Skip to main content
SpringerLink
Log in

A review of research on nanoparticulate flow undergoing coagulation

  • Review Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Nanoparticulate flows occur in a wide range of natural phenomena and engineering applications and, hence, have attracted much attention. The purpose of the present paper is to provide a review of the research conducted over the last decade. The research covered relates to the Brownian coagulation of monodisperse and polydisperse particles, the Taylor-series expansion method of moment, and nanoparticle distributions due to coagulation in pipe and channel flow, jet flow, and the mixing layer and in the process of flame synthesis and deposition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Uchowski, V.: Versuch einer mathematischen theorie der koagulation skinetik kollider losungen. Z. Phys. Chem. 92, 129–168 (1917)

    Google Scholar 

  2. Russel, W.B., Saville, D.A., Schowalter, W.R.: Colloidal Dispersions. Cambridge University Press, Cambridge (1989)

    Book  Google Scholar 

  3. Han, M.Y., Lee, H., Lawler, D.F., Choi, S.: Collision efficiency factor in Brownian coagulation (\(\alpha \)Br) including hydrodynamics and interparticle forces. Water Sci. Technol. 36, 69–75 (1997)

    Article  Google Scholar 

  4. Han, M.Y., Lee, H.: Collision efficiency factor in Brownian coagulation(\(\alpha \)Br): calculation and experimental verification. Colloids Surf. A 202, 23–31 (2002)

    Article  Google Scholar 

  5. Vanni, M., Baldi, G.: Coagulation efficiency of colloidal particles in shear flow. Adv. Colloid Interface Sci. 97, 151–177 (2002)

    Article  Google Scholar 

  6. Chin, C.J., Lu, S.C., Yiacoumi, S.: Fractal dimension of particle aggregates in magnetic fields. Sep. Sci. Technol. 39, 2839–2862 (2004)

    Article  Google Scholar 

  7. Olsen, A., Franks, G., Biggs, S.: An improved collision efficiency model for particle aggregation. J. Chem. Phys. 125, 184906 (2006)

    Article  Google Scholar 

  8. Chun, J., Koch, D.L.: The effects of non-continuum hydrodynamics on the Brownian coagulation of aerosol particles. J. Aerosol Sci. 37, 471–482 (2006)

    Article  Google Scholar 

  9. Feng, Y., Lin, J.Z.: The collision efficiency of spherical dioctyl phthalate aerosol particles in the Brownian coagulation. Chin. Phys. B 17, 4547–4553 (2008)

    Article  Google Scholar 

  10. Wang, Y.M., Lin, J.Z., Feng, Y.: The central oblique collision efficiency of spherical nanoparticles in the Brownian coagulation. Mod. Phys. Lett. B 24, 1523–1531 (2010)

    Article  MATH  Google Scholar 

  11. Chen, Z.L., You, Z.J.: New expression for collision efficiency of spherical nanoparticles in Brownian coagulation. Appl. Math. Mech (English Edition). 31, 851–860 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wang, Y.M., Lin, J.Z.: Attachment efficiency of polydisperse nanoparticles wall-deposition. KONA Powder Part. J. 29, 158–167 (2011)

    Article  Google Scholar 

  13. Zhang, Y.Y., Li, S.Q., Yan, W., Yao, Q., Tse, S.D.: Role of dipole–dipole interaction on enhancing Brownian coagulation of charge-neutral nanoparticles in the free molecular regime. J. Chem. Phys. 134, 084501 (2011)

    Article  Google Scholar 

  14. Wang, Y.M., Lin, J.Z.: The oblique collision efficiency of nanoparticles at different angles in Brownian coagulation. Comput. Math. Appl. 61, 1917–1922 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chen, Z.L., Jiang, R.J., Ku, X.K.: Collision efficiency of brownian coagulation for nanoparticles taking into account the slip boundary condition on the particle surface. Mod. Phys. Lett. B 26, 1250135 (2012)

