 𝐷 = 3𝜋𝜇2𝑑𝑝 𝜌𝑘𝑏𝑇𝐶𝑐 (3.10) where  is the fluid density and Dtube is the tube diameter. From Equation (3.8), the particle transport can be characterized by the Peclet number, which is defined by the ratio of the advection term to the diffusion term, i.e., VDtube/D and; therefore, Peclet number is the multiplication of Reynolds number and Schmidt number, i.e., Pe = ReSc. Finally, the dimensionless parameter () in Equation (3.6) can be expressed as: 𝜁 = 4𝐿 Pe𝐷𝑡𝑢𝑏𝑒 . (3.11) Hence, under the known conditions of tube length and diameter, the penetration efficiency suggested by Gormley and Kennedy can be expressed as a function of the Peclet number (Gormley and Kennedy, 1975). In the later section, we showed the detailed and quantified analysis of the bending effects on the nanoparticle deposition and introduced the relative penetration efficiency (R) defined as the ratio of the penetration efficiency of a sharp-bent tube (SBT) to that of a straight tube (G-K,ST): 𝜂𝑅 = 𝜂𝑆𝐵𝑇(Pe) 𝜂𝐺−𝐾,𝑆𝑇(Pe) . (3.12) 50 3.3 Experimental method The schematic of the experimental set-up is illustrated in Figure 3.1. The silver powder (Ag(s)) was placed on the ceramic tube and evaporated due to high temperature by a tube furnace (Model STF 55433C-1, Lindberg/Blue M, MA, USA). The evaporated silver (Ag(g)) was carried by ultra-high purity grade nitrogen gas (99.999%). Finally, the polydisperse silver nanoparticles (AgNPs) were generated through the condensation process as a result of low temperature at the downstream flow of the ceramic furnace tube. The generated polydisperse AgNPs were charged by a Polonium-210 radioactive source with the diffusion charging distribution (Wiedensohler, 1988; Wiedensohler and Fissan, 1988). The AgNPs were classified by a nano-differential mobility analyzer (Nano-DMA, Model 3085, TSI, MN, USA) with an electrostatic classifier (Model 3080, TSI, MN, USA) to produce monodisperse and singly positive-charged AgNPs with each desired particle size, i.e., dp = 3, 5, 7, 10, 15, 20, 30, and 50 nm, by adjusting the applied voltage to a Nano- DMA (Chen et al., 1998; Rengasamy et al., 2008; Yook and Pui, 2006). The particle size distribution after classifying aerosol flow by using a Nano-DMA was investigated. Briefly, the principle of a Nano-DMA is as follows: Charged polydisperse particles (Boltzmann equilibrium state obtained by Po-201) are introduced into the classification zone inside a DMA. Along the classification zone, the charged particles are deflected by the electrical force, and particles having a very narrow range of electrical mobility (monodisperse particles) exit the DMA through a small slit. The tested particles are AgNPs which are generated by evaporation and condensation technique, i.e., tube furnace. For evaluating the classification performance of the Nano-DMA, the particle size distribution of the classified 51 AgNPs by the Nano-DMA is measured by using a scanning mobility particle sizer. Figure 3.2 showed the results of normalized particle size distribution after classifying aerosol flow by using the Nano-DMA. Sheath air and aerosol flow rates through the Nano-DMA were set as 15 and 1.5 L/min, respectively. Figure 3.2 Particle size distribution after classifying AgNPs aerosol flow by using a Nano- DMA. Figure 3.1 Experimental schematic for measuring penetration efficiency of nanoparticles on a sharp-bent tube. 52 The flow rate of the test section was controlled by the mass flow controller embedded in the aerosol electrometer and insufficient or overflowed flow was replenished by a diluter or was discharged into the air, respectively. The accurately controlled flow rate was introduced to the test section of a sharp-bent tube with dimensions of Dtube = 4.572 mm, A = 14.2 mm, L = 17.5 mm, and B = 6.4 mm (Figure 3.3). The pressure was measured as approximately 100 kPa. The test flow rates through the tube are 0.65, 0.97, 1.61, 2.26, 3.22, and 4.83 L/min corresponding to Reynolds numbers of 200, 300, 500, 700, 1000, and 1500. It should be mentioned that a fully developed flow condition was achieved by installing a straight long tube with a sufficient length corresponding to approximately 100Dtube before the test tube section. The monodisperse and singly positive-charged AgNPs classified by the Nano- DMA were counted by an aerosol faraday cup electrometer (Model 3068B, TSI, MN, USA) which can detect airborne particles down to 2 nm and is widely employed when calibrating a condensation particle counter as a standard method (Järvinen et al., 2018; C. Kim et al., 2016a; Thomas et al., 2018). Since the generated particle size was in sub-100 nm, the multiple charge effect by the diffusion charging was assumed to be neglected. The current (I) was measured by the aerosol faraday cup electrometer and the particle number concentration (Cnum) was calculated as follows: 𝐶𝑛𝑢𝑚 = 𝐼 𝑛𝑝𝑒𝑄 . (3.13) Here, np is the average number of elementary charge units per particle and e is the elementary unit of charge of 1.6×10-19 As. Particle penetration efficiency () was obtained 53 by measuring AgNP concentration upstream (Cnum,up) and downstream (Cnum,down) as: 𝜂 = 𝐶𝑛𝑢𝑚,𝑑𝑜𝑤𝑛 𝐶𝑛𝑢𝑚,𝑢𝑝 . (3.14) A three-way valve was utilized to sample either the upstream or downstream. The lengths of tube lines from the measurement points of the upstream and downstream to the inlet of the electrometer are set to be the same so the effect of the additional particle loss by the diffusion was minimized. Moreover, the conducting tubes were used for the whole transport system to minimize the electrostatic effect on the particle loss (Liu et al., 1985). The lengths from the bending point in the sharp-bent tube to the upstream measurement point (Lup) and the downstream measurement point (Ldown) were set as 80 and 270 mm, respectively. Here, to minimize the particle coagulation effect during particle transport in the test section, the particle number concentration for each particle size was controlled below 2×105 particles/cm3. Under this concentration condition, the estimated reduction rate of particle number concentration is significantly low around 0.002%. To be specific, the actual measurement data showed that the highest particle concentration was 1.4×105 particles/cm3 and the average particle concentration in all experimental cases was 1.6×104 particles/cm3. Before comparing the coagulation effect, we should mention that polydisperse particles are classified as ‘monodisperse particles’ in upstream and downstream measurements. The coagulation effect is well described in the aerosol textbook (Friedlander, 2000). Based on this, the simple aerosol decay model due to ‘monodisperse’ Brownian coagulation can be represented as follows: 𝑑𝐶 𝑑𝑡 = −𝐾𝐶2, (3.15) 54 where K is the monodisperse coagulation coefficient, and C is the particle number concentration. With performing the integration on both sides, the particle number concentration after time t can be represented as 𝐶2 = 𝐶1 1+𝐾𝐶1𝑡 , (3.16) where t is the time which is determined as t = Ltube/V, and C1 is assumed as the initial particle concentration. Because all the tested particles are in the free molecule regime (Kn > 1), the monodisperse coagulation coefficient can be calculated as 𝐾 = 4( 3𝑘𝑏𝑇𝑑𝑝 2𝜌𝑝 ). (3.17) For our experimental conditions, we calculated the monodisperse coagulation coefficient. The average, maximum, and minimum values of the monodisperse coagulation coefficient are 3.71×10-16 m3/s, 6.84×10-16 m3/s (for dp = 50 nm), and 1.68×10-16 m3/s (for dp = 3 nm), respectively. The average, maximum, and minimum ratio of decreased particle number concentration due to coagulation for all experimental data, i.e., 1-C2/C1, are 1.38×10-6, 1.49×10-5, and 1.48×10-10, respectively, which are negligible values. Even though we did not consider the other coagulation effects such as turbulent coagulation, and sedimentation coagulation. The textbook reported that Brownian coagulation effect dominants for particles smaller than 1 μm (Friedlander, 2000). Therefore, we believe that the coagulation effect for our experiment can be neglected. 55 Figure 3.3 Geometry of test-section of a sharp-bent tube. 3.4 Numerical method The numerical analysis was performed to investigate the characteristic of fluid flow in the sharp-bent tube and, therefrom, to provide perspectives on the particle deposition mechanisms for the tube according to different particle sizes and flow rates. The continuity, momentum, and energy equations were simultaneously solved by using a computational fluid dynamic code, ANSYS FLUENT Release 18.1, and the Reynolds stress model was used for considering turbulent flow caused by the curved flow with high 56 Dean number (Chrysler and Sparrow, 1986; Ghaffarpasand et al., 2012; Soh and Berger, 1984). The flow was assumed to be three-dimensional, steady, and incompressible flow. To validate the numerically calculated fluid flow, the velocity profile on a 90° smooth-bent tube was compared with the experimental data obtained by Enayet et al (Enayet et al., 1982). As shown in Figure 3.4, the numerically calculated velocity magnitudes along the radial position showed a good agreement with the experimental data, accurately predicting the biased flow toward the outer wall of the smooth-bent tube. The most of flow passed through the outer wall the biased flow toward the outer wall increased when the flow was developed from 30o to 60o. Mesh independent test was performed, and the results were shown in Figure 3.5. The results showed that there was no significant difference between each mesh count likewise in Figure 3.4. In this study, ‘Mesh 3’ was chosen for comparing the velocity magnitude and secondary flow according to the amount of Reynolds number. It should be noted that the numerical analysis of the flow field was conducted to support and explain the experimentally obtained results of particle deposition. Figure 3.4 Numerically calculated velocity comparison between experimental results and numerical results of a smooth-bent tube: (a) velocity magnitude contour, (b) velocity profile at cross-section of 30o point and (c) velocity profile at cross-section of 60o point. 6 0 2 4 a Exp:(Enayet et al, 1982)b c 57 Figure 3.5 Results of mesh independent test of a sharp-bent tube: (a) velocity magnitude contour results and (b) axial velocity results after a sharp-bent tube from 1 mm. 3.5 Results and discussion 3.5.1 Effect of Schmidt number Particles with a small size, i.e., small inertia, well follow the fluid flow; however, due to the diffusion effect and secondary flow caused by the centrifugal force, the chance for small nanoparticles to be deposited on the tube wall increases. The particle size (dp), i.e., Schmidt number, is one of the important parameters on particle penetration efficiency of the sharp-bent tube, i.e., SBT (L, Dtube, Sc, Re). To investigate the effect of particle size during the particle transport on the sharp-bent tube, the penetration efficiencies of eight different particle sizes, i.e., dp = 3, 5, 7, 10, 15, 20, 30, and 50 nm, were obtained experimentally. Figure 3.6 showed the experimental results of the particle penetration efficiency a b 58 on the sharp-bent tube according to Schmidt number with different Reynolds numbers, i.e., Re = 200, 300, 500, 700, 1000, and 1500. The range of Schmidt number was from 25.46 to 6276 calculated from Equation (3.10). The diffusion coefficient (D) and Schmidt number according to the particle sizes are provided in Table 3.1. As Schmidt number increases, i.e., increasing particle size, the particle penetration efficiency on a sharp-bent tube increases as shown in Figure 3.6. For the lowest Reynolds number, i.e., Re = 200, the particle penetration efficiency on the sharp-bent tube increases from 52.9% at Sc = 25.46 to 99.4% at Sc = 6276. The particle penetration efficiency for the highest Reynolds number, i.e., Re = 1500, increases from 74.0% at Sc = 25.46 to 98.2% at Sc = 6276. Due to the higher diffusion coefficient for the lower Schmidt number, the residence time of the smaller particles before adhering to the tube wall decreased, i.e., tr  D-1, resulting in the longer displacement of the smaller particles at the same time period. In addition to the effect of Schmidt number, the increase in penetration efficiency was observed with increasing Reynolds numbers in Figure 3.6, and the penetration efficiencies of the straight tube and sharp-bent tube as a function of Reynolds number were plotted in Figure 3.7 for more details by comparing each other. 59 Table 3.1 Diffusion coefficient and Schmidt number with different particle sizes. Particle size, dp [nm] Diffusion coefficient, D [m2/s] Schmidt number, Sc [-] 3 5.8765×10-7 25.455 5 2.1256×10-7 70.374 7 1.0897×10-7 137.27 10 5.3785×10-8 278.12 15 2.4200×10-8 618.14 20 1.3783×10-8 1085.3 30 6.2836×10-9 2380.6 50 2.3836×10-9 6275.7 60 Figure 3.6 Effect of Schmidt number on penetration efficiency with different Reynolds numbers: (a) Re = 200, (b) Re = 300, (c) Re = 500, (d) Re = 700, (e) Re = 1000 and (f) Re = 1500. 61 3.5.2 Effect of Reynolds number and comparison between straight and sharp-bent tubes The particle penetration efficiency on the sharp-bent tube (SBT) is a function of flow rate (Q), i.e., Reynolds number. The effect of Reynolds number on particle penetration efficiency of the straight tube and the sharp-bent tube is shown in Figure 3.7 with various particle diameters, i.e., dp = 3, 5, 7, 10, 15, and 20 nm. The penetration efficiency of the straight tube was calculated by Equations (3.4) and (3.6), and the length of the straight tube was set to be the same as the tube length between the upstream and downstream of the T- elbow of the test section, which is 350 mm, i.e., Ltube = Lup + Ldown. In other words, from the comparison results shown in Figure 3.7, the effect of the sharp turn on particle penetration can be clearly observable, resulting in more particle deposition compared to the straight tube case. In general, the penetration efficiency of the sharp-bent tube was lower than the penetration efficiency of the straight tube. In particular, the difference in penetration efficiencies between the sharp-bent tube and the straight tube became more significant when the particle size is smaller. For example, when Re = 200, the difference in the particle penetration efficiencies is 15.6% at Sc = 25.46, 10.1% at Sc = 70.37, and 4.2% at Sc = 1085. This is because the recirculation flow occurred at the corner of the sharp-bent tube and the flow velocity inner tube wall region decreased due to the occurrence of the separation region after the bending point so that the residence time of the nanoparticles of the sharp-bent tube was higher than that of the straight tube. Therefore, the longer residence time in the sharp-bent tube caused more particle loss due to diffusion. When the Reynolds 62 number increased, the penetration efficiency of nanoparticles increased as illustrated in Figure 3.7. This is because even though the radial-directional residence time (tr) which is a function of the root-mean-square displacement, i.e., xrms = (2Dtr)1/2, does not change as Reynolds number increases, the flow-directional residence time (tx) decreases for both straight and sharp-bent tube, i.e., tx = L/V., resulting in increasing the possibility of particles penetrating through the tube. In addition to this effect, additional particle losses due to secondary flow near the tube wall occurred in the sharp-bent tube. In particular, the lower Reynolds number triggered the lower flow rate near the wall. The details of flow patterns inside the sharp-bent tube will be discussed in the following section. 63 Figure 3.7 Effect of Reynolds number on penetration efficiency with different Schmidt numbers: (a) Sc = 25.46, (b) Sc = 70.37, (c) Sc = 137.27, (d) Sc = 278.12, (e) Sc = 618.14 and (f) Sc = 1085.31. 64 3.5.3 Velocity profile and secondary flow Figure 3.8 showed the numerically obtained velocity magnitude and streamline at the cross-section of the midplane along the sharp-bent tube geometry at Reynolds numbers of 200 and 1000. For both Reynolds numbers, recirculation with lower velocities, i.e., blue- colored region, occurs at the corner of the sharp-bent tube. This recirculation flow phenomenon results in the longer residence time of nanoparticles in the sharp-bent tube than in the straight tube case. The flow analysis on the sharp-bent tube well explains the comparison results between the particle penetration efficiency of the straight tube and sharp-bent tube in Figure 3.7. The flow separation and reattachment, due to the curvature effect, were observed at the inner wall after the bending point for both Reynolds numbers. The starting point of the flow separation from the sharp-bent point implies that no significant difference was found between the two Reynolds numbers and similar phenomena were observed in Takamura et al.’s experimental work performed (Takamura et al., 2012). However, the reattachment point, where new streamlines were developed in Figure 3.8, from the sharp- bent point of the high Reynolds number of 1000 was shorter than the case for the low Reynolds number of 200. This might be a consequence of the more active replenishment and, thus, faster recovery of flow at the inner wall due to the stronger secondary flow at the higher Reynolds number. Further details of the secondary flow can be found in Fig 6. 65 Figure 3.8 Velocity magnitude and streamline in the midplane of a sharp-bent tube: (a) low Reynolds number (Re = 200) and (b) high Reynolds number (Re = 1000). 66 Figure 3.9 showed the numerically calculated radial velocity and streamline at the cross-section of the sharp-bent tube at the 1 mm distance away from the bending point at Reynolds numbers of 200 and 1000. The strong secondary flow was generated after the bending point because of a maximized centrifugal force, i.e., mfpV2/R → (max), caused by the minimized curvature radius on the sharp-bent tube, i.e., R → (min), where mfp is the mass of fluid particle and R is the curvature radius. Moreover, due to the higher velocity, the strength of the secondary flow is much stronger at the higher Reynolds number. In addition, the center point position, i.e., the core of the secondary flow, was slightly closer to the inner and side tube wall at the higher Reynolds number. For the continuity of secondary flow, the higher flow rates were established due to the shorter distance from the core of secondary flow to the inner and side walls. In other words, this represents that the flow velocity of the lower Reynolds number near the tube wall was much slower in terms of the secondary flow as well as the overall flow rate. This causes more nanoparticles to be deposited inside the tube when the Reynolds number is low because the lower flow velocity makes longer the residence time for nanoparticles to diffuse to the tube wall. Therefore, this secondary flow analysis strongly supports the experimental data obtained in Figure 3.7, concluding that the lower Schmidt or Reynolds number enhances the particle deposition by reducing the residence time. 67 Figure 3.9 Radial velocity and secondary flow streamline after a sharp-bent tube from 1 mm: (a) low Reynolds number (Re = 200) and (b) high Reynolds number (Re = 1000). 68 3.5.4 Empirical correlation of penetration efficiency on a sharp-bent tube Through the experimental data and flow analysis inside the sharp-bent tube, we confirmed that the particle penetration efficiency on the tube was strongly affected by particle size and flow rate, i.e., Schmidt number and Reynolds number, respectively. Therefore, the particle deposition behaviors inside the tube can be characterized by the Peclet number, which is the dimensionless number obtained by the multiplication of the Schmidt number and Reynolds number. Figure 3.10 showed that the particle penetration efficiency on a straight tube and sharp-bent tube with the same length and diameter of the tubes, i.e., Ltube = 350 mm and Dtube = 4.572 mm, was plotted according to the Peclet number. The penetration efficiency on the straight tube (G-K,ST, black dashed line) was obtained based on the analytical solution denoted in Equation (3.4), and the penetration efficiency on the sharp-bent tube (SBT, symbols, and red solid line) was obtained through the experiment. When the Peclet number increased, the penetration efficiency of both cases increased, as shown in Figure 3.10. Furthermore, the penetration efficiency on the sharp- bent tube was lower compared to the penetration efficiency on the straight tube at each Peclet number. A detailed explanation of the results was already discussed in the previous sections. Based on the penetration efficiency on the sharp-bent tube (SBT) as a function of the Peclet number, the empirical correlation curve was obtained as follows: 𝜂𝐶𝑜𝑟,𝑆𝐵𝑇(Pe) = 1 − 𝐶1Pe 𝐶2. (3.18) The correlated data showed a good agreement with the experimental data at 4×103 < Pe < 69 107. The correlation constants of C1 and C2 in Equation (3.18) were determined as 27.41 and -0.4831, respectively. The coefficient of determination (R2), the sum of squares (SSE), and root mean square error (RMSE) were 0.9446, 0.0258, and 0.0237, respectively. It should be mentioned that all experimentally obtained penetration efficiencies can be placed in a single curve based on the Peclet number, indicating that by simply calculating the Peclet number without considering particle size and flow rate separately, one can accurately predict the particle deposition behavior using the correlation suggested in this study. Figure 3.10 Penetration efficiency comparison of a straight tube and a sharp-bent tube and correlation results as a function of Peclet number. Symbols represent the experimentally obtained penetration efficiency for a sharp-bent tube. 70 As shown by the obtained correlation curve for predicting the penetration efficiency of a sharp-bent tube, the penetration efficiency could be expressed as a function of the Peclet number. Therefore, to further examine the additional deposition by the sharp turn effect quantitatively, the relative penetration efficiency (R) of the sharp-bent tube compared to the straight tube was shown in Figure 3.11 and the data were obtained by Equation (3.12). The relative penetration efficiency can also be obtained by substituting Cor,SBT estimated from the correlation fitting curve instead of SBT in Equation (3.12). The relative penetration efficiency decreased as the Peclet number decreased. This represents that the smaller particle size and lower flow rate enhance the deviation between the straight and sharp-bent tubes, imposing more depositions by the sharp turn. From this analysis, we can draw a conclusion that under the same conditions, e.g., tube length, particle size, and flow rate, the simple change in geometry of the tube affects the particle deposition behavior significantly. 