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The effect of weak inertia on flow through a porous medium. (English) Zbl 0718.76099

Summary: Using the theory of homogenization we examine the correction to Darcy’s law due to weak convective inertia of the pore fluid. General formulae are derived for all constitutive coefficients that can be calculated by numerical solution of certain canonical cell problems. For isotropic and homogeneous media the correction term is found to be cubic in the seepage velocity, hence remains small even for Reynolds numbers which are not very small. This implies that inertia, if it is weak, is of greater importance locally than globally. Existing empirical knowledge is qualitatively consistent with our conclusion since the linear law of Darcy is often accurate for moderate flow rates.

MSC:

76S05 Flows in porous media; filtration; seepage
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[1] DOI: 10.1121/1.391962 · Zbl 0568.73014
[2] Auriault, J. Méc. 16 pp 575– (1977)
[3] DOI: 10.1016/0020-7225(80)90025-7 · Zbl 0435.76072
[4] Adler, Physico-chem. Hydrodyn. 5 pp 287– (1984)
[5] DOI: 10.1017/S0022112082000627 · Zbl 0515.76039
[6] Adler, Physico-chem. Hydrodyn. 5 pp 269– (1984)
[7] Forchheimer, Z. Ver. Deutsch. Ing. 45 pp 1782– (1901)
[8] Ene, J. Méc. 14 pp 73– (1975)
[9] DOI: 10.1007/BF01036526
[10] DOI: 10.1121/1.386945 · Zbl 0519.73038
[11] Brenner, Phil. Trans. R. Soc. Lond. 307 pp 149– (1982)
[12] Brenner, Phil. Trans. R. Soc. Lond. 297 pp 81– (1980)
[13] DOI: 10.1016/0009-2509(64)85051-X
[14] DOI: 10.1016/0020-7225(74)90062-7 · Zbl 0275.76032
[15] Rose, Proc. Inst. Mech. Kngrs 153 pp 154– (1945)
[16] DOI: 10.1002/aic.690190111
[17] Mei, Proc. R. Soc. Lond. 426 pp 391– (1989)
[18] McCorquodale, J. Hydraulic Res. 2 pp 123– (1978)
[19] DOI: 10.1016/0020-7225(79)90022-3 · Zbl 0409.76078
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