Open AccessContinuum Percolation Theory for Saturation Dependence of Air Permeability
Author(s) -
Hunt A. G.
Publication year - 2005
Publication title -
vadose zone journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.036
H-Index - 81
ISSN - 1539-1663
DOI - 10.2136/vzj2005.0134a
Subject(s) - tortuosity , percolation threshold , percolation theory , hydraulic conductivity , saturation (graph theory) , porous medium , permeability (electromagnetism) , conductivity , air permeability specific surface , percolation (cognitive psychology) , materials science , porosity , thermodynamics , mechanics , physics , soil science , chemistry , electrical resistivity and conductivity , geology , mathematics , soil water , composite material , biochemistry , quantum mechanics , combinatorics , neuroscience , membrane , layer (electronics) , biology
Continuum percolation theory has recently been used to find the saturation, S , dependence of the hydraulic conductivity, K ( S ), of probabilistic fractal porous media. Analysis of K ( S ) in conjunction with solute diffusion revealed the presence of a critical volume fraction, θ t , for percolation in natural porous media. For moisture contents within a few percent of θ t , K ( S ) depends on the moisture content as a power of θ − θ t At higher moisture contents, K ( S ) is determined through critical path analysis, which uses continuum percolation theory to find the dependence of a bottleneck (flow‐limiting) pore radius on S The physics near θ t is thus dominated by connectivity and tortuosity issues, but far from θ t by the variations in the radius of a bottleneck pore. Here it is demonstrated that the bottleneck pore radius for air permeability, k a , does not change as a function of saturation. Using the same scaling for the air permeability in the vicinity of the percolation of the air phase as proposed for the hydraulic conductivity in the vicinity of the percolation of the water phase yields results for k a in accordance with experimental data.