Transport in Porous Media

, Volume 48, Issue 3, pp 315–330 | Cite as

Coriolis Effects on Filtration Law in Rotating Porous Media

  • Jean-Louis Auriault
  • Christian Geindreau
  • Pascale Royer


We investigate the filtration law of incompressible viscous Newtonian fluids in rigid non-inertial porous media, for example, rotating porous media. The filtration law is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For finite Ekman numbers the filtration law is shown to resemble a Darcy's law, but with a non-symmetric permeability tensor which depends on the angular velocity of the porous matrix. We obtain the filtration analog of the Hall effect. For large Ekman numbers the filtration law is a small correction to the classical Darcy's law. The corrector is antisymmetric. In this case we recover a structure of law which is similar to phenomenological laws introduced in the literature, but with a dissimilar effective coefficient.

rotating porous media filtration law Ekman homogenisation 


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  1. Arulanandan, K., Thompson, P. Y., Kutter, B. L., Meegoda, N. J., Muraleetharan, K. K. and Yogachandran, C.: 1988, Centrifuge modelling and transport processes for pollutants in soils, J. Geotech. Engng 114(2), 185–205.Google Scholar
  2. Auriault, J.-L.: 1991, Heterogeneous medium. Is an equivalent macroscopic description possible?, Int. J. Engng Sci. 29(7), 785–795.Google Scholar
  3. Auriault, J.-L., Strzelecki, T., Bauer, J. and He, S.: 1990, Porous deformable media saturated by a very compressible fluid: quasi-statics, Eur. J. Mech., A/Solids 9(4), 373–392.Google Scholar
  4. Auriault, J.-L., Geindreau, C. and Royer, P.: 2000, Filtration law in rotating porous media, C.R.A.S. II b 328, 779–784.Google Scholar
  5. Bear, J., Corapcioglu, M. Y. and Balakrishna, J.: 1984, Modeling of centrifugal filtration in unsaturated deformable porous media, Adv. Water Resour. 7, 150–167.Google Scholar
  6. Bensoussan, A., Lions, J.-L. and Papanicolaou, G.: 1978, Asymptotic Analysis for Periodic Structures, North Holland.Google Scholar
  7. Benton G. S. and Boyer D.: 1966, Flow through a rapidly rotating conduit of arbitrary cross-section, J. Fluid Mech. 26(1), 69–79.Google Scholar
  8. Chakrabarti A. and Gupta A. S.: 1981, Nonlinear thermohaline convection in a rotating porous medium, Mech. Res. Com. 8(1), 9–22.Google Scholar
  9. John, J.: 1970, Partial differential equations, in: É. Roubine (ed.), Mathematics Applied to Physics, Springer-Verlag, Berlin.Google Scholar
  10. Johnston J. P., Halleen R. M. and Lezius D. K.: 1972, Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow, J. Fluid Mech. 56(3), 533–557.Google Scholar
  11. Kou, S., Poirier, D. R. and Flemings, C.: 1978, Macrosegregation in rotated remelted ingots, Metall. Trans. B 9B, 711–719.Google Scholar
  12. Kvasha, V. B.: 1985, Multiple-spouted gas-fluidized beds and cyclic fluidization: operation and stability, in: J. F. Davidson, R. Cift and D. Harrison (eds.), Fluidization, 2nd edn., Academic Press, London, pp. 675–701.Google Scholar
  13. Liou, J. J. and Liaw, J. S.: 1987, Thermal convection in a porous medium subject to transient heating and rotation, Int. J. Heat Mass Trans. 30(1), 208–211.Google Scholar
  14. Hart J. E.: 1971, Instability and secondary motion in a rotating channel flow, J. Fluid Mech. 45(2),341–351.Google Scholar
  15. Lezius D. K. and Johnston J. P.: 1976, Roll-cell instabilities in rotating laminar and turbulent channel flow, J. Fluid Mech. 77(1), 153–175.Google Scholar
  16. Lord, A. E.: 1999, Capillary flow in geotechnical centrifuge, Geotech. Test. J. 22(4), 292–300.Google Scholar
  17. Mitchell, R. J.: 1994, Matrix suction and diffusive transport in centrifuge models, Can. Geotech. J. 31, 357–363.Google Scholar
  18. Palm E. and Tyvand P. A.: 1984, Thermal convection in a rotating porous layer, J. Appl. Math. Phys. 35, 122–123.Google Scholar
  19. Patil P. R. and Vaidyanathan G.: 1983, On setting up of convection currents in a rotating porous medium under the influence of variable viscosity, Int. J. Engng. Sci. 21(2), 123–130.Google Scholar
  20. Rudraiah N., Shivakumara I. S. and Friedrich R.: 1986, The effect of rotation on linear and non-linear double-diffusive convection in a sparsely packed, porous medium, Int. J. Heat Mass Trans. 29(9), 1301–1317.Google Scholar
  21. Sanchez-Palencia, E.: 1980, Non Homogeneous Media and Vibration Theory, Vol. 127, Springer, Lecture notes in Physics.Google Scholar
  22. Vadasz, P.: 1993, Fluid flow through heterogeneous porous media in a rotating square channel, Transport in Porous Media 12, 43–54.Google Scholar
  23. Vadasz, P.: 1997, Flow in rotating porous media, in: Prieur du Plessis (ed.), Fluid Transport in Porous Media, Computational Mechanics Publications, Southampton.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Jean-Louis Auriault
    • 1
  • Christian Geindreau
    • 1
  • Pascale Royer
    • 1
  1. 1.Laboratoire Sols Solides Structures (3S), UJF, INPG, CNRSDomaine UniversitaireGrenoble CedexFrance

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