    Article  Google Scholar 

  16. Hawa, T., Zachariah, M.R.: Coalescence kinetics of unequal sized nanoparticles. J. Aerosol Sci. 37, 1–15 (2006)

    Article  Google Scholar 

  17. Wang, Y.M., Lin, J.Z.: Collision efficiency of two nanoparticles with different diameters in Brownian coagulation. Appl. Math. Mech. (English Edition). 32, 1019–1028 (2011)

    Article  MATH  Google Scholar 

  18. Kelkar, A.V., Dong, J.N., Franses, E.I., Corti, D.S.: New models and predictions for Brownian coagulation of non-interacting spheres. J. Colliod Interface Sci. 389, 188–198 (2013)

    Article  Google Scholar 

  19. Muller, H.: Zur Allgemeinen Theorie der Raschen Koagulation. Kolloideihefte 27, 223–250 (1928) (in German)

  20. Friedlander, S.K.: Smoke, Dust and Haze: Fundamentals of Aerosol Behavior. Wiley, New York (2000)

    Google Scholar 

  21. Allen, M.D., Raabe, O.G.: Slip correction measurement of spherical solid aerosol particles in an improved millican apparatus. Aerosol Sci. Technol. 4, 269–286 (1985)

    Article  Google Scholar 

  22. Fuchs, N.A.: The Mechanics of Aerosols. Pergamon, New York (1964)

    Google Scholar 

  23. Otto, E., Fissan, H., Park, S.H., Lee, K.W.: The log-normal size distribution theory of brownian aerosol coagulation for the entire particle size range: part II-analytical solution using Dahneke’s coagulation kernel. J. Aerosol Sci. 30, 17–34 (1999)

    Article  Google Scholar 

  24. Pratsinis, S.E.: Simultaneous nucleation, condensation, and coagulation in aerosol reactor. J. Colloid Interface Sci. 124, 416–417 (1988)

    Article  Google Scholar 

  25. Hulbert, H.M., Katz, S.: Some problems in particle technology: a statistical mechanical formulation. Chem. Eng. Sci. 19, 555–574 (1994)

    Article  Google Scholar 

  26. Lin, J.Z., Chan, T.L., Liu, S., Zhou, K., Zhou, Y., Lee, S.C.: Effects of coherent structures on nanoparticle coagulation and dispersion in a round jet. Int. J. Nonlinear Sci. Numer. Simul. 8, 45–54 (2007)

    Article  Google Scholar 

  27. Upadhyay, R.R., Ezekoye, O.A.: Evaluation of the 1-point quadrature approximation in QMOM for combined aerosol growth laws. J. Aerosol Sci. 34, 1665–1683 (2003)

    Article  Google Scholar 

  28. Pratsinis, S.E.: Receptor models for ambient carbonaceous aerosols. Aerosol Sci. Technol. 10, 258–266 (1989)

    Article  Google Scholar 

  29. Mcgraw, R.: Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27, 255–265 (1997)

    Article  Google Scholar 

  30. Yu, M.Z., Lin, J.Z., Chan, T.L.: A new moment method for solving the coagulation equation for particles in Brownian motion. Aerosol Sci. Technol. 42, 705–713 (2008)

    Article  Google Scholar 

  31. Lee, K.W., Chen, H.: Coagulation rate of polydisperse particles. Aerosol Sci. Technol. 3, 327–334 (1984)

    Article  Google Scholar 

  32. Yu, M.Z., Lin, J.Z.: Binary homogeneous nucleation and growth of water-sulfuric acid nanoparticles using a TEMOM model. Int. J. Heat Mass Transfer 53, 635–644 (2010)

    Article  MATH  Google Scholar 

  33. Wang, W.X., He, Q., Chen, N.A., Xie, M.L.: A simple moment model to study the effect of diffusion on the coagulation of nanoparticles due to Brownian motion in the free molecule regime. Therm. Sci. 16, 1331–1338 (2012)

    Article  Google Scholar 

  34. Lin, J.Z., Chen, Z.L.: A modified TEMOM model for Brownian coagulation of nanoparticles based on the asymptotic solution of the sectional method. Sci. China Technol. Sci. 56, 3081–3092 (2013)

