A theoretical analysis of donnan dialysis across charged porous membranes

Abstract

A previously developed model [1] for the transport of ions in charged capillary tubes is used to determine the effect of membrane properties (average pore radius and surface charge density) and solution concentration on steady-state ion and solution fluxes in two types of Donnan dialysis separations. Specifically, the concentration of a dilute metal ion solution into an acid stripping solution by ion exchange across a cation exchange membrane and the removal of an acid contaminant from a metal ion solution using an anion exchange membrane are studied. The model is able to predict the changes in metal ion flux caused by changes in acid and metal ion concentrations in the strip and feed solutions in the Donnan dialysis experiments performed by Lake and Melsheimer [2]. These effects could not be explained by the mass-transfer resistance model used by Lake and Melsheimer [2] and by others [3,4] to describe ion transport across a charged membrane in Donnan dialysis separations. The time-dependent ion concentrations in well-stirred solutions undergoing Donnan dialysis are also modeled. The results are shown to match the experimental data of Ng and Snyder [4] when the boundary layer resistance are negligible and reasonable values for the membrane pore parameters are assumed.