Skip to main content

Langevin Dynamics Simulation of Transport and Aggregation of Soot Nano-particles in Turbulent Flows


The present paper uses Langevin dynamics (LD) to investigate the aggregation of soot nano-particles in turbulent flows. Interparticle forces are included, and the computation of the individual particles by LD is retained even after aggregate formation such that collision events and locations can be based on center-to-center particle distances without invoking any modelling assumptions of aggregate shape and/or collision frequency. We focus on the interactions between the specific hydrodynamic conditions and the particle properties and their effect on the resulting agglomerates’ morphologies. The morphology is characterized by the fractal dimension, D f . Computations of particle aggregation in homogeneous isotropic turbulence and in shear flows dominated by counter-rotating vortices with a wide range of turbulence intensities and particle sizes indicate that the evolution of the agglomerates’ shapes can be adequately parameterized by the size of the agglomerates and the Knudsen and Péclet numbers, the latter being based on the smallest turbulence scales. The computations further suggest that the shapes of agglomerates of certain sizes are relatively independent of time and relatively insensitive to larger turbulence structures. The fractal dimensions are modelled as functions of radius of gyration, Kn and Pe. The fitted expressions show good agreement with the LD simulations and represent the entire growth process of the agglomerates. A direct comparison of selected aggregates with experimental data shows very good qualitative agreement. A thorough quantitative validation of the evolution of the computed aggregate characteristics is, however, presently hindered by the challenges for and therefore lack of suitable experiments under appropriately controlled conditions.

This is a preview of subscription content, access via your institution.

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


  1. 1.

    Ito, H., Fujita, O., Ito, K.: Agglomeration of soot particles in diffusion flames under microgravity. Combust Flame 99(2), 363–370 (1994)

    Article  Google Scholar 

  2. 2.

    Kusters, K.A., Wijers, J.G., Thoenes, D.: Aggregation kinetics of small particles in agitated vessels. Chem. Eng. Sci. 52, 107–121 (1997)

    Article  Google Scholar 

  3. 3.

    Murr, L. In: Paul, M. (ed.) : Soot: Structure, composition, and health effects, pp 1–63. Nova Science Publishers (2012)

  4. 4.

    Ho, C.A., Sommerfeld, M.: Modelling of micro-particle agglomeration in turbulent flows. Chem. Eng. Sci. 57, 3073–3084 (2002)

    Article  Google Scholar 

  5. 5.

    Mokhtari, T., Chakrabarti, A., Sorensen, C.M., Cheng, C., Vigil, D.: The effect of shear on colloidal aggregation and gelation studied using small-angle light scattering. J. Colloid Interf. Sci. 327, 216–223 (2008)

    Article  Google Scholar 

  6. 6.

    Soos, M., Moussa, A.S., Ehrl, L., Sefcik, J., Wu, H., Morbidelli, M.: Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank. J. Colloid Interf. Sci. 319, 577–589 (2008)

    Article  Google Scholar 

  7. 7.

    Raman, V., Fox, R.O.: Modeling of fine-particle formation in turbulent flames. Annu. Rev. Fluid Mech. 48(1), 159–190 (2016)

    Article  MATH  Google Scholar 

  8. 8.

    Pratsinis, S.E.: Simultaneous nucleation, condensation, and coagulation in aerosol reactors. J. Colloid Interf. Sci. 124(2), 416–427 (1988)

    Article  Google Scholar 

  9. 9.

    Xiong, Y., Pratsinis, S.E.: Gas phase production of particles in turbulent reactive flows. J. Aerosol Sci. 22(5), 637–655 (1991)

    Article  Google Scholar 

  10. 10.

    Guichard, R., Tanière, A., Belut, E., Rimbert, N.: Simulation of nanoparticle coagulation under Brownian motion and turbulence in a differential–algebraic framework: Developments and applications. Int. J. Multiphas. Flow 64, 73–84 (2014)

    Google Scholar 

  11. 11.

    Salenbauch, S., Cuoci, A., Frassoldati, A., Saggese, C., Faravelli, T., Hasse, C.: Modeling soot formation in premixed flames using an extended conditional quadrature method of moments. Combust Flame 162(6), 2529–2543 (2015)

    Article  Google Scholar 

  12. 12.

    Zucca, A., Marchisio, D.L., Barresi, A.A., Fox, R.O.: Implementation of the population balance equation in CFD codes for modelling soot formation in turbulent flames. Chem. Eng. Sci. 61(1), 87–95 (2006)

    Article  Google Scholar 

  13. 13.

    Park, S., Kruis, F., Lee, K., Fissan, H.: Evolution of particle size distributions due to turbulent and brownian coagulation. Aerosol Sci. Tech. 36, 419–432 (2002)

    Article  Google Scholar 

  14. 14.

    Bhatt, J., Lindstedt, R.: Analysis of the impact of agglomeration and surface chemistry models on soot formation and oxidation. P. Combust. Inst. 32(1), 713–720 (2009)

    Article  Google Scholar 

  15. 15.

