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Hydraulic Conductivity of Porous Media at Low Water Content
Author(s) -
Toledo Pedro G.,
Novy Robert A.,
Davis H. Ted,
Scriven L. E.
Publication year - 1990
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1990.03615995005400030007x
Subject(s) - hydraulic conductivity , disjoining pressure , exponent , power law , fractal dimension , mathematics , thermodynamics , soil water , radius , porosity , conductivity , geometry , fractal , content (measure theory) , physics , materials science , mathematical analysis , soil science , geology , composite material , quantum mechanics , wetting , statistics , linguistics , philosophy , computer security , computer science
Abstract Matric potential ψ and hydraulic conductivity K at low water content θ often obey power laws in θ, 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 ψ and K . Specifically, they lead to ψ ∝ θ −1/(3‐ D ) and K ∝ θ 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 ψ and K at low θ. 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 (θ) that we computed using three trial distributions of pore radius.