Permeability of fluid flow through a periodic array of cylinders

The three-dimensional model of an incompressible Newtonian viscous fluid slowly flowing through a periodic array of cylinders is considered. We use homogenization to determine a system of equations that are then solved numerically to calculate the permeability. We determine the permeability as a function of the angle the cylinders make with the bottom surface. Numerical results are obtained using a Taylor–Hood mixed finite element method. The numerical approach is validated by comparing the results with computed results of Rocha and Cruz, for a simple cubic array of spheres, with good agreement. Results are presented for different cylindrical densities and angles. When the flow aligns and is perpendicular to an array of cylinders, the results are validated with experimental data. The spherical part of the permeability is compared with the Kozeny–Carman equation. Applications of these results include modeling fluid flow through biological hairlike structures such as animal hair, glass rods, fiberglass, filter pads, polymer gel, collagen, nylon fibers and natural rice field or trees.