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Original Articles

High-accuracy method for modeling nucleation and growth of particles

ORCID Icon, ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 1033-1052 | Received 09 Jan 2024, Accepted 27 May 2024, Published online: 21 Jun 2024

References

  • Ahmad, H., S. K. Kamarudin, L. J. Minggu, and M. Kassim. 2015. Hydrogen from photo-catalytic water splitting process: A review. Renew. Sustain. Energy Rev. 43:599–610. doi: 10.1016/j.rser.2014.10.101.[Mismatch]]
  • Alphonse, P., K. Muthukumarasamy, and R. Dhairiyasamy. 2023. Nanoparticle size and heat pipe angle impact on the thermal effectiveness of a cylindrical screen mesh heat pipe. Appl. Mech. 4 (3):870–84. doi: 10.3390/applmech4030045.
  • Bakhtar, F., J. B. Young, A. J. White, and D. A. Simpson. 2005. Classical nucleation theory and its application to condensing steam flow calculations. J. Mech. Eng. Sci. 219 (12):1315–33. doi: 10.1243/095440605X8379.
  • Bilodeau, J.-F., and P. Proulx. 1996. A mathematical model for ultrafine iron powder growth in a thermal plasma. Aerosol. Sci. Technol. 24 (3):175–89. doi: 10.1080/02786829608965362.
  • Diab, J., L. Fulcheri, V. Hessel, V. Rohani, and M. Frenklach. 2022. Why turquoise hydrogen will Be a game changer for the energy transition. Int. J. Hydrogen Energy 47 (61):25831–48. doi: 10.1016/j.ijhydene.2022.05.299.
  • Frenkel, J. 1955. Kinetic Theory of Liquids. New York, NY: Dover.
  • Frenklach, M. 1985. Dynamics of discrete distribution for smoluchowski coagulation model. J. Coll. Interface Sci. 108 (1):237–42. doi: 10.1016/0021-9797(85)90256-5.
  • Frenklach, M. 2002. Method of moments with interpolative closure. Chem. Eng. Sci. 57 (12):2229–39. doi: 10.1016/S0009-2509(02)00113-6.
  • Frenklach, M., and S. J. Harris. 1987. Aerosol dynamics modeling using the method of moments. J. Colloid Interface Sci. 118 (1):252–61. doi: 10.1016/0021-9797(87)90454-1.
  • Friedlander, S. K. 1983. Dynamics of aerosol formation by chemical reaction. Ann. NY Acad. Sci. 404:354. doi: 10.1111/j.1749-6632.1983.tb19497.x.
  • Friedlander, S. K. 2000. Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics. Oxford: Oxford University Press.
  • Friedlander, S. K., and C. L. Wang. 1966. Self-preserving particle size distribution for coagulation by brownian motion. J. Colloid. Interface Sci. 22:126–32. doi: 10.1016/0021-9797(66)90073-7.
  • Gaskell, P. H., and A. K. C. Lau. 1988. Curvature-compensated convective-transport: SMART, A new boundedness preserving transport algorithm. Int. J. Numer. Methods Fluids 8:617–41. doi: 10.1002/fld.1650080602.
  • Gelbard, F., and J. H. Seinfeld. 1979. The general dynamics equation for aerosols. J. Colloid. Interface Sci. 68:363–82. doi: 10.1016/0021-9797(79)90289-3.
  • Gelbard, F., Y. Tambour, and J. H. Seinfeld. 1980. Sectional representations for simulating aerosol dynamics. J. Colloid. Interface Sci. 76 (2):541–56. doi: 10.1016/0021-9797(80)90394-X.
  • Giri, A. K. 2010. Mathematical and numerical analysis for coagulation-fragmentation equations. PhD diss., Otto-von-Guericke-Universität Magdeburg; https://pure.mpg.de/rest/items/item_2520116/component/file_2520189/content
  • Girshick, S. L. 1994. Particle nucleation and growth in thermal plasmas. Plasma Sources Sci. Technol. 3 (3):388–94. doi: 10.1088/0963-0252/3/3/023.
