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The use of the finite element method for calculating the thermophoresis velocity of large aerosol particles

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Abstract

The finite element method has been employed to calculate the thermophoresis velocity of solid aerosol particles, the sizes of which are much larger than the mean free path of molecules in a gas. The thermophoretic velocities of axially symmetric particles moving along their rotation axes have been numerically calculated. Cylindrical particles, particles having a shape resulting from rhomb rotation around one of its diagonals, and spheroidal particles have been considered. The data obtained for spheroidal particles have been compared with the available results of analytical calculations.

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References

  1. Yalamov, Yu.I. and Galoyan, V.S., Dinamika kapel’ v neodnorodnykh vyazkikh sredakh (Drop Dynamics in Heterogeneous Viscous Media), Yerevan: Luis, 1985.

    Google Scholar 

  2. Williams, M.M.R. and Loyalka, S.K., Aerosol Science: Theory and Practice, Oxford: Pergamon, 1991.

    Google Scholar 

  3. Epstein, P.S., Z. Phys., 1929, vol. 54, p. 537.

    Article  Google Scholar 

  4. Zheng, F., Adv. Colloid Interface Sci., 2002, vol. 97, p. 225.

    Article  Google Scholar 

  5. Reed, L.D., M.Sc. Thesis (Univ. of Illinois, Urbana-Champaign, IL, 1971).

    Google Scholar 

  6. Yalamov, Yu.I. and Afanas’ev, H.M., Zh. Tekh. Fiz., 1977, vol. 47, p. 1998.

    Google Scholar 

  7. Yalamov, Yu.I. and Safiullin, R.A., Teplofiz. Vys. Temp., 1994, vol. 32, p. 271.

    CAS  Google Scholar 

  8. Yalamov, Yu.I. and Safiullin, R.A., Zh. Tekh. Fiz., 1995, vol. 65, no. 3, p. 1.

    Google Scholar 

  9. Shchukin, E.R., Kareva, N.N., Yalamov, Yu.I., and Shulimanova, Z.L., Zh. Tekh. Fiz., 1999, vol. 69, no. 8, p. 21.

    Google Scholar 

  10. Keh, H.J. and Tu, H.J., Colloids Surf. A, 2001, vol. 176, p. 213.

    Article  CAS  Google Scholar 

  11. Shchukin, E.R., Malai, N.V., and Shulimanova, E.L., Nauchn. Vedom. BelGU: Mat., Fiz., 2015, vol. 41, no. 23, p. 45.

    Google Scholar 

  12. Roldughin, V.I., Kolloidn. Zh., 1983, vol. 45, p. 1134.

    Google Scholar 

  13. Gaidukov, M.N., Melkumyan, M.A., and Yalamov, Yu.I., Inzh.-Fiz. Zh., 1983, vol. 45, p. 508.

    Google Scholar 

  14. Yalamov, Yu.I., Chermoshentsev, A.B., and Chermoshentseva, O.F., High Temperature, 1997, vol. 35, p. 425.

    CAS  Google Scholar 

  15. Mohan, A. and Brenner, H., SIAM J. Appl. Math., 2006, vol. 66, p. 787.

    Article  Google Scholar 

  16. Senchenko, S. and Keh, H.J., Phys. Fluids, 2007, vol. 19, p. 033102.

    Article  Google Scholar 

  17. Chang, Yu.C. and Keh, H.J., J. Aerosol Sci., 2010, vol. 41, p. 180.

    Article  CAS  Google Scholar 

  18. Srivastava, D.K., Yadav, R.R., and Yadav, S., Int. J. Appl. Math. Mech., 2012, vol. 8, p. 17.

    Google Scholar 

  19. Yalamov, Yu.I., Redchits, V.P., and Gaidukov, M.N., Inzh.-Fiz. Zh., 1980, vol. 39, p. 539.

    Google Scholar 

  20. Yalamov, Yu.I., Gukasyan, A.A., and Gaidukov, M.N., Dokl. Akad. Nauk SSSR, 1981, vol. 260, p. 871.

    CAS  Google Scholar 