    Article  Google Scholar 

  35. Xie, M.L., He, Q.: The fundamental aspects of TEMOM model for particle coagulation due to Brownian motion. Part 1: in the free molecule regimes. Int. J. Heat Mass Transfer 70, 1115–1120 (2014)

    Article  Google Scholar 

  36. Chen, Z.L., Lin, J.Z., Yu, M.Z.: Direct expansion method of moments for nanoparticle Brownian coagulation in the entire size regime. J. Aerosol Sci. 67, 28–37 (2014)

    Article  Google Scholar 

  37. De Bleecker, K., Bogaerts, A., Goedheer, W.: Modelling of nanoparticle coagulation and transport dynamics in dusty silane discharges. New J. Phys. 8, 178–181 (2006)

    Article  Google Scholar 

  38. Yin, Z.Q., Lou, M.: Experimental study on nanoparticle deposition in straight pipe flow. Therm. Sci. 16, 1410–1413 (2012)

    Article  Google Scholar 

  39. Lin, J.Z., Liu, S., Chan, T.L.: Nanoparticle migration in a fully developed turbulent pipe flow considering the particle coagulation. Chin. J. Chem. Eng. 20, 679–685 (2012)

    Article  Google Scholar 

  40. Lin, J.Z., Yin, Z.Q., Gan, F.J., Yu, M.Z.: Penetration efficiency and distribution of aerosol particles in turbulent pipe flow undergoing coagulation and breakage. Int. J. Multiph. Flow 61, 28–36 (2014)

    Article  MathSciNet  Google Scholar 

  41. Lin, P.F., Lin, J.Z.: Transport and deposition of nanoparticles in bend tube with circular cross-section. Prog. Nat. Sci. 19, 33–39 (2009)

    Article  Google Scholar 

  42. Lin, P.F., Lin, J.Z.: Prediction of nanoparticle transport and deposition in bends. Appl. Math. Mech. (English Edition). 30, 957–968 (2009)

    Article  MATH  Google Scholar 

  43. Lin, J.Z., Lin, P.F., Yu, M.Z., Chen, H.J.: Nanoparticle transport and coagulation in bends of circular cross section via a new moment method. Chin. J. Chem. Eng. 18, 1–9 (2010)

    Article  Google Scholar 

  44. Lin, J.Z., Lin, P.F., Chen, H.J.: Research on the transport and deposition of nanoparticles in a rotating curved pipe. Phys. Fluids 21, 122001 (2009)

    Article  Google Scholar 

  45. Lin, J.Z., Lin, P.F., Chen, H.J.: Nanoparticle distribution in a rotating curved pipe considering coagulation and dispersion. Sci. China Phys. Mech. Astron. 54, 1502–1513 (2011)

    Article  Google Scholar 

  46. Chan, T.L., Lin, J.Z., Zhou, K., Chan, C.K.: Simultaneous numerical simulation of nano and fine particle coagulation and dispersion in a round jet. J. Aerosol Sci. 37, 1545–1561 (2006)

    Article  Google Scholar 

  47. Lin, J.Z., Chan, T.L., Liu, S., Zhou, Y., Lee, S.C.: Effects of coherent structures on nanoparticle coagulation and dispersion in a round jet. Int. J. Nonlinear Sci. Numer. Simul. 8, 45–54 (2007)

    Article  Google Scholar 

  48. Yin, Z.Q., Lin, J.Z., Zhou, K., Chan, T.L.: Numerical simulation of the formation of pollutant nanoparticles in the exhaust twin-jet plume of a moving car. Int. J. Nonlinear Sci. Numer. Simul. 8, 535–543 (2007)

    Article  Google Scholar 

  49. Yin, Z.Q., Lin, J.Z.: Numerical simulation of the formation of nanoparticles in an impinging twin-jet. J. Hydrodyn. 19, 533–541 (2007)

