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Mathematical model for mixing liquids with a disperse phase in laminar and turbulent regimes in packed-bed flow mixers

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Abstract

A mathematical model for calculating static packed-bed mixers in laminar and turbulent regimes is discussed. The mathematical model is constructed using the theory of mass transfer and turbulent migration of particles when the mass transfer of a finely disperse phase is considered as a kind of diffusion process. Some calculations have been performed and certain dependences of the mixing efficiency on the Reynolds number have been plotted.

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References

  1. Thakur, R.K., Vial, Ch., Nigam, K.D.P., Nauman, E.B., and Djelveh, G., Static mixers in the process industries-a review, Chem. Eng. Res. Des., 2003, vol. 81, no. 7, pp. 787–826.

    Article  CAS  Google Scholar 

  2. Chausov, F.F., Domestic static mixers for the continuous mixing of liquids, Neftehim. Neftegaz. Mashinostr., 2009, no. 3, pp. 11–14

    Google Scholar 

  3. Kulov, N.N. and Gordeev, L.S., Mathematical modeling in chemical engineering and biotechnology, Theor. Found. Chem. Eng., 2014, vol. 48, no. 3, pp. 225–229.

    Article  CAS  Google Scholar 

  4. Barabash, V.M., Begichev, V.I., Belevitskaya, M.A., and Smirnov, N.N., Problems and trends in the development of the theory and practice of mixing of fluid media, Theor. Found. Chem. Eng., 2007, vol. 41, no. 2, pp. 130–136.

    Article  CAS  Google Scholar 

  5. Danilov, Yu.M., Mukhametzyanova, A.G., Deberdeev, R.Ya., and Berlin, A.A., Estimating the efficiency of mixing of liquid components in small tubular turbulent devices, Theor. Found. Chem. Eng., 2011, vol. 45, no. 1, pp. 81–84.

    Article  CAS  Google Scholar 

  6. Laptev, A.G., Farakhov, T.M., and Dudarovskaya, O.G., Efficiency of the turbulent mixing of media in packed flow-through mixers, Neftegaz. Delo, 2012, no. 4, pp. 387–408.

    Google Scholar 

  7. Mednikov, E.P., Turbulentnyi perenos i osazhdenie aerozolei (Turbulent Transport and Deposition of Aerosols), Moscow: Nauka, 1980.

    Google Scholar 

  8. Rossetti, S.J. and Pfeffer, R., Drag reduction in dilute flowing gas-solid suspensions, AIChE J., 1972, vol. 18, pp. 31–39.

    Article  CAS  Google Scholar 

  9. Laptev, A.G., Modeli pogranichnogo sloya i raschet teplomassoobmennykh protsessov (Boundary Layer Models and Calculation of Heat- and Mass-Transfer Processes), Kazan: Kazan. Univ., 2007.

    Google Scholar 

  10. Laptev, A.G. and Farakhov, T.M., Mathematical models of momentum transfer in the boundary layer, J. Eng. Phys. Thermophys., 2013, vol. 86, no. 3, pp. 604–613.

    Article  Google Scholar 

  11. Laptev, A.G. and Farakhov, T.M., Mathematical models and calculation of the hydrodynamic characteristics of a boundary layer, Polythem. Online Sci. J. Kuban State Agrarian Univ., 2012, no. 82, pp. 704–738.

    Google Scholar 

  12. Landau, L.D., Mekhanika sploshnykh sred (Continuum Mechanics), Moscow: Gostekhteorizdat, 1954.

    Google Scholar 

  13. Levich, V.G., Fiziko-khimicheskaya gidrodinamika (Physicochemical Fluid Dynamics), Moscow: Fizmatgiz, 1959.

    Google Scholar 

  14. Prandtl’, L. and Tietjens, O., Hydro- und Aaeromechanik, Berlin: 1929.

    Google Scholar 

  15. Kutateladze, S.S., Conservative properties of near-wall turbulence, Teor. Osn. Khim. Tekhnol., 1971, vol. 5, no. 1, pp. 3–12.

    Google Scholar 

  16. Ramm, V.M., Absorbtsiya gazov (Gas Absorption), Moscow: Khimiya, 1976.

    Google Scholar 

  17. Laptev, A.G., Basharov, M.M., and Farakhova, A.I., Efficiency of turbulent separation of a fine-particle phase in thin-layer settling tanks, Energosberezh. Vodopodg., 2011, no. 5, p. 4346.

    Google Scholar 

  18. Townsend, A.A., The Structure of Turbulent Shear Flow, Cambridge: Cambridge Univ. Press, 1976.

    Google Scholar 

  19. Sokolov, V.N. and Domanskii, I.V., Gazozhidkostnye reaktory (Gas-Liquid Reactors), Leningrad: Mashinostroenie, 1976.

    Google Scholar 

  20. Kagan, A.M., Laptev, A.G., Pushnov, A.S., and Farakhov, M.I., Kontaktnye nasadki promyshlennykh teplomassoobmennykh apparatov (Phase Contact Packings for Industrial Heat and Mass Transfer Apparatuses), Kazan: Otechestvo, 2013.

    Google Scholar 

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Correspondence to O. G. Dudarovskaya.

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Original Russian Text © A.G. Laptev, T.M. Farakhov, O.G. Dudarovskaya, 2015, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2015, Vol. 49, No. 1, pp. 23–31.

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Laptev, A.G., Farakhov, T.M. & Dudarovskaya, O.G. Mathematical model for mixing liquids with a disperse phase in laminar and turbulent regimes in packed-bed flow mixers. Theor Found Chem Eng 49, 21–29 (2015). https://doi.org/10.1134/S004057951501008X

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  • DOI: https://doi.org/10.1134/S004057951501008X

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