Permeability of three-dimensional models of fibrous porous media

Viscous flow through three-dimensional models of fibrous porous media is analysed. The periodic models are based on ordered networks of cylindrical fibres on regular cubic lattices. Numerical solutions are obtained using the spectral boundary element method introduced by Muldowney & Higdon (1995). Results are presented for solid volume fractions ranging from extreme dilution to near the maximum volume fraction for permeable media. Theoretical estimates are derived using slender-body theory and lubrication approximations in the appropriate asymptotic regimes. Comparisons are made with model predictions based on properties of two-dimensional media (Jackson & James 1986), and with results for disordered dispersions of prolate spheroids (Claeys & Brady 1993b).