W. Richard Bowen

Characterisation of nanofiltration membranes for predictive purposes - use of salts, uncharged solutes and atomic force microscopy

Abstract An asymmetric nanofiltration membrane (Hoechst, PES5) has been characterised by three different techniques: modelling of the rejection of simple salts, modelling of the rejection of uncharged solutes and atomic force microscopy. Interpretation of experimental data for the rejection of three salts having common co-ion (LiCl, NaCl, KCl) with model calculations allows a characterisation of the membrane in terms of three parameters: an effective pore radius (rp), the ratio of effective thickness over porosity ( Δx A k ) and an effective charge density (X). Interpretation of experimental data with model calculations for uncharged solutes (Vitamin B12, raffinose, sucrose, glucose, glycerin) allows a characterisation in terms of rp and Δx A k . Atomic force microscopy (AFM) allows direct determination of surface pore radius rps and surface porosity Aks. The AFM images provide direct confirmation of the presence of discrete surface pores in such membranes. Further comparison of the characterisation obtained with salts and that obtained with uncharged solutes shows that it is better to describe the transport through such membranes as occurring through discrete pores rather than using an homogenous description of the membrane structure. It is also shown that the complexity of a “space-charge” description of the electric field distribution in the nanometre dimension pores of such membranes is not warranted. Direct experimental evidence of the charging mechanism of the membranes is provided. Overall characterisation parameters suitable for predictive purposes are suggested.

Characterisation and prediction of separation performance of nanofiltration membranes

Abstract The rejection of single electrolytes at six nanofiltration membranes has been experimentally studied. The membranes were chosen to cover the range from ultrafiltration to reverse osmosis and to represent a diversity of polymers used for membrane fabrication. Such experimental data has been interpreted using a model based on the extended Nernst-Planck equation. The model accounts for the hindered nature of transport in the membranes. Such an interpretation allows a characterisation of the membranes in terms of two parameters, an effective membrane thickness and an effective membrane charge density. The latter may be related to the solution ionic content by means of an isotherm. The method presented also allows an estimation of the effective pore size of the membrane. A knowledge of the effective membrane thickness, effective charge density and effective pore size allows use of the model to predict the separation of mixtures of electrolytes at a membrane. Very good agreement between such a prediction and experimental data has been obtained.

Modelling the performance of membrane nanofiltration—critical assessment and model development

Abstract A critical assessment of previous theoretical descriptions of membrane nanofiltration shows that the good agreement with experimental data is due to the use of the ratio of effective membrane thickness to membrane porosity as an arbitrary fitting parameter. A more rigorous analysis shows that rejection is independent of membrane thickness. A model allowing calculation of uncharged solute rejection on the basis of a single membrane parameter (pore radius) is developed. The theoretical description is based on a hydrodynamic model of hindered solute transport in pores. The dependence of solute chemical potential on pressure is included, although its effect is shown to be small. A variation of solvent viscosity with pore radius is also included. For pores of a single size, such variation has no effect on rejection, though it will become important for overall membrane rejection if a pore size distribution is included. The good agreement between this model and experimental data confirms that uncharged solute rejection in nanofiltration membranes may be well-described by such a continuum model. A two-parameter model (pore radius and membrane charge) for electrolyte rejection has been developed that includes dielectric exclusion in the form of an energy barrier to ion partitioning into the pores. Reassessment of the pore dielectric constant using NaCl rejection at the isoelectric point of a Desal-DK membrane resulted in significantly better agreement with experimental rejection data than use of the high frequency solvent dielectric constant for an oriented layer of water molecules at the pore walls. The predicted values of effective membrane charge density were not only significantly reduced in magnitude, and hence more realistic, than those from previous models, but their variation with concentration for divalent salts was in better agreement with physical models of ion adsorption. The theoretical descriptions of the present paper are developed more rigorously than those previously published. Their overall agreement with experimental data is good and the resulting membrane parameters are likely to be more closely related to physical membrane properties than those obtained from previous models. The descriptions are useful for membrane process assessment and prediction. They also provide a sound basis for further developments.

Theoretical descriptions of membrane filtration of colloids and fine particles: An assessment and review

Abstract Membrane separation technology is a novel and highly innovative process engineering operation. Membrane processes exist for most of the fluid separations encountered in industry. The most widely used are membrane ultrafiltration and microfiltration, pressure driven processes which are capable of separating particles in the approximate size ranges of 1 to 100 nm and 0.1 to 10 μm, respectively. The design of membrane separation processes, like all other processes, requires quantitative expressions relating material properties to separation performance. The factors controlling the performance of ultra- and microfiltration are extensively reviewed. There have been a number of seminal approaches in this field. Most have been based on the rate limiting effects of the concentration polarisation of the separated colloids at the membrane surface. Various rigorous, empirical and intuitive models exist, which have been critically assessed in terms of their predictive capability and applicability. The decision as to which of the membrane filtration models is the most correct in predicting permeation rates is a matter of difficulty and appears to depend on the nature of the dispersion to separated. Recommendations are made as to which of the existing models can be most appropriately applied to different types of dispersions.

