Calculation of the hydrodynamic permeability of gels and gel-filled microporous membranes

A new approach to the calculation of gel hydrodynamic permeability is presented in which the gel is modeled as an assemblage of spheres whose radius is a function of the gel concentration. Scaling methods coupled with the electrostatic persistence length are used to estimate the correlation length in equivalent semidilute solutions. The correlation length is taken to be equal to the sphere diameter in an assemblage, and the hydrodynamic permeability of the assemblage is calculated using the Brinkman and Happel models. It is shown that the calculated permeabilities are fully in accord with experimental data reported in the literature for membranes with incorporated poly(acrylamide) gels, as well as data reported in this work for membranes containing charged gels composed of poly(4-vinyl-N-benzylpyridinium salts).