Effects of charge on osmotic reflection coefficients of macromolecules in porous membranes

A computational model was developed to predict the effects of solute and pore charge on the osmotic reflection coefficients (sigma(o)) of spherical macromolecules in cylindrical pores. Results were obtained for particles and pores of like charge and fixed surface charge densities, using a theory that combined low Reynolds number hydrodynamics with a continuum, point-charge description of the electrical double layers. In this formulation steric and/or electrostatic exclusion of macromolecules from the vicinity of the pore wall creates radial variations in osmotic pressure. These, in turn, lead to the axial pressure gradient that drives the osmotic flow. Due to the stronger exclusion that results from repulsive electrostatic interactions, sigma(o) with charge effects always exceeded that for an uncharged system with the same solute and pore size. The effects of charge stemmed almost entirely from particle positions within a pore being energetically unfavorable. It was found that the required potential energy could be computed with sufficient accuracy using the linearized Poisson-Boltzmann equation, high charge densities notwithstanding. In principle, another factor that might influence sigma(o) in charged pores is the electrical body force due to the streaming potential. However, the streaming potential was shown to have little effect on sigma(o), even when it markedly reduced the apparent hydraulic permeability.