Production of Nanoparticles in Thermal Plasmas: A Model Including Evaporation, Nucleation, Condensation, and Fractal Aggregation

  • Norma Yadira Mendoza Gonzalez
  • Mbark El Morsli
  • Pierre Proulx
Peer Reviewed


In this work a coupled model for the production of nanoparticles in an inductively coupled plasma reactor is proposed. A Lagrangian approach is used to describe the evaporation of precursor particles and an Eulerian model accounting for particle nucleation, condensation, and fractal aggregation. The models of the precursor and nanoparticles are coupled with the magneto-hydrodynamic equations describing the plasma. The purpose of this study is to develop a model for the synthesis of particles in a thermal plasma reactor, which can be used to optimize industrial reactors. The growth of aggregates is considered by introducing a power law exponent D f. Results are compared qualitatively and quantitatively with existing experimental data from plasma reactors at a relatively large laboratory scale. The results obtained from the model confirm the previously observed importance of the quench strategy in defining the morphology of the nanoparticles.


CFD modeling fractal particles ICP plasmas method of moments nanoparticle synthesis 


  1. 1.
    F.E. Kruis, H. Fissan, A. Peled, Synthesis of Nanoparticles in the Gas Phase for Electronic, Optical and Magnetic Applications—A Review. J. Aerosol Sci. 29(5-6), 511–535 1998 CrossRefGoogle Scholar
  2. 2.
    P.C. Kong, E. Pfender, Thermal Plasma Synthesis of Ceramics—A Review. Heat Transfer Therm. Plasma Process. ASME 161, 1–8 (1991)Google Scholar
  3. 3.
    G. Vissokov, I. Grancharov, T. Tsvetanov. On the Plasma-Chemical Synthesis of Nanopowders. Plasma Sci. Technol. 5, 2039–2050 2003CrossRefGoogle Scholar
  4. 4.
    N.Y. Mendoza-Gonzalez, B.M. Goortani, P. Proulx. Numerical Simulation of Silica Nanoparticles Production in a RF Plasma Rector: Effect of Quench, Mater. Sci. Eng. C 27(5-8), 1265–1269 2007CrossRefGoogle Scholar
  5. 5.
    N.Y. Mendoza-Gonzalez, B.M. Goortani, P. Proulx. Numerical Study of the Synthesis of Nanoparticles in an Inductively Coupled Plasma Reactor. Czech. J. Phys. 56-B, B1263–B1270 2006CrossRefGoogle Scholar
  6. 6.
    M. Shigeta, T. Watanabe, H. Nishiyama. Numerical Investigation for Nanoparticle Synthesis in an RF Inductively Coupled Plasma. Thin Solid Films, 457, 192–200 2004CrossRefGoogle Scholar
  7. 7.
    R. Bolot, C. Coddet, C. Schreuders, M. Leparoux, S. Siegmann Modeling of an Inductively Coupled Plasma for the Synthesis of Nanoparticles, J. Therm. Spray Technol. 16(5-6), 690–697 2007CrossRefGoogle Scholar
  8. 8.
    R. Ye, J.G. Lian, T. Ishigaki. Controlled Synthesis of Alumina Nanoparticles Using Inductively Coupled Thermal Plasma with Enhanced Quenching. Thin Solid Fims 515(9), 4251–4257 2007CrossRefGoogle Scholar
  9. 9.
    B.M. Goortani, P. Proulx, S. Xue, N.Y. Mendoza-Gonzalez, Controlling Nanostructure in Thermal Plasma Processing: Moving from Highly Aggregated Porous Structure to Spherical Silica Nanoparticles. Powder Technol. 175, 22–32 2007CrossRefGoogle Scholar
  10. 10.
    C.R. Kaplan, J.W. Gentry Agglomeration of Chain-Like Combustion Aerosols due to Brownian Motion. Aerosol Sci. Technol. 8, 11–28 1988CrossRefGoogle Scholar
  11. 11.
    A. Kazakov and M. Frenklach, Dynamic Modeling of Soot Particle Coagulation and Aggregation: Implementation with the Methods of Moments and Application to High-Pressure Laminar Premixed Flames, Combust. Flame, 1998, 114, p 484-501Google Scholar
  12. 12.
    R.J. Samson, G.W. Mulholland, J.W. Gentry. Structural Analysis of Soot Aggregates. Langmuir 3, 272–281 1987CrossRefGoogle Scholar