  21. Leong, K.H., J. Aerosol Sci., 1984, vol. 15, p. 511.

    Article  Google Scholar 

  22. Williams, M.M.R., J. Phys. D: Appl. Phys., 1986, vol. 19, p. 1631.

    Article  Google Scholar 

  23. Malai, N.V. and Shchukin, E.R., Zh. Tekh. Fiz., 2003, vol. 73, no. 9, p. 39.

    Google Scholar 

  24. Keh, H.J. and Ou, C.L., Aerosol Sci. Technol., 2004, vol. 38, p. 675.

    Article  CAS  Google Scholar 

  25. D’yakonov, S.N. and Ryumshin, B.V., Differ. Uravn. Protsessy Upravl., 2006, no. 2, p. 1.

    Google Scholar 

  26. Chang, Yu.C. and Keh, H.J., AIChE J., 2009, vol. 55, p. 35.

    Article  CAS  Google Scholar 

  27. Keh, H.J. and Chang, Yu.C., Phys. Fluids, 2009, vol. 21, p. 062001.

    Article  Google Scholar 

  28. Chang, Yu.C. and Keh, H.J., Phys. Fluids, 2010, vol. 22, p. 113305.

    Article  Google Scholar 

  29. Malay, N.V. and Mironova, N.N., Univ. J. Phys. Appl., 2014, vol. 8, p. 251.

    Google Scholar 

  30. Hecht, F., J. Numer. Math., 2012, vol. 20, p. 251.

    Article  Google Scholar 

  31. Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, Logg, A., Mardal, K.A., and Wells, G., Eds., Berlin: Springer, 2012.

  32. Cantwell, C.D., Moxey, D., Comerford, A., et al., Comput. Phys. Commun., 2015, vol. 192, p. 205.

    Article  CAS  Google Scholar 

  33. Reddy, J.N. and Gartling, D.K., The Finite Element Method in Heat Transfer and Fluid Dynamics, Boca Raton: CRC, 2010.

    Google Scholar 

  34. Pozrikidis, C., Introduction to Theoretical and Computational Fluid Dynamics, Oxford: Oxford Univ. Press, 2011.

    Google Scholar 

  35. Glowinski, R., in Handbook of Numerical Analysis, Amsterdam: Elsevier, 2003, vol. 9, p. 3.

    Google Scholar 

  36. Segal, I.A., Finite Element Methods for the Incompressible Navier–Stokes Equations, Delft: Delft Univ. of Technology, 2015.

    Google Scholar 

  37. Li, H., J. Comput. Appl. Math., 2011, vol. 235, p. 5155.

    Article  Google Scholar 

  38. Ganesan, S. and Tobiska, L., Int. J. Numer. Methods Fluids, 2008, vol. 57, p. 119.

    Article  Google Scholar 

  39. Delone, B.N., Izv. Akad. Nauk SSSR, Otd. Mat. Estestv. Nauk, Ser. Mat., 1934, no. 4, p. 793.

    Google Scholar 

  40. Roberts, J.E. and Thomas, J.M., in Handbook of Numerical Analysis, Amsterdam: Elsevier, 1991, vol. 2, p. 523.

    Google Scholar 

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Authors and Affiliations

  1. Pskov State University, pl. Lenina 2, Pskov, 180000, Russia

    S. I. Grashchenkov

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  1. S. I. Grashchenkov
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Correspondence to S. I. Grashchenkov.

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Original Russian Text © S.I. Grashchenkov, 2017, published in Kolloidnyi Zhurnal, 2017, Vol. 79, No. 1, pp. 25–31.

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Grashchenkov, S.I. The use of the finite element method for calculating the thermophoresis velocity of large aerosol particles. Colloid J 79, 35–41 (2017). https://doi.org/10.1134/S1061933X17010069

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  • DOI: https://doi.org/10.1134/S1061933X17010069

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