Skip to main content
SpringerLink
Log in

Front roughening in three-dimensional imbibition

  • Solids and Liquids
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract.

We investigate the structure and dynamics of the interface between two immiscible liquids in a three-dimensional disordered porous medium. We apply a phase-field model that includes explicitly disorder and discuss both spontaneous and forced imbibition. The structure of the interface is dominated by a length scale ξ× which arises from liquid conservation. We further show that disorder in the capillary and permeability act on different length scales and give rise to different scalings and structures of the interface properties. We conclude with a range of applications.

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

  • M.I.J. van Dijke, K.S. Sorbie, J. Pet. Sci. Eng. 39, 201 (2003)

    Article  Google Scholar 

  • J. Rosinski, Am. Ink Maker 71, 40 (1993)

    Google Scholar 

  • J. Aspler, Nordic Pulp Paper Res. J. 1, 68 (1993)

    Google Scholar 

  • N. Poulin, P. Tanguy, J. Aspler, L. Larrondo, Can. J. Chem. Eng. 75, 949 (1997)

    Article  Google Scholar 

  • C.J. Ridgway, P.A.C. Gane, Nordic Pulp Paper Res. J. 17, 119 (2002)

    Google Scholar 

  • M.J. Blunt, M.D. Jackson, M. Piri, P.H. Valvatne, Adv. Water Resour. 25, 1069 (2002)

    Article  Google Scholar 

  • A. Leventis, D.A. Verganelakis, M.R. Halse, J.B. Webber, J.H. Strange, Transp. Porous Media 39, 143 (2000)

    Article  Google Scholar 

  • J.S. Ceballos-Ruano, T. Kupka, D.W. Nicoll, J.W. Benson, M.A. Ioannidis, C. Hansson, M.M. Pintar, J. Appl. Phys. 91, 6588 (2002)

    Article  ADS  Google Scholar 

  • N.M. Abboud, Transp. Porous Media 30, 199 (1998)

    Article  Google Scholar 

  • W. Hwang, S. Redner, Phys. Rev. E 63, 021508 (2001)

    Article  ADS  Google Scholar 

  • M. Alava, M. Dubé, M. Rost, Adv. Phys. 53, 83 (2004)

    Article  ADS  Google Scholar 

  • R. Lenormand, J. Phys. Cond. Mat. 2, SA79 (1990)

  • M. Sahimi, Rev. Mod. Phys. 65, 1393 (1993)

    Article  ADS  Google Scholar 

  • A.M. Tartakovsky, S.P. Neuman, R.J. Lenhard, Phys. Fluids 15, 3331 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  • D. Ronen, H. Scher, M.J. Blunt, Trans. Porous Media 28, 159 (1997)

    Article  Google Scholar 

  • R.G. Hughes, M.J. Blunt, Trans. Porous Media 40, 295 (2000)

    Article  Google Scholar 

  • E. Aker, K.J. Maloy, A. Hansen, Phys. Rev. E 61, 2936 (2000)

    Article  ADS  Google Scholar 

  • M Dubé, F. Mairesse, J.P. Boisvert, Y. Voisin, Submitted, IEEE Trans. Image Analysis (2005)

  • A.-L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)

  • M. Dubé, B. Chabot, C. Daneault, M. Alava, Pulp & Paper Canada 106, 24 (2005)

    Google Scholar 

  • H. Leschhorn, T. Nattermann, S. Stepanow, L.-H. Tang, Ann. Physik 6, 1 (1997)

    ADS  Google Scholar 

  • J.M. Schwarz, D.S. Fisher, Phys. Rev. E 67, 021603 (2003)

    Article  ADS  Google Scholar 

  • S.V. Buldyrev, S. Havlin, H.E. Stanley, Physical A 200, 200 (1993)

    Article  ADS  Google Scholar 

  • A. Rosso, W. Krauth, Phys. Rev. Lett. 87, 187002 (2001)

    Article  ADS  Google Scholar 

  • J. Bear, Y. Bachmat, Introduction to modeling of transport phenomena in porous media (Kluwer Academic, Dordrecht, 1991)

  • T.J. Senden, M.A. Knackstedt, M.B. Lyne, Nordic Pulp Paper Res. J. 15, 554 (2000)

    Google Scholar 

  • C.J. Ridgway, P.A.C. Gane, J. Schoelkopf, J. Coll. Int. Sci. 252, 373 (2002)

    Article  Google Scholar 

  • D.E. Eklund, P.J. Salminen, Tappi Journal 69, 116 (1986)

    Google Scholar 

  • L.A. Richard, Physics (N.Y.) 1, 318 (1931)

    Google Scholar 

  • J. Asikainen, S. Majaniemi, M. Dubé, J. Heinonen , T. Ala-Nissila, Eur. Phys. J. B 30, 253 (2002)

    Article  ADS  Google Scholar 

  • R. Chandler, J. Koplik, K. Lerman, J.F. Willemsen, J. Fluid. Mech. 119, 249 (1982)

