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Hydraulic permeability of ordered and disordered single-layer arrays of cylinders.

The hydraulic permeability of single-layer fibrous media is studied through two-dimensional (2D) and three-dimensional Navier-Stokes based flow simulations. As simple representations of such materials, one-dimensional arrays of parallel cylinders as well as two-dimensional arrays of perpendicularly crossing cylinders were used. The distance between the cylinders was either constant (ordered layers) or variable (disordered layers). For both 1D and 2D ordered layers, we propose a geometrical scaling rule for the hydraulic permeability as a function of cylinder radius and solid volume fraction (porosity), which is a modification of a scaling rule previously reported by Clague and co-workers. The proposed modification is based on theoretical considerations and leads to significantly improved correspondence with simulation results. The hydraulic permeability of unstructured layers is found to be higher than that of structured layers of equal porosity for both 1D and 2D arrays. We propose a single parameter that can be easily determined experimentally to characterize the degree of disorder, as well as a generally valid correction factor in the proposed geometrical scaling rule to account for the influence of disorder on the hydraulic permeability.