    Wu, M., Friedlander, S.: Enhanced power-law agglomerate growth in the free-molecule regime. J. Aerosol Sci. 24, 273–282 (1993)

    Article  Google Scholar 

  16. 16.

    Sundaram, S., Collins, L.: Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct Numerical Simulations. J. Fluid Mech. 335, 75–109 (1997)

    Article  MATH  Google Scholar 

  17. 17.

    Zhou, Y., Wexler, A., Wang, L.: On the collision rate of small particles in isotropic turbulence. II. Finite inertia case. Phys. Fluids 10(5), 1206–1216 (1998)

    Article  Google Scholar 

  18. 18.

    Wang, L.P., Wexler, A.S., Zhou, Y.: On the collision rate of small particles in isotropic turbulence. i. zero-inertia case. Phys. Fluids 10, 266–276 (1998)

    Article  Google Scholar 

  19. 19.

    Brunk, B.K., Koch, D.L., Lion, L.W.: Turbulent coagulation of colloidal particles. J. Fluid Mech. 364, 81–113 (1998)

    Article  MATH  Google Scholar 

  20. 20.

    Reade, W., Collins, L.: A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation. J. Fluid Mech. 415, 45–64 (2000)

    Article  MATH  Google Scholar 

  21. 21.

    Balakin, B., Hoffmann, A.C., Kosinski, P.: The collision efficiency in a shear flow. Chem. Eng. Sci. 68(1), 305–312 (2012)

    Article  Google Scholar 

  22. 22.

    Almohammed, N., Breuer, M.: Modeling and simulation of agglomeration in turbulent particle-laden flows: a comparison between energy-based and momentum-based agglomeration models. Powder Technol. 294, 373–402 (2016)

    Article  Google Scholar 

  23. 23.

    Derksen, J.J.: Direct simulations of aggregates in homogeneous isotropic turbulence. Acta. Mech. 224(10), 2415–2424 (2013)

    Article  MATH  Google Scholar 

  24. 24.

    Derksen, J.J.: Direct numerical simulations of aggregation of monosized spherical particles in homogeneous isotropic turbulence. Aiche. J. 58(8), 2589–2600 (2012)

    Article  Google Scholar 

  25. 25.

    Mountain, R., Mulholland, G., Baum, H.: Simulation of aerosol agglomeration in the free molecular and continuum flow regimes. J. Colloid Interf. Sci. 114(1), 67–81 (1986)

    Article  Google Scholar 

  26. 26.

    Meakin, P.: Models for colloidal aggregation. Annu. Rev. Phys. Chem. 39(1), 237–267 (1988)

    Article  Google Scholar 

  27. 27.

    Gutsch, A., Pratsinis, S., Loffler, F.: Agglomerate’s structure and growth rate by trajectory calculations of monomer-cluster collisions. J. Aerosol. Sci. 26(2), 187–& (1995)

    Article  Google Scholar 

  28. 28.

    Mitchell, P., Frenklach, M.: Particle aggregation with simultaneous surface growth. Phys. Rev. E 67, 061,407 (2003)

    Article  Google Scholar 

  29. 29.

    Videcoq, A., Han, M., Abélard, P., Pagnoux, C., Rossignol, F., Ferrando, R.: Influence of the potential range on the aggregation of colloidal particles. Physica A 374(2), 507–516 (2007)

    Article  Google Scholar 

  30. 30.

    Isella, L., Drossinos, Y.: Nanoparticle agglomeration by Langevin simulations. Phys. Rev. E 82, 011,404 (2010)

    Article  Google Scholar 

  31. 31.

    Schutte, K.C.J., Portela, L.M., Twerda, A., Henkes, R.A.W.M.: Hydrodynamic Perspective on Asphaltene Agglomeration and Deposition. Energ. Fuel 29(5), 2754–2767 (2015)

    Article  Google Scholar 

  32. 32.

    Markutsya, S., Fox, R.O., Subramaniam, S.: Characterization of sheared colloidal aggregation using Langevin dynamics simulation. Phys. Rev. E 89(6) (2014)

  33. 33.

    Schaefer, D.: Fractal models and the structure of materials. Mrs Bull 13, 22–27 (1988)

    Article  Google Scholar 

  34. 34.

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

    Article  Google Scholar 

  35. 35.

    Lazaridis, M., Drossinos, Y.: Multilayer resuspension of small identical particles by turbulent-flow. Aerosol Sci. Technol. 28, 548–560 (1998)

    Article  Google Scholar 

  36. 36.

    Rothenbacher, S., Messerer, A., Kasper, G.: Fragmentation and bond strength of airborne diesel soot agglomerates. Part. Fibre Toxicol. 5, 9 (2008)

    Article  Google Scholar 

  37. 37.

    Inci, G., Arnold, A., Kronenburg, A., Weeber, R.: Modeling nanoparticle agglomeration using local interactions. Aerosol. Sci. Tech. 48(8), 842–852 (2014)

    Article  Google Scholar 

  38. 38.

