A numerical calculation of the hydraulic permeability of three-dimensional disordered fibrous media

Hydraulic permeabilities of polymeric membranes and gels are of interest both for calculating fluid flow rates and hindered diffusion coefficients. We have calculated hydraulic permeabilities for monomodal and bimodal, periodic and random fibrous media. Hydrodynamic interactions between fibers are calculated by applying a numerical version of slender body theory to a collection of fibers in a cubic cell many Brinkman screening lengths in dimension. Results for random media are obtained by averaging over many ensembles of fibers. To account for the surrounding medium, the line distribution of point forces along the fiber axes are replicated throughout space by using the Ewald summation technique. Results for periodic media agree with previous theoretical results up to a fiber volume fraction of 50% for parallel flow and 40% for transverse flow. Hydraulic permeabilities calculated for three-dimensional, disordered media with monomodal and bimodal distributions of fiber radius are compared with existing theories and with experimentally determined hydraulic permeabilities for a range of fiber volume fractions. Specific calculations are performed for agarose and collagen/proteoglycan gel systems, which are well described as bimodal fibrous media and are relevant to bioseparations and physiological systems, respectively.