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Transport in Porous Media

, Volume 26, Issue 1, pp 89–98 | Cite as

Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore

  • Peter K. Kitanidis
  • Bruce B. Dykaar
Article

Abstract

This article presents a series solution to the velocity in a two-dimensional long sinusoidal channel. The approach is based on a stream function formulation of the Stokes problem and a series expansion in terms of the width to the length ratio, which is considered small. Results show how immobile zones may appear and even flow separation and nonturbulent eddies, even in the absence of prima facie dead-end pores. It is shown that the flow tends to concentrate in strips connecting pore throats.

Stokes flow pore-scale hydrodynamics analytical solution multiple-scales method stream function biharmonic equation periodic flow. 

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References

  1. Bear, J.: 1972, Dynamics of Fluids in Porous Media, American Elsevier, New York.Google Scholar
  2. Brenner, H., and Edwards, D. A.: 1993, Macrotransport Processes, Butterworth-Heinemann, Boston.Google Scholar
  3. Chen, B., Cunningham, A., Ewing, R., Peralta, R. and Visser, E.: 1994, Two-dimensional modeling of microscale transport and biotransformation in porous media, Numer. Methods Partial Differential Equations 10, 65–83.Google Scholar
  4. Hasegawa, E. and Izuchi, H.: 1983, On steady flow through a channel consisting of an uneven wall and a plane wall. Part 1. Case of no relative motion in two walls, Bull. JSME 26(214), 514–520.Google Scholar
  5. Dykaar, B. B.: 1994, Macroflow and macrotransport in heterogeneous porous media, PhD Thesis, Stanford Univ. Civ. Eng.Google Scholar
  6. Dykaar, B. B. and Kitanidis, P. K.: 1996, Macrotransport of a biologically reacting solute through porous media, Water Resour. Res. 32(2), 307–320.Google Scholar
  7. Edwards, D.A., Shapiro, M., Bar-Yoseph, P. and Shapira, M.: 1990, The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders, Phys. Fluids A 2(1), 45–55.Google Scholar
  8. Edwards, R. A., Shapiro, M., Brenner, H. and Shapira, M.: 1991, Dispersion of inert solute in spatially periodic two-dimensional model porous media, Transport in Porous Media 6, 337–358.Google Scholar
  9. Freeze, R. A. and Cherry, J. A.: 1979, Groundwater, Prentice-Hall, New York.Google Scholar
  10. Gale, J. E., Rouleau, A. and Atkinson, L. C.: 1985, Hydraulic properties of fractures, in Memoires. Hydrogeology of Rocks of Low Permeability, International Association of Hydrogeologists, Tucson, AZ, pp. 1-11.Google Scholar
  11. Happel, J. and Brenner, H.: 1983, Low-Reynolds Number Hydrodynamics, Kluwer, Boston.Google Scholar
  12. Hinch, E. J.: 1991, Perturbation Methods, Cambridge Univ. Press, Cambridge.Google Scholar
  13. Hull, L. C., Miller, J. D. and Clemo, T.M.: 1987, Laboratory and simulation studies of solute transport in fracture networks, Water Resour. Res. 23(8), 1505–1513.Google Scholar
  14. Kundu, P. K.: 1990, Fluid Mechanics, Academic Press, San Diego.Google Scholar
  15. Pozrikidis, C.: 1987, Creeping flow in two-dimensional channels, J. Fluid Mech. 180, 495–514.Google Scholar
  16. Pozrikidis, C.: 1992, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge Univ. Press.Google Scholar
  17. Raven, K. G., Novakowski, K. S. and Lapcevic, P. A.: 1998, Interpretation of field tracer tests of a single fracture using a transient solute storage model, Water Resour. Res. 24(12), 2019–2032.Google Scholar
  18. Zimmerman, R. W., Kumar, S. and Bodvarsson, G. S.: 1991, Lubrication theory analysis of the permeability of rough-walled fractures, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 28(4), 325–331.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Peter K. Kitanidis
    • 1
  • Bruce B. Dykaar
    • 1
  1. 1.Stanford UniversityStanfordU.S.A

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