Analytical determination of viscous permeability of fibrous porous media

In this study, the permeability of ordered fibrous media towards normal and parallel flow is determined analytically. In this approach, porous material is represented by a "unit cell" which is assumed to be repeated throughout the media. Several fiber arrangements including: touching and non-touching arrays are considered. Modeling ID touching fibers as a combination of Channel-like conduits, a compact relationship is proposed to predict permeability. Employing an integral technique and assuming a parabolic velocity profile within the unit cells, analytical relationships are developed for pressure drop for rectangular arrangements. The developed models are successfully compared with existing experimental data collected by others for square arrangement over a wide range of porosity. Due to the random nature of the porous micro structures, determination of exact permeability of real fibrous media is impossible. However, the analyses developed for ordered unit cells enable one to predict the trends observed in experimental data. Moreover, it is shown that the proposed normal flow permeability of square unit cell serves as a lower bound for the permeability of fibrous media. The effects of unit cell aspect ratio and fibers diameter on the permeability are also investigated. It is noted that with an increase in the aspect ratio the normal permeability decreases while, the parallel permeability remains constant. It is also shown that the permeability of fibrous media is related to the diameter of fibers squared.