71 Figure 3.11 Penetration efficiency comparison of a straight tube and a sharp-bent tube and correlation curve fitting curve as a function of Peclet number. Symbols represent the experimentally obtained penetration efficiency for a sharp-bent tube. 3.6 Conclusions The present study reports (1) the variation of penetration efficiency according to the particle size and flow rate, (2) the characteristic of fluid flow on the sharp-bent tube, and (3) the empirical correlation fitting curve for predicting the penetration efficiency of the sharp-bent tube. First, the fluid flow on the sharp-bent tube was systematically investigated by particle deposition experiments employing different-sized particles and 72 flow rates. We found that particle size and flow rate highly affected the penetration efficiency on the sharp-bent tube. When the particle size and flow rate decreased, the ratio of nanoparticle radial-directional residence time to flow directional residence time, i.e., tr/tx, decreased, resulting in more particle losses on both straight and sharp-bent tubes. However, through the comparison between straight and sharp-bent tubes, we found that the additional particle loss in the sharp-bent tube occurred as the Schmidt number and Reynolds number decreased. For example, the overall penetration efficiency of the sub-10 nm particles in the sharp-bent tube was approximately or more than 10% lower compared to the straight tube case. Second, to explain the experimental results of the additional particle loss caused by the sharp-bent tube, the numerical analysis of fluid flow in the sharp-bent tube was performed. The numerically calculated flow field showed two common features: the recirculation pattern at the corner of the sharp-bent tube and the separated and reattachment flow at the inner wall after the bending point. In addition to the two common features, the strength and center position of the secondary flow were carefully investigated according to the different Reynolds numbers. We found that at the higher Reynolds number, the strength of the secondary flow increased, and the core of the secondary flow moved toward the inner and side tube wall, which resulted in the fast flow velocity and thus higher penetration efficiency. From the flow simulation, the experimentally obtained deposition behaviors can be efficiently explained. Third, based on the experimental results obtained by conducting various parametric studies and employing dimensionless numbers, the empirical correlation fitting 73 curve was suggested to predict the nanoparticle penetration efficiency on the sharp-bent tube as a function of Peclet number: 𝜂𝐶𝑜𝑟,𝑆𝐵𝑇 = 1 − 𝐶1Pe 𝐶2, with C1 = 27.41 and C2 = - 0.4831 in the range of 4×103 < Pe < 107. To the best of our knowledge, there is no study to present the empirical correlation fitting curve for predicting the particle penetration efficiency on the sharp-bent tube. As compared to the penetration efficiency on the straight tube, the relative penetration efficiency on the sharp-bent tube was evaluated. The relative penetration efficiency increases from 78.7% for Pe = 4×103 to 99.1% for Pe = 107. The strong diffusion transport rate, i.e., small-sized particles, and weak advection transport rate, i.e., low flow rate, induced more particle losses due to secondary flow after the bending point, drawing the decreased relative particle efficiency. 74 Chapter 4 Numerical investigation of nanoparticle deposition location and pattern on a sharp-bent tube wall 4.1 Introduction Nanoparticles become one of the important research topics as the development of nanotechnology brings enormous benefits to various fields such as energy (Ma and Zou, 2018; Modi et al., 2020; Peng et al., 2018; Sheikholeslami et al., 2018; Wang and Cheng, 2019; Watanabe et al., 2018) and semiconductor (Jiang et al., 2019; Morales and Lieber, 1998; Saha et al., 2018; Wang et al., 2017) industries. Within the growing field of nanotechnology, there is a need for synthesizing and manufacturing nanoparticles via plasma synthesis (Lin et al., 2005; Saito et al., 2009; Vollath, 2008), chemical vapor deposition (D. S. Choi et al., 2016; Rezaei et al., 2014), flame synthesis (Strobel et al., 2006; Wegner and Pratsinis, 2004), and laser ablation (Streubel et al., 2016). In this regard, the loss of manufactured nanoparticles during the manufacturing process should be reduced for obtaining a high yield of production. Meanwhile, gas-based nanofluids are considered a potential candidate for improving the heat transfer performance in gas-cooled nuclear 75 power plants (Williams, 2015) as well as solar energy collectors (de Risi et al., 2013; Potenza et al., 2017). Moreover, the enhancement of heat transfer performance in liquid- based nanofluids has been reported by various researchers (Cai et al., 2020; Haridas et al., 2015; Hashimoto et al., 2020; Rajput and Srivastava, 2016; Srinivas Rao and Srivastava, 2014). However, deterioration of heat transfer performance occurs when nanoparticles settle and form a layer on the surface, resulting in reduced heat transfer efficiency (Das et al., 2006), similar to fouling in heat exchangers (Wang et al., 2019; Zhang et al., 2019) or heat sinks (Oguntala et al., 2018; Sarafraz et al., 2017). Technological advances in the semiconductor industry have led to reduced minimum pitch size and increased wafer size (Hu et al., 2016; Kwak et al., 2018b; Lallart et al., 2018). As a result, the size of particles that causes semiconductor failure has decreased, and thus controlling particle contamination attracts great attention (Cho et al., 2019; D. Kim et al., 2016; Sato et al., 2003; Woo et al., 2018). One example of particle contamination problems that may occur during a semiconductor process is that deposited particles in a pipeline are resuspended and cause secondary deposition/contamination on wafers (C. Kim et al., 2016a; Kim et al., 2015; Ziskind, 2006). Therefore, it is imperative to carefully investigate the characteristics of fluid flow and particle deposition and penetration during nanoparticle transport to improve production yields and quality in various applications. Many researchers have studied nanoparticle deposition or penetration in a straight tube (Gormley and Kennedy, 1975; Ingham, 1991, 1984; Martonen et al., 1996). Nanoparticle transport on a straight tube can be easily predicted owing to its simple 76 geometry; however, it is much more complicated to predict particle behaviors on a curved tube even though it is more practically important. This is because most of the transport systems have complex pipelines consisting of bent tubes and finite elbow tubes for effective utilization of limited space. In the last decades, lots of studies have been performed on particle deposition or penetration in a curved tube (Cong et al., 2017; Inthavong, 2019; McFarland et al., 1997; Peters and Leith, 2004a, 2004b; Pui et al., 1987; Sun et al., 2013, 2011; Sun and Lu, 2013; Tsai and Pui, 1990). Pui et al. presented the empirical correlation curve for obtaining penetration efficiency on a 90o smooth-bent tube in the particle size range from 2.5 to 10 μm by using Stokes number, i.e., Stk = (pVdp2Cc)/(9Dtube) (Pui et al., 1987), and the work on the smooth-bent tube was further improved by a numerical simulation (Tsai and Pui, 1990). McFarland et al. modified Pui et al.’s correlation curve (Pui et al., 1987) by considering the bent angle and curvature ratio for characterizing aerosol penetration for dp = 5–15 μm (McFarland et al., 1997). Peters and Leith measured the deposition efficiency of micro-sized particles with a size range from 5 to 150 μm in curved industrial ducts and considered the effective surface area of the bent tube to modify Pui et al’s work (Pui et al., 1987) (Peters and Leith, 2004a, 2004b). The penetration of large particles, i.e., dp = 1–16 μm (Sun et al., 2011) and dp = 0.7–100 μm (Sun et al., 2013; Sun and Lu, 2013) were further investigated to examine variable influencing factors such as duct configuration and concentration non-uniformity. Cong et al. numerically investigated particle penetration efficiency by considering the particle-wall collision effect for dp = 0.1–20 μm (Cong et al., 2017). Inthavong presents a comprehensive analysis of micro-sized particle deposition in 90o smooth-bent tubes for dp = 1–100 μm (Inthavong, 2019). The main findings in the above-mentioned studies showed that particle 77 deposition is significantly enhanced at large Stokes numbers due to inertial impaction and gravitational depositions. However, most of these studies (Cong et al., 2017; Inthavong, 2019; McFarland et al., 1997; Peters and Leith, 2004a, 2004b; Pui et al., 1987; Sun et al., 2013, 2011; Sun and Lu, 2013; Tsai and Pui, 1990) only focused on micro-sized particles on smooth-bent tubes and did not clearly report the particle deposition patterns and locations in the tubes. Nanoparticles have very different deposition mechanisms from those for micro-sized particles and, thereby, deposition patterns differ significantly. Most recent studies on nanoparticle transport mainly focused on determining deposition or penetration efficiency without analyzing particle deposition patterns or locations. Wang et al. experimentally measured the nanoparticle penetration efficiency on 90° smooth-bent tubes and sharp-bent tubes for dp = 5–15 nm (Wang et al., 2002). Ghaffarpasand et al. measured the nanoparticle penetration efficiency on 90° smooth-bent tubes and showed the experimental results as a function of Stokes number for dp = 3–17 nm (Ghaffarpasand et al., 2012). However, Stokes number of nanoparticles in this size range is generally neglected because the inertia of nanoparticles is insignificant (Ghaffarpasand et al., 2012; Lee and Gieseke, 1994; Lin et al., 2015). Additionally, particle depositions on smooth-bent coils (Yook and Pui, 2006) and 180° smooth-bent tubes (Lin et al., 2015) were reported. Despite the above-mentioned extensive studies on particle deposition in curved pipes, the main focus of past research lies in the determination of particle deposition or penetration efficiency. Consequently, there is still the main challenge regarding deposition locations and patterns of sub-10 nm particles. Even though characterizing particle 78 deposition and penetration is an active and vibrant research field, to our best knowledge, there is no study reporting nanoparticle deposition patterns and locations on a sharp-bent tube, which are crucial for the prevention and control of contamination sources in variable industrial applications. Therefore, the objectives of the present study are to analyze deposition locations and patterns on sharp-bent tubes for dp = 1–10 nm and to explore the various effects on the deposition behavior of the nanoparticles. 4.2 Numerical method 4.2.1 Computational domain Figure 4.1 illustrates the dimensions of the sharp-bent tube, i.e., elbow connection, (Model 6LV-4MW-9, Swagelok, OH, USA) which is widely employed in various industries, especially in the semiconductor industry. The blue arrow and green dotted line represent the flow direction and center line, respectively. The sharp-bent tube is parallel to the y-axis (xz plane), and the origin of the coordinate is on the inner bending point as shown in Figure 4.1. The outer bending region is a quadrant circle shape. The diameter of the sharp-bent tube (Dtube) was set 4.572 mm. To obtain the fully developed flow before the flow entering the sharp-bent tube, the inlet length of the sharp-bent tube (Linlet) was set as approximately 102Dtube. To figure out the flow and particle deposition pattern after the bending point, the outlet length of the sharp-bent tube (Loutlet) was set to be 62Dtube. 79 Figure 4.1 Schematic of the calculation domain and descriptions on a sharp-bent tube. 4.2.2 Numerical approach To simulate the flow field of the sharp-bent tube, the continuity, momentum, and energy equations were simultaneously solved by using a computational fluid dynamic (CFD) code, ANSYS FLUENT Release 18.1 (Kwak et al., 2018a, 2017). A sharp-bent curved flow was considered a turbulent flow because the strong secondary flow is generated after the bending point, and its Dean number (De), i.e., De = Re(2R/Dtube)-0.5, is 80 much higher than the value of 370 owing to the minimized curvature radius on the sharp- bent tube, i.e., R → 0 (Chrysler and Sparrow, 1986; Ghaffarpasand et al., 2012; Kwak et al., 2020; Soh and Berger, 1984). Therefore, the Reynolds stress model with enhancement wall treatment, which is one of the accurate Reynolds-averaged Navier-Stokes (RANS) models for characterizing a curved pipe flow, was employed to analyze the flow field in the sharp-bent tube (McFarland et al., 1997; Zhang et al., 2012). For considering the enhancement wall treatment, the dimensionless distance from the tube wall (y+) was set to less than 1 to meet the refinement of grid size according to the guideline suggested by Zhang et al. (Zhang et al., 2012). The grid size of the first cell near the tube wall was selected as 14.37 m and a growth factor of 1.2 was applied until the next tenth cell. The grid independence study was carried out by changing the grid size from 0.1Dtube to 0.04Dtube, i.e., the numbers of grid cells were approximately 0.7 million to 4.9 million. We optimized the number of grid cells to shorten the numerical calculation time without distorting the local fluid velocities. Therefore, in this study, the grid size and the number of grid cells were chosen as 0.06Dtube and approximately 2.1 million, respectively. The flow was assumed to be three-dimensional, steady, and incompressible. The governing equations employed in the numerical simulation, i.e., averaged continuity and RANS equation, were shown below. Averaged continuity equation: ∂𝑣?̅? 𝜕𝑥𝑖 = 0. (4.1) 81 RANS equation: 𝜌𝑣?̅? ∂𝑣?̅? 𝜕𝑥𝑗 = 𝜕 𝜕𝑥𝑗 (−?̅?𝛿𝑖𝑗 + 2𝜇𝑆𝑖𝑗̅̅̅̅ + 𝜏𝑖𝑗 𝑅 ), (4.2) where xi is the position vector component, vi is the fluid velocity component, ρ is the fluid density, p is the pressure, μ is the dynamic viscosity, δij is the Kronecker delta function, Sij = 0.5(∂vi/∂xj+∂vj/∂xi) is the strain rate tensor, and the overbar indicates the average value, and 𝜏𝑖𝑗 𝑅 is Reynolds stress which was determined by the Reynolds stress model. The Semi- Implicit Method for Pressure Linked Equations (SIMPLE) algorithm in a pressure-based solver was employed to calculate the flow field with coupled pressure and velocity. The momentum and energy equations were spatially discretized by implementing a second- order upwind scheme, and we used a first-order upwind scheme for the spatial discretization of Reynolds stress equations. The iterative calculation was terminated when all relative errors fell below 10–5. The inlet bulk mean velocities (V) through the sharp-bent tube were set to be 0.327, 0.982, 1.636, and 3.272 m/s corresponding to Reynolds numbers (Re) of 100, 300, 500, and 1,000. The pressure outlet condition was chosen for the exit of the sharp-bent tube. 4.2.3 Particle transport modeling For nanoparticles, diffusion serves as the main deposition mechanism among several particle deposition mechanisms including gravitational sedimentation, inertial impaction, thermophoresis, electrophoresis, and diffusion (Friedlander, 2000; Hinds, 1982; 82 J. H. Kim et al., 2006; Kim et al., 2014; Lee et al., 2012; Lee and Yook, 2015). Brownian diffusion resulting from collisions between fluid molecules and particles suspended in a fluid was theoretically characterized by Einstein (Einstein, 1905). The Brownian diffusion coefficient (D) is expressed as follows (Hinds, 1982): 𝐷 = 𝑘𝑏𝑇𝐶𝑐 3𝜋𝜇𝑑𝑝 , (4.3) where kb is the Boltzmann’s constant, T is the absolute temperature, Cc is the slip correction factor,  is the fluid dynamic viscosity, and dp is the particle diameter. For simulating sub- 100 nm particle-laden flow, drag force and Brownian diffusion were considered. A single- particle tracking method (Lagrangian approach) was employed, and particle behavior was assumed to be not affecting the continuous fluid flow. The particle force balance equation can be expressed as follows: 𝑑𝒗𝒑 𝑑𝑡 = 𝒇𝑫 + 𝒇𝑩, (4.4) where vp is the particle velocity vector and fD, and fB is the drag force and Brownian force per unit particle mass, respectively. The particle force balance equation was calculated using the numerical method with the analytic and Runge-Kutta schemes, in combination with the Automated Tracking Scheme recommended by ANSYS FLUENT owing to a numerical stability issue (ANSYS, 2011). In the sub-100 nm particle-laden flow, Stokes’ drag law should be modified by considering a slip correction factor. Therefore, fD is defined as follows: 𝒇𝑫 = 18𝜇 𝜌𝑝𝑑𝑝 2𝐶𝑐 (𝒗 − 𝒗𝒑), (4.5) 83 where the dynamic viscosity () was assumed to be 1.8325×10-5 kg/(ms), p is the particle density, v is the fluid velocity vector, and Cc is the slip correction factor. Kim et al. calculated the slip correction factor by measuring the electrical mobility of the certified polystyrene latex nanoparticles as a function of pressure, and the slip correction factor can be obtained as follows (Kim et al., 2005): 𝐶𝑐 = 1 + ( 2𝜆 𝑑𝑝 ) (1.165 + 0.483 exp (− 0.997 2𝜆/𝑑𝑝 )) , (4.6) where the mean free path () was assumed to be 67.3 nm. The influence of the Brownian motion was considered by using a Gaussian white noise random process with a spectral intensity (So) as follows (Li and Ahmadi, 1992): 𝑆𝑜 = 216𝜈𝑘𝑏𝑇 𝜋𝟐𝜌𝑑𝑝 5( 𝜌𝑝 𝜌 ) 2 𝐶𝑐 , (4.7) where  is the kinematic viscosity,  is the fluid density, and p is the particle density. The amplitude of the Brownian force can be represented as follows: 𝑓𝐵𝑖 = 𝜁𝑖√ 𝜋𝑆𝑜 ∆𝑡 , (4.8) where i is the zero-mean, unit-variance-independent Gaussian random numbers, which are bounded by -1 and +1, and t is the time step. For evaluating the coagulation effect, the modified Smoluchowski equation was used (Prakash et al., 2003). To be specific, the bulk residence time of nanoparticles can be estimated based on bulk flow velocity and tested tube length. In this study, the bulk flow 84 velocities through the tube were set to be 0.327, 0.982, 1.636, and 3.272 m/s corresponding to Reynolds numbers (Re) of 100, 300, 500, and 1,000. The length of the tested tube is less than 155 mm. Therefore, the bulk residence times of nanoparticles are around 0.47, 0.16, 0.09, and 0.05 s, corresponding to Re = 100, 300, 500, and 1,000, respectively. To evaluate the coagulation effect under these conditions, we used the modified Smoluchowski equation (Prakash et al., 2003) as follows: 𝑑𝐶𝑛𝑢𝑚,𝑘 𝑑𝑡 = 1 2 ∑ ∑ 𝜒𝑖𝑗𝑘𝛽(𝑣𝑖 , 𝑣𝑗) 𝑀 𝑗=2 𝐶𝑛𝑢𝑚,𝑖𝐶𝑛𝑢𝑚,𝑗 𝑀 𝑖=2 − 𝐶𝑛𝑢𝑚,𝑘 ∑ 𝛽(𝑣𝑖 , 𝑣𝑘) 𝑀 𝑖=2 𝐶𝑛𝑢𝑚,𝑖. (4.9) Where Cnum is the particle number concentration (Cnum = 2×1011 particles/m3), M is the number of volume nodes (M = 101), and vi is the particle volume at node i. i = 1 represents the monomer (e.g. dp,i=1 = 1, 3, 5, or 10 nm). χijk is the size-splitting operator for nodes i, j, and k, and β(vi, vj) is the collision kernel between nodes i and j in the free molecule regime (Kn > 1) (Friedlander, 2000), which are defined as follows: 𝜒𝑖𝑗𝑘 = { 𝑣𝑘+1−(𝑣𝑖+𝑣𝑗) 𝑣𝑘+1−𝑣𝑘 , if 𝑣𝑘 ≤ 𝑣𝑖 + 𝑣𝑗 ≤ 𝑣𝑘+1 (𝑣𝑖+𝑣𝑗)−𝑣𝑘−1 𝑣𝑘−𝑣𝑘−1 , if 𝑣𝑘−1 ≤ 𝑣𝑖 + 𝑣𝑗 ≤ 𝑣𝑘 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 , (4.10) and 𝛽(𝑣𝑖, 𝑣𝑘) = ( 3 4𝜋 ) 1/6 ( 6𝑘𝑏𝑇 𝜌𝑝 ) 1/2 ( 1 𝑣𝑖 + 1 𝑣𝑗 ) 1/2 (𝑣𝑖 1/3 + 𝑣𝑗 1/3 ) 2 . (4.11) Based on these equations, the normalized averaged particle size (= dp,avg(t)/dp,i=1) and normalized particle concentration (= Cnum,i=1(t)/Cnum,i=1(t=0)) is calculated, as shown in Figure 4.2. The maximum relative difference (caused by whether coagulation effect 85 presents or not) is less than 10-5 %, and 10-4 % for particle size and particle concentration, respectively. Therefore, the coagulation effect can be neglected in this study. Figure 4.2 Evaluation of coagulation effect during penetrating the sharp-bent tube: (Left) Calculated normalized averaged particle size (=dp,avg(t)/dp,i=1); (Right) Calculated normalized particle concentration (=Cnum,i=1(t)/Cnum,i=1(t=0)). 4.2.4 Particle injection model As the flow field and particle motion are interpreted in different ways, it is necessary to compensate for the resulting differences, i.e., the flow field is analyzed using the Eulerian method, and the particle motion is calculated using the Lagrangian method. Especially, using the Lagrangian particle model with uniform particle distribution cannot represent the nonuniform flow field such as fully developed flow. To solve this issue, the number or concentration of particles was modified by considering the flow velocity when calculating the particle deposition efficiency. To be specific, Tsai et al. (Tsai and Pui, 1990) calculated the particle deposition efficiency in a toroidal coordinate system by considering 86 the axial velocity (uaxial), particle concentration (Cnum), and the area of the i-th control volume (Ai), i.e.,  = (ith C.V. impacted uaxial,i Cnum,iAi)/(all C.V.’s uaxial,iCnum,iAi). Recently, Yook et al. developed a statistical Lagrangian particle tracking (SLPT) model which can be used for nonuniform flow fields in a two-dimensional axisymmetric domain (Yook et al., 2007). Even though the SLPT model can be applied to the simple two-dimensional system for calculating the particle deposition efficiency, it is not appropriate for complex systems such as particle deposition in three-dimensional geometry. To apply the Lagrangian approach the particle number distribution at the particle injection plane was determined based on aerosol mass flow rate, and its algorithm is shown in Figure 4.3. The local number of particles injected at the i-th element (Nin,i) was assumed to be proportional to the local aerosol mass flow rate (ṁp,i) as follows: 𝑁𝑖𝑛,𝑖 ∝ ?̇?𝑝,𝑖 = 𝜌𝑝𝑣𝑖𝐴𝑖, (4.12) where vi and Ai are the fluid velocity and area of the i-th element, respectively. Once the total number of injected particles (Nin) is defined, Nin,i can be determined as follows: 𝑁𝑖𝑛,𝑖 = 𝑁𝑖𝑛𝜓𝑖, (4.13) where 𝜓𝑖 = ?̇?𝑝,𝑖 ∑ ?̇?𝑝,𝑘 𝑛 𝑘=1 . (4.14) Particles were sequentially placed in randomized locations within the i-th element until the number of particles reached Nin,i. Specifically, in this study, as the fully developed 87 fluid flow was assumed before entering the sharp-bent region, the local aerosol mass flow rate (ṁp,i) can be represented within the cylindrical coordinate system as follows: ?̇?𝑝,𝑖 = 𝜌𝑝𝑣𝑖(𝑟?̅?)2𝜋𝑟?̅?∆𝑟, (4.15) where 𝑣𝑖(𝑟?̅?) = 2𝑉𝑎𝑣𝑔 (1 − 𝑟?̅? 2 (𝐷𝑡𝑢𝑏𝑒/2)2 ). (4.16) Here, r = ri - ri-1 and 𝑟?̅? = (ri + ri-1)/2. In this study, 0.1 million particles were injected for statistically reliable results, and the exemplary distribution of the injected particles at the injection plane is shown in Figure 4.4. 88 Figure 4.3 Algorithm for determining particle injection positions based on the aerosol mass flow rate. 89 Figure 4.4 Distribution of 0.1 million particles at the injection plane based on aerosol mass flow rate. 4.3 Experimental method Figure 4.5 shows the schematic diagram of the experimental setup for measuring the deposition efficiency of nanoparticles on a sharp-bent tube. The silver nanoparticles (AgNPs) or glucose nanoparticles (C6H12O6NPs) were generated by using a tube furnace (Model STF 55433C-1, Lindberg/Blue M, MA, USA) or an electrospray aerosol generator (ES, Model 3480, TSI, MN, USA), respectively. Silver powder (Ag) placed on the ceramic 90 tube inside the tube furnace was evaporated due to high temperature, and the silver vapor was carried by the ultra-high purity grade nitrogen gas (99.999%). Through the condensation process resulting from the low temperature at the downstream flow of the ceramic tube, AgNPs were generated. The temperature of the tube furnace was set to 1100 oC. For the generation of C6H12O6NPs, we prepared 1 ml of the 0.01 M glucose solution (C6H12O6(aq)) and adjusted the electrical conductivity of the solution by adding 0.02 ml of the 0.05 M ammonium acetate solution (CH3COONH4(aq)). The prepared sample was placed in the sample chamber in the ES. We controlled the liquid flow rate through a 40- m capillary tube, whose end was immersed in the sample, by adjusting the chamber pressure. By applying the high voltage to the sample, highly charged droplets were generated and carried with sheath air. The highly charged droplets become smaller droplets as the pressure of expansion created by surface charge becomes larger than the pressure created by surface tension, i.e., exceeding the Rayleigh limit. The very small droplets dispersed from the ES were dried by a diffusion dryer, and finally, C6H12O6NPs were generated (Gomez and Tang, 1994; Lee et al., 2019b, 2019a, 2017a; Taflin et al., 1989). In this study, we used the liquid flow rate through the capillary tube of approximately 0.32 L/min and the applied high voltage of 3.0 kV to form the cone-jet mode, which is considered a proper dispersion mode at the tip of the capillary tube (Hogan et al., 2006). Depending on the experimental purpose, we employed a three-way valve to choose either AgNP or C6H12O6NP generating system as shown in Figure 4.5. 91 Figure 4.5 Schematic of the experimental setup for measuring nanoparticle deposition efficiency of nanoparticles on a sharp-bent tube. An orifice was used as a flow restrictor in order that the aerosol flow rate was set to be 1.0 L/min. The overflowed flow was discharged into the air through a HEPA filter. A Polonium-210 radioactive source was used for neutralizing the generated polydisperse AgNPs or C6H12O6NPs. The diluter for mixing airborne nanoparticles with clean air was used, and the clean air flow rate was measured by using a mass flow meter (Model 4140, TSI, MN, USA) and set to 0.6 L/min. To assure fully developed flow before entering the test tube section, a straight long tube with a length of approximately 100Dtube was installed. A three-way valve was employed to sample either the upstream or downstream. To minimize the measurement error caused by the additional particle loss during the particle transportation from the upstream and downstream sampling point to the three-way valve, the length of each sampling tube line was set to be the same. Furthermore, to prevent particle loss by the electrostatic effect, the conducting material of the tube was used for the entire transport system (Liu et al., 1985). 