  • Girshick, S. L., P. Agarwal, and D. G. Truhlar. 2009. Homogeneous nucleation with magic numbers: Aluminum. J. Chem. Phys. 131 (13):134305. doi: 10.1063/1.3239469.
  • Girshick, S. L., and C. P. Chiu. 1989. Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis. Plasma Chem. Plasma Process. 9 (3):355–69. doi: 10.1007/BF01083672.
  • Girshick, S. L., and C.-P. Chiu. 1990. Kinetic nucleation theory: A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor. J. Chern. Phys. 93 (2):1273–7. doi: 10.1063/1.459191.
  • Girshick, S. L., C.-P. Chiu, and P. H. McMurry. 1990. Time-dependent aerosol models and homogeneous nucleation rates. Aerosol. Sci. Technol. 13 (4):465–77. doi: 10.1080/02786829008959461.
  • Hoecker, C., F. Smail, M. Bajada, M. Pick, and A. Boies. 2016. Catalyst nanoparticle growth dynamics and their influence on product morphology in a CVD process for continuous carbon nanotube synthesis. Carbon 96:116–24. doi: 10.1016/j.carbon.2015.09.050.
  • Hoecker, C., F. Smail, M. Pick, L. Weller, and A. M. Boies. 2017. The dependence of CNT aerogel synthesis on sulfur-driven catalyst nucleation processes and a critical catalyst particle mass concentration. Sci. Rep. 7 (1):14519. doi: 10.1038/s41598-017-14775-1.
  • Inguva, P. K., K. C. Schickel, and R. D. Braatz. 2022. Efficient numerical schemes for population balance models. Comput. Chem. Eng. 162:107808. doi: 10.1016/j.compchemeng.2022.107808.
  • Jacobson, M. Z., and R. P. Turco. 1995. Simulating condensational growth, evaporation, and coagulation of aerosols using a combined moving and stationary size grid. Aerosol. Sci. Technol. 22 (1):73–92. doi: 10.1080/02786829408959729.
  • Kappler, P., P. Ehrburger, J. Lahaye, and J. B. Donnet. 1979. Fine carbon particle formation by carbon-vapor condensation. J. Appl. Phys. 50 (1):308–16. doi: 10.1063/1.325660.
  • Katoshevski, D., and J. H. Seinfeld. 1997a. Analytical solution of the multicomponent aerosol general dynamic equation—without coagulation. Aerosol. Sci. Technol. 27 (4):541–9. doi: 10.1080/02786829708965493.
  • Katoshevski, D., and J. H. Seinfeld. 1997b. Analytical-numerical solution of the multicomponent aerosol general dynamic equation-with coagulation. Aerosol. Sci. Technol. 27 (4):550–6. doi: 10.1080/02786829708965494.
  • Khrabry, A. I., E. M. Smirnov, and D. K. Zaytsev. 2010. Solving the convective transport equation with several high-resolution finite volume schemes: Test computations. In Computational fluid dynamics, ed. A. Kuzmin, 535–40. Berlin, Heidelberg: Springer. doi: 10.1007/978-3-642-17884-9_67.
  • Kim, K. S., G. Cota-Sanchez, C. T. Kingston, M. Imris, B. Simard, and G. Soucy. 2007. Large-scale production of single-walled carbon nanotubes by induction thermal plasma. J. Phys. D. Appl. Phys. 40 (8):2375–87. doi: 10.1088/0022-3727/40/8/S17.
  • Kim, K. S., and T. H. Kim. 2019. Nanofabrication by thermal plasma jets: From nanoparticles to low-dimensional nanomaterials. J. Appl. Phys. 125 (7):070901. doi: 10.1063/1.5060977.
