Estimation and influence of long range solute. Membrane interactions in ultrafiltration

Abstract

A new method of estimating the interaction energy between a spherical particle and the wall of a straight cylindrical pore is developed. Based on the method, the variations of the apolar (Lifshitz-van der Waals), electrostatic, and polar (acid-base) interactions between spherical particles and pore walls have been determined for different radial positions of the particle and particle to pore size ratios. Using the estimates of the total interaction comprising the above three components, the thermodynamic (equilibrium) and hydrodynamic parameters characterizing the transport of aqueous macromolecular solutions in membrane pores have been determined using the hydrodynamic approach. Estimates of the permeate flux and solute rejection are obtained by combining the transport model within the membrane pore with the film theory for transport in the boundary layer adjacent to the membrane. The results illustrate the influence of long-range interactions, especially the polar repulsion, on the transport and separation characteristics of membrane pores. Comparisons of the results with the hydrodynamic theory using hard-sphere interactions indicate that the long-range interactions are very important for ultrafiltration membranes with small pores (<100 nm). In the ultrafiltration of aqueous macromolecular solutions using hydrophilic membranes, the polar acid-base repulsion exerts the dominating influence on the distribution coefficient, osmotic reflection coefficient, intrinsic rejection, and the permeate flux.