92 The nanoparticle size distribution of upstream and downstream was measured by a scanning mobility particle sizer (SMPS) consisting of a nano-differential mobility analyzer (Nano-DMA, Model 3085, TSI, MN, USA), an electrostatic classifier (Model 3080, TSI, MN, USA), and an ultrafine condensation particle counter (UCPC, Model 3776, TSI, MN, USA). The flow rates of aerosol and sheath air through the Nano-DMA were set to be 1.5 and 10 L/min, respectively. The 120-s scanning time and 30-s retrace time were selected for the SMPS measurements. The deposition efficiency of nanoparticles on a sharp-turn tube (dep) was determined by obtaining the ratio of the downstream concentration (Cnum,down) to the upstream concentration (Cnum,up) and calculated as: 𝜂𝑑𝑒𝑝 = 1 − 𝐶𝑛𝑢𝑚,𝑑𝑜𝑤𝑛 𝐶𝑛𝑢𝑚,𝑢𝑝 . (4.17) 4.4 Result and discussion 4.4.1 Velocity magnitude and streamline in the midplane of a sharp-bent tube In the presence of a three-dimensional flow field, the flow is often considered to consist of two components: the primary flow and the secondary flow. The directions of the primary flow and secondary flow are parallel to and perpendicular to the main fluid flow, respectively. Figure 4.6 shows the normalized velocity magnitude and streamline in the midplane (cross section in the xz plane) of a sharp-bent tube according to various Reynolds numbers, i.e., Re = (a) 100, (b) 300, (c) 500, and (d) 1,000. In this study, the axial and radial 93 directions were defined as perpendicular and parallel directions to each cross section in Figure 4.6a, respectively. Before further analysis of the flow characteristics in a sharp-bent tube, the correctness of the simulation method used in this study was verified by examining flow fields in smooth-bent tubes with bend angles of 30o and 60o. The curvature radius and diameter of the tube of the reference model (Enayet et al., 1982) were 134.4 mm and 48 mm, respectively. The numerically obtained velocity magnitudes at various locations inside the tubes were compared with the experimental work conducted by Enayet et al. (Enayet et al., 1982), and the comparison results are in good agreement as confirmed in Figure 4.7. Therefore, our simulation method for characterizing flow field in a tube with a bent structure was employed for further study. In Figure 4.6, before the flow enters the sharp-bent region, the fluid flow is not affected by the bending structure of the tube. Because the inlet length of the sharp-bent tube, Linlet = 102Dtube, is longer than the hydrodynamic entry length (0.05DtubeRe), a fully developed velocity profile is observed at Ain-Aout. At the bending point (Bin-Bout), the fluid flow at the inner side of the tube (Bin) is slightly more accelerated compared to the one for the outer side (Bout). The recirculation occurs at the corner of the outer bending point where the flow has relatively lower velocities, i.e., blue-colored region, for all Reynolds numbers. After the sharp-bent point, the separation of the flow occurs at the inner wall and the locations of the flow separation for all Reynolds numbers are similar. This finding was also observed in the work of Takamura et al. (Takamura et al., 2012). Furthermore, the faster fluid flow, i.e., the red-colored region, near the outer wall occurs, following which the velocity gradually decreases as the flow is developing. Furthermore, after the bending point, the streamlines near the inner wall at a high Reynolds number gradually approached the 94 streamline near the outer wall. At a low Reynolds number, on the other hand, the streamlines are relatively parallel to the main flow direction. This phenomenon at a high Reynolds number demonstrates that the secondary flow after the bending point is stronger than the low Reynolds number. Figure 4.6 Velocity magnitude and streamline in a sharp-bent tube at y = 0 surface (xz plane) for different Reynolds numbers: (a) Re = 100; (b) Re = 300; (c) Re = 500; (d) Re = 1,000. 95 Figure 4.7 Normalized velocity magnitude along the radial position in a smooth-bent tube obtained by the present numerical simulation (red line) and experimental work done by Enayet et al. (blue rectangle) under two different Reynolds number conditions (Enayet et al., 1982). 4.4.2 Axial velocity at the cross-section of a sharp-bent tube Figure 4.8 shows that the normalized axial velocity on a sharp-bent tube at various cross-sections, i.e., Ain-Aout (surface at x = -8 mm), Bin-Bout (surface at x = z), Cin-Cout (surface at z = -1 mm), Din-Dout (surface at z = -3 mm), Ein-Eout (surface at z = -5 mm), and Fin-Fout (surface at z = -7 mm) represented in Figure 4.6a, according to various Reynolds 96 numbers, i.e., Re = (a) 100, (b) 300, (c) 500, and (d) 1,000. The axial velocity is defined as the velocity perpendicular to each cross-section. The concentric contour line was observed in Ain-Aout owing to the insignificant impact of the sharp-bent tube on the flow before entering the bending region. At the bending point (Bin-Bout), the overall axial velocity significantly decreases compared to the axial velocity at the cross-section of Ain-Aout. More interestingly, in the cross-section of Bin-Bout, as the Reynolds number increases, the blue-colored region (crescent-shaped region) with the very slow axial velocity becomes lighter along the outer line (Bout), meaning the axial velocity becomes relatively higher at the outer corner of the bending point. The crescent-shaped region with the slightly higher velocity might be a consequence of the stronger recirculation around the bending point as shown in the streamline in Figure 4.6. The results of the axial velocity after the bending region (C to F) show that most of the fluid flow is deviated toward the outer region of the tube, regardless of Reynolds number. Therefore, the outward-sloping flow is likely to cause most of the nanoparticles, which have a less inertial effect, to lean toward the outer region. In the cross-sections of Cin-Cout and Din-Dout, as the Reynolds number increases, the region with the slower axial velocity, i.e., the blue-colored region near Cin and Din, gradually becomes narrower and moves toward the center of the tube. Furthermore, the boundary layer for higher Reynolds numbers after the bending section becomes thinner as clearly seen in the outer region of each location (Cout, Dout, Eout, and Fout). These phenomena might be caused by the stronger secondary flow at a higher Reynolds number, resulting in penetrating closer to the tube wall. 97 Figure 4.8 Axial velocity on a sharp-bent tube at various cross-sections (Ain-Aout, Bin-Bout, Cin-Cout, Din-Dout, Ein-Eout, and Fin-Fout) for different Reynolds numbers: (a) Re=100; (b) Re=300; (c) Re= 500; (d) Re=1,000. 4.4.3 Secondary flow in the cross-section of a sharp-bent tube Figure 4.9 illustrates the normalized radial velocity and the secondary flow streamline on a sharp-bent tube at various cross-sections, i.e., Ain-Aout, Bin-Bout, Cin-Cout, Din-Dout, Ein-Eout, and Fin-Fout, according to various Reynolds numbers, i.e., Re = (a) 100, (b) 300, (c) 500, and (d) 1,000. Before the bending point, there are no secondary flow 98 patterns as shown in the figure for Ain-Aout. At the bending point (Bin-Bout), the crescent- shaped region with the lower radial velocity is observed along the outer wall (Bout), and, as the Reynolds number increases, the relatively higher radial velocity (lighter blue) appears. The curved streamlines formed near the Bout location (θ = 0o) at lower Reynolds number (Re = 100) are closer to the center of the tube wall while, at higher Reynolds number (Re = 1,000), they are formed much closer to the outer wall, indicating the thinner boundary layer thickness. Consequently, this represents the stronger secondary flow occurs at a higher Reynolds number, more deeply penetrating the tube's outer wall. Figure 4.9 Radial velocity and secondary flow on a sharp-bent tube at various cross- sections (Ain-Aout, Bin-Bout, Cin-Cout, Din-Dout, Ein-Eout, and Fin-Fout,) for different Reynolds number: (a) Re=100; (b) Re=300; (c) Re= 500; (d) Re=1,000. 99 To give a quantitative explanation of the secondary flow boundary layer, the normalized secondary flow boundary layer thickness, δrad,i, is defined as the distance from the tube wall at which uradial/umean = i. Here, i represents the value of normalized radial velocity. Figure 4.10 shows the secondary flow boundary layer thickness values as a function of azimuthal angle for i = 0.01 (a and d), 0.05 (b and e), and 0.10 (c and f). Based on the quantitative results shown in Figure 4.10 and radial velocity contours in Figure 4.9, we clearly see that the thinner secondary flow boundary layer thickness indicates a higher normalized radial velocity. To be specific, δrad,i for the Bin-Bout section at θ > 90o has lower values, i.e., thinner boundary layer, as depicted in Figure 4.10 (a-c), and the overall normalized radial velocities for Bin-Bout section, are higher at θ > 90o compared to at θ < 90o, as illustrated in Figure 4.9. . The pronounced difference in secondary flow boundary layer thickness at Bin-Bout section between each Reynolds number occurs at θ = 0o. For the Cin-Cout section, the relatively strong secondary flow, i.e., thinner boundary layer, occurs at around θ = 90o, compared to the secondary flow strength at near θ = 0 and 180o. These results are supported by the previous work from Yook and Pui (Yook and Pui, 2006). They reported that secondary boundary layer thickness in a curved flow with a high Reynolds number was thinner, resulting in a stronger secondary flow. Based on the results, the distance from the tube wall at uradial/umean = 0.1 near the outer wall at the Bin-Bout section was estimated as 438 and 27.1 µm for Re = 100 and 1,000, respectively. 100 Figure 4.10 Secondary flow boundary layer thickness at Bin-Bout (surface at x = z), and Cin- Cout (surface at z = -1 mm) with various Reynolds numbers (Re = 100, 300, 500, and 1,000). After the bending point, the streamlined patterns for the secondary flow at the different Reynolds numbers show clear differences. The area of the closed streamlines formed around the vertex gradually decreases as the flow is developing. The center of the vortices caused by the secondary flow tends to be closer to the wall as the Reynolds number increases, resulting in faster radial velocity near the tube wall owing to the continuity of secondary flow. Moreover, when comparing between (Cin-Cout) and (Din-Dout, Ein-Eout, and Fin-Fout) locations, the vortices of the secondary flow move slightly toward the center of the tube as the flow is developing from the C to F location. In addition to these patterns of the secondary flow, the overall magnitude of the normalized radial velocity gradually decreases as the flow is developing. The relatively faster radial velocity is confirmed at the Cin-Cout location when the Reynolds number becomes higher. Therefore, it can be summarized that the higher Reynolds number and the less developed flow (closer to the 101 bending point) result in faster radial velocity near the tube wall. 4.4.4 Deposition efficiency according to particle size To validate the numerical results and investigate the effect of particle size on particle deposition behavior in the sharp-bent tube, the deposition efficiency on the sharp- bent tube was numerically and experimentally obtained. Figure 4.11 shows the comparison of the deposition efficiency on a sharp-bent tube as a function of particle diameter between four cases at Re = (a) 500, (b) 1,000, and (c) 1,500: AgNPs furnace-SMPS experiment (triangular symbols); C6H12O6NPs electrospray-SMPS experiment (inverted triangular symbols); AgNPs electrometer experiment performed by Kwak et al. (Kwak et al., 2020) (rectangular symbols); present numerical simulation (circular symbols with line). In general, the overall trend of the present numerically calculated results agreed well with the various experimental data, as shown in Figure 4.11. As the particle size decreases, the deposition efficiency on a sharp-bent tube sharply increases. This is because the smaller particles result in not only the shorter radial-directional residence time (tr) due to a higher Brownian diffusion coefficient (D), i.e., tr  tB  Dtube2/8D (Hinds, 1982; Kwak et al., 2020; Yook et al., 2010; Yook and Ahn, 2009) but also the higher concentration near the outer wall because of the smaller particles with smaller inertia, well following the main stream flow (Lee et al., 2014). The numerical and experimental results show that there are fewer deposited particles with higher Reynolds numbers, especially for smaller particles. This is due to the fact that as Reynolds number increases, the axial-directional residence time, i.e., ta  L/uaxial, decreases while the radial-directional residence time (tr) is almost maintained, 102 resulting in less particle deposition on the tube wall. Figure 4.11 Nanoparticle deposition efficiency on a sharp-bent tube for different Reynolds numbers: (a) Re = 500; (b) Re = 1,000; (c) Re = 1,500. To examine the effect on the thermophoretic effect caused by the heated tube wall situation, we compared the relative importance of the Brownian diffusion effect and thermophoretic effect by introducing two criteria, i.e., the ratio of the radial-directional residence time of a particle influenced by the thermophoretic effect to Brownian diffusion 103 (ψtime = tTH/tB) and the ratio of Brownian diffusion coefficient to thermophoretic diffusion coefficient (ψD = D/DTH) (Hedayati and Domairry, 2016; Rajput and Srivastava, 2016). If the value of ψtime or ψD is greater than 1.0, it implies that the Brownian diffusion effect contributes more to particle deposition, whereas if the value of ψtime or ψD is less than 1.0, the thermophoretic effect has more influence on particle deposition than Brownian diffusion effect. The radial-directional residence time of a particle under the thermophoretic effect (tTH) can be determined by calculating the thermophoretic velocity of a particle, which can be obtained by the thermal gradient in the fluid (VTH = 0.55µ∇T/ρT) (Hinds, 1982; Waldmann and Schmitt, 1966), i.e., tTH  Dtube/2VTH. The thermophoretic diffusion coefficient (DTH) can be calculated by considering the volumetric particle concentrations, i.e., DTH = 0.26kµφ/(ρ(2k+kp)). The thermal conductivity of the sub-10 nm particles (kP) is evaluated by the relation with the thermal conductivity of the bulk materials (kp = dpkbulk/λe,b) (Warrier and Teja, 2011). The reference material was selected as silver nanoparticles with the bulk thermal conductivity (kbulk) of 424 W/(mK), and the mean free path of electrons in the bulk state is 49.10 nm (Warrier and Teja, 2011). Table 4.1 compares each radial-directional residence time in a temperature gradient of 1,000 K/m, diffusion coefficient in a volumetric particle concentration of 1.0%, and the calculated ratios as a function of particle size, i.e., ψD and ψtime. Here, the temperature gradient of 1000 K/m and volumetric particle concentration of 1.0% were chosen for maximizing the thermophoretic effect (Hinds, 1982; Rajput and Srivastava, 2016). Therefore, the thermophoretic effect under the condition in the present numerical study can be reasonably neglected because both criteria values were estimated much greater than 1.0, i.e., ψtime and ψD ≫ 1.0. However, it should be noticed that particle deposition efficiency is expected to be affected by several 104 other competing mechanisms including the thinned or disrupted thermal boundary layer by the presence of nanoparticles and the coupled effect of hydrodynamic and thermal boundary layers under the heated tube wall case (Haridas et al., 2015; Rajput and Srivastava, 2016; Srinivas Rao and Srivastava, 2014). Table 4.1 Comparison of Brownian diffusion effect and thermophoretic diffusion effect at different particle sizes. dp [nm] Brownian diffusion effect Thermophoretic diffusion effect Ratio D [m2/s] tB [s] DTH [m2/s] tTH [s] ψD [-] ψtime [-] 1 5.26×10-6 1.24×10-1 1.16×10-10 4.11×101 4.52×104 3.32×102 3 5.88×10-7 1.11×100 3.90×10-11 4.11×101 1.51×104 3.70×101 5 2.13×10-7 3.07×100 2.34×10-11 4.11×101 9.09×103 1.34×101 10 5.38×10-8 1.21×101 1.17×10-11 4.11×101 4.60×103 3.39×100 4.4.5 Deposition location and pattern To investigate the patterns of the deposited particles before and after the sharp- bent point, the cumulative number of deposited particles (Ndep) was examined according to the position at the x- and z-coordinate as shown in Figure 4.12. The slope of the cumulative number of deposited particles, i.e. |d(Ndep)/dx| or |d(Ndep)/dz|, gradually decreases before the flow passes the sharp-bent point (x-coordinate). This is because the particle concentration gradually decreases as the particle-laden flow passes through the straight tube (Gormley and Kennedy, 1975; Shi et al., 2004). However, after passing 105 through the sharp-bent point, although the particle concentration has already been decreased, the slope of the cumulative number of deposited particles is significantly increased right after the bending point, following which it maintains rather than the case before passing the sharp-bent point (except for a few cases of low Reynolds number). It is interesting to note that with a lower Reynolds number and smaller particle size, the slope of the cumulative number of deposited particles at -7 mm < z < -3 mm is similar to the slope for the particles deposited at -7 mm < x < 0 mm in the straight tube region. This might be due to the fact that at Din-Dout (z = -3 mm) and Ein-Eout (z = -5 mm) the magnitude of radial velocity and secondary flow is relatively small at low Reynolds number, as shown in Figure 4.9a. Notably, it is true that stronger secondary flow occurs at a higher Reynolds number and enhances particle deposition. However, it does not mean higher Reynolds number results in a higher deposition rate, which is generally not true, because the particle deposition is significantly enhanced at a lower Reynolds number due to the enhanced diffusional deposition. Therefore, there should be caution in analyzing the results in Figure 4.12. 106 Figure 4.12 Cumulative number of deposited particles on a sharp-bent tube according to the position at the x- and z-coordinate for different Reynolds numbers and different particle sizes: (a) dp = 1 nm; (b) dp = 3 nm; (c) dp = 5 nm; (d) dp = 10 nm. To identify the location of the particle deposition in the longitudinal tube direction more macroscopically, a local deposition enhancement factor (LDEF) was introduced to examine the relative amount of the deposited particles for each section (Shi et al., 2004). The LDEF is defined as follows: LDEF = 𝑁𝑑𝑒𝑝,𝑖/𝐴𝑖 𝑁𝑑𝑒𝑝,𝑡𝑜𝑡/𝐴𝑡𝑜𝑡 , (4.18) 107 where Ndep is the number of deposited particles, and A is the area of the inner wall of the tube. The subscripts of i and tot indicate the section location and total, respectively. A higher LDEF represents more particles posited at the unit area compared to other sections. In this study, we divided the sharp-bent tube into six sections. Sections 1 and 3 occupy 1.78Dtube (=8.1 mm) in each direction from the origin, and Section 2 represents the edge of the sharp-bent tube. The remaining Sections 4, 5, and 6 are the regions with a tube length of 10Dtube (=45.7 mm). In Section 3, right after the bending region, the highest LDEF was obtained. This indicates that most of the particles are deposited right after the bending region owing to the strong secondary flow induced by the sharp-bent tube. Notably, despite the strong secondary flow at Section 2 (bending point), the relatively low LDEF was estimated. This is because the aerosol mass flow rate is very low at Section 2 due to the low axial velocity near Bout where particle deposition occurs; therefore, fewer particles pass through Section 2, resulting in less deposition. For Sections 1 and 2, the relatively small difference in LDEFs was obtained between different Reynolds numbers, but for Section 3, the relatively small LDEFs were estimated at Re = 100 compared to other LDEFs for Re = 300, 500, and 1,000. This means that the stronger secondary flow associated with a higher Reynolds number enhances the particle deposition in Section 3. Moreover, it should be noted that as an LDEF value is affected by the upstream particle concentration, gradually decreasing LDEF values were obtained along the straight region at Sections 4, 5, and 6. 108 Figure 4.13 Local deposition enhancement factor (LDEF) on a sharp-bent tube at each section for various Reynolds numbers and particle sizes. To systematically analyze the particle deposition pattern along the azimuthal angles in Section 3 where most of the particles are deposited, we introduced the relative deposition efficiency (ηdep,R), which is defined as follows: 𝜂𝑑𝑒𝑝,𝑅(𝜃) = ∫ 𝑁𝑑𝑒𝑝,𝑧(𝜃 ∗) 𝑑𝜃∗ 𝜃+22.5° 𝜃−22.5° ∫ 𝑁𝑑𝑒𝑝,𝑧(𝜃∗) 𝑑𝜃∗ 360° 0° , (4.19) where θ is the azimuthal angle, and the outer part of the tube wall is represented as θ = 0. Ndep,z is the number of deposited particles in a specific range in the z-direction. Figure 4.14 shows the results of the particle deposition pattern at the bending point (Section 3) for various locations and particle sizes. Regardless of Reynolds number and particle size, the patterns of particle deposition show that more particles are deposited at the outer region, i.e.,  = 0 or 360o, and fewer particles were deposited at the inner region, i.e.,  = 180o, resulting in the V-shaped curve in the figure. This is because the higher 109 nanoparticle concentration is formed near the outer wall due to the higher normalized axial velocity, i.e., higher mass flow rate carrying more particles (Figure 4.8). Therefore, the difference in the relative deposition efficiency along the azimuth direction is mainly caused by the outward-sloping flow. On the other hand, the results of the relative deposition efficiency show that particles are uniformly deposited along the azimuthal angles as the Reynolds number increases as shown in Figure 4.14d. This might be the consequence of the strong secondary flow at a high Reynolds number, carrying particles uniformly to the entire azimuthal angles, i.e., well mixed. Therefore, particle deposition patterns show a sharp V-shaped curve at a low Reynolds number and a blunt V-shaped curve at a high Reynolds number. 110 Figure 4.14 Particle deposition pattern right after the bending point, obtained by calculating relative deposition efficiency at various locations and particle sizes for different Reynolds numbers: (a) Re=100; (b) Re=300; (c) Re= 500; (d) Re=1,000. 4.5 Conclusions In the present study, we reported the characteristics of fluid flow and particle behavior on a sharp-bent tube at various conditions. Numerical simulations for analyzing nanoparticle deposition efficiency, location, and pattern on a sharp-bent tube were 111 conducted by applying the modified single-particle tracking method based on aerosol mass flow rate. The developed numerical model was validated by comparing the numerical deposition efficiency to the systematic experiments on AgNPs and C6H12O6NPs deposition in a sharp-bent tube. Based on the numerical simulations of a sharp-bent tube, we found several important findings as follows: 1) Numerical analysis of the flow field in a sharp-bent tube revealed that at a high Reynolds number, strong secondary flow, developed after the flow passed the bending point, penetrated closer to the tube's inner wall. Furthermore, as Reynolds number increased, the vortices caused by the secondary flow moved toward the tube wall, carrying more nanoparticles and enhancing the deposition. The secondary flow was observed better at the region closer to the bending point, i.e., less developed flow after the bending region, following which it became weaker along the downstream flow. 2) Nanoparticle deposition efficiency was obtained as a function of Reynolds number and particle size. We found that the deposition efficiency on a sharp-bent tube was affected by several factors. In general, lower Reynolds number and smaller particle size enhanced deposition by diffusion of nanoparticles. In a sharp-bent tube, outward- sloping flow and secondary flow also enhanced the deposition of nanoparticles by carrying them closer to the tube wall. Notably, the stronger secondary flow was observed at a higher Reynolds number. This means the particle deposition can be enhanced at a high Reynolds number by creating a strong secondary flow and thus promoting the diffusional deposition due to the shorter radial-directional residence time. Therefore, the simulation approach introduced in this study can be widely used to 112 predict the rate of particle deposition quantitatively even in complex conditions or geometries. 