Skip to main content
SpringerLink
Log in

Effect of the magnetic field on the hydrodynamic permeability of a membrane

  • Published:
Colloid Journal Aims and scope Submit manuscript

Abstract

The present paper concerns the influence of the magnetic field on the permeability of a membrane of solid cylindrical particles covered with porous layer. Here, we have considered the flow along the axis of cylinder and the alignment of uniform magnetic field is assumed to be perpendicular to the axis. The Brinkman equation is used for flow through porous region and Stokes equation is used for flow through clear fluid region. To model flow through assemblage of particles, cell model technique has been used i.e. the porous cylindrical shell is assumed to be confined within a hypothetical cell of same geometry. The stress jump condition has been employed at the fluid-porous interface and all four alternative conditions Happel, Kuwabara, Kvashnin and Mehta-Morse/Cunningham are used at the hypothetical cell. Effect of the Hartmann number on the hydrodynamic permeability of the membrane is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics. Dordrecht: Kluwer, 1991.

    Google Scholar 

  2. Happel, J., Motai, T., and Uchida, S. Ind. Eng. Chem., 1954, vol. 46, p. 1194.

    Article  Google Scholar 

  3. Happel, J., A.I.Ch.E., 1958, vol. 4, p. 197.

    Article  CAS  Google Scholar 

  4. Happel, J., A.I.Ch.E., 1959, vol. 5, p. 174.

    Article  CAS  Google Scholar 

  5. Kuwabara, S., J. Phys. Soc. Japan, 1959, vol. 14, p. 527.

    Article  Google Scholar 

  6. Epstein, N. and Masliyah, J.H., Chem. Eng. J., 1972, vol. 3, p. 169.

    Article  CAS  Google Scholar 

  7. Neale, G., Epstein, N., and Nader, W., Chem. Eng. Sci., 1973, vol. 28, p. 1865.

    Article  CAS  Google Scholar 

  8. Mehta, G.D. and Morse, T.F., J. Chem. Phys., 1975, vol. 63, p. 1878.

    Article  CAS  Google Scholar 

  9. Cunningham, E., Proc. Roy. Soc. (London). A, 1910, vol. 83, p. 357.

    Article  Google Scholar 

  10. Kvashnin, A.G., Fluid Dynamics, 1979, vol. 14, p. 598.

    Article  Google Scholar 

  11. Dassios, G., Hadjinicolaou, M., Coutelieris, F.A., and Payatakes, A.C., Q. Appl. Math., 1995, vol. 52, p. 157.

    Google Scholar 

  12. Dassios, G., Hadjinicolaou, M., Coutelieris, F.A., and Payatakes, A.C., Int. J. Eng. Sci., 1995, vol. 33, p. 1465.

    Article  Google Scholar 

  13. Veerapaneni, S. and Wiesner, M.R., J. Colloid Interface Sci., 1996, vol. 177, p. 45.

    Article  CAS  Google Scholar 

  14. Datta, S. and Deo, S., Proc. Ind. Acad. Sci. (Math. Sci.), 2002, vol. 112, p. 463.

    Article  Google Scholar 

  15. Datta, S. and Deo, S., Indian J. Pure Appl. Math., 2002, vol. 33, p. 903.

    Google Scholar 

  16. Deo, S., Sadhana, 2004, vol. 29, p. 381.

    Article  Google Scholar 

  17. Kim, A.S. and Yuan, R., J. Membrane Sci., 2005, vol. 249, p. 89.

    Article  CAS  Google Scholar 

  18. Deo, S. and Yadav, P.K., Int. J. Math. Math. Sci. (2008), doi: 10.1155/2008/651910.

  19. Deo, S. and Gupta, B.R., Acta Mechanica, 2009, vol. 203, p. 241.

    Article  Google Scholar 

  20. Deo, S., J. Porous Media, 2009, vol. 12, p. 347.

    Article  CAS  Google Scholar 

