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Hydraulic Conductivity of Porous Media at Low Water Content

Dep. of Chemical Engineering and Materials Science, 421 Washington Ave. S.E, Univ. of Minnesota, Minneapolis, MN 55455

*Corresponding author.

ABSTRACT

Matric potential and hydraulic conductivity K at low water content often obey power laws in , but the exponents of these are largely empirical. Theories of fractal geometry and of thin-film physics provide a basis for the observed power-law behavior of and K. Specifically, they lead to ^–1/(3-D) and K ^{3/m(3 – D)}, where D is the Hausdorff dimension of the surface between the pore space and grains or matrix, and m is the exponent in the relation of disjoining pressure II and film thickness h, i.e., II h^–m. These power laws may increase the reliability of extrapolating measurements of and K at low . Using the data of Nimmo and Akstin (1988) to test our ideas, we found that, in the case of water in soils, m < 1 and, across length scales between 5 µm and 20 µm, 2.1 < D < 2.7. In the limit of smooth pore walls, D = 2. The measured hydraulic conductivities lie between upper and lower bounds of K() that we computed using three trial distributions of pore radius.

Received for publication April 27, 1989.