    Article  Google Scholar 

  50. Fujitani, Y., Hirano, S., Kobayashi, S., Tanabe, K., Suzuki, A., Furuyama, A., Kobayashi, T.: Characterization of dilution conditions for diesel nanoparticle inhalation studies. Inhalation Toxicol. 21, 200–209 (2009)

    Article  Google Scholar 

  51. Chan, T.L., Zhou, K., Lin, J.Z., Liu, C.H.: Vehicular exhaust gas-to-nanoparticle conversion and concentration distribution in the vehicle wake region. Int. J. Nonlinear Sci. Numer. Simul. 11, 581–593 (2010)

    Article  Google Scholar 

  52. Zhu, J.Z., Qi, H.Y., Wang, J.S.: Nanoparticle dispersion and coagulation in a turbulent round jet. Int. J. Multiph. Flow 54, 22–30 (2013)

    Article  Google Scholar 

  53. Yu, M.Z., Lin, J.Z., Chen, L.H., Chan, T.L.: Large eddy simulation of a planar jet flow with nanoparticle coagulation. Acta Mech. Sin. 22, 293–300 (2006)

    Article  MATH  Google Scholar 

  54. Yu, M.Z., Lin, J.Z., Chen, L.H.: Nanoparticle coagulation in a planar jet via moment method. Appl. Math. Mech. (English Edition). 28, 1445–1453 (2007)

    Article  MATH  Google Scholar 

  55. Lu, Y.H.: Nanoparticle nucleation and coagulation in a submerged jet: theoretical prediction and simulation. Int. J. Nonlinear Sci. Numer. Simul. 10, 1189–1200 (2009)

    Article  Google Scholar 

  56. Das, S., Garrick, S.C.: The effects of turbulence on nanoparticle growth in turbulent reacting jets. Phys. Fluids 22, 103303 (2010)

    Article  Google Scholar 

  57. Loeffler, J., Das, S., Garrick, S.C.: Large eddy simulation of titanium dioxide nanoparticle formation and growth in turbulent jets. Aerosol Sci. Technol. 45, 616–628 (2011)

    Article  Google Scholar 

  58. Garrick, S.C., Wang, G.H.: Modeling and simulation of titanium dioxide nanoparticle synthesis with finite-rate sintering in planar jets. J. Nanopart. Res. 13, 973–984 (2011)

    Article  Google Scholar 

  59. Settumba, N., Garrick, S.C.: Direct numerical simulation of nanoparticle coagulation in a temporal mixing layer via a moment method. J. Aerosol Sci. 34, 149–167 (2003)

    Article  Google Scholar 

  60. Settumba, N., Garrick, S.C.: A comparison of diffusive transport in a moment method for nanoparticle coagulation. J. Aerosol Sci. 35, 93–101 (2004)

    Article  Google Scholar 

  61. Garrick, S.C., Lehtinen, K.E.J., Zachariah, M.R.: Nanoparticle coagulation via a Navier–Stokes/nodal methodology: evolution of the particle field. J. Aerosol Sci. 37, 555–576 (2006)

    Article  Google Scholar 

  62. Wang, G.H., Garrick, S.C.: Modeling and simulation of titania formation and growth in temporal mixing layers. J. Aerosol Sci. 37, 431–451 (2006)

    Article  Google Scholar 

  63. Lin, J.Z., Liu, Y.H.: Nanoparticle nucleation and coagulation in a mixing layer. Acta Mech. Sin. 26, 521–529 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  64. Xie, M.L., Yu, M.Z., Wang, L.P.: A TEMOM model to simulate nanoparticle growth in the temporal mixing layer due to Brownian coagulation. J. Aerosol Sci. 54, 32–48 (2012)

    Article  Google Scholar 

  65. Rosner, D.E., Pyykonen, J.J.: Bivariate moment simulation of coagulating and sintering nanoparticles in flames. AIChE J. 48, 476–491 (2002)

    Article  Google Scholar 

  66. Kim, H.J., Jeong, J.I., Park, Y.: Modeling of generation and growth of non-spherical nanoparticles in a co-flow flame. J. Nanopart. Res. 5, 237–246 (2003)