  13. 13.
    T. Matsoukas, S.K. Friedlander. Dynamics of Aerosol Agglomerate Formation. J. Colloid Interface Sci. 146(2), 495–506 1991CrossRefGoogle Scholar
  14. 14.
    M.K. Wu, S.K. Friedlander. Enhanced Power Law Agglomerate Growth in the Free Molecular Regime. J. Aerosol Sci. 24, 273–282 1993CrossRefGoogle Scholar
  15. 15.
    Y. Xiong, S.E. Pratsinis. Formation of Agglomerate Particles by Coagulation and Sintering part I: A Two Dimensional Solution of the Population Balance Equation. J. Aerosol Sci. 24, 283–300 1993CrossRefGoogle Scholar
  16. 16.
    F. Kruis, K. Kusters, S. Pratsinis, Simple Model for the Evolution of the Characteristics of Aggregate Particles Undergoing Coagulation and Sintering. Aerosol Sci. Technol. 19, 514–526 1993CrossRefGoogle Scholar
  17. 17.
    J. I. Jeong, M. Choi. A Sectional Method for the Analysis of Growth of Polydisperse Non-Spherical Particles Undergoing Coagulation and Coalescence. J. Aerosol Sci. 32, 565–582 2001CrossRefGoogle Scholar
  18. 18.
    J.I. Jeong, M. Choi. Analysis of Non-Spherical Polydisperse Particle Growth in a Two-Dimensional Tubular Reactor. J. Aerosol Sci. 34, 713–732 2003CrossRefGoogle Scholar
  19. 19.
    F. Aristizabal, R.J. Munz, and D. Berk, Modeling of the Production of Ultra Fine Aluminium Particles in Rapid Quenching Turbulent Flow, Aerosol Sci. Technol., 2006, 37, p 162–189Google Scholar
  20. 20.
    T. Adona, “The Study of a Novel Thermal Process for the Production of Fumed Silica,” PhD Thesis, McGill University, Canada, 1998Google Scholar
  21. 21.
    J.F. Bilodeau, “Modélisation de la Croissance de Poudres Ultrafines en Réacteur à Plasma Thermique (Modeling of the Ultra Fine Particle Growth in a Thermal Plasma Reactor),” PhD Thesis, Université de Sherbrooke, Canada, 1994, in FrenchGoogle Scholar
  22. 22.
    B.M. Goortani, N.Y. Mendoza, and P. Proulx, Synthesis of SiO2 Nanoparticles in RF Plasma Reactors: Effect of Feed Rate and Quench Gas Injection, Int. J. Chem. Reactor Eng., 2006, 4:A33, p 1-18Google Scholar
  23. 23.
    M.I. Boulos. Flow Temperature Fields in the Fire-Ball of an Inductively Coupled Plasma. IEEE Trans. Plasma Sci. 4, 28–39 1976CrossRefGoogle Scholar
  24. 24.
    S. Xue, P. Proulx, M.I. Boulos. Extended-Field Electromagnetic Model for Inductively Coupled Plasma. J. Phys. D: Appl. Phys. 34, 1897–1906 2001CrossRefGoogle Scholar
  25. 25.
    R. Bolot, J. Li, and C. Coddet, Some Key Advices for the Modeling of Plasma Jets using Fluent, Proceedings of the International Thermal Spray Conference, ITSC 2005, 2-4 May 2005, (Basel, Switzerland), DVS Verlag GmbH, Düsseldorf, Germany, CD-Room, ISBN: 3-87155-793-5Google Scholar
  26. 26.
    R. Ye, P. Proulx, M.I. Boulos. Particle Turbulent Dispersion and Loading Effects in an Inductively Coupled Radio Frequency Plasma. J. Phys. D: Appl. Phys., 33(17), 2154–2162 2000CrossRefGoogle Scholar
  27. 27.
    M. Shigeta, H. Nishiyama. Numerical Analysis of Metallic Nanoparticle Synthesis Using RF Inductively Coupled Plasma Flows. Trans. ASME, 127, 1222–1230 2005CrossRefGoogle Scholar
  28. 28.
    P. Proulx, J. Mostaghimi, M.I. Boulos. Heating of Powers in an RF Inductively Coupled Plasma Under Dense Loading Conditions, Plasma Chem. Plasma Process. 7(1), 29–53 1987CrossRefGoogle Scholar
  29. 29.
    M.I. Boulos, W.H. Gauvin. The Plasma Jet as a Chemical Reactor, a Proposed Model. Can. J. Chem. Eng. 52(3), 355–363 1974CrossRefGoogle Scholar
  30. 30.
    L. Talbot, R.K. Chen, R.W. Schefer, D.R. Willis. Thermophoresis of Particles in a Heated Boundary Layer. J. Fluid Mech. 101(4), 737–758 1980CrossRefGoogle Scholar
