Mathematical Modeling of Microfiltration in a Rectangular Channel

  • S. T. Antipov
  • A. I. KlyuchnikovEmail author


In formulating problems concerning physical models of hydrodynamic processes, it is generally impossible objectively to take into account quantitatively most factors because of their wide diversity and variability. Another significant impediment is the absence of a unified and universally accepted theory of mass transfer in micro- and ultrafiltration. Noteworthy is the particular complexity of transmembrane transfer with developed flow instabilities of varying intensity because any (even insignificant) change in the process parameters of micro- and ultrafiltration leads to different conditions of the formation (or destruction) of the surface layer, which inevitably influences boundary conditions. In this work, it was shown that a one-parameter diffusion model can be adapted to the membrane separation process by taking into account the permeability of one of the walls of a rectangular channel under consideration. The flow pattern was studied to determine the behavior of the solute concentration field on the membrane surface and to evaluate the efficiency of measures taken to reduce the concentration polarization in hydrodynamic methods by varying the velocity.


mathematical modeling microfiltration membrane module concentration polarization specific permeability equations of flow of viscous incompressible liquid diffusion model flow pattern 



  1. 1.
    Akhmadiev, F.G., Farakhov, M.I., Bekbulatov, I.G., and Isyanov, Ch.Kh., Mathematical modeling of filtering process of two-phase suspensions in tubular filters under nonisothermal conditions, Theor. Found. Chem. Eng., 2016, vol. 50, no. 1, pp. 41–51. CrossRefGoogle Scholar
  2. 2.
    Gan, Q., Howell, J.A., Field, R.W., England, R., Bird, M.R., O’Shaughnessy, C.L., and McKechinie, M.T., Beer clarification by microfiltration — Product quality control and fractionation of particles and macromolecules, J. Membr. Sci., 2001, vol. 194, no. 2, pp. 185–196. CrossRefGoogle Scholar
  3. 3.
    Hunt, J.W., Brouchaert, C.J., Raal, J.D., Treffry-Goatley, K., and Buckley, C.A., The unsteady-state modelling of cross-flow microfiltration, Desalination, 1987, vol. 64, pp. 431–442. CrossRefGoogle Scholar
  4. 4.
    Babenyshev, S.P., Chernov, P.S., and Mamai, D.S., Modeling of the membrane filtration of liquid systems, Nauchn. Zh. Kuban. Gos. Agrar. Univ., 2012, no. 76 (02), pp. 1–11.Google Scholar
  5. 5.
    Bazhenov, V.I. and Ustyuzhanin, A.V., Mathematical model for biological purification of wastewater taking into account hydrodynamic and non-steady-state conditions, Vestn. Irkutsk. Gos. Tekh. Univ., 2014, no. 11 (94), pp. 128–133.Google Scholar
  6. 6.
    Gorbunova, Yu.A. and Timkin, V.A., Hydrodynamics of microfiltration and ultrafiltration separation of milk and curd, Agrar. Vestn. Urala, 2016, no. 6 (148), p. 70.Google Scholar
  7. 7.
    Lobasenko, B.A. and Pavskii, V.A., Determination of the concentration of solutes in the boundary layer on the membrane surface, Izv. Vyssh. Uchebn. Zaved., Pishch. Tekhnol., 2001, nos. 2–3, p. 68.Google Scholar
  8. 8.
    Semenov, A.G., Evolution of the gel contamination of a membrane during tangential ultrafiltration of a solution of a high-molecular compound, Tekh. Tekhnol. Pishch. Proizvod., 2011, no. 1 (20), p. 1.Google Scholar
  9. 9.
    Bekker, V.F., Modelirovanie khimiko-tekhnologicheskikh ob"ektov upravleniya: uchebnoe posobie (Modeling of Chemical Engineering Processes: A Textbook), Moscow: RIOR-INFRA–M, 2014, 2nd ed.Google Scholar
  10. 10.
    Timashev, S.F., Fizikokhimiya membrannykh protsessov (The Physicochemistry of Membrane Processes), Moscow: Khimiya, 1998.Google Scholar
  11. 11.
    Bryk, M.T., Ul’trafil’tratsiya (Ultrafiltration), Kiev: Naukova Dumka, 1989.Google Scholar
  12. 12.
    Schmitz, P., Houi, D., and Wandelt, B., Hydrodynamic aspects of crossflow microfiltration: Analysis of particle deposition at the membrane surface, J. Membr. Sci., 1992, vol. 71, nos. 1–2, pp. 29–40. CrossRefGoogle Scholar
  13. 13.
    Antipov, S.T., Kretov, I.T., Shakhov, S.V., and Klyuchnikov, A.I., Concentration polarization in beer clarification, Pivo Napitki, 2001, no. 3, p. 18.Google Scholar
  14. 14.
    Antipov, S.T., Shakhov, S.V., Ryazanov, A.N., Klyuchnikov, A.I., Blyakhman, D.A., and Vasil’chenko, A.N., RF Patent 2147459, Byull. Izobret., 2000, no. 11.Google Scholar
  15. 15.
    Laptev, A.G. and Lapteva, E.A., Determination of turbulent mixing coefficients in one- and two-phase media using the Taylor model, Fundam. Issled., 2015, no. 2, p. 2810.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Voronezh State University of Engineering TechnologiesVoronezhRussia

Personalised recommendations