AIChE Journal, Vol.54, No.1, 32-41, 2008
"Mixing Rules" for estimating the hydraulic permeability of fiber mixtures
While theoretical results for the hydraulic permeability of fibrous media are typically based on a single type of fiber in an ordered array, many synthetic or biological materials are composed of fibers which differ in size, charge, orientation, or other characteristics. It is desirable to be able to estimate the permeability of such a mixture from its composition and the properties of the individual fiber types. Toward that end, we compared four "mixing rules" proposed in the literature, each based on differing approximations of the hydrodynamic interactions between multiple fiber types. To provide data for charged fibers, the open-circuit hydraulic permeabilities of periodic arrays of fibers with different surface charge densities and/or radii were computed using finite element methods. Based on these data for charged fibers, as well as published results for arrays of uncharged fibers of differing radii and/or orientation, we compared the four mixing rules for 64 cases. In some situations there were several-fold differences among the predicted hydraulic permeabilities. Nonetheless, a volume-weighted averaging of the resistivities of individual fiber types was found to be reasonably reliable, giving an overall root-mean-square error of 24%. This mixing rule was equally applicable to systems containing charged or neutral fibers. (C) 2007 American Institute of Chemical Engineers.