Hydraulic permeability of (un)bounded fibrous media using the lattice Boltzmann method

Several articles have been written regarding the hydraulic permeability of ordered and disordered fibrous media. Here, we explore wall effects on hydraulic permeabilities for ordered and disordered media using the lattice Boltzmann (LB) simulation method. Simulation results are found to be in excellent agreement with the semi analytic result of Sangani and Acrivos, and simulation results for disordered media are in good agreement with the results of Jackson and James and Higdon and Ford's fcc lattice. The macroscopic behavior, the hydraulic permeability, shows a distinct connection with the geometry of the system. This connection is explored and elucidated for ordered and disordered media. Finally, hydraulic permeabilities for bounded media at various wall separations are presented for both ordered and disordered media and results are compared with hydraulic permeabilities calculated for the unbounded media, and a phenomenological correlation is presented to facilitate rapid prediction of hydraulic permeabilities for both unbounded and bounded fibrous media.