Skip to main content
Log in

Effect of magnetic field on the hydrodynamic permeability of a membrane built up by porous spherical particles

  • Published:
Colloid Journal Aims and scope Submit manuscript

Abstract

In this paper, an analysis of steady, axi-symmetric Stokes flow of an electrically conducting viscous incompressible fluid through spherical particle covered by porous shell in presence of uniform magnetic field is presented. To model flow through the swarm of spherical particles, cell model technique has been used, i.e. porous spherical shell is assumed to be confined within a hypothetical cell of the same geometry. At the fluid-porous interface, the stress jump boundary condition for tangential stresses along with continuity of normal stress and velocity components are used. Four known boundary conditions on the hypothetical surface were considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta−Morse’s) condition. The effect of stress jump coefficient, Hartmann number, and dimensionless permeability of the porous region as well as particle volume fraction on the hydrodynamic permeability and streamlines were discussed. The patterns of streamlines were also obtained.

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

Access this article

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, J., Low Reynolds Number Hydrodynamics, Dordrecht: Kluwer, 1991.

    Google Scholar 

  2. Uchida, S., Int. Sci. Technol. Univ. Tokyo (in Japan), 1954, no. 3, p. 97.

    Google Scholar 

  3. Happel, J., AIChE J., 1958, vol. 4, p. 197.

    Article  CAS  Google Scholar 

  4. Happel, J., AIChE J., 1959, vol. 5, p. 174.

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. Cunningham, E., Proc. R. Soc. London A, 1910, vol. 83, p. 357.

    Article  Google Scholar 

  9. Brinkman, H.C., Appl. Sci. Res., 1947, vol. A, p. 27.

    Google Scholar 

  10. Grosan, T., Postelnicu, A., and Pop, I., Transp. Porous Media, 2010, vol. 81, p. 89.

    Article  Google Scholar 

  11. Barman, B., Indian J. Pure Appl. Math., 1996, vol. 27, p. 1244.

    Google Scholar 

  12. Dassios, G., Hadjinicolaou, M., and Payatakes, A.C., Q. Appl. Math., 1994, vol. 52, p. 157.

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Zlatanovski, T., Q. J. Mech. Appl. Math., 1999, vol. 52, p. 111.

    Article  Google Scholar 

  15. Yadav, P.K. and Deo, S., Meccanica, 2012, vol. 47, p. 1499.

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  18. Kuznetsov, A.V., Appl. Sci. Res., 1996, vol. 56, p. 53.

    Article  CAS  Google Scholar 

  19. Kuznetsov, A.V., Int. J. Heat Mass Transfer, 1998, vol. 41, p. 2556.

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  21. Srivastava, A.C. and Srivastava, N., Z. Angew. Math. Phys., 2008, vol. 56, p. 821.

    Article  Google Scholar 

  22. Prakash, J. and Raja Sekhar, G.P., Meccanica, 2012, vol. 47, p. 1079.

    Article  Google Scholar 

  23. Perepelkin, P.V., Starov, V.M., and Filippov, A.N., Colloid J., 1992, vol. 54, p. 139.

    CAS  Google Scholar 

  24. Vasin, S.I., Starov, V.M., and Filippov, A.N., Colloid J., 1996, vol. 58, p. 291.

    CAS  Google Scholar 

  25. Vasin, S.I., Starov, V.M., and Filippov, A.N., Colloid J., 1996, vol. 58, p. 282.

    CAS  Google Scholar 

  26. Vasin, S.I. and Filippov, A.N., Colloid J., 2004, vol. 66, p. 261.

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  30. Yadav, P.K., Tiwari, A., Deo, S., Filippov, A.N., and Vasin, S.I., Acta Mech., 2010, vol. 215, p. 193.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Chaudhary, S. and Kumar, P., Meccanica, 2014, vol. 49, p. 69.

    Article  Google Scholar 

  34. Ishak, A., Nazar, R., and Pop, I., Meccanica, 2009, vol. 44, p. 369.

    Article  Google Scholar 

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

    Google Scholar 

  36. Jayalakshmamma, D.V., Dinesh, P.A., and Sankar, M., Mapana J. Sci., 2011, vol. 10, p. 11.

    Google Scholar 

  37. Tiwari, A., Deo, S., and Filippov, A., Colloid J., 2012, vol. 74, p. 515.

    Article  CAS  Google Scholar 

  38. Srivastava, B.G., Yadav, P.K., Deo, S., Singh, P.K., and Filippov, A.N., Colloid J., 2014, vol. 76, p. 725.

    Article  CAS  Google Scholar 

  39. Liu, S. and Masliyah, J., Chem. Eng. Commun., 1996, vols. 148–150, p. 653.

    Article  Google Scholar 

  40. Nield, D.A. and Bejan, A., Convection in Porous Media, New York: Springer, 2006, p. 3.

    Google Scholar 

  41. Volfkovich, Yu.M., Filippov, A.N., and Bagotsky, V.S., Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology, London: Springer, 2014.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pramod Kumar Yadav.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yadav, P.K., Deo, S., Singh, S.P. et al. Effect of magnetic field on the hydrodynamic permeability of a membrane built up by porous spherical particles. Colloid J 79, 160–171 (2017). https://doi.org/10.1134/S1061933X1606020X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061933X1606020X

Navigation