Application of the Charge Regulation Model to Transport of Ions through Hydrophilic Membranes: One-Dimensional Transport Model for Narrow Pores (Nanofiltration)

The charge regulation concept is combined with the Navier-Stokes and Nernst-Planck equations to describe the ion retention of nanofiltration membranes consisting of narrow cylindrical pores. The charge regulation approach replaces the assumption of a constant charge or a constant potential at the membrane pore surface, and accounts for the influence of pH, salt concentration, and type of electrolyte on ion retention. In the current model, radial concentration and potential gradients are considered to be negligibly small (valid for narrow enough pores), resulting in a one-dimensional transport description. The model describes typical experimental data for nanofiltration membranes, such as the change of ion retention with pore radius, ion concentration, pH, and pressure both for monovalent and multivalent ions. For a constant solvent velocity, the model in some cases predicts an optimum pore size for retention. Nonequal retentions for anions and cations are predicted at low and high pH values, as well as a minimum solvent velocity for very low salt concentrations. For higher salt concentrations, and at a fixed pressure difference, an increase in solvent velocity with increasing ion concentrations is predicted, in agreement with other one-dimensional transport descriptions found in the literature, but in contrast to some experimental data

Electrolyte retention of supported bi-layered nanofiltration membranes

The electrolyte separation behaviour of a supported bi-layered ceramic membrane is investigated experimentally and the measured ion retentions are compared with the predictions of a site-binding transport model with no adjustable parameters. Due to the difference in iso-electric point between its two separating layers, the bi-layered system is expected to perform better over a large pH range compared with a membrane with only one type of selective layer. The separating layers in the membrane are a microporous silica and a mesoporous -alumina (pore sizes of 0.8 and 2 nm, respectively) and their retention is studied for a binary electrolyte solution of NaCl at 1 mol/m3 for pH values between 4 and 10. Because of its smaller pores and high charge, the silica layer mainly determines the membrane retention at neutral and alkaline pH, while the -alumina layer has a significant impact on the NaCl retention at 4 < pH< 5. The model predictions are in good agreement with the experimental data for Na+ at 4 < pH< 9 and for Cl− at the whole pH range. For a pH of 4, the predicted chloride retention is lower than the sodium retention while the experimental data show the opposite effect. © 2005 Elsevier B.V. All rights reserved

Electric Field Mediated Ion Transport Through Charged Mesoporous Membranes

The transport of ions from aqueous solutions through a stacked Au/alpha-alumina/gamma-alumina/Au membrane under the influence of a dc potential difference is reported. The membrane shows high cation permselectivity at ionic strengths of ~1 mM at pH 4.3-6.5, which is associated with a combination of anion adsorption and double-layer overlap inside the pores of the gamma-alumina layer. The cation flux can be controlled by ionic strength, dc potential difference and pH