3) Lastly, we examined the deposition location and pattern of nanoparticles on the sharp- bent tube. We observed a significant increase in the cumulative number of deposited particles right after the flow passed the sharp-bent point, meaning the bending geometry largely enhanced the deposition of nanoparticles. More interestingly, the particle deposition pattern along the azimuthal angles at Section 3 (refer to Figure 4.13 for the location) showed that depending on the Reynolds number, the deposition pattern displayed significant differences. At a low Reynolds number, much more particles were deposited at the outer region owing to the higher axial velocity near the outer wall compared to the side or inner walls. However, at a high Reynolds number, it was found that particles were uniformly deposited along the azimuthal angles owing to the strong secondary flow that carried particles to the entire azimuthal angles. The introduced numerical method and findings on the deposition location might be very useful in various applications such as cause analysis of decreased heat exchange efficiency and deteriorated semiconductor yield due to particle contamination. In the future, furthermore, it would be important to investigate the nanoparticle deposition location and pattern under various conditions such as turbulent flow regimes, different working fluids, and developing flow regimes. 113 Chapter 5 Numerical study of nanoparticle penetration characteristics in forked tubes using tracking particle identification 5.1 Introduction Advances in nanomaterial technology have brought significant advantages to fields such as energy, semiconductors, and health industries; as a result, many nanoparticle synthesis methods have been developed (Mezhericher et al., 2018; Ranjan et al., 2016; Streubel et al., 2016; Strobel et al., 2006). Accordingly, it has become necessary to study nanoparticle loss and penetration during the transport process to obtain high production yields. Meanwhile, the importance of nanoparticle transport has been highlighted in various applications such as enhanced heat transfer performance with nanofluids in heat exchangers or heat sinks (Haridas et al., 2015; Ho et al., 2020; Lyu et al., 2020; Modi et al., 2020; Potenza et al., 2017), particulate contamination control in semiconductor manufacturing processes (Hu et al., 2016; Kwak et al., 2018b; Lee and Yook, 2015; Woo et al., 2018), and inhalation of drug/toxic/virus aerosols in humans (Dong et al., 2018; Haghnegahdar et al., 2019; Shi et al., 2004). Transport systems for these applications are 114 generally composed of complicated tubing systems with several branched structures or inlets/outlets to improve the process efficiency (Ho et al., 2020; Lyu et al., 2020; Patil et al., 2020; Shi et al., 2004; Shui et al., 2018). The interaction of several effects on nanoparticles and fluid flow, including Brownian diffusion, drag force, and secondary flow, determines the nanoparticle transport characteristics such as deposition on tubular walls or in branched regions (Kwak et al., 2020; Shi et al., 2004). Gormley and Kennedy developed an equation for determining the nanoparticle penetration efficiency in a straight tube under a fully developed parabolic velocity inlet condition (Gormley and Kennedy, 1975). However, their analytical solution is not suitable for many realistic applications that consist of curved pipe systems in which a secondary flow effect appears, resulting in a complex particle motion (Kwak et al., 2020; Olin and Dal Maso, 2020; Wang et al., 2002; Yook and Pui, 2006; Zhao et al., 2020). Several studies have investigated changes in particle deposition/penetration efficiency due to secondary flow in curved tubes. Pui et al. used the Stokes number (Stk) to propose an empirical correlation equation to obtain (or predict) the penetration efficiency in 90° smooth-bent tubes over a particle diameter (dp) range of 2.5 to 10 μm (Pui et al., 1987). McFarland et al. further developed the correlation curve of Pui et al. (Pui et al., 1987) by considering the curvature ratio and bend angle for dp = 5–15 μm (McFarland et al., 1997). Cong et al. numerically examined the particle penetration efficiency in 90° smooth-bent tubes, including the effect of the particle wall collision model for dp = 0.1–20 μm (Cong et al., 2017). Inthavong presented a unifying correlation curve for 90° smooth-bent tubes with various geometrical combinations over a particle size range of 1–100 μm (Inthavong, 2019). Guo et al. numerically revealed that the particle deposition efficiency in a 90° smooth-bent 115 tube with a circular cross-section was higher than that of a square cross-section (Guo et al., 2020). The above studies showed that particle deposition is significantly increased in curved tubes at large Stokes numbers because of inertial collision and gravitational deposition enhanced by the secondary flow (Cong et al., 2017; Guo et al., 2020; Inthavong, 2019; McFarland et al., 1997; Pui et al., 1987). However, most of these studies focused only on micron-sized particles in curved tubes and examined macroscopic penetration/deposition efficiency without analyzing microscopic regions in the tubes (Cong et al., 2017; Guo et al., 2020; Inthavong, 2019; McFarland et al., 1997; Pui et al., 1987). Generally, the transport mechanisms of micron-sized particles in a curved flow shown in the abovementioned studies (Cong et al., 2017; Guo et al., 2020; Inthavong, 2019; McFarland et al., 1997; Pui et al., 1987) cannot be applied when examining the characteristics of nanoparticle transport because nanoparticles have a small inertial force and are highly affected by diffusion (Ghaffarpasand et al., 2012; Kwak et al., 2020; Lin et al., 2015; Olin and Dal Maso, 2020; Wang et al., 2002). An early experimental study on nanoparticle penetration characteristics was carried out by Wang et al.; they systematically investigated the diffusional loss in 90° smooth-bent and sharp-bent tubes by comparing the results with the Gormley and Kennedy analytical solution (Gormley and Kennedy, 1975) for dp = 5–15 nm (Wang et al., 2002). Ghaffarpasand et al. conducted experiments in a straight and 90° smooth-bent tube and obtained the nanoparticle penetration efficiency and deposition velocity as a function of the Stokes number for particle sizes of 3–17 nm (Ghaffarpasand et al., 2012). Lin et al. performed a numerical study on cylindrical nanoparticles through a curved tube; the results showed that the degree of non-uniformity of particle concentration distribution increased 116 with increasing Stokes number and Reynolds number in a 90° smooth-bent tube (Lin et al., 2020). Ghaffarpasand et al. and Lin et al. observed different trends in nanoparticle penetration, showing that the penetration efficiency started to decrease at specific Stokes numbers of 0.024 (Ghaffarpasand et al., 2012) and 0.02 (Lin et al., 2020), respectively. Yook and Pui experimentally measured the nanoparticle penetration efficiency in smooth- bent coils and presented a correlation fitting curve by considering the secondary flow boundary thickness and Brownian diffusion for dp = 3–50 nm (Yook and Pui, 2006). Lin et al. developed a numerical model for predicting nanoparticle penetration efficiency in a 180° smooth-bent tube for dp = 8–550 nm as a function of the Schmidt and Dean numbers (Lin et al., 2015). Our previous study (Kwak et al., 2020) experimentally investigated nanoparticle penetration efficiency and presented a correlation fitting curve for a sharp- bent tube for dp = 3–50 nm. Olin and Maso presented the numerically obtained nanoparticle penetration efficiency with a constant and developed concentration profile; they also presented a correlation fitting curve for dp < 23 nm in 90° smooth-bent tubes (Olin and Dal Maso, 2020). However, most of these studies were limited to simple, single-curved tube geometries (Ghaffarpasand et al., 2012; Gormley and Kennedy, 1975; Kwak et al., 2020; Lin et al., 2020, 2015; Olin and Dal Maso, 2020; Yook and Pui, 2006). Therefore, it is necessary to further investigate more complicated tubing systems and compare the results. Furthermore, forked tubes with tree-like branching structures are widely utilized in various industries to provide working fluids into systems with multiple inputs; they are also present in the respiratory system (lungs) and circulatory system (blood vessels). In the present study, the penetration characteristics of sub-100 nm nanoparticles were investigated by tracking individual particles in a forked tube with a tree-like 117 branching structure at Reynolds numbers ranging from 370 to 2000. To track individual particles in the forked tube, a modified single-particle tracking analysis based on the aerosol mass flow rate was employed; the validity of the numerical analysis method was demonstrated by comparing the obtained deposition efficiency with the experimental results. According to our research, this is the first time that the penetration characteristics of sub-100 nm nanoparticles have been systematically investigated for a forked tube by employing the detailed contours of particle distribution, concentration, and identification (ID) at cross-sections under various conditions. Furthermore, we suggested a simple but powerful correlation equation as a function of the Peclet number for predicting nanoparticle deposition efficiency for the forked tube and compared the results with those for straight and single sharp-bent tubes. 5.2 Method 5.2.1 Numerical method Figure 5.1 shows the geometry of the forked tube used in this study. The forked tube comprises six elbow connections (Model 6LV-4MW-9, Swagelok, OH, USA) and three union tees (Model 6LV-4MW-3, Swagelok, OH, USA). The forked tube had one inlet and four outlets, made with glands (Model 6LV-4-VCR-3-4, Swagelok, OH, USA), and male nuts (Model SS-4-VCR-4, Swagelok, OH, USA). The two outlets on each side of the initial fork are called the outer and inner outlets, respectively, as shown in Figure 5.1b; each component was welded together. The dimensions of the forked tube in Figure 5.1b 118 and 1c are Dtube = 4.572 mm, L1 = 40.4 mm, L2 = 67.2 mm, L3 = 120.8 mm, L4 = 46.2 mm, L5 = 23.5 mm, and L6 = 10.414 mm. The bending region of the elbow connections had a quadrant-circle shape, as illustrated in Figure 5.1c. Half of the forked tube was simulated as a calculation domain because of the symmetric geometry with respect to the x-y plane. Figure 5.1 Geometry of forked tube: (a) photo of a forked tube; (b) computational domain of forked tube; (c) schematic view of elbow connection (left) and union tee (right). A computational fluid dynamics (CFD) software package, ANSYS FLUENT 119 Release 18.1, simulates the flow fields and particle trajectories. The flow fields were considered a continuous phase, i.e., the Eulerian method; the particle trajectories were treated as a discrete phase that exchanges mass and momentum with the continuous phase, i.e., the Lagrangian method. The resulting differences caused by these two different methods were compensated by using a modified single-particle tracking analysis based on aerosol mass flow rate; a detailed description of the flow-rate-weighted particle tracking method is available in our previous work (Kwak et al., 2021b). As the curved flow with a high Dean number (De), i.e., De = Re(2R/Dtube)-0.5, was considered turbulent flow, the Reynolds-averaged Navier-Stokes (RANS) equation was used to solve the continuous phase flow (Chrysler and Sparrow, 1986; Ghaffarpasand et al., 2012; Soh and Berger, 1984). It is worthwhile to mention that the authors’ previous work shows that our simulation results by using the RANS equation on the curved flow agreed well with the experimental data (Kwak et al., 2021b). The governing equations, namely the averaged continuity and RANS equations, were simplified with the assumptions of steady and incompressible flow. The simplified governing equations are as follows. Averaged continuity equation: ∂𝑣?̅? 𝜕𝑥𝑖 = 0. (5.1) RANS equation: 𝜌𝑣?̅? ∂𝑣?̅? 𝜕𝑥𝑗 = 𝜕 𝜕𝑥𝑗 (−?̅?𝛿𝑖𝑗 + 2𝜇𝑆𝑖𝑗̅̅̅̅ + 𝜏𝑖𝑗 𝑅 ), (5.2) where xi is the position vector component, vi is the fluid velocity component, ρ is the fluid 120 density, p is the pressure, μ is the dynamic viscosity, δij is the Kronecker delta function, Sij = 0.5(∂vi/∂xj+∂vj/∂xi) is the strain rate tensor, and overbar indicates the average; Reynolds stress (𝜏𝑖𝑗 𝑅 ) is defined as follows: 𝜏𝑖𝑗 𝑅 = −𝜌𝑣𝑖′𝑣𝑗′̅̅ ̅̅ ̅̅ , (5.3) where v′ is the zero-mean fluctuating velocity. We used the Reynolds stress model (RSM), which is considered an accurate model for determining the Reynolds stress in the RANS equation (ANSYS, 2011; McFarland et al., 1997; Zhang et al., 2012). Zhang et al. found that the RSM combined with enhanced wall treatment gave accurate results on particle deposition efficiency and the particle deposition pattern, compared to the RSM with a standard wall function (Zhang et al., 2012). Therefore, the RSM with enhanced wall treatment was used to solve the continuous phase. To apply the enhanced wall treatment, the first grid cell size was set to 34 m, i.e., y+ ≈ 1, and a growth factor of 1.2 was applied for each cell until the fifth cell. The grid independence study was performed by changing the number of grid cells from 1.4 million to 5.1 million; we did not find any significant distortion from the number of grids at 2.2 million. To achieve more accurate results, the number of grids was chosen as 5.1 million. The results of the grid independence study are presented in Figure 5.2. 121 Figure 5.2 Results of the grid-independent study. For considering the enhanced wall treatment, the dimensionless distance from the tube wall (y+) was set to one and the grid size of the first cell near the tube wall was selected as 34 m with a growth factor of 1.2 until the next fifth cell. All results from grid independent study showed that there is no significant difference. But, at first union tee, the symmetry of the flow velocity contour is slightly broken until Mesh 2 (1.61 million). From Mesh 3 (2.19 million), the velocity contour started not to be distorted. For getting more accurate results of particle penetration, the number of grids was chosen as 5.1 million. 122 The inlet boundary condition was set to the velocity inlet with a parabolic velocity profile. The mean velocity was 1.218, 1.624, 2.030, 3.249, 4.873, and 6.497 m/s corresponding to Reynolds numbers of 370, 500, 620, 1000, 1500, and 2000, respectively. The four outlets of the forked tube were set to the outflow boundary conditions with the same flow rate weightage. The semi-implicit method was used for the pressure-linked equations algorithm and double-precision solver. The criterion for terminating the numerical calculations of the continuous phase was set to less than 10–6. In the particle tracking method, the trajectory of discrete phase particles was estimated by 𝑑𝑥𝑝,𝑖 𝑑𝑡 = 𝑣𝑝,𝑖, (5.4) where xp,i is the particle position vector, and vp,i is the particle velocity component. It was assumed that there were no interactions between the individual particles and that the particles were spherical. The particle force balance equation was used to determine the particle position vector. The particle force balance equation used was: 𝑚𝑝 𝑑𝑣𝑝,𝑖 𝑑𝑡 = 3𝜋𝜇𝑑𝑝(𝑣𝑖−𝑣𝑝,𝑖) 𝐶𝑐 +𝑚𝑝𝜁𝑖√ 6𝜋𝑑𝑝𝜇𝑘𝑏𝑇 ∆𝑡𝐶𝑐 , (5.5) where mp is the particle mass, dp is the particle diameter, i is a Gaussian random number with zero mean and unit variance, kb is Boltzmann’s constant, T is the absolute temperature, t is the time step; Cc is the slip correction factor, computed as follows (Kim et al., 2005): 123 𝐶𝑐 = 1 + Kn (1.165 + 0.483 exp(−0.997/Kn)), (5.6) where Kn is the Knudsen number, defined as the ratio of the mean free path to the particle radius, i.e., 2λ/dp. The two terms on the right-hand side of Equation (5.5) represent the drag force and Brownian force, respectively. The number of time steps was set to 109 to calculate all particle trajectories without exception. When the particles reached the tube wall, the particle tracking calculations for those particles were terminated, and they were considered to be deposited on the tube wall. The coupled ordinary differential equations, i.e., Equation (5.4) and Equation (5.5), were discretized and computed using Runge–Kutta methods (Cash and Karp, 1990). We introduced dimensionless variables and dimensionless numbers to establish a dimensionless equation for the particle force balance and to characterize the particle penetration behavior. The dimensionless particle velocity and fluid velocity components were obtained by being divided by the bulk mean velocity, i.e., vi/V and vp,i/V, and the dimensionless time was defined as t/τp, where the relaxation time was denoted as 𝜏𝑝 = 𝜌𝑝𝑑𝑝 2𝐶𝑐 18𝜇 . (5.7) The important dimensionless numbers, i.e., Reynolds number (Re), Schmidt number (Sc), and Peclet number (Pe) are defined as Re = 𝜌𝑉𝐷𝑡𝑢𝑏𝑒 𝜇 , (5.8) Sc = 𝜇/𝜌 𝐷 , (5.9) 124 and Pe = ReSc, (5.10) where Dtube is the tube diameter, and the diffusion coefficient (D) can be expressed as 𝐷 = 𝑘𝑏𝑇𝐶𝑐 3𝜋𝜇𝑑𝑝 . (5.11) By introducing dimensionless variables, the dimensionless form of Equation (5.5) can be rearranged as follows: 𝑑𝑣𝑝,𝑖 ∗ 𝑑𝑡∗ = (𝑣𝑖 ∗ − 𝑣𝑝,𝑖 ∗ ) + 𝜁𝑖 Pe √2𝐷𝑡𝑢𝑏𝑒 2 ∆𝑡𝐷 , (5.12) where the superscript asterisk (*) represents the dimensionless variable. From Equation (5.12), it is expected that particle behavior is highly affected by the Peclet number, describing the relative importance of the diffusion and advection effects. Here, it is noted that the turbulence effects on particle motion, e.g., discrete random walk (DRW), are not considered, the difference in modeling results with and without the turbulence effects on the particle motion can exist. For particle injection, the conventional Lagrangian particle tracking method cannot be applied to flow fields with a parabolic velocity profile, i.e., pipe flow, as in this study, because it is only suitable for a uniform particle distribution at the injection plane. Therefore, a modified single-particle tracking analysis based on aerosol flow rate was employed (Kwak et al., 2021b). The local number of particles injected at the ith element (Nin,i) was calculated as follows: 125 𝑁𝑖𝑛,𝑖 = 𝑁𝑖𝑛 ?̇?𝑝,𝑖 ∑ ?̇?𝑝,𝑖 𝑛 𝑖=1 , (5.13) where Nin is the total number of injected particles, ṁp,i is the local aerosol mass flow rate at the ith element, and n is the number of elements. The particles numbered Nin,i was placed in randomized locations within the i-th element. In the present study, the total number of injected particles and the number of elements was set to 20,000 and 100, respectively. To track the particle movement as the injected particles passed through the forked tube, all individual particles were assigned an identification (ID) number. The first particle ID number was designated as the particle located at the center of the tube cross-section, and the particle ID number increased for the particles closer to the tube wall (Figure 5.3c). The results of the injected particle distribution, normalized particle concentration, and particle ID designation are shown in Figure 5.3. As clearly seen in Figure 5.3a (also in Figure 5.3b), because of the use of the flow-rate-weighted particle injection method, more particles were placed near the center of the tube through which the higher flow rate passes (i.e., a higher concentration in the center). Figure 5.3 Particle injection positions based on aerosol mass flow rate: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. 126 5.2.2 Experimental method Figure 5.4 shows the experimental setup for measuring the nanoparticle deposition efficiency in a forked tube. Silver nanoparticles (AgNPs) were generated through the evaporation and condensation method with silver powder placed on a ceramic tube in a tube furnace (Model STF 55433C-1, Lindberg/Blue M, MA, USA) (Scheibel and Porstendörfer, 1983). AgNPs were transported from the furnace using ultra-high-purity nitrogen gas (99.999%). Soft X-rays were used to charge the AgNPs. The multiple charge effect by soft X-ray irradiation was neglected because the size of the tested particles was sub-100 nm. A nano-differential mobility analyzer (Nano-DMA, Model 3085, TSI, MN, USA) and an electrostatic classifier (Model 3080, TSI, MN, USA) were used to produce monodisperse and singly positively charged AgNPs. The flow rates of sheath air and aerosol through the Nano-DMA were set to 15 and 1.5 L/min, respectively. For the entire aerosol transport system, electrically conductive tubing was used to minimize particle losses. The overflow or insufficient air flow was discharged or replenished through a high-efficiency particulate air filter. A straight long tube with a length of approximately 100Dtube was used to achieve a fully developed flow with a parabolic velocity profile at the inlet of the forked tube. A three-way valve was employed for sampling either upstream (directly to a detector) or downstream (through the forked tube). The flow rates were adjusted using two mass flow controllers (MFC #1 and #2 in Figure 5.4, Model 1179A, MKS Instruments, MA, USA) and a mass flow controller integrated into the aerosol electrometer (AEM, Model 3068B, TSI, MN, USA). The downstream flow rates of MFC 127 #1, MFC #2, and AEM were controlled to be Q, 2Q, and Q, respectively. The upstream flow rate controlled by the AEM was 4Q. The setup illustrated in Figure 5.4 was used to measure the concentration of AgNPs coming from the outer outlet of the forked tube; connections were altered appropriately to test the inner outlet. The total flow rates (4Q) of downstream and upstream were 1.6, 3.2, and 6.4 L/min, corresponding to Reynolds numbers of 500, 1000, and 2000, respectively. Figure 5.4 Experimental setup for measuring nanoparticle deposition efficiency on forked tubes. The AEM measured the current of the charges carried by the positively charged AgNPs at the upstream or downstream; therefore, the number of monodisperse and singly positively charged AgNPs (N) was calculated as follows: 128 𝑁 = 𝑖𝑡𝑒𝑥𝑝. 𝑛𝑝𝑒 , (5.14) where i is the current measured using the AEM, np is the average number of elementary charge units per particle (1 #-1), texp. is the sampling time (60 s), and e is the elementary unit of charge of 1.6×10-19 As. The penetration efficiency of two outer or two inner outlets (i) was obtained by considering the symmetrical geometry of the forked tube outlets, as shown in Figure 5.1b, and can be calculated as 𝜂𝑖 = 2𝑁𝑑𝑜𝑤𝑛,𝑖 𝑁𝑢𝑝 , where 𝑖 = { 𝐴 for the outer outlet 𝐵 for the inner outlet , (5.15) and the subscripts of up and down represent the upstream and downstream values, respectively; the outer and inner outlets are shown in Figure 5.1. Notably, the penetration efficiency of each outlet should be between 0 and 0.5, i.e, 0 ≤ i ≤ 0.5. The particle deposition efficiency (dep) is obtained as follows: 𝜂𝑑𝑒𝑝 = 1 − (𝜂𝐴 + 𝜂𝐵). (5.16) 5.3 Results and discussion 5.3.1 Nanoparticle deposition efficiency A parametric study was performed to numerically investigate the effects of the Schmidt number and Reynolds number on the particle deposition efficiency of the forked tube. The tested particle sizes were 1, 2, 3, 5, 7, 10, 20, 30, 50, and 100 nm. The calculated 129 Schmidt numbers are presented in Table 5.1. The total flow rates of the forked tube were set to 1.2, 1.6, 2.0, 3.2, 4.8, and 6.4 L/min. To validate the calculated particle deposition efficiencies through the numerical method, we experimentally obtained the particle deposition efficiencies for the 18 cases with particle sizes of 3, 5, 7, 10, 20, and 50 nm and flow rates of 1.6, 3.2, and 6.4 L/min; each experiment was repeated three times. Table 5.1 Schmidt number with different particle sizes. Particle size [nm] Schmidt number [-] 1 2.84 2 11.3 3 25.5 5 70.4 7 137 10 278 20 1090 30 2380 50 6280 100 22000 Experimentally obtained particle penetration, and deposition was shown in Table 5.2. For adjusting the particle sizes of each case, the temperature of the tube furnace was varied from 1000 to 1200 °C. (The size of nanoparticles generated by the evaporation and condensation method is large at high temperatures.) For achieving accurate data from the experiment, we measured particle penetration efficiency three times for each outlet. 