Modelling the retention of ionic components for different nanofiltration membranes

Retention measurements with salt solutions of NaCl, Na2SO4, MgCl2, MgSO4 and LaCl3 were carried out for four commercial nanofiltration membranes. The retention of ionic components was analyzed by the Donnan-steric partitioning pore model (DSPM), that describes the solute transport through a membrane using the extended Nernst–Planck equation. The analysis made it possible to evaluate the membrane charge density, which showed that the charge density is not constant but depends very much on the salt and its concentration; this phenomenon was found for all membranes and is attributed to ion adsorption on the membrane material. For magnesium and lanthanum salts this could lead to a change in the sign of the membrane charge from a negative to a positive value. Theoretical calculations strengthened this finding.

Dynamic ultrafiltration model for charged colloidal dispersions: A Wigner-Seitz cell approach

A rigorous, dynamic mathematical model for predicting the rate of ultrafiltration of charged colloidal dispersions is developed. The model is based on sophisticated descriptions of the particle-particle interactions within filter cakes which are responsible for controlling permeation rates. Electrostatic (double layer) interactions are accounted for by means of a Wigner-Seitz cell approach, including a numerical solution of the non-linear Poisson-Boltzmann equation, which is known to give an excellent description of the configurational electrostatic interaction energy of particle assemblages. London-van der Waals forces are calculated using a computationally efficient means of approximating screened, retarded Lifshitz-Hamaker constants. Hydration forces are included by utilising mathematical expressions derived from the latest results obtained with surface-forces apparatus. Configurational entropy effects are calculated using an equation of state giving excellent agreement with molecular dynamic data. Electroviscous effects are also accounted for. These descriptions of particle-particle interactions in assemblages are used to develop an a priori model, with no adjustable parameters, that allows quantitative prediction of the rate of filtration of charged colloidal dispersions as a function of zeta-potential, particle composition (through the Hamaker constant), ionic strength, applied pressure, particle radius and membrane resistance. This is a dynamic model which takes into account the variation of local specific cake resistance as a function of both position in the cake and time. The predictions of the model are systematically investigated, showing the great importance of taking particle-particle interactions into account for ultrafiltration. A comparison with experimental filtration data for colloidal silica shows that the model is in excellent agreement with such data.

Modelling of membrane nanofiltration—pore size distribution effects ☆

Abstract The effects of log-normal pore size distributions on the rejection of uncharged solutes and NaCl at hypothetical nanofiltration membranes have been assessed theoretically. The importance of pore radius-dependent properties such as solvent viscosity and dielectric constant is increased by the introduction of a pore size distribution in calculations. However, the effect of porewise variation in viscosity is less apparent when considered at a defined applied pressure rather than at a defined flux, showing a further advantage of basing theoretical analysis of nanofiltration in terms of applied pressure. Truncated pore size distributions gave better agreement than full distributions with experimental rejection data for a Desal-DK nanofiltration membrane. Such truncation is in agreement with the findings of atomic force microscopy (AFM). Analysis of uncharged solute rejection data alone could not give useful information about membrane pore size distribution. Neither could such a distribution be obtained quantitatively directly from AFM images. However, use of the shape of the distribution obtained by AFM in conjunction with experimental rejection data for an uncharged solute allows calculation of corrected distributions. Importantly, incorporation of such a corrected pore size distribution in calculations of NaCl rejection gave better agreement with experimental data, compared to calculations assuming uniform pores, at high pressure, the region of industrial interest.

Analysis of the Salt Retention of Nanofiltration Membranes Using the Donnan–Steric Partitioning Pore Model

The performance of four commercial nanofiltration membranes was analyzed by the Donnan–steric partitioning pore model (DSPM) that describes solute transport through a membrane using the extended Nernst-Planck equation. Retention measurements were carried out as a function of the permeate flux for uncharged solutes, which allowed characterization of the membranes in terms of an effective membrane pore radius and the ratio of an effective membrane thickness to the porosity. Retention measurements with single salt solutions of NaCl, Na2SO4, MgCl2, and MgSO4 clearly showed the effect of ion concentration and ion valence on the retention. The DSPM model was used to evaluate the effective membrane charge density by analyzing the retention of single salt solutions. The analysis showed that the charge density is not constant but depends very much on the salt and its concentration. This is attributed to ion adsorption on the membrane material. For magnesium salts this could lead to a positive membrane charge. This...

Atomic force microscope studies of membranes: Surface pore structures of Cyclopore and Anopore membranes

Non-contact atomic force microscopy has been used to investigate the surface pore structure of Cyclopore and Anopore microfiltration membranes in air. Three Cyclopore membranes and three Anopore membranes of different pore sizes were studied. Excellent high resolution images were obtained. Analysis of the images gave quantitative information on the surface pore structure, in particular the pore size distribution. Non-contact AFM is an excellent means of obtaining such information for microfiltration membranes.

Atomic force microscopy studies of nanofiltration membranes: surface morphology, pore size distribution and adhesion

Abstract Atomic force microscopy has been used to quantify surface morphology, pore size distributions and particle adhesion for three nanofiltration membranes. It was found that the mean pore diameters were ∼ 1 nm and that the relative sizes corresponded to measured separation performance. Adhesion of polystyrene particles was greater than that of silica particles, due partly to greater electrostatic double-layer repulsion between the negatively charged membranes and silica, and partly to short-range repulsive interactions associated with the silica surface. It is likely that short-range repulsive interactions are also responsible for the low adhesion of the negatively charged silica particles even at the membrane which was positively charged.