    Article  MATH  ADS  Google Scholar 

  • C.-H. Lam, V.K. Horváth, Phys. Rev. Lett. 85, 1238 (2000)

    Article  ADS  Google Scholar 

  • M. Dubé, M. Rost, K.R. Elder, M. Alava, S. Majaniemi, T. Ala-Nissila, Phys. Rev. Lett. 83, 1628 (1999)

    Article  ADS  Google Scholar 

  • M. Dubé, M. Rost, M. Alava, Eur. Phys. J. B 15, 691 (2000)

    Article  ADS  Google Scholar 

  • M. Dubé, M. Rost, K.R. Elder, M. Alava, S. Majaniemi, T. Ala-Nissila, Eur. Phys. J. B 15, 701 (2000)

    Article  ADS  Google Scholar 

  • M. Dubé, S. Majaniemi, M. Rost, K.R. Elder, M. Alava, T. Ala-Nissila, Phys. Rev. E 64, 051605 (2001)

    Article  ADS  Google Scholar 

  • A. Hernández-Machado, J. Soriano, A.M. Lacasta, M.A. Rodríguez, L. Ramírez-Piscina, J. Ortín, Europhys. Lett. 55, 194 (2001)

    Article  ADS  Google Scholar 

  • I. Mitkov, D.M. Tartakovsky, C.L. Winter, Phys. Rev. E 58 R5245, (1998)

  • P. Papatzacos, Trans. Porous Media 49, 139 (2002)

    Article  MathSciNet  Google Scholar 

  • This compressibility arises from the finite curvature of the potential wells but only introduces a minor perturbation. On long time scales, the fluid is essentially incompressible, cf., the discussion above equation (4)

  • J. Soriano, J.J. Ramasco, M.A. Rodríguez, A. Hernández-Machado, J. Ortín, Phys. Rev. Lett. 89, 026102 (2002)

    Article  ADS  Google Scholar 

  • D. Jasnow, J. Viñals, Phys. of Fluids 7, 747 (1996)

    Google Scholar 

  • E. Pauné, J. Casademunt, Phys. Rev. Lett. 90, 144504 (2003)

    Article  ADS  Google Scholar 

  • D. Wilkinson, J.F. Willemsen, J. Phys. A: Math. Gen. 16, 3365 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  • E.W. Washburn, Phys. Rev. 17, 273 (1921)

    Article  ADS  Google Scholar 

  • M. Rost, L. Laurson, M. Dubé, M. Alava, Phys. Rev. Lett. 98, 054502 (2007)

    Article  ADS  Google Scholar 

  • T. Laurila, C. Tong, S. Majaniemi, I. Huopaniemi, T. Ala-Nissila, Eur. Phys. J. B 46, 553 (2005)

    Article  ADS  Google Scholar 

  • D. Wilkinson, Phys. Rev. A 34, 1380 (1986)

    Article  ADS  Google Scholar 

  • D. Geromichalos, F. Mugele, S. Herminghaus, Phys. Rev. Lett. 89, 104503 (2002)

    Article  ADS  Google Scholar 

  • J.-F. Gouyet, B. Sapoval, M. Rosso, Phys. Rev. B 37, 1832 (1988)

    Article  ADS  Google Scholar 

  • J. Soriano, A. Mercier, R. Planet, A. Hernández-Machado, M.A. Rodríguez, J. Ortín, Phys. Rev. Lett. 95, 104501 (2005)

    Article  ADS  Google Scholar 

  • See e.g., R. Kant, Phys. Rev. E 53, 5749 (1996). For a self-affine interface, the the roughness exponent, χ< 1, leads to w(L)/L →0 asymptotically at large distances. This implies that \({\cal C}(z) \sim e^{-z/w}\). The result equation (39) is for the special case of an interface with Gaussian fluctuations.

    Article  ADS  Google Scholar 

  • V. Vuorinen, HUT project report (2003)

  • J. Ketoja, K. Niskanen, in 12th Fundamental Research Symposium (Oxford, 2001)

Download references

Author information

Authors and Affiliations

  1. Centre de Recherche en Pâtes et Papiers, Université du Québec à Trois-Rivières, C.P. 500, Trois-Rivières Québec, G9A 5H7, Canada

    M. Dubé & C. Daneault

  2. Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, 02015, HUT, Finland

    V. Vuorinen & M. Alava

  3. Abteilung Theoretische Biologie, IZMB, Universität Bonn, Kirschallee 1, 53115, Bonn, Germany

    M. Rost

Authors
  1. M. Dubé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Daneault
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Vuorinen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Alava
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Rost
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Rost.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dubé, M., Daneault, C., Vuorinen, V. et al. Front roughening in three-dimensional imbibition. Eur. Phys. J. B 56, 15–26 (2007). https://doi.org/10.1140/epjb/e2007-00085-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2007-00085-7

PACS.

Search

Navigation