130 Reynolds number (Re) and Schmidt number (Sc) were calculated by using Equation (5.8) and Equation (5.9), respectively. The number of particles (N) was calculated by Equation (5.14). Each experiment data was averaged for 60 seconds of measurement data. We assumed that the multiple charge effect by soft X-ray was negligible. The particle penetration efficiency of each outlet (i) was calculated by using Equation (5.15). Particle deposition efficiency (dep) was calculated by using Equation (5.16). The experimental data and the comparison between the data and numerical results are shown in Figure 5.5. Table 5.2 Experimentally obtained particle penetration and deposition. Re[-] Sc[-] Run i(Outlet) Upstream Downstream i [-] dep[-] Iup [fA] Nup [#] Idown[fA] Ndown [#] 500 25.2 1 A 16.2 6.08×106 2.27 8.51×105 0.280 0.476 B 17.5 6.56×106 2.13 7.99×105 0.243 2 A 16.4 6.15×106 2.03 7.61×105 0.248 0.511 B 16.4 6.15×106 1.98 7.43×105 0.241 3 A 16.3 6.11×106 2.44 9.15×105 0.299 0.441 B 16.7 6.26×106 2.17 8.14×105 0.260 70.4 1 A 117.6 4.41×107 19.9 7.46×106 0.338 0.329 B 117.2 4.40×107 19.5 7.31×106 0.333 2 A 116.7 4.38×107 20.0 7.50×106 0.343 0.330 B 117.3 4.40×107 19.2 7.20×106 0.327 3 A 117.9 4.42×107 19.6 7.35×106 0.332 0.359 B 117.4 4.40×107 18.1 6.79×106 0.308 137 1 A 472.8 1.77×108 94.5 3.54×107 0.400 0.233 B 472.1 1.77×108 86.6 3.25×107 0.367 2 A 473.6 1.78×108 94.6 3.55×107 0.399 0.234 B 471.3 1.77×108 86.3 3.24×107 0.366 3 A 474.7 1.78×108 93.6 3.51×107 0.394 0.221 B 469.8 1.76×108 90.4 3.39×107 0.385 278 1 A 543.2 2.04×108 116.4 4.37×107 0.429 0.159 B 540.1 2.03×108 111.3 4.17×107 0.412 2 A 538.8 2.02×108 116.5 4.37×107 0.432 0.161 B 554.4 2.08×108 112.6 4.22×107 0.406 3 A 541.1 2.03×108 115.9 4.35×107 0.428 0.166 B 554.8 2.08×108 112.5 4.22×107 0.406 1090 1 A 2.18×103 8.18×108 517.4 1.94×108 0.475 0.057 B 2.21×103 8.29×108 517.5 1.94×108 0.468 131 2 A 2.17×103 8.14×108 512.9 1.92×108 0.473 0.057 B 2.19×103 8.21×108 515.0 1.93×108 0.470 3 A 2.17×103 8.14×108 508.4 1.91×108 0.469 0.065 B 2.19×103 8.21×108 511.2 1.92×108 0.467 6280 1 A 342.5 1.28×108 84.6 3.17×107 0.494 0.014 B 358.5 1.34×108 88.2 3.31×107 0.492 2 A 343.9 1.29×108 83.9 3.15×107 0.488 0.043 B 373.8 1.40×108 87.6 3.29×107 0.469 3 A 344.7 1.29×108 87.9 3.30×107 0.510 0.008 B 370.1 1.39×108 89.2 3.35×107 0.482 1000 25.2 1 A 6.67 2.50×106 1.19 4.46×105 0.357 0.301 B 6.32 2.37×106 1.08 4.05×105 0.342 2 A 5.48 2.06×106 1.02 3.83×105 0.372 0.358 B 6.97 2.61×106 0.939 3.52×105 0.269 3 A 6.70 2.51×106 0.859 3.22×105 0.256 0.425 B 7.04 2.64×106 1.12 4.20×105 0.318 70.4 1 A 68.1 2.55×107 13.0 4.88×106 0.382 0.259 B 67.9 2.55×107 12.2 4.58×106 0.359 2 A 65.2 2.45×107 12.6 4.73×106 0.387 0.229 B 63.0 2.36×107 12.1 4.54×106 0.384 3 A 66.4 2.49×107 12.3 4.61×106 0.370 0.262 B 64.2 2.41×107 11.8 4.43×106 0.368 137 1 A 371.8 1.39×108 78.6 2.95×107 0.423 0.152 B 368.1 1.38×108 78.3 2.94×107 0.425 2 A 373.6 1.40×108 78.9 2.96×107 0.422 0.150 B 366.6 1.37×108 78.3 2.94×107 0.427 3 A 374.1 1.40×108 79.4 2.98×107 0.424 0.152 B 364.9 1.37×108 77.3 2.90×107 0.424 278 1 A 546.8 2.05×108 124.8 4.68×107 0.456 0.098 B 559.1 2.10×108 124.6 4.67×107 0.446 2 A 567.4 2.13×108 127.0 4.76×107 0.448 0.099 B 548.4 2.06×108 124.4 4.67×107 0.454 3 A 572.6 2.15×108 130.4 4.89×107 0.455 0.099 B 551.2 2.07×108 122.8 4.61×107 0.446 1090 1 A 1.70×103 6.38×108 415.8 1.56×108 0.489 0.034 B 1.68×103 6.30×108 400.8 1.50×108 0.477 2 A 1.70×103 6.38×108 414.6 1.55×108 0.488 0.039 B 1.63×103 6.11×108 385.3 1.44×108 0.473 3 A 1.67×103 6.26×108 394.8 1.48×108 0.473 0.036 B 1.61×103 6.04×108 395.1 1.48×108 0.491 6280 1 A 548.8 2.06×108 128.6 4.82×107 0.469 0.032 B 570.9 2.14×108 142.4 5.34×107 0.499 2 A 555.9 2.08×108 128.4 4.82×107 0.462 0.043 B 571.8 2.14×108 141.6 5.31×107 0.495 3 A 565.5 2.12×108 127.8 4.79×107 0.452 0.054 B 543.8 2.04×108 134.2 5.03×107 0.494 2000 25.2 1 A 17.2 6.45×106 3.37 1.26×106 0.392 0.206 B 17.8 6.68×106 3.58 1.34×106 0.402 2 A 16.3 6.11×106 3.08 1.16×106 0.378 0.263 B 17.9 6.71×106 3.21 1.20×106 0.359 132 3 A 16.8 6.30×106 3.32 1.25×106 0.395 0.240 B 17.2 6.45×106 3.14 1.18×106 0.365 70.4 1 A 436.0 1.64×108 90.2 3.38×107 0.414 0.178 B 446.8 1.68×108 91.3 3.42×107 0.409 2 A 434.2 1.63×108 90.3 3.39×107 0.416 0.171 B 438.9 1.65×108 90.6 3.40×107 0.413 3 A 434.6 1.63×108 89.7 3.36×107 0.413 0.175 B 437.3 1.64×108 90.1 3.38×107 0.412 137 1 A 377.4 1.42×108 84.8 3.18×107 0.449 0.117 B 384.0 1.44×108 83.3 3.12×107 0.434 2 A 374.5 1.40×108 84.0 3.15×107 0.449 0.126 B 387.9 1.45×108 82.6 3.10×107 0.426 3 A 375.0 1.41×108 82.5 3.09×107 0.440 0.125 B 384.4 1.44×108 83.7 3.14×107 0.435 278 1 A 828.8 3.11×108 183.7 6.89×107 0.443 0.110 B 801.4 3.01×108 178.8 6.71×107 0.446 2 A 816.3 3.06×108 183.6 6.89×107 0.450 0.100 B 795.0 2.98×108 179.0 6.71×107 0.450 3 A 819.9 3.07×108 181.8 6.82×107 0.443 0.108 B 794.3 2.98×108 178.3 6.69×107 0.449 1090 1 A 2.72×103 1.02×109 660.4 2.48×108 0.486 0.027 B 2.71×103 1.02×109 660.3 2.48×108 0.487 2 A 2.74×103 1.03×109 661.0 2.48×108 0.482 0.036 B 2.73×103 1.02×109 656.8 2.46×108 0.481 3 A 2.72×103 1.02×109 658.3 2.47×108 0.484 0.036 B 2.73×103 1.02×109 654.9 2.46×108 0.480 6280 1 A 349.2 1.31×108 85.4 3.20×107 0.489 0.031 B 333.6 1.25×108 80.0 3.00×107 0.480 2 A 344.2 1.29×108 78.5 2.94×107 0.456 0.053 B 377.1 1.41×108 92.5 3.47×107 0.491 3 A 357.1 1.34×108 87.0 3.26×107 0.487 0.049 B 373.3 1.40×108 86.5 3.24×107 0.463 133 Figure 5.5 Comparison of nanoparticle penetration efficiency on a forked tube at each outlet between numerical and experimental results: (a) Re=500; (b) Re=1000; (c) Re=2000. Lines represent the numerically calculated penetration efficiency on forked tubes. Symbols with error bars represent the experimentally obtained penetration efficiency on forked tubes. Figure 5.6 compares the numerically and experimentally obtained nanoparticle deposition efficiency on the forked tube according to Schmidt number with different Reynolds numbers. Particles with smaller Schmidt numbers are more affected by diffusion; thus, the particle deposition efficiency on the forked tube decreases when the Schmidt number increases. When the Reynolds number increases, the diffusion effect of particles on the deposition is reduced because of the increasing advection transport rate. This is because when flow-directional advection is dominant, the particle residence time in the tube decreases, resulting in a lower particle deposition efficiency. Furthermore, the experimentally obtained nanoparticle deposition efficiency data show good agreement with the numerically calculated results, with a small overall discrepancy of 3.3%. Therefore, the present numerical model can accurately predict the particle penetration phenomena in complex tubing systems such as forked tubes. 134 Figure 5.6 Comparison between numerical and experimental results for nanoparticle deposition efficiency in forked tubes: (a) Re = 500; (b) Re = 1000; (c) Re = 2000. Solid lines and open circular symbols with error bars represent the numerical and experimental deposition efficiency in a forked tube, respectively. 5.3.2 Flow characteristics The flow characteristics of the forked tube change significantly when the flow forks in two directions (i.e., a union tee) or changes direction by 90° (i.e., an elbow connection), which are the connecting components used in the forked tube. Figure 5.7 and Figure 5.8 show the flow field visualization when the flow passes through the union tee and elbow connection, respectively. To characterize the flow fields, we have presented two cases of flow field visualization results for the lowest and highest Reynolds numbers, i.e., 135 Re = 370 and 2000, for the sake of brevity. The vortex cores (green region) are represented by Q* = 0.1. Here, the normalized Q-criterion (Q*) (Fazle Hussain, 1986; Fu et al., 2013; Inthavong, 2019; Liu et al., 2017) is defined as Q* = Q/Qmax, where Q = 0.5(ΩijΩij−SijSij), and Ωij = 0.5(∂vi/∂xj−∂vj/∂xi); it can be seen that the higher the normalized Q-criterion, the relatively stronger the vortex flow or secondary flow. The walls inside and outside the curve of the flow turning direction are termed the “inner wall” and “outer wall,” respectively, as shown in Figure 5.7 and Figure 5.8. After a sudden change in the flow direction, the vortex flow is formed closer to the inner wall than the outer wall in both the union tee and elbow connections. The streamlines uniformly released from each component inlet surface are represented by grey lines. To emphasize the effect of strong vortex flow, the streamlines that are released from the surface with Q* = 0.8 are marked in red in Figure 5.7 and Figure 5.8. Most parts of the streamlines in the vortex cores (green region) have different directions to the main flow direction (normal to the tube cross-section). Moreover, when comparing the cases between Re of 370 and 2000, the distortion of the streamlines occurs more significantly at a large Reynolds number after the main flow direction changes. It is worth mentioning that although more significant distortion due to secondary flow occurs at a higher Reynolds number, this does not mean that the overall particle deposition is enhanced. Compared to the case with a lower Reynolds number, the diffusion effect on particle deposition is reduced because of the shorter particle residence time at the higher Reynolds number, giving a lesser chance for the particles to be deposited on the wall. Therefore, these complex phenomena are intertwined, and it is important to investigate detailed particle behavior through simulations. 136 Figure 5.7 Effects of union tee on flow streamlines and vortex cores: (left) Re = 370; (right) Re = 2000. Green regions represent the vortex cores with Q* = 0.1; grey lines represent the streamlines uniformly released from the union tee inlet; red lines represent the streamlines released from the surface with Q* = 0.8. 137 Figure 5.8 Effects of elbow connection on flow streamlines and vortex cores: (left) Re = 370; (right) Re = 2000. Green regions represent the vortex cores with Q* = 0.1; grey lines represent the streamlines uniformly released from the elbow connection inlet; red lines represent the streamlines released from the surface with Q* = 0.8. 138 5.3.3 Particle concentration and ID Figures 5.9-5.13 and 5.15-5.17 show the particle distribution, normalized particle concentration, and particle ID contours observed at the cross-sections marked in each figure. It should be noted that the difference in each particle location in the streamwise direction at a specific time does not affect the contour results, (i.e., once particles are passed through the cross-section marked in each figure, the coordinate of particles is recorded). The contour results provide specific information on the trajectory changes of the particles when passing through the forked tube. The contour data in Figures 5.10-5.13 and 5.15-5.17 were extracted from the plane with a large x value in the coordinate system, i.e., the right side, as the forked tube has symmetrical geometry. Figure 5.9 shows the behavior and position of particles when particles pass through a section of the straight tube before the bent region of the forked tube once the particles are injected at the inlet. Compared to Figure 5.3 (i.e., contours at the injection plane), the particle distribution or normalized particle concentration contour in Figure 5.9 shows that when the Reynolds number and particle size are small, fewer particles are observed near the tube wall because of particle loss caused by the diffusion effect. However, when the Reynolds number and particle size are large (e.g., Re = 2000 and dp = 100 nm), the smallest difference in the normalized particle concentration between the center of the tube and the vicinity of the tube wall is observed, resulting in particles being more evenly distributed throughout. Notably, the particles can travel further without deposition on the tube wall at large Peclet numbers (i.e., large Re and particle size), proportional to the ratio of the radial- directional residence time (tr) to the flow-directional residence time (tx), i.e., tr/tx ∝ Pe 139 (Kwak et al., 2020; Yook et al., 2010; Yook and Ahn, 2009). Figure 5.9 Particle penetration characteristics before first union tee with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. As shown in Figure 5.9c, most particles pass through the tube in the flow direction without mixing when the Reynolds number and particle size are large. However, for small Re and particle size (e.g., Re = 370 and dp = 3 nm), the clarity of the colored boundaries is blurred, meaning that particle mixing occurs even in the straight section of the path (less mixing effect). This is because, in general, sub-100 nm particles have low inertia but a large diffusion coefficient. Therefore, the smaller particles tend to mix better with the 140 surrounding particles owing to the strong diffusion effect. Figure 5.10 shows the particle penetration characteristics after passing through the first union tee. A distinct feature in Figures 5.10a and 5.10b is that a particle-free zone, marked with red dotted lines in Figure 5.10a, can be seen with a crescent or hook shape. This phenomenon can be explained by the particle ID contour shown in Figure 5.10c; it is clearly seen that the particles with high ID numbers (i.e., red color) are concentrated in the crescent-shaped region. These particles with the high ID numbers were initially near the tube wall before passing through the union tee (Figure 5.9c), but they were transported to the region by the swirling vortex flow caused by the geometry of the bend. A similar trend was observed in Figure 5.7, which shows a sudden change in streamlines due to vortex flow. The streamlines passing through the strong vortex flow region (i.e., red solid lines in Figure 5.7) start near the wall in the inlet of the union tee but exit in a direction that is slightly biased toward the inner wall from the center in the outlet. In addition, as shown in Figure 5.9b, as small particles (dp = 3 nm) with high ID numbers have a low normalized particle concentration in the vicinity of the tube wall in the inlet, the volume of the fluid with far fewer particles in this region moves along with the swirl flow and forms a particle- free zone (red dotted lines) in Figure 5.10a. However, the particle-free zone is barely observed in the case of the larger particles (dp = 100 nm) because, in the initial state of the particle distribution, the larger particles have a relatively high normalized concentration near the tube wall. 141 Figure 5.10 Particle penetration characteristics after first union tee with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. The red dotted line in (a) marks the particle-free zone. As clearly seen in Figure 5.10c, the effect of the Reynolds number is more significant than that of the particle size. The shape of the contour does not change significantly between the dp range of 3 nm and 100 nm, but it changes significantly for different Reynolds numbers. Furthermore, at a large Reynolds number, i.e., Re = 2000, the particles initially positioned at the center of the tube before passing the union tee (i.e., blue color for ID numbers) are concentrated on the outer wall. Otherwise, these particles with blue-colored ID numbers are widely distributed along the surface of the tube wall at low Reynolds numbers. As shown in Figures 5.10a and 5.10b, the larger the Reynolds number and the 142 smaller the particle size, the more particles are projected toward the outer wall after they pass through the first union tee as smaller particles, with lower inertia, are more likely to follow the flow streamlines (Kwak et al., 2021b; Lee et al., 2014). Further, as the Reynolds number increases, the particle-free zone gradually spreads toward the inner wall with a crescent shape, indicating that a high Reynolds number causes strong vortex flows and results in a non-uniform particle distribution at the first union tee. Figure 5.11 presents contour information on the section distant from the exit of the union tee. As the flow develops along the straight path, the particle-free zone faded in Figure 5.11a compared to that in Figure 5.10a. Furthermore, fading the zone is recognized more clearly for the smaller particles because of the strong diffusion effect that makes the particle distribution more uniform. 143 Figure 5.11 Particle penetration characteristics before first elbow connection with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. The particle penetration characteristics of the forked tube after the first elbow connection are shown in Figure 5.12. Similar to the particle distribution after the first union tee, the smaller the particle size and the larger the Reynolds number, the more pronounced the particle-free zone after the first elbow connection. However, comparing the particle distribution and the particle ID contour in Figure 5.10 and Figure 5.12, the particle-free zone for the first union tee occurred at a high particle ID number (red color particles in Figure 5.10c); however, for the first elbow connection, the particle-free zone occurred for lower particle ID numbers (green or blue color particles), as shown in Figure 5.12c. These results are highly supported by the streamlined investigation shown in Figure 5.8. The 144 starting point of streamlines in the strong vortex flow (red solid lines in Figure 5.8) was located near the wall at the inlet of the elbow connection, but the endpoint of streamlines with strong vortex flow was found at the center of the tube. Therefore, the particles near the wall (green and blue ID numbers in Figure 5.10c or Figure 5.11c) were transported to the center of the tube when they passed through the elbow connection. Figure 5.12 Particle penetration characteristics after first elbow connection for various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. Interestingly, we found that the particle distribution and particle concentration for Re = 370 and dp = 10 nm (Figure 5.12) has two distinct particle-free zones. Comparing the 145 particle ID contour with the particle distribution and concentration contour under these conditions, the following conclusions can be made: (1) the center of the particle-free zone is caused by low particle ID numbers; (2) the particle-free zone along the outer wall (right- side tube wall in Figure 5.12) is triggered by high particle ID numbers. Even though particles with high ID numbers (for Re = 370 and dp = 3 nm) have a clear particle-free zone in the straight line section (Figure 5.9) and the first tee union (Figure 5.10), the particle- free zone along the right tube wall is only faintly seen compared to that of Re = 370 and dp = 10 nm. This is attributed to the fact that the low Reynolds number and small particle size result in a low Peclet number, i.e., low tr/tx; therefore, the particle random motion in the radial direction becomes more dominant. Figure 5.13 Particle penetration characteristics before second union tee with various particle sizes and Reynolds numbers: (a) particle distribution; (b) normalized particle concentration; (c) particle ID. 146 The above results imply that particles with high ID numbers are located near the tube wall before passing through the first union tee (Figure 5.9c) and progress toward the inner wall when passing through the union tee (Figure 5.10c). A similar trend is observed in the sudden change in the streamline due to vortex flow, as shown in Figure 5.7. The streamlines passing through the strong vortex flow region (red solid lines in Figure 5.7) start near the wall in the inlet of the union tee but exit in a direction that is slightly biased toward the inner wall from the center in the outlet. To clarify and support the particle movement caused by passing through the elbow connection, the individual particle trajectories before and after the first elbow connection are presented in Figure 5.14. Figure 5.14 Individual particle trajectory results of dp = 100 nm at first elbow connection. The initial position represents the particle position before passing through the first elbow connection (Figure 5.11). The position after passing the elbow connection represents the particle position after passing through the first elbow connection (Figure 5.12). Here, we can categorize the three different groups of particles: (Group 1) initial particle position near the tube wall (pale yellow), (Group 2) initial particle position with tube centerline (pale orange), and (Group 3) initial particle position between Group 1 and Group 2 (pale green). The arrow direction indicates the particle movement trend. 147 After the first elbow connection, the particle-laden flow was divided as it passed through the second union tee. Figure 5.15 depicts the particle penetration characteristics after the second union tee, connected to two different outlets, i.e., the outer and inner outlets, as shown in Figure 5.1b. Interestingly, although the particle ID contour patterns were completely different before the first union tee (Figure 5.9c) and before the second union tee (Figure 5.13c), the overall particle ID contour after the second union tee (Figure 5.15c) shows a pattern similar to that shown in Figure 5.10c. A simple explanation for pattern similarities is that the particle IDs of the particles located at the center of the tube are blue in Figure 5.9 (before the first union tee) and Figure 5.13 (before the second union tee), but the particle IDs for the particles near the wall are red. In addition, it should be noted that the flow rate through each outlet after the second union tee is reduced to a quarter of the total flow rate. Nevertheless, a particle-free zone can be observed at the outer and inner outlets for Re = 2000 and dp = 3 nm (Figures 5.15a and 5.15d). However, the locations of the particle-free zone for the outer and inner outlets for Re = 2000 and dp = 3 nm are different. Specifically, the particle-free zone for the outer outlet is confirmed near the inner wall of the second union tee while the inner outlet shows two particle-free zones, i.e., one near the inner wall and the other along the outer wall also observed in Figures. 5.12a and 5.12b with Re = 370 and dp = 10 nm. This is because the particle-free zone along the outer wall after the second union tee originates from the previous particle-free zone in Figure 5.13 (before entering the second union tee), which is formed in the inner outlet direction based on a semi-circle; the particle-free zone near the inner wall of the second union tee is derived from the particle deposition on the tube wall. 148 Figure 5.15 Particle penetration characteristics after second union tee with various particle sizes and Reynolds numbers: top diagrams (a, b, c) represent particles toward the outer outlet in Figure 5.1b; bottom diagrams (d, e, f) represent particles toward the inner outlet in Figure 5.1b; (a, d) particle distribution; (b, e) normalized particle concentration; (c, f) particle ID. 149 Figure 5.16 Particle penetration characteristics before second elbow connection with various particle sizes and Reynolds numbers: top diagrams (a, b, c) represent particles toward the outer outlet in Figure 5.1b; bottom diagrams (d, e, f) represent particles toward the inner outlet in Figure 5.1b; (a, d) particle distribution; (b, e) normalized particle concentration; (c, f) particle ID. 150 After the second elbow connection, similar to the second union tee, unique particle penetration characteristics are observed for the particles toward both the outer and inner outlets, as shown in Figure 5.17. The particle concentration after the second elbow connection tends to be higher near the outer wall, and this feature is more pronounced with a larger Reynolds number and smaller particles, similar to the penetration characteristics of the first elbow connection. Furthermore, even though particle-laden flow passes through the forked tube, which is a complicated tube system compared to a straight tube, the particles do not mix well except in the case of a low Reynolds number and small particle size, as observed through particle ID analysis. 