    Chokshi, A., Tielens, A.G.G.M., Hollenbach, D.: Dust coagulation. Astrophys. J. 407, 806–819 (1913)

    Article  Google Scholar 

  39. 39.

    Pantina, J., Furst, E.: Colloidal aggregate micromechanics in the presence of divalent ions. Langmuir 22, 5282–5288 (2006)

    Article  Google Scholar 

  40. 40.

    Kerr, R.M.: Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58 (1985)

    Article  MATH  Google Scholar 

  41. 41.

    Thajudeen, T., Gopalakrishnan, R., Jr, C.J.H.: The collision rate of nonspherical particles and aggregates for all diffusive Knudsen numbers. Aerosol Sci. Tech. 46(11), 1174–1186 (2012)

    Article  Google Scholar 

  42. 42.

    Melas, A.D., Isella, L., Konstandopoulos, A.G., Drossinos, Y.: Friction coefficient and mobility radius of fractal-like aggregates in the transition regime. Aerosol Ssci. Tech. 48(12), 1320–1331 (2014)

    Article  Google Scholar 

  43. 43.

    Zhang, C., Thajudeen, T., Larriba, C., Schwartzentruber, T.E., Jr, C.J.H.: Determination of the scalar friction factor for nonspherical particles and aggregates across the entire Knudsen number range by direct simulation Monte Carlo (DSMC). Aerosol Sci. Tech. 46(10), 1065–1078 (2012)

    Article  Google Scholar 

  44. 44.

    Friedlander, S.: Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics. Oxford University Press (2000)

  45. 45.

    Saffman, P.G., Turner, J.S.: On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16–30 (1956)

  46. 46.

    Zurita-Gotor, M., Rosner, D.: Effective diameters for collisions of fractal-like aggregates: Recommendations for improved aerosol coagulation frequency predictions. J. Colloid Interf. Sci. 255(1), 10–26 (2002)

    Article  Google Scholar 

  47. 47.

    Meyer, C., Deglon, D.: Particle collision modeling - a review. Miner Eng. 24, 719–730 (2011)

    Article  Google Scholar 

  48. 48.

    Goudeli, E., Eggersdorfer, M.L., Pratsinis, S.E.: Coagulation-Agglomeration of Fractal-like Particles: Structure and Self-Preserving Size Distribution. Langmuir 31 (4), 1320–1327 (2015)

    Article  Google Scholar 

  49. 49.

    Kostoglou, M., Konstandopoulos, A.: Evolution of aggregate size and fractal dimension during Brownian coagulation. J. Aerosol. Sci. 32(12), 1399–1420 (2001)

    Article  Google Scholar 

  50. 50.

    Arnold, A., Lenz, O., Kesselheim, S., Weeber, R., Fahrenberger, F., Roehm, D., Kosovan, P., Holm, C.: Espresso 3.1: Molecular Dynamics Software for Coarse-Grained Models. In: Griebel, M., Schweitzer, M.A. (eds.) Meshfree Methods for Partial Differential Equations VI, Lecture Notes in Computational Science and Engineering, vol. 89, pp 1–23. Springer, Berlin Heidelberg (2013)

  51. 51.

    Becker, V., Briesen, H.: Tangential-force model for interactions between bonded colloidal particles. Phys. Rev. E 78, 061,404 (2008)

    Article  Google Scholar 

  52. 52.

    Isella, L., Drossinos, Y.: On the friction coefficient of straight-chain aggregates. J. Colloid Interf. Sci. 356(2), 505–512 (2011)

    Article  Google Scholar 

  53. 53.

    Tumolva, L., Park, J.Y., suk Kim, J., Miller, A.L., Chow, J.C., Watson, J.G., Park, K.: Morphological and Elemental Classification of Freshly Emitted Soot Particles and Atmospheric Ultrafine Particles using the TEM/EDS. Aerosol Sci. Tech. 44(3), 202–215 (2010)

    Article  Google Scholar 

  54. 54.

    Garza, K.M., Soto, K.F., Murr, L.E.: Cytotoxicity and reactive oxygen species generation from aggregated carbon and carbonaceous nanoparticulate materials. Int. J. Nanomed. 3, 83–94 (2008)

    Article  Google Scholar 

  55. 55.

    Maricq, M., Xu, N.: The effective density and fractal dimension of soot particles from premixed flames and motor vehicle exhaust. J. Aerosol Sci. 35(10), 1251–1274 (2004)

    Article  Google Scholar 

  56. 56.

    Hwang, W., Eaton, J.: Creating homogeneous and isotropic turbulence without a mean flow. Exp. Fluids 36(3), 444–454 (2004)

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to A. Kronenburg.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.


The authors acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) as part of the Collaborative Research Center (SFB) 716 held by the University of Stuttgart.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Inci, G., Kronenburg, A., Weeber, R. et al. Langevin Dynamics Simulation of Transport and Aggregation of Soot Nano-particles in Turbulent Flows. Flow Turbulence Combust 98, 1065–1085 (2017).

Download citation


  • Aggregation
  • Dissipation rate
  • Langevin dynamics
  • Soot particles
  • Turbulence