Darcy Permeability of Agarose-Glycosaminoglycan Gels Analyzed Using Fiber-Mixture and Donnan Models

Agarose-glycosaminoglycan (GAG) membranes were synthesized to provide a model system in which the factors controlling the Darcy (or hydraulic) permeability could be assessed in composite gels of biological relevance. The membranes contained a GAG (chondroitin sulfate) that was covalently bound to agarose via terminal amine groups, and the variables examined were GAG concentration and solution ionic strength. The addition of even small amounts of GAG (0.4 vol/vol %) resulted in a twofold reduction in the Darcy permeability of 3 vol/vol % agarose gels. Electrokinetic coupling, caused by the negative charge of the GAG, resulted in an additional twofold reduction in the open-circuit permeability when the ionic strength was decreased from 1 M to 0.01 M. A microstructural hydrodynamic model was developed, based on a mixture of neutral, coarse fibers (agarose fibrils), and fine, charged fibers (GAG chains). Heterogeneity within agarose gels was modeled by assuming that fiber-rich, spherical inclusions were distributed throughout a fiber-poor matrix. That model accurately predicted the Darcy permeability when the ionic strength was high enough to suppress the effects of charge, but underestimated the influence of ionic strength. A more macroscopic approach, based on Donnan equilibria, better captured the reductions in Darcy permeability caused by GAG charge.