    Article  Google Scholar 

  67. Tsantilis, S., Pratsinis, S.E.: Narrowing the size distribution of aerosol-made titania by surface growth and coagulation. J. Aerosol Sci. 35, 405–420 (2004)

    Article  Google Scholar 

  68. Kostoglou, M., Konstandopoulos, A.G., Friedlander, S.K.: Bivariate population dynamics simulation of fractal aerosol aggregate coagulation and restructuring. J. Aerosol Sci. 37, 1102–1115 (2006)

    Article  Google Scholar 

  69. Morgan, N.M., Wells, C.G., Goodson, M.J., Kraft, M., Wagner, W.: A new numerical approach for the simulation of the growth of inorganic nanoparticles. J. Comput. Phys. 211, 638–658 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  70. Morgan, N., Kraft, M., Balthasar, M., Wong, D., Frenklach, M., Mitchell, P.: Numerical simulations of soot aggregation in premixed laminar flames. Proc. Combust. Inst. 31, 693–700 (2007)

    Article  Google Scholar 

  71. Starchenko, V., Muller, M., Lebovka, N.: Growth of polyelectrolyte complex nanoparticles: computer simulations and experiments. J. Phys. Chem. C 112, 8863–8869 (2008)

    Article  Google Scholar 

  72. Yu, M.Z., Lin, J.Z., Chen, L.H., Chan, T.L.: Effect of precursor loading on non-spherical \(\text{ TiO }_{2}\) nanoparticle synthesis in a diffusion flame reactor. Chem. Eng. Sci. 63, 2317–2329 (2008)

    Article  Google Scholar 

  73. Yu, M.Z., Lin, J.Z., Chan, T.L.: Numerical simulation of nanoparticle synthesis in diffusion flame reactor. Powder Technol. 181, 9–20 (2008)

  74. Aristizabal, F., Munz, R.J., Berk, D.: Turbulent modeling of the production of ultra fine aluminum particles: scale-up. Aerosol Sci. Technol. 42, 556–565 (2008)

    Article  Google Scholar 

  75. Zhao, H., Liu, X.F., Tse, S.D.: Effects of pressure and precursor loading in the flame synthesis of titania nanoparticles. J. Aerosol Sci. 40, 919–937 (2009)

    Article  Google Scholar 

  76. De Filippo, A., Sgro, L.A., Lanzuolo, G., D’Alessio, A.: Probe measurements and numerical model predictions of evolving size distributions in premixed flames. Combust. Flame 156, 1744–1754 (2009)

    Article  Google Scholar 

  77. Chen, K.L., Elimelech, M.: Aggregation and deposition kinetics of fullerene (c-60) nanoparticles. Langmuir 22, 10994–11001 (2006)

    Article  Google Scholar 

  78. Kim, D.S., Hong, S.B., Kim, Y.J., Lee, K.W.: Deposition and coagulation of polydisperse nanoparticles by Brownian motion and turbulence. J. Aerosol Sci. 37, 1781–1787 (2006)

    Article  Google Scholar 

  79. Liu, N., Liu, C.L., Zhang, J., Lin, D.H.: Removal of dispersant-stabilized carbon nanotubes by regular coagulants. J. Environ. Sci. 24, 1364–1370 (2012)

    Article  Google Scholar 

Download references

Acknowledgments

The project was supported by the Major Program of the National Natural Science Foundation of China (Grant 11132008).

Author information

Authors and Affiliations

  1. Institute of Fluid Measurement and Simulation, China Jiliang University, Hangzhou, 310018, China

    Jianzhong Lin & Linlin Huo

  2. Institute of Fluid Engineering, Zhejiang University, Hangzhou, 310027, China

    Jianzhong Lin

Authors
  1. Jianzhong Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linlin Huo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianzhong Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, J., Huo, L. A review of research on nanoparticulate flow undergoing coagulation. Acta Mech Sin 31, 292–302 (2015). https://doi.org/10.1007/s10409-015-0398-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-015-0398-5

Keywords

Search

Navigation