The European Physical Journal B

, Volume 64, Issue 3–4, pp 433–436 | Cite as

Inertial capture in flow through porous media

  • J. S. AndradeJr.Email author
  • A. D. Araújo
  • T. F. Vasconcelos
  • H. J. Herrmann


We investigate through numerical calculation of non-Brownian particles transported by a fluid in a porous medium, the influence of geometry and inertial effects on the capture efficiency of the solid matrix. In the case of a periodic array of cylinders and under the action of gravity, our results reveal that δSt, where δ is the particle capture efficiency, and St is the Stokes number. In the absence of gravity, we observe a typical second order transition between non-trapping and trapping of particles that can be expressed as δ ∼ (StSt c ) α , with an exponent α ≈ 0.5, where St c is the critical Stokes number. We also perform simulations for flow through a random porous structure and confirm that its capture behavior is consistent with the simple periodic model.


47.56.+r Flows through porous media 47.55.Kf Particle-laden flows 05.70.Jk Critical point phenomena 83.80.Hj Suspensions, dispersions, pastes, slurries, colloids 


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  1. 1.
    J. Bear, Dynamics of Fluids in Porous Materials (Elsevier, New York, 1972)Google Scholar
  2. 2.
    F. A. Dullien, Porous Media — Fluid Transport and Pore Structure (Academic, New York, 1979)Google Scholar
  3. 3.
    M. Sahimi, Flow and Transport in Porous Media and Fractured Rock (VCH, Boston, 1995)zbMATHGoogle Scholar
  4. 4.
    D.L. Koch, R.J. Hill, Annu. Rev. Fluid Mech. 33, 619 (2001)CrossRefADSGoogle Scholar
  5. 5.
    C. Tien, Granular Filtration of Aerosols and Hydrosols (Butterworths, Boston, 1989)Google Scholar
  6. 6.
    C. Ghidaglia, L. de Arcangelis, J. Hinch, E. Guazzelli, Phys. Rev. E 53, R3028 (1996); C. Ghidaglia, L. de Arcangelis, J. Hinch, E. Guazzelli, Phys. Fluids 8, 6 (1996)CrossRefADSGoogle Scholar
  7. 7.
    J. Lee, J. Koplik, Phys. Fluids 13, 1076 (2001)CrossRefADSGoogle Scholar
  8. 8.
    H. Marshall, M. Sahraoui, M. Kaviany, Phys. Fluids 6, 507 (1993)CrossRefADSGoogle Scholar
  9. 9.
    L.M. Levin, Izdatel’stvo Academii Nauk SSSR (1961), Eng. Transl. Foreing Techn. Div. Doc. No. FTD-HT-23-1593-67; N.A. Fuchs, The Mechanics of Aerosols (Pergamon, New York, 1964); D.B. Ingham, L.T. Hildyard, M.L. Hildyard, J. Aerosol Sci. 21, 935 (1990)Google Scholar
  10. 10.
    S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2001)Google Scholar
  11. 11.
    A.D. Araujo, J.S. Andrade Jr, H.J. Herrmann, Phys. Rev. Lett. 97, 138001 (2006)CrossRefADSGoogle Scholar
  12. 12.
    S.V. Patankar, Numerical Heat Transfer and Fluid Flow (Hemisphere, Washington DC, 1980); the FLUENT (trademark of FLUENT Inc.) fluid dynamics analysis package has been used in this studyzbMATHGoogle Scholar
  13. 13.
    J.S. Andrade Jr, D.A. Street, T. Shinohara, Y. Shibusa, Y. Arai, Phys. Rev. E 51, 5725 (1995); H.E. Stanley, J.S. Andrade Jr, S. Havlin, H.A. Makse, B. Suki, Physica A 266, 5 (1999); J.S. Andrade Jr, U.M.S. Costa, M.P. Almeida, H.A. Makse, H.E. Stanley, Phys. Rev. Lett. 82, 5249 (1999)CrossRefADSGoogle Scholar
  14. 14.
    J.K. Comer, C. Kleinstreuer, C.S. Kim, J. Fluid Mech. 435, 55 (2001)zbMATHADSGoogle Scholar
  15. 15.
    S.A. Morsi, A.J. Alexander, J. Fluid Mech. 55, 193 (1972)zbMATHCrossRefADSGoogle Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  • J. S. AndradeJr.
    • 1
    Email author
  • A. D. Araújo
    • 1
  • T. F. Vasconcelos
    • 1
  • H. J. Herrmann
    • 1
  1. 1.Departamento de FísicaUniversidade Federal do CearáFortaleza, CearáBrazil

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