  • Kim, K. S., C. T. Kingston, D. Ruth, M. Barnes, and B. Simard. 2014. Synthesis of high quality single-walled carbon nanotubes with purity enhancement and diameter control by liquid precursor Ar–H2 plasma spraying. Chem. Eng. J. 250:331–41. doi: 10.1016/j.cej.2014.03.117.
  • Kruis, F. E., K. A. Kusters, S. E. Pratsinis, and B. Scarlett. 1993. A simple model for the evolution of the characteristics of aggregate particles undergoing coagulation and sintering. Aerosol. Sci. Technol. 19 (4):514–26. doi: 10.1080/02786829308959656.
  • Kumar, S., and D. Ramkrishna. 1997. On the solution of population balance equations by discretization—III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 52 (24):4659–79. doi: 10.1016/S0009-2509(97)00307-2.
  • Landgrebe, J. D., and S. E. Pratsinis. 1990. A discrete-sectional model for particulate production by gas-phase chemical reaction and aerosol coagulation in the free-molecular regime. J. Colloid Interface Sci. 139 (1):63–86. doi: 10.1016/0021-9797(90)90445-T.
  • Lee, K. W., J. Chen, and J. A. Gieseke. 1984. Log-normally preserving size distribution for brownian coagulation in the free-molecule regime. Aerosol. Sci. Technol. 3 (1):53–62. doi: 10.1080/02786828408958993.
  • Leonard, B. P. 1979. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19 (1):59–98. doi: 10.1016/0045-7825(79)90034-3.
  • Leonard, B. P. 1991. The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput. Methods Appl. Mech. Eng. 88 (1):17–74. doi: 10.1016/0045-7825(91)90232-U.
  • Li, Z. H., D. Bhatt, N. E. Schultz, J. I. Siepmann, and D. G. Truhlar. 2007. Free energies of formation of metal clusters and nanoparticles from molecular simulations: Aln with n = 2 − 60. J. Phys. Chem. C 111 (44):16227–42. doi: 10.1021/jp073559v.
  • Liu, L., X. Zhang, L. Yang, L. Ren, D. Wang, and J. Ye. 2017. Metal nanoparticles induced photocatalysis. Natl. Sci. Rev. 4 (5):761–80. doi: 10.1093/nsr/nwx019.
  • Liu, X. H., L. Zhong, S. Huang, S. X. Mao, T. Zhu, and J. Y. Huang. 2012. Size-dependent fracture of silicon nanoparticles during lithiation. ACS Nano. 6 (2):1522–31. doi: 10.1021/nn204476h.
  • Maisser, A., K. Barmpounis, M. B. Attoui, G. Biskos, and A. Schmidt-Ott. 2015. Atomic cluster generation with an atmospheric pressure spark discharge generator. Aerosol. Sci. Technol. 49 (10):886–94. doi: 10.1080/02786826.2015.1080812.
  • Mitrakos, D., E. Hinis, and C. Housiadas. 2007. Sectional modeling of aerosol dynamics in multi-dimensional flows. Aerosol. Sci. Technol. 41 (12):1076–88. doi: 10.1080/02786820701697804.
  • Moniruzzaman, C. G., H. G. Park, and K. Y. Park. 2007. Analysis of iron particle growth in aerosol reactor by a discrete-sectional model. Korean J. Chem. Eng. 24 (2):299–304. doi: 10.1007/s11814-007-5051-y.
  • Nazari, M. A., R. Ghasempour, and M. H. Ahmadi. 2019. A review on using nanofluids in heat pipes. J. Therm. Anal. Calorim. 137:1847–55. doi: 10.1007/s10973-019-08094-y.
  • Nemchinsky, V. A., and M. Shigeta. 2012. Simple equations to describe aerosol growth. Modell. Simul. Mater. Sci. Eng. 20:045017. doi: 10.1088/0965-0393/20/4/045017.
  • Okeke, I. J., B. A. Saville, and H. L. MacLean. 2023. Low carbon hydrogen production in Canada via natural gas pyrolysis. Int. J. Hydrogen Energy 48 (34):12581–99. doi: 10.1016/j.ijhydene.2022.12.169.
