Fluid flow through three-dimensional fibrous porous media

A system of self-consistent equations for determining the hydrodynamic resistance of dilute fibrous porous media in the case of arbitrary low Reynolds numbers and arbitrary random packing of the fibers in the media is derived on the basis of a multiple-scattering hydrodynamic theory. The equations obtained are applied to the case of isotropic packing of the fibers and to the anisotropic case when all the fibers are orthogonal to the direction of fluid flow. Equations are derived and analyzed for the velocity correlation function in a random fibrous medium. The longitudinal and transverse diffusion coefficients of a passive impurity embedded in the fluid are calculated.