Spontaneous imbibition in parallel layers of packed beads

Regular Article


The imbibition of a wetting fluid in a homogeneous porous medium follows the diffusion-like behavior described by Washburn. The impregnation of a two-layered porous medium by a wetting fluid due to capillary action has been previously described to have two fronts, one saturating the medium and the other, leading front, which propagates in finer pores. Here, we report that the leading front is governed by the porous structure and is not always in the finer pores. Based on the experiments in a layered porous medium of permeability varying perpendicular to the direction of flow, we show that the permeability of the adjacent layers plays a significant role in determining the leading front amongst the layers. We have also developed an analytical model which describes the flow dynamics in the layered porous medium. The model predicts the condition for which the leading front in the larger pores is followed by the front in the finer pores. This condition is also verified experimentally.

Graphical abstract


Flowing Matter: Interfacial phenomena 


  1. 1.
    C. Nicolaides, B. Jha, L. Cueto-Felgueroso, R. Juanes, Water Resour. Res. 51, 2634 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    L. Chaudhari, N. Hadia, S. Mitra, M. Vinjamur, Energy Sources, Part A: Recovery Util. Environ. Eff. 33, 948 (2011)CrossRefGoogle Scholar
  3. 3.
    M.A. Celia, S. Bachu, J.M. Nordbotten, K.W. Bandilla, Water Resour. Res. 51, 6846 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    M.T. Elenius, S.E. Gasda, in Computational Methods in Geologic CO2 Sequestration, Adv. Water Resour. 62, Part C, 499 (2013)Google Scholar
  5. 5.
    K. Tang, K. Chau, C. Kan, J. Fan, Sci. Rep. 5, 9689 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    A. Attou, G. Ferschneider, Chem. Eng. Sci. 54, 5031 (1999)CrossRefGoogle Scholar
  7. 7.
    N.S.K. Gunda, M. Singh, L. Norman, K. Kaur, S.K. Mitra, Appl. Surf. Sci. 305, 522 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    R. Lucas, Colloid Polym. Sci. 23, 15 (1918)Google Scholar
  9. 9.
    E. Washburn, Phys. Rev. 17, 273 (1921)ADSCrossRefGoogle Scholar
  10. 10.
    D. Shou, L. Ye, J. Fan, Appl. Phys. Lett. 104, 231602 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    M. Kitron-Belinkov, A. Marmur, T. Trabold, G.V. Dadheech, Langmuir 23, 8406 (2007)CrossRefGoogle Scholar
  12. 12.
    G. Mason, N.R. Morrow, J. Colloid Interface Sci. 141, 262 (1991)CrossRefGoogle Scholar
  13. 13.
    M. Reyssat, L. Courbin, E. Reyssat, H. Stone, J. Fluid Mech. 615, 335 (2008)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    J. Gorce, I. Hewitt, D. Vella, Langmuir 32, 1560 (2016)CrossRefGoogle Scholar
  15. 15.
    M. Hultmark, J.M. Aristoff, H.A. Stone, J. Fluid Mech. 678, 600 (2011)CrossRefGoogle Scholar
  16. 16.
    A. Budaraju, J. Phirani, S. Kondaraju, S.S. Bahga, Langmuir 32, 10513 (2016)CrossRefGoogle Scholar
  17. 17.
    S. Chibbaro, Eur. Phys. J. E 27, 99 (2008)CrossRefGoogle Scholar
  18. 18.
    F. Diotallevi, L. Biferale, S. Chibbaro, G. Pontrelli, F. Toschi, S. Succi, Eur. Phys. J. ST 171, 237 (2009)CrossRefGoogle Scholar
  19. 19.
    J. Bear, Dynamics of Fluids in Porous Media, Vol. 1 (American Elsevier, New York, 1972)Google Scholar
  20. 20.
    M. Reyssat, L.Y. Sangne, E.A. Van Nierop, H.A. Stone, EPL 86, 56002 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    J. Bico, D. Qué, Europhys. Lett. 61, 348 (2003)ADSCrossRefGoogle Scholar
  22. 22.
    M. Dong, F. Dullien, J. Zhou, Trans. Porous Media 31, 213 (1998)CrossRefGoogle Scholar
  23. 23.
    D. Qué, Europhys. Lett. 39, 533 (1997)ADSCrossRefGoogle Scholar
  24. 24.
    S. Das, P.R. Waghmare, S.K. Mitra, Phys. Rev. E 86, 067301 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    S. Das, S.K. Mitra, Phys. Rev. E 87, 063005 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • S. Ashraf
    • 1
  • G. Visavale
    • 1
  • S. S. Bahga
    • 2
  • J. Phirani
    • 1
  1. 1.Department of Chemical EngineeringIndian Institute of Technology DelhiHauz Khas, New DelhiIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of Technology DelhiHauz Khas, New DelhiIndia

Personalised recommendations