151 Figure 5.17 Particle penetration characteristics after second elbow connection with various particle sizes and Reynolds numbers: top diagrams (a, b, c) represent particles toward the outer outlet in Figure 1b; bottom diagrams (d, e, f) represent particles toward the inner outlet in Figure 1b; (a, d) particle distribution; (b, e) normalized particle concentration; (c, f) particle ID. 152 Figure 5.18 illustrates how the particles are divided between the outer and inner outlets according to the initial particle position at the main inlet of the forked tube. At Re = 370, for particles initially injected from the center of the forked tube inlet, i.e., particle IDs from 1 to 5000, the probability of passing through the outer outlet is higher than that of other particle IDs; on the contrary, the closer to the tube wall, i.e., increasing particle IDs, the higher the probability of passing through the inner outlet. However, at Re = 1000 and Re = 2000, the particles introduced near the center of the tube and the wall of the tube were more likely to go to the outer outlets, while the particles injected in regions other than the center and vicinity of the wall (i.e., particle ID from 5001 to 15000) were more likely to go to the inner outlets. These results are also clearly seen from the particle ID contour analysis in Figure 5.15, which shows that the particles with the dark blue and red colored ID numbers (center and near the wall) appeared more in Figure 5.15c (outer outlet direction); particle ID contours in Figure 5.15f consisted of the light blue/green/orange colored particle IDs (other regions). Therefore, it can be concluded that most of the particles injected near the center, or the tube wall are directed to the outer outlets because of the secondary flow effect. 153 Figure 5.18 Ratio of particles divided by second union tee and effect of particle initial location at the inlet of the forked tube with various particle sizes and Reynolds numbers. Particle ID number in the x-axis indicates the middle of a group of particle ID numbers, e.g., 2500 represents the particle ID from 1 to 5000, and 17500 represents the particle ID from 15001 to 20000. The contour of the inserted quadrant is a visualization of the resulting ratios. A and B outlets represent the outer and inner outlets, respectively. The darker the color, the more particles progress toward the outer outlet (A outlet) direction. 5.3.4 Effect of Peclet number The nanoparticle deposition efficiency on the tubing system is strongly influenced by the Reynolds number and particle size. Based on the dimensionless particle force balance equation (Equation (5.12)), the nanoparticle deposition efficiency is expected to 154 be expressed as a function of the Peclet number, the dimensionless number obtained by the multiplication of the Reynolds and Schmidt numbers. Figure 5.19 illustrates the nanoparticle deposition efficiency on a forked tube for various Peclet numbers. Open and closed symbols represent the numerically and experimentally obtained deposition efficiencies for a forked tube, respectively. The nanoparticle deposition efficiency for a forked tube decreases as the Peclet number increases, as shown in Figure 5.19. Based on the experimental and numerical results of the deposition efficiency for a forked tube, the correlation fitting curve for predicting the deposition efficiency (dep,FT) is obtained as a function of the Peclet number as follows: 𝜂𝑑𝑒𝑝,𝐹𝑇(Pe) = 𝐶1Pe 𝐶2. (5.17) The correlation constants of C1 and C2 were determined to be 13.75 and -0.3798, respectively. The coefficient of determination (R2), the sum of squares (SSE), and root mean square error (RMSE) were 0.9753, 0.0855, and 0.0335, respectively. The correlated data are in good agreement with the numerical and experimental data, with an overall discrepancy of less than 2.8%. It should be noted that the numerically and experimentally obtained nanoparticle deposition efficiencies are in a single correlation curve as a function of Peclet numbers, and the nanoparticle deposition efficiency can be accurately predicted by simply calculating the Peclet number. 155 Figure 5.19 Nanoparticle deposition efficiency on a forked tube as a function of Peclet number. 5.3.5 Comparison of deposition efficiency between different tube geometries To further investigate the comparison of nanoparticle deposition efficiencies between a straight tube, a sharp-bent tube, and a forked tube, the deposition efficiencies of a straight tube and a sharp-bent tube were obtained from previous studies. Gormley and Kennedy analytically predicted the nanoparticle penetration efficiency on a straight tube (dep,ST) using the dimensionless parameter () (Gormley and Kennedy, 1975): 156 𝜂𝑑𝑒𝑝,𝑆𝑇(𝜁) = { 2.56𝜁2/3 − 1.2𝜁 − 0.177𝜁4/3 1 − 0.819𝑒−3.657𝜁 − 0.097𝑒−22.3𝜁 − 0.032𝑒−57𝜁 𝑓𝑜𝑟 𝜁 < 0.02 𝑓𝑜𝑟 𝜁 ≥ 0.02 . (5.18) The dimensionless parameter can be expressed by comparing the flow-directional residence time (tx) and the radial-directional residence time (tr), obtained as follows: 𝜁 = 𝑡𝑥 2𝑡𝑟 = 4𝐿𝑆𝑇,𝑒𝑞 Pe𝐷𝑡𝑢𝑏𝑒 , (5.19) and 𝐿𝑆𝑇,𝑒𝑞 = 4𝑉𝐹𝑇 𝜋𝐷𝑡𝑢𝑏𝑡𝑒 2 , (5.20) where LST,eq is the length of a straight tube, equivalent to the total length of the forked tube in this study (i.e., LST,eq = 243.7 mm). Therefore, the nanoparticle penetration efficiency for a straight tube only depends on the Peclet number under known conditions of straight tube length and diameter, i.e., dep,ST (Pe, LST,eq, Dtube)→dep,ST (Pe). From our previous study, the nanoparticle deposition efficiency for a sharp-bent tube (dep,SBT) can be expressed as a function of the Peclet number in the range of 4×103 < Pe < 107 (Kwak et al., 2020): 𝜂𝑑𝑒𝑝,𝑆𝐵𝑇(Pe) = 27.41Pe −0.4831. (5.21) A forked tube contains two consecutive elbow connections, i.e., two sharp-bent tubes. The nanoparticle deposition efficiency for a forked tube (dep,FT) can be expected to be larger than that calculated for two consecutive elbow connections (dep,2×SBT), because the additional deposition caused by the two union tees is ignored. Accounting for the change in the Peclet number due to two union tees, the nanoparticle deposition efficiency 157 for two consecutive sharp-bent tubes (dep,2×SBT) in a forked tube can be estimated as follows: 𝜂𝑑𝑒𝑝,2×𝑆𝐵𝑇(Pe) = 1 − (1 − 𝜂𝑑𝑒𝑝,𝑆𝐵𝑇(Pe/2)) (1 − 𝜂𝑑𝑒𝑝,𝑆𝐵𝑇(Pe/4)) (5.22) In Figure 5.20, the particle deposition efficiencies for a straight tube, a sharp-bent tube, two consecutive sharp-bent tubes, and a forked tube are plotted according to the Peclet number. As expected, the nanoparticle deposition efficiency decreased for all cases with increasing Peclet number. Interestingly, the deposition efficiency results for two consecutive sharp-bent tubes (Equation (5.22)), seem to be overestimated compared with the deposition efficiency of a forked tube (Equation (5.17)). Our previous investigation (Kwak et al., 2021b) showed that most nanoparticles were deposited on the outer wall after passing through the elbow tube connection at a low Peclet number. Furthermore, most of the particles are located in the vicinity of the outer wall after the first and second union tees, as shown in Figure 5.10 and Figure 5.15 (outer wall after the first and second union tee = inner wall before the first and second elbow connection), which is different from the assumption for the results of a single elbow tube, i.e., uniformly distributed. These results are supported by Figure 5.21. As more particles are in the vicinity of the outer wall after the union tee (more particles are in the vicinity of the inner wall before the elbow connection), fewer particles are deposited because of an elbow connection; thus, the deposition efficiency of two consecutive sharp-bent tubes is overestimated compared to the deposition efficiency of a forked tube. 158 Figure 5.20 Nanoparticle deposition efficiencies for straight tube, sharp-bent tube (elbow connection), two consecutive sharp-bent tubes (2×sharp-bent tube), and forked tube as a function of Peclet number. 159 Figure 5.21 Penetration efficiency of different particle locations at the inlet of the forked tube with various particle sizes (dp = 3, 10, and 100 nm) and Reynolds number (Re = 370, 1000, and 2000). Section number 1 is the inlet of the forked tube (Figure 5.3); Section number 2 is the inlet of the first union tee (Figure 5.9); Section number 3 is the outlet of the first union tee (Figure 5.10); Section number 4 is the inlet of the first elbow connection (Figure 5.11); Section number 5 is the outlet of the first elbow connection (Figure 5.12); Section number 6 is the inlet of the second union tee (Figure 5.13); Section number 7 is the outlet of the second union tee (Figure 5.15); Section number 8 is the inlet of the second elbow connection (Figure 5.16); Section number 9 is the outlet of the second elbow connection (Figure 5.17). The blue solid line with a circle symbol represents the particle ID number from 1 to 5000; The light blue dashed line with a triangular symbol represents the particle ID number from 5001 to 10000; The orange dash-dotted line represents the particle ID number from 10001 to 15000; The red dash-dot-dotted line represented the particle ID number from 15001 to 20000. 160 5.4 Conclusion In this study, the sub-100 nm nanoparticle penetration characteristics were investigated by tracking individual particles in a forked tube (tree-like branching tube) at Reynolds numbers ranging from 370 to 2000. We used a CFD software package to simulate the flow fields and particle trajectories. The Eulerian and Lagrangian methods were used to calculate the flow fields and particle trajectories, respectively. The resulting differences caused by these two different methods were compensated by implementing a modified single-particle tracking analysis based on the aerosol mass flow rate. To track the injected particles at the inlet of the forked tube, each injected particle was given a particle ID. To validate the simulation results, the numerically calculated deposition efficiencies were compared with the experimental results. The experimentally obtained deposition efficiency showed good agreement with the numerically calculated results (overall error of 3.3%). After validating the numerical method, we further investigated the effect of secondary flow induced by the union tee and elbow connections in the forked tube by visualizing the flow streamlines and vortex core regions; the vortex flow formed closer to the inner wall than the outer wall in the union tee and elbow connections after the sudden change in the flow direction. Severe distortion of the streamlines in the vortex core region was observed; this occurred more significantly at higher Reynolds numbers. The particle distribution, normalized particle concentration, and particle ID contours on the important cross-sections (e.g., before and after the union tees and elbow connections) were examined to investigate the details of the particle behaviors in the forked tube. In the straight tube section (between the inlet and the first union tee), a smaller 161 Reynolds number and particle size enhanced the particle deposition on the tube wall because of the longer residence time through the main flow direction and higher diffusivity of the particles, i.e., tr/tx. For a higher Reynolds number and larger particle size, the particles were evenly distributed throughout, and little mixing occurred with the surrounding particles. After the first union tee, a crescent-shaped particle-free zone was created, attributed to the fact that particles located near the tube wall at the initial state were lost due to their deposition on the tube wall. This particle-free zone moved to the inner wall of the tube because of the secondary flow after the union tee. In addition, a particle-free zone can be clearly seen for small particles because large particles have relatively high normalized concentrations near the tube wall before the union tee compared to small particles. After the first elbow connection, the particle-free zone became clearer for smaller particle sizes and larger Reynolds numbers. However, when comparing the particle distribution and the particle ID contour at the first union tee and the first elbow connection, the particle-free zone at the first union tee occurred at a high particle ID number but at the first elbow connection, the particle-free zone occurred for low particle ID numbers. Moreover, the particle distribution for Re = 370 and dp = 10 nm had two distinct particle- free zones. After the second union tee and elbow connection, we found that different particle-free zones were created depending on the different outlets due to non-uniformly distributed particles in the tube. In addition, by examining the ratio of particles divided by the second union tee, considering the initial injected particle location at the forked tube inlet, we found that the higher the Reynolds number, the more injected particles near the tube wall at the forked tube (Particle ID 15001–20000) were directed to the outer outlet. Lastly, we suggested that the nanoparticle deposition efficiency correlation curve 162 for the forked tube was a function of the Peclet number. By comparing the nanoparticle deposition efficiencies for two consecutive sharp-bent tubes, we found that single elbow tube correlation results were overestimated for the forked tube due to non-uniformly distributed particles in the forked tube. 163 Chapter 6 Nanoparticle resuspension or removal on forked tubes using the pulsed air jet, ultrasonication, and acid dissolution method 6.1 Introduction For recent several years, technical progress in the semiconductor industry triggers the semiconductor device fabrication node to shrink and the size of wafers to grow bigger; consequently, contamination by undesired particles is greatly affecting the semiconductor manufacturing yield. These undesired particles would come from physical or chemical vapor deposition, etching processes, and other fabrication processes. Since adhesive force is proportional to 1 power of diameter and removal force is proportional to 2 or 3 power of diameter (i.e., FAdh∝dp, Frem∝dp2 or dp3), the smaller particles, sub-micron particles, are difficult to remove from the surface (Hinds, 1982). We aim to evaluate particle removal or resuspension efficiency using a pulsed air jet, ultrasonication, and acid dissolution method. Among the many techniques of surface cleaning, the surface cleaning process can be divided into wet-cleaning methods and dry-cleaning methods. In the wet-cleaning methods, ultrasonic or megasonic cleaning has been a promising method for sub-micron 164 particles in the semiconductor industry due to its convenient operation (Bakhtari et al., 2006; Huang et al., 2009). Even though ultrasonic or megasonic cleaning is currently employed in wafer cleaning in manufacturing, the fundamental physical explanation of how the particle is removed from the surface by using megasonic has not been fully understood. Bath-type and stream-type of megasonic cleaning methods are used to remove surface particles. The dry-cleaning process is another well-known method to remove surface particles without using liquid through an air jet. The main advantage of the dry- cleaning method is that the process is more simplified than the wet-cleaning method since there is no procedure to remove the water on the surface after the cleaning process. High- speed air jets generated by a nozzle blow off the particulate contaminants from the surface. In addition, cryogenic particle-laden air jet (e.g. CO2, Argon, Nitrogen) is also popular in surface cleaning industries (Hwang et al., 2011; Lee et al., 2009; McDermott and Butterbaugh, 2008; Sherman, 2016). For ultrasonic or megasonic cleaning which is one of the well-known wet-cleaning methods, there are two principal mechanisms (Kohli and Mittal, 2009): Cavitation, and Acoustic streaming. Cavitation is the constructive interference of sonic energy causing the formation of rarified bubbles in the cleaning solution. When these bubbles are ruptured by a moving sonic wave, they create tiny jets in a fluid which can affect the particles on the surface to be removed. In acoustic streaming, the bulk motion of fluid occurs. The particle contaminants that get removed from the surface are carried away, and therefore, are prevented from re-depositing on the surface. However, in previous studies, the dominant cleaning mechanisms are different from each other. Some researchers suggested that acoustic streaming is the main cleaning mechanism, and they neglected the cavitation effect 165 on removing particles from the surface. They considered the drag force due to the acoustic streaming effect as a dominant particle resuspension mechanism (Bakhtari et al., 2006; Busnaina et al., 1995; BUSNAINA and GALE, 1997; Karimi et al., 2010; Olim, 1997; Zhang et al., 1999). On the other hand, other researchers asserted that acoustic streaming has a little direct effect on the particle removal process and reported that interface sweeping torque and pressure gradient torque due to oscillating bubbles, i.e., cavitation effect, are much stronger than acoustic streaming torque (J. Choi et al., 2016; W. Kim et al., 2009). This controversy is caused by the fact that analytical approaches were conducted without a concrete understanding of the fundamental mechanism of dynamics around surface particles. There are several important parameters in the air jet cleaning method such as particle diameter, the gas pressure in the jet nozzle, the distance between the nozzle tip, the jet impinging angle, and the scanning speed of the air jet (Gotoh et al., 1995, 1994a, 1994b; Masuda et al., 1994; Okazaki et al., 2008a). The particle removal efficiency (PRE) increases with the increasing pressure drop (∆Pn) (Mittal and Jaiswal, 2015). The longer distance (d) between the nozzle and the surface, the higher-pressure drop is required to get the same PRE (Mittal and Jaiswal, 2015). These relationships could be explained by the different dynamic pressure, which represents the energy of the air jet between the nozzle and surface according to each operating condition such as pressure drop (∆Pn) in the jet nozzle and distance (d). The effect of impinging angle (θ) on the PRE was also investigated (Masuda et al., 1994). The different impinging angles produce different PREs due to the changes in jet expanding width (δ). In terms of the practical approach regarding the air jet cleaning method, the removal surface or the air jet nozzle should not be stationary but 166 moved (Masuda et al., 1994). The effect of the scanning speed (vs) was also investigated (Okazaki et al., 2008a): with increasing the scanning speed, the PRE decreases due to the shorter residence time. The PRE can be improved by using the pulsed-jet method instead of the normal jet (Okazaki et al., 2008b). However, the fundamental mechanism of surface particle removal by the pulsed-jet method is not established yet, and several different hypotheses have been suggested by many researchers (Otani et al., 1995, 1994; Ziskind et al., 2002). Ziskind et al. mentioned that the local velocity at any point decreases with time until the steady state is reached (Ziskind et al., 2002). Therefore, the removal force acting on the particles at the initial state of each pulse is maximum. Moreover, the velocity inside the boundary layer becomes higher at the initial state compared to the one at the steady state. However, the works by Otani and other researchers reported that because the PRE per the number of pulsed-air jets, i.e., PRE/number of pulses, remains almost constant during the exposures to consecutive pulse air jets, the preservation of adhesion force distribution might exist (Otani et al., 1995, 1994). Even though the PRE was obtained under different operating conditions through several experiments, the mechanism of surface particle removal has not been established yet. It is also difficult to predict the reliable PRE for each operating condition and to determine the optimal cleaning operation conditions due to the complicated interaction between each variable, e.g.., ∆Pn, d, θ, vs, and RH. However, to our best knowledge, there are no studies to investigate nanoparticle resuspension or removal rate on complicated tube systems. We prepared the forked tube and the geometry of the forked tube was presented in Figure 6.1. The forked tube employed in the present study had five openings that correspond to one inlet and four outlets made with glands and male nuts. The forked tube is composed of three union tees (Model 6LV- 167 4MW-3, Swagelok, OH, USA) and six elbow connections (Model 6LV-4MW-9, Swagelok, OH, USA). The dimensions of the forked tube are Dtube = 4.572 mm, A1 = 40.4 mm, A2 = 67.2 mm, A3 = 90.7 mm, B1 = 46.2 mm, and B2 = 23.5 mm. Figure 0.1 Geometry of forked tube (Dtube = 4.572 mm, A1 = 40.4 mm, A2 = 67.2 mm, A3 = 90.7 mm, B1 = 46.2 mm, and B2 = 23.5 mm). 168 The objective of this study is to investigate nanoparticle resuspension rates on forked tubes by using various methods: pulsed air jet, ultrasonication, and acid dissolution. Fluorescent and AgNPs were deposited by using the aerosol method on forked tubes. AgNPs resuspension or removal efficiency using pulsed air jet, ultrasonication, or acid dissolution methods were presented. 6.2 Particle deposition and resuspension or removal on 200 mm wafers 6.2.1 Deposition by Electrophoresis Figure 6.2 describes the polystyrene latex (PSL) nanoparticle deposition on 200 mm wafers by controlling electrophoresis. The schematic of the deposition chamber in Figure 6.2 can be found in Figure 5 in Yook et al.’s paper (Yook et al., 2008). PSL nanoparticles were generated by using an atomizer or nebulizer. To remove unintended particles such as residue particles, a differential mobility analyzer (Model 3081, TSI, MN, USA) was employed. The deposition spot size was controlled by adjusting the supplied voltage. The electrical mobility (Zp) of DMA (Knutson and Whitby, 1975) and a charged particle from the equivalence between electrophoresis and Stokes’ drag force acting on the particle (Hinds, 1982) can be expressed as follows. 