  • O’Sullivan, D., and S. Rigopoulos. 2022. A conservative finite volume method for the population balance equation with aggregation, fragmentation, nucleation and growth. Chem. Eng. Sci. 263:117925. doi: 10.1016/j.ces.2022.117925.
  • Ozawa, S., S. Takahashi, H. Fukuyama, and M. Watanabe. 2011. Temperature dependence of surface tension of molten iron under reducing gas atmosphere. J. Phys. Conf. Ser. 327:012020. doi: 10.1088/1742-6596/327/1/012020.
  • Panda, S., and S. E. Pratsinis. 1995. Modeling the synthesis of aluminum particles by evaporation-condensation in an aerosol flow reactor. Nanostruct. Mater. 5 (7–8):755–67. doi: 10.1016/0965-9773(95)00292-M.
  • Patzschke, C. F., B. Parkinson, S. Raman, D. C. Dankworth, and K. Hellgardt. 2023. Turquoise hydrogen: Methane pyrolysis as a low-CO2 source of H2. In Methane conversion routesstatus and prospects, eds. V. Galvita and R. Bos, vol. 76, Chapter 2, 34–65. London: Royal Society of Chemistry. doi: 10.1039/9781839160257-00034.
  • Pilinis, C., K. P. Capaldo, A. Nenes, and S. N. Pandis. 2000. MADM-A new multicomponent aerosol dynamics model. Aerosol. Sci. Technol. 32 (5):482–502. doi: 10.1080/027868200303597.
  • Prakash, A., A. P. Bapat, and M. R. Zachariah. 2003. A simple numerical algorithm and software for solution of nucleation, surface growth, and coagulation problems. Aerosol. Sci. Technol. 37 (11):892–8. doi: 10.1080/02786820300933.
  • Pratsinis, S. E. 1988. Simultaneous nucleation, condensation, and coagulation in aerosol reactors. J. Colloid. Interface Sci. 124 (2):416–27. doi: 10.1016/0021-9797(88)90180-4.
  • Rao, N. P., and P. H. McMurry. 1989. Nucleation and growth of aerosol in chemically reacting systems: A theoretical study of the near-collision-controlled regime. Aerosol. Sci. Technol. 11 (2):120–32. doi: 10.1080/02786828908959305.
  • Rhee, S. K. 1970. Wetting of ceramics by liquid aluminum. J. Am. Ceram. Soc. 53 (7):386–9. doi: 10.1111/j.1151-2916.1970.tb12138.x.
  • Shigeta, M., Y. Hirayama, and E. Ghedini. 2021. Computational study of quenching effects on growth processes and size distributions of silicon nanoparticles at a thermal plasma tail. Nanomaterials 11 (6):1370. doi: 10.3390/nano11061370.
  • Shigeta, M., M. Tanaka, and E. Ghedini. 2019. Numerical analysis of correlation between arc plasma fluctuation and nanoparticle growth-transport under atmospheric pressure. Nanomaterials 9 (12):1736. doi: 10.3390/nano9121736.
  • Slezov, V. V., and J. Schmelzer. 1994. Kinetics of formation and growth of a new phase with a definite stoichiometric composition. J. Phys. Chem. Solids 55 (3):243–51. doi: 10.1016/0022-3697(94)90139-2.
  • Slezov, V. V., and J. Schmelzer. 2002. Kinetics of formation of a phase with an arbitrary stoichiometric composition in a multicomponent. Phys. Rev. E 65 (3):031506. doi: 10.1103/PhysRevE.65.031506.
  • Slezov, V. V., J. Schmelzer, and Y. Y. Tkatch. 1996. Number of clusters formed in nucleation-growth processes. J. Chem. Phys. 105 (18):8340–51. doi: 10.1063/1.472689.
