Mathematical Model of Transfer and Deposition of Finely Dispersed Particles in a Turbulent Flow of Emulsions and Suspensions

  • A. G. Laptev
  • M. M. Basharov

The problem of modeling turbulent transfer of finely dispersed particles in liquids has been considered. An approach is used where the transport of particles is represented in the form of a variety of the diffusion process with the coefficient of turbulent transfer to the wall. Differential equations of transfer are written for different cases, and a solution of the cell model is obtained for calculating the efficiency of separation in a channel. Based on the theory of turbulent transfer of particles and of the boundary layer model, an expression has been obtained for calculating the rate of turbulent deposition of finely dispersed particles. The application of this expression in determining the efficiency of physical coagulation of emulsions in different channels and on the surface of chaotic packings is shown.


mass transfer of particles turbulent diffusion structure of flow cellular model physical coagulation 


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  1. 1.
    E. P. Mednikov, Turbulent Transfer and Deposition of Aerosols [in Russian], Nauka, Moscow (1980).Google Scholar
  2. 2.
    Chemist′s and Technologist′s New Handbook, Processes and Apparatuses of Chemical Technologies, Pt. 1 [in Russian], ANO NPO "Professional," St. Petersburg (2004).Google Scholar
  3. 3.
    V. V. Kafarov and M. B. Glebov, Mathematical Simulation of Basic Processes of Chemical Industries [in Russian], Vysshaya Shkola, Moscow (1991).Google Scholar
  4. 4.
    A. G. Laptev, M. M. Basharov, and A. I. Farakhova, Determining the efficiency of subjecting finely dispersed emulsions to physical coagulation in a packed layer under turbulent conditions, Therm. Eng., 60, No. 9, 669−675 (2013).CrossRefGoogle Scholar
  5. 5.
    S. G. D′yakonov, V. I. Elizarov, and A. G. Laptev, Theoretical Principles and Simulation of the Processes of Separation of Substances [in Russian], Izd. Kazansk. Univ., Kazan (1993).Google Scholar
  6. 6.
    V. M. Ramm, Absorption of Gases [in Russian], Khimiya, Moscow (1976).Google Scholar
  7. 7.
    A. G. Laptev and E. A. Lapteva, Determination of the coefficients of turbulent mixing in single- and two-phase media by Taylor′s model, Fundam. Issled., No. 2, 2810−2814 (2015).Google Scholar
  8. 8.
    M. O. Sivolotskii and O. V. Chagin, Obtaining emulsions in a static mixer with a new internal vertical device, Sovr. Naukoemk. Tekhnol. Region. Prilozh., 38, No. 2, 108−113 (2014).Google Scholar
  9. 9.
    M. É. Aérov, O. M. Todes, and D. A. Narinskii, Stationary Granular-Bed Apparatuses [in Russian], Khimiya, Leningrad (1979).Google Scholar
  10. 10.
    I. A. Aleksandrov, Mass Transfer in Rectification and Absorption of Multicomponent Mixtures [in Russian], Khimiya, Leningrad (1975).Google Scholar
  11. 11.
    A. G. Laptev, E. A. Lapteva, and T. M. Farakhov, Models of transport phenomena in random packed and granular beds, Theor. Found. Chem. Eng., 49, No. 4, 388−395 (2015).CrossRefGoogle Scholar
  12. 12.
    A. G. Laptev and M. M. Basharov, Efficiency of Heat and Mass Transfer and of the Separation of Heterogeneous Media in Apparatuses of the Oil and Gas Chemical Complex [in Russian], Tsentr Innovats. Tekhnol., Kazan (2016).Google Scholar
  13. 13.
    M. I. Farakhov, A. G. Laptev, and M. M. Basharov, Modernization of the apparatuses of liquid purification of dispersed phase at an oil-chemical complex, Teor. Osn. Khim. Tekhnol., 49, No. 6, 132−138 (2015).Google Scholar
  14. 14.
    S. S. Kutateladze, Heat Transfer and Hydrodynamic Resistance [in Russian], Énergoatomizdat, Moscow (1990).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Kazan State Power Engineering UniversityKazanRussia
  2. 2.Public Corporation TANEKONizhnekamskRussia

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