𝑍𝑝 = 𝑄𝑠ℎ 𝑙𝑛( 𝑟2,𝐷𝑀𝐴 𝑟1,𝐷𝑀𝐴 ) 2𝜋𝑉𝐷𝑀𝐴𝐿𝐷𝑀𝐴 = 𝑛𝑝𝑒𝐶𝑐 3𝜋𝜇𝑑𝑝 , (6.1) where Qsh is the sheath flow rate of DMA, VDMA is the voltage applied to the center rod of DMA, and r1,DMA, r2,DMA and LDMA are the inner radius, outer radius, and length of DMA, 169 respectively. np is the average number of elementary charge units per particle (particle-1), e is the elementary unit of charge of 1.6×10-19 As, dp is the particle diameter, µ is the gas dynamic viscosity of 1.8325×10-5 kg/ms and Cc is the slip correction factor which was calculated as follows (Kim et al., 2005): 𝐶𝑐 = 1 + Kn (1.165 + 0.483 exp(−0.997/Kn)), (6.2) where Kn is Knudsen number which is defined as the ratio of the mean free path to particle radius, i.e., 2λ/dp. For calculating the particle deposition size on 200 mm wafers, we assumed that the time for the charged PSL nanoparticle to drift the space between the wafer surface and aerosol outlet (tz) should be the same as the time for the PSL nanoparticle to travel in the radial direction (tr) which can be expressed as follows (Yook et al., 2008): 𝑡𝑧 = 𝑙𝑔 𝑣𝑧 = 𝜋𝑠2𝑙𝑔 4𝑄𝑖𝑛,𝑐ℎ𝑎𝑚𝑏𝑒𝑟 = 𝑡𝑟, (6.3) where lg is the space between the wafer surface and aerosol outlet, s is the deposition spot size, and Qin,chamber is the flow rate through the deposition chamber. the drift velocity in the z-direction (vz) can be computed as follows: 𝑣𝑧 = 𝑍𝑝𝐸, (6.4) the electric field strength (E) was calculated by 𝐸 = 𝑉𝑑/𝑙𝑔, (6.5) where Vd is the voltage applied to the bottom plate. Therefore, we can determine the deposition spot size as follows (Yook et al., 2008): 170 𝑠 = √ 12𝜇𝑄𝑖𝑛,𝑐ℎ𝑎𝑚𝑏𝑒𝑟𝑑𝑝𝑙𝑔 𝑛𝑝𝑒𝐶𝑐𝑉𝑑 . (6.6) Figure 6.2 Experiment setup for PSL nanoparticle deposition on 200 mm wafers by controlling electrophoresis. The example results of PSL 102 nm particle deposition by controlling electrophoresis as shown in Figure 6.3. The deposited particle size, number, and spot size were measured by using a wafer surface scanner (WSS, KLA-Tencor SP1 TBI in Entegris, MN). The controlled spot size was calculated by using Equation (6.6). The calculated deposition spot size was very similarly measured with the actual deposited spot size and generated PSL nanoparticle size was reasonably measured when comparing the size bin results of WSS. It is noted that there was some contamination by a wafer-handling tweezer (wafer pick) as shown in Figure 6.3a. 171 Figure 6.3 PSL nanoparticle deposition results which are determined by the wafer surface scanner: (a) 102 nm raw data of 200 mm wafer full scanning result; (b) magnified wafer scanning results in controlled spot size; (c) particle deposition results in different size bin channel; (d) 102nm particle count of each size bin channel; (e) PSL 300, 600, 900 nm deposition results. To deposit the larger size of particles in 200 mm wafers, we also tested with PSL 300 nm, 600 nm, and 900 nm as shown in Figure 6.3e. Even though we successfully controlled the particle deposition spot size, we failed to get uniform deposition results for the cases of 300 nm, 600 nm, and 900 nm. The tested particle size of each different location 172 (#1~#9) and applied voltage (Vd) was summarized in Table 6.1. The example magnified image of Figure 6.3e is presented in Figure 6.4a. We found the particle pattern on 200 mm wafers, these results are affected by a 90-degree smoothly bent tube at the aerosol chamber inlet, as shown in Figure 6.4b. An extended crescent shape was observed when passing through a smoothly 90-degree bend tube. A bent tube can form the secondary flow inside the tube. This phenomenon can be explained by the particle-laden flow characteristics on forked tubes which is sophisticatedly described in Chapter 5. Table 6.1 The tested particle size of each different location (#1~#9) and applied voltage (Vd) of the experiment are in Figure 6.3e. Location #1 #2 #3 #4 #5 #6 #7 #8 #9 dp [nm] 300 300 300 300 300 600 600 900 900 Vd [V] 1500 3000 4500 6000 7500 5000 8000 6000 9000 173 Figure 6.4 (a) Examples of magnified images of Figure 6.3 and PSL 300 nm nanoparticle deposition results which are determined by the wafer surface scanner, (b) 90-degree bend tube at the aerosol deposition chamber inlet. 6.2.2 Direct deposition method To uniformly deposit particles on 200 mm wafers and minimize the secondary flow effect, the PSL particles were directly deposited on 200 mm wafers, as shown in Figure 6.5. The solution which contains PSL particles continuously supply to the electrospray by using a syringe pump with a flow feeding rate of 0.3 ml/h. The deposition experiment time was set to 4 min. The applied voltage at the outlet of the electrospray nozzle was 4 kV. The tested PSL particle size is 1.6 µm. 174 Figure 6.5 Experiment setup for 1.6 µm PSL particles to be directly deposited on 200 mm wafers. 6.2.3 PSL 1.6 µm resuspension or removal by a pulsed air jet If the air jet cleaning is applied to remove the particles on the surface, removal forces are categorized as aerodynamic drag force and aerodynamic lift force, as shown in Figure 6.6a. When calculating the drag and lift force, the flow velocity at the center of the particle was utilized. Since the flow velocity steadily increases with distance from the surface, the actual drag force which acts on the particles is slightly higher than the center of the particles (Lee et al., 2017b). Therefore modified drag force (Goldman et al., 1967; Lee et al., 2017b; O’Neill, 1968; Sharma et al., 1992) and lift force (Busnaina et al., 1993; 175 Mezhericher et al., 2018) can be expressed as follows: 𝐹𝐷𝑟𝑎𝑔 = 3𝑓𝜋𝜇𝑢𝑐𝑑𝑝 𝐶𝑐 , (6.7) and 𝐹𝐿𝑖𝑓𝑡 = 1.615𝑑𝑝 2𝑢𝑐√𝜌𝜇 𝑑𝑢 𝑑𝑦 | 𝑦=𝑑𝑝/2 . (6.8) Here, the dimensionless coefficient of force acting on the sphere (f) was determined as 1.7009 (O’Neill, 1968). Generally, the drag force is much bigger than the lift force. The removal force is proportional to dp. Therefore, the smaller particles are difficult to remove or be resuspended. There are two major particle adhesion forces which are the Van der Waals force and capillary force, as shown in Figure 6.6b. Condensation of water vapor around the particle-substrate contact area forms a meniscus. The formed meniscus will add capillary force, and it significantly enhances the adhesion between the particle and the substrate. Van der Waals force and capillary force (Ahmadi et al., 2007) can be determined as follows. 𝐹𝑉𝐷𝑊 = 𝐴𝑑𝑝 12𝑧0 2, (6.9) and 𝐹𝐶 = 2𝜋𝜎𝑑𝑝[sin 𝛼 sin(𝜃 + 𝛼) + cos 𝜃]. (6.10) Here, A is the Hamaker constant, zo is the separation distance between particle and substrate, 176 and σ is the surface tension of water (=0.0735 N/m). The angle α and wetting angle θ are described in Figure 6.6b. Van der Waals forces could be substituted by other adhesion models such as JKR (Davies, 1973), DMT (Derjaguin et al., 1975), and TPL (Tsai et al., 1991)” model. The total adhesion force could be estimated by summation of these two forces, i.e., FAdh ≈ (FVDW+FC). Therefore, the total adhesion force including Van der Waals force and capillary force is proportional to the particle diameter (FAdh∝dp). Based on calculated adhesion force and particle removal forces, the particle detachment model could be modeled. As shown in Figure 6.6d, there are three detachment modes: sliding, rolling and lifting. Each detachment mode equation comes from the force and moment balance equation in each axis. Sliding detachment mode: 𝐹𝐷𝑟𝑎𝑔 > 𝑘𝑠(𝐹𝐴𝑑ℎ − 𝐹𝐿𝑖𝑓𝑡). (6.11) Lifting detachment mode: 𝐹𝐿𝑖𝑓𝑡 > 𝐹𝐴𝑑ℎ. (6.12) Rolling detachment mode: 0.87𝑑𝑝𝐹𝐷𝑟𝑎𝑔 + 𝑎𝐹𝐿𝑖𝑓𝑡 > 𝑎𝐹𝑎𝑑ℎ. (6.13) If the moment resulting from drag and lift is bigger than the moment coming from total adhesion force, the particle is detached. The rolling detachment mode is also called Torque analysis (Lee et al., 2017b). Among the three detachment modes, the rolling detachment mode is considered the initial detachment mechanism (Lee et al., 2017b). In the air jet 177 cleaning, since generally the flow velocity coming from the air jet nozzle is extremely high, the flow would be turbulent flow in terms of Reynolds number. The velocity profile near the surface resulting from turbulent flow in the boundary layer is not simply calculated. Moreover, the drag and lift forces are functions of flow velocity. Before applying the particle detachment model, the velocity profile near the wall should be determined. 178 Figure 6.6 (a) Particle removal force by air jet; (b) particle adhesion force; (c) free body diagram; (d) particle resuspension mechanisms: sliding, rolling, and lifting. 179 To validate the flow field resulting from impinging air jet, the reference model (Loureiro and Silva Freire, 2012) which clearly illustrated boundary conditions and geometric information, and the overall experimental set-up was carefully chosen by considering the similar boundary conditions and abundant velocity flow profile data near the wall. To simplify the reference model, turbulent, steady state, and two-dimensional axis symmetry conditions were assumed, as shown in Figure 6.7. The height of the air nozzle (Htube) is 1350 mm, the diameter of the air nozzle (D) is 43.5 mm, and the length of impinging bottom plate wall (Dplate) is 840 mm. By using Computational Fluid Dynamic software, ANSYS FLUENT, impinging air jet flow field is calculated. The boundary condition at the air nozzle inlet was set as velocity inlet with 17 m/s, i.e., the corresponding Reynolds number is approximately 47,100, and the exit of air was set as pressure outlet with ambient pressure (101 kPa). Figure 6.7 Computational domain for numerically investigating impinging air jet. 180 Figure 6.8 shows the numerically calculated velocity field. For the impinging air jet, there are two regions; one is the stagnation region and the other one is the wall jet region. At the center of the air jet, there is a stagnation point at which flow velocity is zero. After the stagnation point, the flow velocity near the wall steadily increases with the distance from the center. This region is called a stagnation region. After the stagnation region, the flow velocity near the wall steadily decreased. This region is referred to as the wall jet region. For obtaining the velocity near the impinging wall, the friction velocity was calculated as follows: 𝑢𝜏 = √ 𝜏𝑤 𝜌𝑤 . (6.14) Compare with the other theory and empirical models (Beltaos and Rajaratnam, 1974; Poreh et al., 1964; Tu and Wood, 1996; Viegas and Janeiro Borges, 1986), in the wall jet region, the present numerical data shows good agreement with experiment data and various models. In the stagnation region, the numerical results slightly overestimated the friction velocity. But the trend is the same as the theoretical model and the error between them is also acceptable. 181 Figure 6.8 Numerically calculated velocity field of impinging air jet and validation results of friction velocity with various model and experimental results. 182 Figure 6.9 illustrates the particle resuspension experiment setup by using a pulsed air jet. The experiment was performed in Entegris class 10 cleanroom. The pulsed air was controlled by a solenoid valve and the flow rate was measured by three mass flow meters (Model 4045, TSI, MN, USA). The nozzle diameter was chosen as 2.38 mm for generating high-pressure air. The distance between the air jet nozzle inlet and the 200 mm wafer surface was set as 1 cm. The pressure was measured as 53 kPa. The pulsed air was fired 10 times through a solenoid valve, and 10 seconds of air was added to make pulsed air, and the air was blocked for 10 seconds. Figure 6.9 Particle resuspension experiment setup by using pulsed air jet: (a) experiment setup schematic; (b) a photo of experiment setup; mechanisms: (c) nozzle with a diameter of 2.38 mm. 183 Figure 6.10 shows the results of the particle resuspension experiment before and after the pulsed air jet. The tested PSL particle size was 1.6 µm. The particle deposition method was described in Figure 6.5. The experimental results show that particles were hardly resuspended by the air jet experiment. Ahmadi et al theoretically calculated that critical friction velocities should be larger than at least 10~100 m/s for removing sub- micron particles, i.e., dp< 1 µm (Ahmadi et al., 2007). But the calculated friction velocities of the reference model (Loureiro and Silva Freire, 2012) were smaller than 2 m/s, as shown in Figure 6.8b. This might be the reason why particles were not resuspended by the pulsed air jet. In this study, one of our objectives is to remove sub-micron particles, the air jet method is not appropriate to remove silver nanoparticles. Figure 6.10 Particle resuspension experiment before and after pulsed air jet result: (a) particle scatter diagram before pulsed air jet; (b) particle scatter diagram after pulsed air jet; (c) contour diagram before pulsed air jet; (d) contour diagram after pulsed air jet. 184 6.3 Nanoparticle deposition on forked tubes 6.3.1 Fluorescent nanoparticle Pui et al. suggested the measurement method by using fluorescent particles for evaluating the particle deposition efficiency on a 90o smooth-bent pipe (Pui et al., 1987). By using a vibrating orifice aerosol generator, they generated monodisperse micro-sized liquid particles in which uranine was dissolved. They got deposition efficiency by comparing the total mass of uranine on the bending section and on the outlet filter section. For a fluorescent tracer, fluorescein sodium salt (C20H10Na2O5, Cas 518-48-8, Mw = 376.27 kg/mol) was purchased by Sigma-Aldrich Co. Ltd (St. Louis, MO, USA). The fluorescein sodium salt is easily dissolvable in water (solubility of C20H10Na2O5 in water is ~ 1 g/L). The excitation and emission wavelength ranges of fluorescein sodium salt are 400-550 nm and 500-650 nm, respectively (S. C. Kim et al., 2021; Kwak et al., 2021a). To measure the fluorescent signals, Turner Digital Fluorometer (TDF, Model 450, Barnstead/Thermolyne, IA, USA) was employed. The working principle of TDF is that excitation energy which is generated by the quartz-halogen lamp (λ = 340-750 nm) is filtered by a Narrow Band filter (NB440 filter, Model 45F01-05, Barnstead/Thermolyne, IA, USA), as shown in Figure 6.11. Because of the NB440 filter, the sample solutions which contain fluorescein sodium salt is only excited by the specific wavelength of 440-460 nm. The emitted light is also filtered by using Sharp-Cut 500 (SC500) emission filter. The digital number (DN) of the fluorescence signal (FS) was measured by TDF. 12×75 mm culture tubes (Product no. 99445-12, Corning, NY, USA) with sample solutions were placed into the fluorometer for measuring the fluorescent signal. As shown in Figure 6.12, the integrated fluorescent signal 185 and fluorescent tracer concentration can be represented as a log-log linear relation (Gaigalas et al., 2005). The best-fitted results are as follows (Kwak et al., 2021a): 𝑙𝑜𝑔 𝐶𝑓 = 4.314 + 1.064(FS). (6.15) Here, Cf is fluorescent tracer concentration in ng/L (ppt), and FS is the integrated fluorescent signal measured by fluorometer in digital number (DN). Figure 6.11 (a) Schematic of fluorometer working mechanism. (b) Fluorescein sodium salt emission and excitation wavelength and fluorometer light excitation and emission filter wavelength. NB and SC refer to narrow band, and sharp-cut, respectively (Kwak et al., 2021a). Quartz-Halogen Lamp [340~750 nm] NB 440 filter SC 500 filter Sample Light detector a b 186 Figure 6.12 Comparison between fluorescence signal measured by fluorometer and fluorescent tracer concentration. The red solid line indicates the fitting curve results (Kwak et al., 2021a). The fluorescent nanoparticle deposition on a forked gas line experiment setup was illustrated in Figure 6.13a. Fluorescent nanoparticles were generated by using an electrospray aerosol generator (ES, Model 3480, TSI, MN, USA). We prepared 1 ml of fluorescein sodium salt solution with less than 0.05 mM and adjusted the electrical conductivity of the solution by adding 0.02 ml of the 0.02 M ammonium acetate solution for generating fluorescent nanoparticles. Since particle deposition efficiency is highly affected by the particle size and the fluorometer cannot provide the generated particle size 187 data, the generated particle size distribution was monitored by using a scanning mobility particle sizer (SMPS) which is combined with a nano-differential mobility analyzer (Nano- DMA, Model 3085, TSI, MN, USA), an ultrafine condensation particle counter (UCPC, Model 3776, TSI, MN, USA), and an electrostatic classifier (Model 3080, TSI, MN, USA). The generated fluorescent nanoparticles were assumed as monodisperse and the example of measured particle size distribution was illustrated in Figure 6.13b. It was assumed that the number of generated nanoparticles was the same as the amount collected in the filter. To prevent the particle shifting phenomenon due to the flow rate difference, the flow rate through the forked gas line and the flow rate toward the filter was set to be the same. Figure 6.13 (a) Fluorescent nanoparticle deposition on a forked gas line experiment setup; (b) fluorescent nanoparticle size distribution measured by SMPS; (c) fluorescent nanoparticle collecting method for upstream concentration. 188 After the deposition experiment, forked gas lines and filters were each placed in a sealed zipper storage bag and immersed in 100 ml of deionized water. The shaker was set at 200 rpm for 30 minutes so that fluorescent nanoparticles were sufficiently soluble in water. Each sample concentration was measured by TDF and calculated by using Equation (6.15). The nanoparticle deposition efficiency on a forked gas line was obtained by comparing fluorescein nanoparticles concentration obtained in forked gas lines (CFT) and filters (Cfilter) solution and calculated as follows: 𝜂𝑑𝑒𝑝 = 𝐶𝐹𝑇 𝐶𝑓𝑖𝑙𝑡𝑒𝑟 . (6.16) The experimental results and particle deposition efficiency was summarized in Table 6.2. It should be noticed that since TDF was a mass-based measurement device, the size of monodisperse particles was obtained by volume-based particle size distribution from SMPS. The correlation fitting curve for predicting the forked gas line deposition efficiency based on electrometer measurement and numerical simulation results was 𝜂𝑑𝑒𝑝,𝐹𝑇,𝑐𝑜𝑟(Pe) = 13.75Pe −0.3798, (6.17) where Pe is the Peclet number, and dep,FT,cor is the predicted nanoparticle deposition efficiency on a forked gas line. Since the total flow rates through the forked gas line were set to be 1 L/min and the particle size measured through SMPS was 23.3 nm, the corresponding Reynolds number was calculated as 310 and the corresponding Schmidt number was calculated as 1460 (Kwak et al., 2023, 2021b, 2020). The predicted nanoparticle deposition efficiency of fluorescent nanoparticles on forked gas lines experiment was calculated as approximately 10% (Kwak et al., 2023). The averaged 189 experimentally measured deposition results by using fluorescent nanoparticles were approximately 13.2% as presented in Table 6.2. Table 6.2 Experiment result of fluorescent nanoparticle deposition on a forked gas line experiment. Volume mode size was measured by SMPS. The measured value was determined by fluorescence signal. The calculated concentration was determined by using a correlation Equation (6.15). Deposition efficiency was calculated by comparing fluorescein nanoparticles concentration obtained in forked gas lines (CFT) and filters (Cfilter) solution data by using Equation (6.16). The averaged experimentally measured deposition results by using fluorescent nanoparticles were approximately 13.2%. Volume mode size [nm] Measured value in a filter[DN] Measured value in a forked gas line [DN] Calculated concentration in a filter [ppt] Calculated concentration in a forked gas line [ppt] Deposition efficiency [%] 23.3 0.535 0.114 10592 2044 19.3 0.728 0.063 14700 1088 7.4 0.282 0.041 5359 689 12.9 6.3.2 Silver nanoparticle For inter-comparing the results measured by different instruments, we performed the feasibility test as shown in Figure 6.14a. The amount of generated silver nanoparticles (AgNPs) was measured by a condensation particle counter (CPC, Model 3772, TSI, MN, USA) and single particle inductively coupled plasma mass spectrometry (sp-ICPMS, Model NexION 350 ICP-MS, PerkinElmer, MA, USA). To minimize the contamination in the sample solution, sp-ICPMS was operated in the Applied Materials class 1000 190 cleanroom. For generating large size of spherical silver nanoparticles, we employed the 1st furnace-agglomerate chamber-2nd furnace system (S. C. Kim et al., 2009). Due to the high temperature of the 1st tube furnace (Model STF 55433C-1, Lindberg/Blue M, MA, USA), the silver powder which was placed on the ceramic tube evaporated. By using ultra-high purity grade nitrogen gas (99.999%), the evaporated silver was carried. As a result of the low temperature downstream of the tube furnace, the small size of silver nanoparticles was created through the condensation process. This small size of silver nanoparticles (AgNPs) had agglomerated with each other due to large residence time in the agglomerate chamber. By slightly melting the surface of agglomerated silver nanoparticles in the 2nd tube furnace (Model HTF55322A, Lindberg/Blue M, MA, USA), those nanoparticles become a spherical shape as shown in Figure 6.14b. The generated spherical AgNPs were charged by a Polonium-210 radioactive source with the diffusion charging distribution (Wiedensohler, 1988; Wiedensohler and Fissan, 1988). The AgNPs were classified by a nano-differential mobility analyzer (Nano-DMA, Model 3085, TSI, MN, USA) with an electrostatic classifier (Model 3080, TSI, MN, USA) to produce monodisperse and singly positive-charged AgNPs with sizes of 50 nm. The temperature of the first and second-stage tube furnace was set to 1200 oC, and 600 oC, respectively. Sheath air and aerosol flow rates through the Nano-DMA were set as 15 and 1.5 L/min, respectively. To obtain silver nanoparticle solutions for use as a sample for sp-ICPMS, the dissolvable electrospun nanofiber membrane (ENM) was fabricated. The polymer for fabricating the dissolvable ENM was chosen as polyethylene oxide (PEO, Cas 25322-68- 3, Mw = 1,000,000 kg/mol). The detailed ENM fabrication process was described in the author's previous publication (S. C. Kim et al., 2020). The 50 nm spherical silver 191 nanoparticles were tested, and the deposition time varied from 30 to 90 minutes. The results of the feasibility test for interchangeably using the CPC and sp-ICPMS methods are presented in Figure 6.14c. A strong correlation between sp-ICPMS and CPC particle counts was obtained. It is worthwhile to mention that, to our best knowledge, this is the first time to present the intercomparison results between sp-ICPMS and CPC. Figure 6.14 (a) Experiment setup for obtaining the large size of silver nanoparticle and comparing CPC and sp-ICPMS; (b) description of silver nanoparticle collecting method for measuring sp-ICPMS and SEM image of ENM and collected spherical silver nanoparticles; (c) Intercomparison results between CPC and sp-ICPMS. 192 6.4 Nanoparticle resuspension or removal on forked tubes 6.4.1 Clean air transport Figure 6.15 illustrates the silver nanoparticles resuspension experiment during the clear air transport. Three different conditions were evaluated: (1) clean air test performed with HEPA filter without a forked tube (Figure 6.15a); (2) baseline test performed with HEPA filter with a clean (before deposition) forked tube; (3) AgNPs resuspension test with HEPA filter with a dirty (after deposition) forked tube (Figure 6.15b). For the dirty forked tube, 50 nm AgNPs are deposited with the estimated number of approximately 2 x 107 particles which was determined by the correlation deposition efficiency equation, i.e., Equation (6.17) and CPC cumulative particle count number. Figure 6.15 Experiment setup for resuspension during clean air transport: (a) clean air test; (b) experiment set-up for silver nanoparticles resuspension test. 193 Figure 6.16 shows the 50 nm AgNPs resuspension experimental results during clean air transport. We conducted a clean air transport experiment for nine hours. Fig 56a shows the real-time cumulative particle number results. We found that the measured number of particles in the gas passed through the dirty gas line and the clean air test results were almost the same. The resuspension rate of 50 nm AgNPs is approximately 25 particles/hour without considering the clean air test. These results show that the resuspended nanoparticles from the complicated gas line systems might not be a contamination source during the semiconductor industry manufacturing process. Figure 6.16 Experiment results of resuspension during clean air transport: (a) real-time cumulative particle number results; (b) Comparison of each experiment results between clean air test, baseline test, 1-hour resuspension test, and 9-hour resuspension test. 6.4.2 Pulsed air jet experiment The contamination during the manufacturing process would occur after a strong turbulent flow inside the forked tube. To evaluate the resuspension rate before and after the 194 air jet cleaning method on forked tubes, we performed a pulsed air jet experiment on a forked tube as shown in Figure 6.17. The pulsed purified nitrogen gas was injected 60 times. The nitrogen gas was added to make a pulsed signal for one second and then supplied nitrogen gas was blocked for three seconds. The pulsed air jet experiment was performed in the Applied Materials class 10 cleanroom. Figure 6.17 Experiment setup for particle resuspension by using a pulsed air jet. After the pulsed air jet resuspension experiment, the degree of contamination on the forked tube was evaluated by using Semi F70 which includes a laser particle counter (LPC) and condensation particle counter (CPC). The experiment results were summarized in Table 6.3. Here, we also got similar results that were obtained in the 200 mm wafer experiment in Figure 6.10. There was no significant difference between forked tubes with and without pulsed air jet cleaning. Therefore, we believe that the aerosol detecting method, i.e., LPC or CPC, is not useful to evaluate the particle resuspension or removal efficiency and the pulsed air jet cleaning method is not appropriate to remove sub-100 nm AgNPs. 