In this study, the transverse permeability of fibrous porous media is studied both experimentally and theoretically. A scale analysis technique is employed for determining the transverse permeability of various fibrous matrices including square, staggered, and hexagonal arrangements of unidirectionally aligned fibers, as well as simple two-directional mats and simple cubic structures. In the present approach, the permeability is related to the porosity, fiber diameter, and tortuosity of the medium. In addition, the pressure drop in several samples of tube banks of different arrangements and metal foams are measured in the creeping flow regime. The pressure-drop results are then used to calculate the permeability of the samples. The developed compact relationships are successfully verified through comparison with these experimental results and the data reported by others. Our results suggest that fiber orientation has an important effect on the permeability; however, these effects are more pronounced in low porosities, i.e., ɛ<0.7.

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The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement.

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