Vol. 32, issue 06, article # 3

Beresnev S.A., Vasiljeva M.S., Kochneva L.B. Motion of fractal-like aggregates: settling velocity of particles and thermophoresis. // Optika Atmosfery i Okeana. 2019. V. 32. No. 06. P. 437–442 [in Russian].
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The theoretical approach for calculations of fractal-like particles characteristics on the basis of gas-kinetic results for homogeneous spheres is presented. It consists in replacement of a real fractal aggregate by an equivalent sphere with the mobility radius and approximations of the density and heat conductivity of the aggregate by their effective values. The validity of the method has been confirmed in the comparison with the known experimental data. The theory suggested has two important restrictions: fractal aggregate should consist from a great number of primary particles (100 and more) and primary particles should be monodisperse. Violation of these conditions leads to considerable divergence between theoretical and experimental results.


settling velocity, thermophoresis, fractal-like particles


  1. Beresnev S.A., Vasil'eva M.S., Gryazin V.I., Kochneva L.B. Fotoforez fraktalo-podobnykh agregatov sazhi: mikrofizicheskaya model', sravnenie s eksperimentom i vozmozhnye atmosfernye proyavleniya // Optika atmosf. i okeana. 2017. V. 30, N 6. P. 457–462; Beresnev S.A., Vasil’eva M.S., Gryazin V.I., Kochneva L.B. Photophoresis of fractal-like soot aggregates: Microphysical model, comparison with experiment, and possible atmospheric manifestations // Atmos. Ocean. Opt. 2017. V. 30, N 6. P. 527–532.
  2. Beresnev S.A., Chernyak V.G., Fomyagin G.A. Motion of a spherical particle in a rarefied gas. Part 2. Drag and thermal polarization // J. Fluid Mech. 1990. V. 219. P. 405–421.
  3. Beresnev S., Chernyak V. Thermophoresis of a spherical particle in a rarefied gas: Numerical analysis based on the model kinetic equations // Phys. Fluids. 1995. V. 7, N 7. P. 1743–1756.
  4. Sorensen C.M. The mobility of fractal aggregates: A review // Aerosol Sci. Technol. 2011. V. 45. P. 765–779.
  5. Allen M.D., Raabe O.G. Slip correction measurements of spherical solid aerosol particles in animproved Millikan apparatus // Aerosol Sci. Technol. 1985. V. 4. P. 269–286.
  6. Yon J., Bescond A., Ouf F.-X. A simple semi-empirical model for effective density measurements of fractal aggregates // J. Aerosol Sci. V. 87. P. 28–37.
  7. Nan C.-W., Birringer R., Clarke D.R., Gleiter H. Effective thermal conductivity of particulate composites with interfacial thermal resistance // J. Appl. Phys. 1997. V. 81, N 10. P. 6692–6699.
  8. Evans W., Prasher R., Fish J., Meakin P., Phelan P., Keblinski P. Effect of aggregation and interfacial thermal resistance on thermal conductivity of nanocomposites and colloidal nanofluids // Int. J. Heat Mass Transfer. 2008. V. 51. P. 1431–1438.
  9. Suzuki S., Dobashi R. Effect of particle morphology on the thermophoretic behavior of soot particle // 20th Int. Colloq. Dyn. Expl. React. Syst. (ICDERS2005). Montreal. 2005. P. 205-1–4.
  10. Suzuki S., Kawana K., Dobashi R. Effect of particle morphology on thermophoretic velocity of aggregated soot particles // Int. J. Heat Mass Transfer. 2009. V. 52. P. 4695–4700.
  11. Baron P.A., Willeke K. Aerosol measurement: Principles, techniques, and applications. New York: Wiley-Interscience, 2001. 1172 p.
  12. Karasev V.V., Onischuk A.A., Glotov O.G., Baklanov A.M., Pilyugina E.A., Kiskin A.B., Zarko V.E. Formation of titania nanoparticles via combustion of the pyrotechnic mixture // Proc. 35th Int. Ann. Conf. of ICT. Karlsruhe. 2004. P. 139-1–12.
  13. Messerer A., Niessner R., Pöschl U. Thermophoretic deposition of soot aerosol particles under experimental conditions relevant for modern diesel engine exhaust gas systems // J. Aerosol Sci. 2003. V. 34. P. 1009–1021.
  14. Brugière E., Gensdarmes F., Ouf F.X., Yon J., Coppalle A. Increase in thermophoretic velocity of carbon aggregates as a function of particle size // J. Aerosol Sci. 2014. V. 76. P. 87–97.
  15. Yahiaa L.A.A., Gehin E., Sagot B. Application of the Thermophoretic Annular Precipitator (TRAP) for the study of soot aggregates morphological influence on their thermophoretic behavior // J. Aerosol Sci. 2017. V. 113. P. 40–51.