195 Table 6.3 The experiment result of resuspension after the pulsed air jet experiment. The two-stage of tube furnace system instead of the single-stage of tube furnace was employed for generating spherical 50 nm AgNPs, as shown in Figure 6.14a at the University of Minnesota (UMN). Pulsed air jet cleaning was performed as illustrated in Figure 6.17 at Applied Materials (AMAT). The estimated deposited nanoparticles were calculated by Equation (6.17). UMN Applied Materials AgNPs size [nm] Deposition Time [min] Upstream NPs [particles] Estimated Dep. NPs [particles] Pulsed Air Jet Cleaning Semi F70 LPC [particles /ft 3 ] CPC [particles /ft 3 ] 50 60 3.12 x 10 8 1.75 x 10 7 No 2 2 2.54 x 10 8 1.43 x 10 7 Yes 5 <1 30 1.51 x 10 8 8.48 x 10 6 No 22 <1 1.48 x 10 8 8.31 x 10 6 Yes 3 <1 6.4.3 Ultrasonication To increase the particle removal or resuspension efficiency (PRE) for removing sub-100 nm AgNPs, the ultrasonication method was employed. Ultrasonic frequencies and power of experiment condition were 78 kHz, and 1200 W, respectively. The power density of ultrasonication (U/S) was approximately 200 W/in2. Each forked tube was filled with 7.5 ml of deionized water and sealed with red plastic caps for preventing the unwanted particles from coming into forked tubes, i.e. for internal surface ultrasonication, as shown in Figure 6.18a. 196 Figure 6.18 Internal surface high-power ultrasonication for silver nanoparticle resuspension: (a) a photo of immersed forked tubes in high power ultrasonic bath with capped with red plastic caps; (b) a photo of the first high-power ultrasonic plastic rack to hold forked tubes; (c) a photo of the second high power ultrasonic plastic rack to hold forked tubes. Internal surface high-power ultrasonication was performed on two different racks which hold the forked tube in an ultrasonic bath. The first ultrasonication was performed on the plastic rack and the second ultrasonication was performed on the metal rack which was depicted in Figure 6.18b and Figure 6.18c. The particle removal or resuspension efficiency based on predicted nanoparticle deposition efficiency (PREcor) was expressed as follows: PRE𝑐𝑜𝑟 = 𝑁𝑟𝑒𝑠,𝑈/𝑆 𝑁𝑢𝑝×𝜂𝑑𝑒𝑝,𝐹𝑇,𝑐𝑜𝑟(Pe) . (6.18) 197 Here, Nres,U/S is the number of resuspended particles during the ultrasonication, dep,FT,cor is the predicted nanoparticle deposition efficiency on a forked tube by Equation (6.17), and Nup is the number of upstream cumulative particles and can be calculated as follows: 𝑁𝑢𝑝 = 𝑄𝐶𝑛𝑢𝑚𝑡𝑒𝑥𝑝, (6.19) where Q is the total flow rate passing through the forked tube, Cnum is the particle number concentration measured by CPC or electrometer, and texp is the deposition experiment time. For depositing 50 nm AgNPs on forked tubes, the total flow rate was set as 1.0 L/min, corresponding Reynolds number is 310. The deposition experiment times were set at 15, 30, and 60 minutes. The estimated deposited nanoparticles were determined as 5.62% by Equation (6.17). The summarized results of the particle deposition experiment and particle resuspension by ultrasonication are presented in Table 6.4. The averaged PREcor during the first ultrasonication and the second ultrasonication was measured as 2.28%, and 6.04%, respectively. Therefore, PREcor of 50 nm AgNPs increased with the use of a metal rack (Figure 6.18b) compared to the use of a plastic rack (Figure 6.18c). The averaged total PREcor during the first ultrasonication and the second ultrasonication was measured as 8.33%. 198 Table 6.4 Experiment result of resuspension by high power ultrasonication (U/S or WRS). It should be noticed that the total flow rate of the forked tube was set to 1.0 L/min (Re = 310) and the two-stage of tube furnace system instead of the single-stage of tube furnace was employed for generating spherical 50 nm AgNPs as shown in Figure 6.14a. Internal surface high-power ultrasonication was performed as illustrated in Figure 6.18a at Applied Materials. The 1st U/S and 2nd U/S were performed on a plastic rack (Figure 6.18b) and a metal rack (Figure 6.18c), respectively. The estimated deposited nanoparticles were calculated as 5.62% by Equation (6.17). UMN Applied Materials Total PREcor [%] AgNPs size [nm] Upstream NPs [particles] Estimated Deposition NPs [particles] sp-ICPMS (AgNPs analysis) 1 st U/S [particles] 2 nd U/S [particles] Total (1+2) [particles] 50 7.40 x 107 4.16 x 106 1.16 x 105 5.17 x 105 6.33 x 105 15.23 7.38 x 10 7 4.15 x 106 1.30 x 105 3.81 x 105 5.11 x 105 12.32 1.46 x 10 8 8.20 x 106 2.65 x 105 3.33 x 105 5.98 x 105 7.29 1.58 x 10 8 8.88 x 106 1.76 x 105 3.95 x 105 5.70 x 105 6.42 3.02 x 10 8 1.70 x 107 7.24 x 104 3.06 x 105 3.78 x 105 2.23 3.02 x 10 8 1.70 x 107 3.62 x 105 7.36 x 105 1.10 x 105 6.48 6.4.4 Ultrasonication and dissolution by acid extraction Before concluding the PRE by ultrasonication, particle deposition efficiency and PRE were verified once more by using another method, i.e., ultrasonication and particle dissolution by acid extraction method. For using the particle dissolution by acid extraction method, mass concentration measured by ICP-MS and particle concentration measured by sp-ICPMS was calibrated with 40 nm AgNPs. The 40 nm AgNPs suspension solution with a mass concentration of 697 ppb (ppb = µg/L) was prepared. The prepared mother sample solution was diluted with the dilution factor (DF) of 10, 50, 250, 2.5k, 12.6k, 25.3k, 50.6k, and 126k. Particle 199 concentration of the diluted sample solutions with DF of 2.5k, 12.6k, 25.3k, 50.6k, and 126k was measured by sp-ICPMS. Mass concertation of every sample was dissolved by 3 wt.% nitric acid (HNO3) and measured by ICPMS. Particle concentration of samples with DF of 1, 10, 50, and 250 were estimated based on the measured particle concentration value of samples with DF = 2.5k. The calibration results for the acid extraction method are presented in Figure 6.19 and the calibration equation is (𝐶𝑛𝑢𝑚 in particles/ml) = 844,694 × (𝐶𝑚𝑎𝑠𝑠 in ppb). (6.20) Here, Cnum is the particle number concentration measured or estimated by sp-ICPMS, and Cmass is the mass concentration measured by ICP-MS. Figure 6.19 40 nm silver nanoparticles calibration results for acid extraction performed by Applied Materials. For 3 wt.% HNO3. 200 Figure 6.20 illustrates the experiment procedures of each step for evaluating particle deposition by aerosol method, particle resuspension by high-power ultrasonication, and dissolution by acid extraction. Particle deposition by aerosol method (Step 1 in Figure 6.20) was conducted at the University of Minnesota (UMN). Particle resuspension by high- power ultrasonication and particle dissolution by acid extraction was carried out at Applied Materials (AMAT). Figure 6.20 Experiment procedures for evaluating particle deposition rate by aerosol method, particle resuspension rate by high power ultrasonication, and dissolution rate by acid extraction. Before depositing AgNPs on forked tubes, the forked tube was carefully cleaned through a series of procedures: (1) soaking the entire forked tube in 20 v/v% HNO3 for 15 minutes; (2) Rinsing the forked tube with deionized water; (3) Drying forked tube through blowing nitrogen gas; (4) Repeat procedure step (1~3). For the #14 forked tube, the internal 201 HNO3 circulation method was additionally performed for 15 minutes with the condition of 60 Psi with a flow rate of 5 L/min. After performing the cleaning process, the cleanliness of forked tubes was evaluated by using Step 2 in Figure 6.20. The summarized cleaning process of each forked tube and cleanliness results were presented in Table 6.5. It should be noticed that the order of resuspended particles number by high power ultrasonication was 105 after the cleaning process. Table 6.5 Cleaning process of each forked tube and evaluated cleanliness of forked tubes before particle deposition experiment. Forked tube Cleaning method sp-ICPMS Mode size of AgNPs [nm] Number of AgNPs [particles] #14 HNO3 Int Cir + 2 × HNO3Soak 24 4.08×105 #18 2 × HNO3 Soak 34 1.14×105 #21 2 × HNO3 Soak 44 1.14×105 #22 2 × HNO3 Soak 45 1.07×105 For the AgNPs deposition by aerosol method (Step 1 in Figure 6.20), 40 nm AgNPs were deposited by using the forked tube particle deposition setup. For generating spherical 40 nm AgNPs, the two-stage of tube furnace system instead of the single-stage of tube furnace was employed in Figure 6.14a. The total flow rate of the forked tube was set to 1.6 L/min (Re = 500). The deposition experiment time (texp) was set to 60 minutes. The number of upstream cumulative particles (Nup) was calculated by Equation (6.19). The predicted deposition efficiency value was calculated as 5.51% by Equation (6.17). The AgNPs 202 deposition results are presented in Table 6.6. It should be noticed that the estimated deposited particles number of forked tubes was around 9×107 ~10×107 which value is approximately 1,000 times higher than the number of AgNPs on the forked tube before the deposition experiment. Table 6.6 AgNPs deposition results (Step 1 in Figure 6.20). Forked tube Average upstream particle concentration [particles/cm3] Total measured particle number in upstream [particles] Estimated number of deposited particles [particles] #14 1.82×104 1.75×109 9.64×107 #18 1.73×104 1.66×109 9.15×107 #21 1.72×104 1.65×109 9.09×107 #22 1.69×104 1.62×109 8.93×107 The deposited AgNPs on the internal tube wall of forked tubes were resuspended by high-power ultrasonication with 78 kHz and 1200 W (Step 2 in Figure 6.20). 7.5 ml of deionized water was used for filling the inside of the forked tubes and each inlet and outlet of forked tubes was sealed by red plastic caps as shown in Figure 6.18a. The immersed forked tubes in the ultrasonic bath were sonicated for 15 minutes. After the ultrasonication, the samples are analyzed by sp-ICPMS to determine the number of resuspended AgNPs. The resuspension results were summarized in Table 6.7 and Figure 6.21. 203 Table 6.7 The resuspension results (Step 2 in Figure 6.20) of AgNPs in the internal surface of forked tubes by 200 W/in2 high power ultrasonication (1200 W and 78 kHz) which is depicted in Figure 6.18a. Forked tubes were filled with 7.5 mL of deionized water and sonicated twice for 15 minutes. Forked tube Number of resuspended particles during the 1st ultrasonication [particles] Number of resuspended particles during the 2nd ultrasonication [particles] Total number of resuspended particles during the 1st and 2nd ultrasonication [particles] #14 2.42×106 1.71×106 4.13×106 #18 1.71×106 0.16×106 1.86×106 #21 0.87×106 2.61×106 3.47×106 #22 2.64×106 0.24×106 2.87×106 Figure 6.21 Particle resuspension results (Step 2 in Figure 6.20) of AgNPs in the internal surface of forked tubes by 200 W/in2 high power ultrasonication (1200 W and 78 kHz). Forked tubes were filled with 7.5 mL of deionized water and sonicated twice for 15 minutes. The raw data of these results were shown in Table 6.7. 204 In Step 3 in Figure 6.20, the rest of the 40 nm AgNPs in the interior of each forked tube after two times of ultrasonication was dissolved in 3 wt.% HNO3 solution with three times. For dissolving the remaining AgNPs in the internal surface of forked tubes by acid extraction, the samples are prepared as presented in Table 6.8. The solution samples were analyzed by using ICP-MS and the number of AgNPs dissolved by acid solution was calculated by using Equation (6.20). Table 6.9 and Figure 6.22 shows the results of the measured mass concentration of dissolved remaining AgNPs on each forked tube and the converted number of AgNPs dissolved by acid solution. It should be noticed that the 40 nm AgNPs particle deposition experiment was not performed on the #20 forked tube which was utilized as baseline results. Table 6.8 Sample preparation for the remaining AgNPs in the internal surface of gas lines by acid extraction with 3 wt.% HNO3 (For Step 3 in Figure 6.20). Extraction @ @1 @2 @3 Solution volume [mL] 4.0 4.0 7.5 Time [min) 5 5 15 Table 6.9 Measured mass concentration of dissolved AgNPs solution extracted from each forked tube (Step 3 in Figure 6.20). The converted number of particles was calculated by the calibration curve, as shown in Figure 6.19 and Equation (6.20). Note: AgNPs were not deposited on the #20 forked tube. Forked tube / Extraction Measured mass concentration [ppb] Converted number of particles [particles] Total number of dissolved particles [particles] @1 @2 @3 @1 @2 @3 #20 0.364 0.264 0.663 1.23×106 8.92×105 4.20×106 6.32×106 #14 2.458 3.504 3.169 8.30×106 1.18×107 2.01×107 4.02×107 #18 2.101 3.589 2.506 7.10×106 1.21×107 1.59×107 3.51×107 #21 2.896 1.801 9.027 9.78×106 6.08×106 5.72×107 7.31×107 #22 13.989 3.769 1.032 4.73×107 1.27×107 6.54×106 6.65×107 205 Figure 6.22 Particle dissolution results (Step 3 in Figure 6.20) of AgNPs in the internal surface of forked tubes by 3 wt.% HNO3. Each dissolution method were described in Table 6.8. The converted number of particles was calculated by the calibration curve, as shown in Figure 6.19 and Equation (6.20). The raw data of these results were shown in Table 6.9. The number of deposited particles can be estimated by MS analysis (Ndep,MS) as follows: 𝑁𝑑𝑒𝑝,𝑀𝑆 = 𝑁𝑟𝑒𝑠,𝑈/𝑆 + 𝑁𝑑𝑖𝑠,𝑎𝑐𝑖𝑑. (6.21) Here, Nres,U/S is the number of resuspended particles by high power ultrasonication, and Ndis,acid is the number of dissolved particles by acid solution. By comparing the number of passing through the forked tube particles (Nup) based on the upstream of deposition experiment data and the number of deposited particles can be estimated by MS analysis, the particle deposition efficiency based on MS analysis (ηdep,FT,MS) can be measured as follows: 206 𝜂𝑑𝑒𝑝,𝐹𝑇,𝑀𝑆 = 𝑁𝑑𝑒𝑝,𝑀𝑆 𝑁𝑢𝑝 . (6.22) The particle removal or resuspension efficiency based on MS analysis (PREMS) was expressed as follows: PRE𝑀𝑆 = 𝑁𝑟𝑒𝑠,𝑈/𝑆 𝑁𝑑𝑒𝑝,𝑀𝑆 . (6.23) The summary of each step's results (e.g., Table 6.6, Table 6.7, and Table 6.9), ηdep,FT,MS, PREcor, and PREMS was presented in Table 6.10. Table 6.10 Summary of 40 nm AgNPs deposition, resuspension, and dissolution results. The experimental deposition efficiency (ηdep,FT,MS), particle resuspension or removal efficiency (PREMS) was based on MS analysis, and particle resuspension or removal efficiency (PREcor) was based on correlation DE results. Particle DEs of estimated deposited particles based on correlation results and numerical results are 5.51%, and 2.67%, respectively. Forked tube Particle deposition (Step 1 in Figure 6.20) at UMN Particle resuspension (Step 2 in Figure 6.20) and dissolution (Step 3 in Figure 6.20) at AMAT ηdep,FT,MS [%] PREcor [%] PREMS [%] Total measured particle number in upstream (Nup, [particles]) Estimated deposited particles based on correlation results (Ndep,cor, [particles]) Estimated deposited particles based on numerical results [particles] Total number of resuspended particles during ultrasonication (Nres,U/S, [particles]) Total number of dissolved particles (Ndis,acid, [particles]) Total number of removed particles during ultrasonication and dissolution (Ndep,MS, [particles]) #14 1.75×109 9.64×107 4.67×107 4.13×106 4.02×107 4.43×107 2.53 4.28 9.31 #18 1.66×109 9.15×107 4.43×107 1.86×106 3.51×107 3.70×107 2.23 2.04 5.04 #21 1.65×109 9.09×107 4.41×107 3.47×106 7.31×107 7.65×107 4.64 3.22 4.54 #22 1.62×109 8.93×107 4.33×107 2.87×106 6.65×107 6.94×107 4.28 3.34 4.14 207 Figure 6.23 compares the number of resuspended 40 nm AgNPs by high-power ultrasonication (Nres,U/S), and the number of removed 40 nm AgNPs by both of high power ultrasonication acid solution (Nres,U/S+Ndis,acid). The 40 nm AgNPs removal or resuspension efficiency based on MS analysis (PREMS) was approximately 5.76%. Figure 6.23 Estimated number of removed particles was evaluated by (1) ultrasonication and (2) the sum of ultrasonication and acid extraction methods. For validating the particle deposition efficiency estimated by each different evaluation method, Figure 6.24 was presented. The blue line with the small-closed circle 208 symbol in Figure 6.24 was a numerically calculated result. The Blue open circle with the error bar in Figure 6.24 was experimentally measured data. The Red dashed line in Figure 6.24 is the correlation results which are described in Equation (6.17). The green rectangular symbol with an error bar in Figure 6.24 was experimentally estimated data by a series of steps in Figure 6.20 and Equation (6.22). In addition, it should be noticed that if considering the controlled forked tube sample for removing the background silver nanoparticles in Table 6.9, the averaged ηdep,FT,MS was 3.04% which is more similar to the numerical simulation results (2.67%). Each different evaluation method can successfully predict particle deposition efficiency. Figure 6.24 Comparison of particle deposition efficiency on forked tubes of each different evaluation method. Figure 6.25 shows the results of particle removal or resuspension efficiency (PRE). Blue rectangular represents the particle removal or resuspension efficiency based on 209 predicted nanoparticle deposition efficiency (PREcor) by Equation (6.18). The red inversed triangle represents the particle removal or resuspension efficiency based on MS analysis (PREMS) by Equation (6.23). PREs of 50 nm AgNPs were summarized in Table 6.5 and PREs of 40 nm AgNPs were summarized in Table 6.10. The results show that the large size of AgNPs is more easily detached by ultrasonication. However, averaged PRE is lower than 10%, therefore the ultrasonication cannot efficiently resuspend AgNPs from forked tubes. Figure 6.25 Particle removal or resuspension efficiency (PRE) is based on the different particle deposition efficiency by ultrasonication. 210 6.5 Conclusion In this study, we evaluate nanoparticle resuspension on forked tubes with various methods: pulsed air jet, ultrasonication, and acid dissolution. We deposited particles on two different surfaces: 200 mm wafers and forked tubes. For depositing particles on 200 mm wafers, PSL particles were deposited by electrophoresis and direct deposition method. On the forked tubes, fluorescent, and AgNPs were deposited by using the aerosol method, and pulsed air jet, and ultrasonication resuspension or removal efficiency for AgNPs was evaluated. We successfully controlled the deposition spot size by electrophoresis, but due to the secondary flow effect on the bending part, we confirmed some patterns on 200 mm wafers for particles with a larger size of 300 nm PSL. By using the direct deposition method, we evaluated the PSL 1.6 µm removal efficiency by using a pulsed air jet, resulting in nearly fewer particles resuspended. We confirmed that 50 nm AgNPs were hardly resuspended by using the ultrasonication method, and PRE was confirmed as less than 10%. For validating particle deposition efficiency and low PRE, we used ultrasonication and particle dissolution by acid extraction method. 40 nm AgNPs were deposited by using the aerosol method. Through the systematic approach at Applied Materials, we verified that particle deposition efficiency can be successfully estimated through correlation results and numerical results. However, the particle removal efficiency of 40 nm AgNPs is still under 10%. Based on the series of experimental results for PRE, we confirmed that the small size of AgNPs is hardly resuspended through ultrasonication. 211 Chapter 7 Semi-empirical equation for determining the nanofiber pressure drop by considering the slip effect 7.1 Introduction PM1.0, PM2.5, and PM10 indicate particulate matter (PM) less than 1.0, 2.5, and 10 μm, respectively. Several scientific reports found associations between air pollution and mortality (Bell, 2004; Chen et al., 2014; Dockery et al., 1993; Jhun et al., 2014; Samet et al., 2000; Schwartz et al., 2018; Zanobetti and Schwartz, 2008). In addition to this, PM2.5 can transport over thousands of kilometers of distance and can remain airborne for weeks (Aguilera et al., 2020; Pui et al., 2014; Tai et al., 2010; Wilson and Suh, 1997). For these reasons, to protect public health, the U.S. Environmental Protection Agency (USEPA) established the PM2.5 standard, and progressively strengthen its standard which is currently 35µg/m3 over a 24-h period and 12µg/m3 for the annual average (Pui et al., 2014). Therefore, it is very important to control and remove the particulate matter in our life. To remove the large size of particles like PM2.5, and PM10, with large inertia, an inertial particle separator, e.g. cyclone separator, zigzag separator, and impactor, can be 212 employed (Cheon et al., 2017; M.-W. Kim et al., 2021; Kim et al., 2013; Lim et al., 2021; Noh et al., 2020; Park et al., 2015). However, nano-sized particles like ultrafine particles (particulate matter less than 0.1 μm) or PM1.0 with low inertia are difficult to remove by using inertial particle separator systems. Therefore, among the various efforts to remove airborne particles, air filtration is one of the most cost-effective and popular methods to control and reduce exposure to airborne particles (Bian et al., 2018; Fisk and Chan, 2017; Kang et al., 2019; S. C. Kim et al., 2020; Singer et al., 2017; Yang et al., 2017; Zaatari et al., 2014). For example, outdoor air is purified by a series of aerosol filtration systems using high-efficiency particulate air (HEPA) filters (which can remove at least 99.97% of particles with a size of 0.3 µm) and ultra-low particulate air (ULPA) filters (which can remove at least 99.9995% of particles with a size of 0.12 µm) to keep a particle-free environment inside the semiconductor manufacturing facilities (Donovan, 1990; Heumann, 1997; C. Kim et al., 2016b; S. C. Kim et al., 2020, 2006). Also, to reduce the airborne particle concentration from the outdoor air, minimum efficiency reporting values (MERV) filters (which capture larger particles between 0.3 and 10 µm) or HEPA filters are frequently used in the air handling unit (AHU), fan coil unit (FCU), or the heating, ventilation, and air-conditioning (HVAC) systems (Bian et al., 2018; Chen et al., 2021). In addition to this, under the current COVID-19 pandemic situation, the importance of respirators using filter media has been proven for preventing SARS-CoV-2 virus transmission (Ou et al., 2020; Pei et al., 2020). Recently, the particle size of interest becomes smaller due to the narrower spacing between nodes in the semiconductor chips (Kwak et al., 2018b; Lee et al., 2020; SamsungNewsroom, 2022) and the toxicity of nanoparticles in human health (Huang et al., 213 2017; Khalili Fard et al., 2015; Kochar et al., 2022; Liu et al., 2014). As a result, air filter media must be denser and thicker to improve filtration efficiency at nano-sized particles, increasing filter pressure drop and thus increasing total operating costs (S. C. Kim et al., 2020). Nanofiber filter media which consists of nanometer-scale fiber has been introduced and studied for reducing the pressure drop across the filter media, (i.e. reducing the operating cost) as well as increasing particle collection efficiencies (Choi et al., 2017; Leung et al., 2009; Xia et al., 2018; Zhao et al., 2016). Knudsen number (Kn) is an important dimensionless quantity that allows for characterizing the boundary conditions of a fluid flow. Knudsen number is defined as the ratio of the molecular mean free path length (λ) to a representative physical length (Lchar), i.e., Kn = λ/Lchar. The physical length in the fibrous filter is the radius of the fiber (df/2), i.e., Lchar = df/2. 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