Hydraulic permeability of fibrous porous media

In this study, the hydraulic permeability for viscous flow through fibrous media of high porosity is investigated theoretically. Fibrous media in one-dimensional (1D), two-dimensional (2D) or three-dimensional (3D) structure are approximated as consisting of repetitive unit cells based on Voronoi Tessellation approximation and volume averaging method. In the new model, the hydraulic permeability of fibrous media is described as a function of porosity and fiber radius as well as geometrical formation factors including the degree of randomness (viz. randomness of fiber distribution) and fiber orientation. In particular, the slip effect for flow through superfine fibrous media is analytically studied. The prediction of the new model for fibrous media with porosity greater than 0.7 is highly consistent with the analytical, experimental and numerical results found in the literature. It is further demonstrated that randomly packed fibrous media have larger permeability than regular ones, the hydraulic permeability of fibrous media increases with increasing of through-plane orientation, but is less dependent on in-plane fiber orientation, and the slip effect on the longitudinal hydraulic permeability is greater than the perpendicular one.