Transport in Porous Media

, Volume 109, Issue 3, pp 711–726 | Cite as

Stokes Flow Through a Boolean Model of Spheres: Representative Volume Element

  • B. Abdallah
  • F. Willot
  • D. Jeulin


The Stokes flow is numerically computed in porous media based on 3D Boolean random sets of spheres. Two configurations are investigated in which the fluid flows inside the spheres or in the complementary set of the spheres. Full-field computations are carried out using the Fourier method of Wiegmann (2007). The latter is applied to large system sizes representative of the microstructure. The overall permeability of the two models as well as the representative volume element are estimated as a function of the pore volume fraction. We give numerical estimates for the asymptotic behavior of the permeability in the dilute limit for the solid phase, and close to the percolation threshold of the pores. FFT maps of the velocity field are presented, for increasing values of the pore volume fraction. The patterns of the local velocity field is analyzed using various morphological criteria. The tortuosity of the streamlines is found to be much higher than the geometrical tortuosity, for both models. The histograms of the velocity field are computed at increasing pore volume fraction. The covariance of orientation is used to characterize the spatial correlation of the velocity field.


Porous media Stokes flow FFT methods Representative volume element Tortuosity Streamlines 



The research leading to the results presented has received funding from the European Union’s Seventh Framework Programme (FP7/2007–2013) for the Fuel Cells and Hydrogen Joint Technology Initiative under Grant agreement 303429. The authors thank an anonymous referee for useful remarks.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Center for Mathematical Morphology, Mines ParisTechPSL Research UniversityFontainebleauFrance

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