  • Smirnov, B. M. 2000. Clusters and small particles: In gases and plasmas. Berlin, Germany: Springer Science & Business Media.
  • Smirnov, B. M. 2006. Principles of statistical physics. Berlin, Germany: Wiley VCH.
  • Smirnov, B. M. 2010. Cluster processes in gases and plasmas. Weinheim: Wiley-VCH.
  • Smith, N. R., N. J. Shaviv, and H. Svensmark. 2016. Approximate analytical solutions to the condensation-coagulation equation of aerosols. Aerosol. Sci. Technol. 50 (6):578–90. doi: 10.1080/02786826.2016.1168921.
  • Suck, S. H., and J. R. Brock. 1979. Evolution of atmospheric aerosol particle size distributions via brownian coagulation: Numerical simulation. J. Aerosol. Sci. 10:581–90. doi: 10.1016/0021-8502(79)90020-X.
  • Tacu, M., A. Khrabry, and I. D. Kaganovich. 2020. Convenient analytical formula for cluster mean diameter and diameter dispersion after nucleation burst. Phys. Rev. E 102 (2–1):022116. doi: 10.1103/PhysRevE.102.022116.
  • Tanaka, Y., K. Shimizu, K. Akashi, K. Onda, Y. Uesugi, T. Ishijima, S. Watanabe, S. Sueyasu, and K. Nakamura. 2020. High rate synthesis of graphene-encapsulated silicon nanoparticles using pulse-modulated induction thermal plasmas with intermittent feedstock feeding. Jpn. J. Appl. Phys. 59 (SH):SHHE07. doi: 10.35848/1347-4065/ab71db.
  • Tsang, T. H., and A. Rao. 1988. Comparison of different numerical schemes for condensational growth of aerosols. Aerosol. Sci. Technol. 9 (3):271–7. doi: 10.1080/02786828808959214.
  • Wu, J.J., and R.C. Flagan. (1988). A discrete-sectional solution to the aerosol dynamic equation. J. Colloid. Interface Sci. 123 ( 2):339–352. doi: 10.1016/0021-9797(88)90255-X.
  • Wyslouzil, B. E., and J. Wölk. 2016. Overview: Homogeneous nucleation from the vapor phase—The experimental science. J. Chem. Phys. 145 (21):211702. doi: 10.1063/1.4962283.
  • Yan, C., X. Yang, H. Zhao, H. Zhong, G. Ma, Y. Qi, B. E. Koel, and Y. Ju. 2021. Controlled Dy-doping to nickel-rich cathode materials in high temperature aerosol synthesis. Proc. Combust. Inst. 38 (4):6623–30. doi: 10.1016/j.proci.2020.06.332.
  • Yatom, S., A. Khrabry, J. Mitrani, A. Khodak, I. Kaganovich, V. Vekselman, B. Stratton, and Y. Raitses. 2018. Synthesis of nanoparticles in carbon arc: Measurements and modeling. MRS Commun. 8 (3):842–9. doi: 10.1557/mrc.2018.91.
  • Zhalehrajabi, E., N. Rahmanian, S. Zarrinpashne, and P. Balasubramanian. 2014. Investigation of the Growth of Particles Produced in a Laval Nozzle. Part. Sci. Technol. 32 (6):595–601. doi: 10.1080/02726351.2014.933459.
  • Zhang, H., G. Sharma, S. Dhawan, D. Dhanraj, Z. Li, and P. Biswas. 2020. Comparison of discrete, discrete-sectional, modal and moment models for aerosol dynamics simulations. Aerosol. Sci. Technol. 54 (7):739–60. doi: 10.1080/02786826.2020.1723787.
  • Zhang, X., Z. Liu, M. Tanaka, and T. Watanabe. 2021. Formation mechanism of amorphous silicon nanoparticles with additional counter-flow quenching gas by induction thermal plasma. Chem. Eng. Sci. 230:116217. doi: 10.1016/j.ces.2020.116217.

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