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• W1966137892 abstract "By starting from the linearized Navier-Stokes equation for the fluid and the elastic wave equation for the solid frame of a porous medium, the first-principles definition of the frequency-dependent permeability ensuremath{kappa}(ensuremath{omega}) and the recipe for its calculation are derived through the application of the homogenization procedure. It is shown systematically that, in the limit of wavelength much larger than the typical pore size, the fluid may be regarded as incompressible in the permeability calculation, and the solid-frame displacement acts as an additional pressure source term for the fluid flow. The physics underlying the generic asymptotic frequency dependence of ensuremath{kappa}(ensuremath{omega}) is introduced through its analytic solution in the case of a cylindrical tube. To calculate ensuremath{kappa}(ensuremath{omega}) for periodic porous media models, we have formulated a finite-element approach for the numerical solution of the incompressible fluid equations at low and intermediate frequencies and of the Laplace equation at high frequencies. The numerical results for the sinusoidally modulated tube, the fused-spherical-bead lattice, and the fused-diamond lattice indicate a large range of values for the static permeability ${ensuremath{kappa}}_{0}$ as well as the other asymptotic parameters such as the tortuosity ensuremath{alpha} and the surface length parameter ensuremath{Lambda} as defined by Johnson et al. However, despite their variability, almost all the numerical data on periodic models are shown to satisfy the approximate scaling relation ensuremath{kappa}(ensuremath{omega})ensuremath{simeq}${ensuremath{kappa}}_{0}$f(ensuremath{omega}/${ensuremath{omega}}_{0}$), where ${ensuremath{omega}}_{0}$ is a characteristic frequency particular to the medium, and f is a universal function independent of microstructures. We advance arguments that delineate the physical reason for this scaling behavior as well as the condition for its validity. The scaling prediction is then generalized to the case of random porous media through both numerical simulations and the critical-path argument. Our theory gives a simple explanation to the observed correlations in sedimentary rocks, and the scaling prediction is supported by experimental ensuremath{kappa}(ensuremath{omega}) measurements on fused glass beads and crushed-glass samples." @default.
• W1966137892 created "2016-06-24" @default.
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• W1966137892 date "1989-06-01" @default.
• W1966137892 modified "2023-10-18" @default.
• W1966137892 title "First-principles calculations of dynamic permeability in porous media" @default.
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• W1966137892 doi "https://doi.org/10.1103/physrevb.39.12027" @default.
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