  21. Davis, R.H. and Stone, H.A., Chem. Eng. Sci., 1993, vol. 48, p. 3993.

    Article  CAS  Google Scholar 

  22. Filippov, A.N., Vasin, S.I., and Starov, V.M., Colloids Surf. A, 2006, vols. 282–283, p. 272.

    Article  Google Scholar 

  23. Vasin, S.I., Filippov, A.N., and Starov, V.M., Adv. Colloid Interface Sci., 2008, vol. 139, p. 83.

    Article  CAS  Google Scholar 

  24. Vasin, S.I. and Filippov, A.N., Colloid J., 2009, vol. 71, p. 31.

    Article  CAS  Google Scholar 

  25. Vasin, S.I. and Filippov, A.N., Colloid. J., 2009, vol. 71, p. 141.

    Article  CAS  Google Scholar 

  26. Vasin, S.I., Filippov, A.N., and Sherysheva, E.E., Colloid. J., 2011, vol. 73, p. 303.

    Article  CAS  Google Scholar 

  27. Ochoa-Tapia, J.A and Whitaker, S., Int. J. Heat Mass Transfer, 1995, vol. 38, p. 2635.

    Article  CAS  Google Scholar 

  28. Ochoa-Tapia, J.A and Whitaker, S., Int. J. Heat Mass Transfer, 1995, vol. 38, p. 2647.

    Article  CAS  Google Scholar 

  29. Raja Sekhar, G.P and Amaranath, T., Mech. Res. Commun., 1996, vol. 23, p. 449.

    Article  Google Scholar 

  30. Bhattacharyya, A. and Raja Sekhar, G.P., Chem. Eng. Sci., 2004, vol. 59, p. 4481.

    Article  CAS  Google Scholar 

  31. Srivastava, A.C. and Srivastava, N., ZAMP, 2005, vol. 56, p. 821.

    Article  Google Scholar 

  32. Deo, S., Filippov, A.N., Tiwari, A., et al., Adv. Colloid Interface Sci., 2011, vol. 164, p. 21.

    Article  CAS  Google Scholar 

  33. Vasin, S.I., Sherysheva, E.E., and Filippov, A.N., Colloid J., 2011, vol. 73, p. 167.

    Article  CAS  Google Scholar 

  34. Gold, R.R., J. Fluid Mech., 1962, vol. 13, p. 505.

    Article  Google Scholar 

  35. Globe, S., Phys. Fluids, 1959, vol. 2, p. 404.

    Article  Google Scholar 

  36. Mazumdar, H.P., Ganguly, U.N., and Venkatesan, S.K., Indian J. Pure Appl. Math., 1996, vol. 27, p. 519.

    Google Scholar 

  37. Haldar, K. and Ghosh, S.N., Indian J. Pure Appl. Math., 1994, vol. 25, p. 345.

    Google Scholar 

  38. Suri, P.K. and Suri, P.R., Indian J. Pure Appl. Math., 1981, vol. 12, p. 907.

    Google Scholar 

  39. Ramchandra Rao, A. and Deshikachar, K.S., J. Indian Inst. Sci. 1988, vol. 68, p. 247.

    Google Scholar 

  40. Bali, R. and Awasthi, U., Appl. Math. Comput., 2007, vol. 188, p. 1635.

    Article  Google Scholar 

  41. Varshney, G., Katiyar, V.K., and Kumar, S., Int. J. Eng, Sci. Tech., 2010, vol. 2, p. 67.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333031, India

    Ashish Tiwari

  2. Department of Mathematics, University of Allahabad, Allahabad, 211002, India

    Satya Deo

  3. Department of Higher Mathematics, Gubkin Russian State University of Oil and Ga, Leninsky Prospect, 65, Moscow, 119991, Russia

    Anatoly Filippov

Authors
  1. Ashish Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Satya Deo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anatoly Filippov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tiwari, A., Deo, S. & Filippov, A. Effect of the magnetic field on the hydrodynamic permeability of a membrane. Colloid J 74, 515–522 (2012). https://doi.org/10.1134/S1061933X1204014X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061933X1204014X

Keywords

Search

Navigation