  31. 31.
    H. Ounis, G. Ahmadi, J.B. McLaughlin. Brownian Diffusion of Submicrometer Particles in the Viscous Sublayer, J. Colloid Interface Sci. 143(1), 266–277 1991CrossRefGoogle Scholar
  32. 32.
    A. Li, G. Ahmadi. Dispersion and Deposition of Spherical Particles from Point Sources in a Turbulent Channel Flow. Aerosol Sci. Technol. 16(4), 209–226 1992CrossRefGoogle Scholar
  33. 33.
    W.E. Ranz, W.R. Marshall. Evaporation from Drops, Part I, Chem. Eng. Prog. 48(3), 141–146 1952Google Scholar
  34. 34.
    W.E Ranz, W.R Marshall. Evaporation from Drops, Part II, Chem. Eng. Prog. 48(4), 173–180 1952Google Scholar
  35. 35.
    S.L. Girshick, C.P. Chiu. Kinetic Nucleation Theory: A New Expression for the Rate of Homogeneous Nucleation from an Ideal Supersaturated Vapor. J. Chem. Phys. 93, 1273–1277 1990CrossRefGoogle Scholar
  36. 36.
    J.H. Seinfeld. Atmospheric Chemistry and Physics of Air Pollution. John Wiley & Sons, New York, 1986Google Scholar
  37. 37.
    G.M. Phanse, S.E. Pratsinis. Theory for Aerosol Generation in Laminar Flow Condensers. Aerosol Sci. Technol. 11(2), 100–119 1989CrossRefGoogle Scholar
  38. 38.
    S. Vemury, S. Pratsinis. Self-Preserving Size Distributions of Agglomerates J. Aerosol Sci. 26, 175–185 1995CrossRefGoogle Scholar
  39. 39.
    G.W. Mulholland, R.J Samson, R.D. Mountain, M.H. Ernst Cluster Size Distribution for Free Molecular Agglomeration. Energy Fuels 2, 481–486 1988CrossRefGoogle Scholar
  40. 40.
    D. Lindackers, M. Strecker, P. Roth, C. Janzen, S.E. Pratsinis. Formation and Growth of SiO2 Particles in Low Pressure H2/O2/Ar Flames Doped with SiH4. Combust. Sci. Technol. 123, 287–315 1997CrossRefGoogle Scholar
  41. 41.
    E. Pantos, J.B. West, W.H. Dokter, H.F. Van Garderen, R.A. Van Santen. Growth and Aging Phenomena in Silica Gels, J. Sol-Gel Sci. Technol. 2, 273–276 1994CrossRefGoogle Scholar
  42. 42.
    C.G. Wells, N.M. Morgan, M. Kraft, W. Wagner. A New Method for Calculating the Diameter of Partially-Sintered Nanoparticles and its Effect on Simulated Particle Properties. Chem. Eng. Sci. 64(1), 158–166 2006CrossRefGoogle Scholar
  43. 43.
    M. Frenklach, S.J. Harris. Aerosol Dynamics Modeling Using the Method of Moments. J. Colloid Interface Sci. 118, 252–261 1987CrossRefGoogle Scholar
  44. 44.
    M.I. Boulos, P. Fauchais, and E. Pfender, Thermal Plasmas: Fundamentals and Applications, Plenum Press, New York, 1994Google Scholar
  45. 45.
    P. Proulx, J. Mostaghimi, M.I. Boulos. Plasma-Particle Interaction Effects in Induction Plasma Modeling Under Dense Loading Conditions. Int. J. Heat Mass Transfer 28, 1327–1336 1985CrossRefGoogle Scholar
  46. 46.
    M. Shigeta, T. Watanabe. Numerical Investigation of Cooling Effect on Platinum Nanoparticle Formation in Inductively Coupled Thermal Plasmas. J. Appl. Phys. 103, 074903 2008CrossRefGoogle Scholar
  47. 47.
    J.F. Bilodeau, P. Proulx. A Mathematical Model for Ultrafine Iron Powder Growth in a Thermal Plasma, Aerosol Sci. Technol. 24, 175–189 1996CrossRefGoogle Scholar
  48. 48.
    M. Shigeta, T. Watanabe. Two Dimensional Analysis of Nanoparticle Formation in Induction Thermal Plasmas with Counterflow Cooling, Thin Solid Films, 103, 4415–4422 2008Google Scholar

Copyright information

© ASM International 2008

Authors and Affiliations

  • Norma Yadira Mendoza Gonzalez
    • 1
  • Mbark El Morsli
    • 1
  • Pierre Proulx
    • 1
  1. 1.Laboratoire de Modélisation Mathématique des Procédés Chimiques OPPUS, Chemical Engineering DepartmentUniversité de SherbrookeSherbrookeCanada

Personalised recommendations