Theory of pressure-driven transport of neutral solutes and ions in porous ceramic nanofiltration membranes

Hindered transport theory and homogeneous electro-transport theory are used to calculate the limiting, high volume flux, rejection of, respectively, neutral solutes and binary electrolytes by granular porous nanofiltration membranes. For ceramic membranes prepared from metal oxides it is proposed that the membrane structural and charge parameters entering into the theory, namely the effective pore size and membrane charge density, can be estimated from independent measurements: the pore radius from the measured hydraulic radius using a model of sintered granular membranes and the effective membrane charge density from the hydraulic radius and the electrophoretic mobility measurements on the ceramic powder used to prepare the membrane. The electro-transport theory adopted here is valid when the membrane surface charge density is low enough and the pore radius is small enough for there to be strong electrical double layer overlap in the pores. Within this approximation the filtration streaming potential is also derived for binary electrolytes.     

Nanofiltration membranes synthesized from hyperbranched polyethyleneimine

Four nanofiltration membranes, two negatively and two positively charged, were fabricated by interfacial polymerization. Three different amines, ethylenediamine (EDA), diethylenetriamine (DETA), and hyperbranched polyethyleneimine (PEI) were selected to react with two acyl chlorides, trimesoyl chloride (TMC) and terephthaloyl chloride (TPC). The two membranes containing hyperbranched PEI, PEI/TPC and PEI/TMC, are positively charged at the operational pH. But the other two membranes, EDA/TMC and DETA/TMC, are negatively charged. It is found that the two PEI membranes own special rejection characters during nanofiltration. The PEI/TPC membrane has a similar pore size to the EDA/TMC membrane but owns simultaneously the higher salt rejection and permeation flux. The PEI/TMC has a pore size as large as 1.5 nm and still has a higher NaCl rejection than the EDA/TMC membrane of which the pore size as small as 0.43 nm. We consider that the special rejection characters are derived from the special structure of PEI. The hyperbranched structure allows some of the charged amine groups drifting inside the pores and interacting with the ions in the pathway. The drifting amines increase salt rejection but have little effect on water permeation. It implies that a high flux and high rejection membrane for desalting can be obtained by attaching freely rotating charged groups.     

Effect of the Univalent Cation Adsorption on the Nanofiltration Membrane Selectivity

The selective, filtration, and electrokinetic properties of an OPMN-KMZ nanofiltration membrane are studied with respect to the aqueous solutions of the chlorides of alkali metals and ammonium within a concentration range from 10^–4 to 10^–1 mol/l. The dependences of the charge of the membrane pore surface and the rejection of cations of centinormal solutions of the aforementioned salts and protons on pH are obtained. The membrane isoelectric points corresponding to the centinormal solution of each salt are determined. The minima of the membrane selectivity with respect to the corresponding cations of salts are revealed in the region of isoelectric points. It is shown that, for univalent cations in the regime of convective diffusion, the coefficient of electrolyte rejection by the membrane correlates with the adsorption potential of cations (counterions) at the pore surface of a selective layer.     

Analysis of the pressure-induced potential arising through composite membranes with selective surface layers

When a pressure gradient is applied through a charged selective membrane, the transmembrane electrical potential difference, called the filtration potential, results from both the applied pressure and induced concentration difference across the membrane. In this work we investigate the electrokinetic properties relative to both active and support layers of a composite ceramic membrane close to the nanofiltration range. First, the volume charge density of the active layer is obtained by fitting a transport model to experimental rejection rates (which are controlled by the active layer only). Next, the value of the volume charge density is used to compute the theoretical filtration potential through the active layer. For sufficiently high permeate volume fluxes, the concentration difference across the active layer becomes constant, which allows assessing the membrane potential of the active layer. Experimental measurements of the overall filtration potential arising through the whole membrane are performed. The contribution of the support layer to this overall filtration potential is put in evidence. That implies that the membrane potential of the active layer cannot be deduced directly from the overall filtration potential measurements. Finally, the contribution of the support layer is singled out by subtracting the theoretical filtration potential of the active layer from the experimental filtration potential measured across the whole membrane (i.e., support + active layers). The amphoteric behavior of both layers is put in evidence, which is confirmed by electrophoretic measurements carried out with the powdered support layer and by recently reported tangential streaming potential measurements.     

Flux enhancement during Dean vortex tubular membrane nanofiltration: 13. Effects of concentration and solute type

Controlled centrifugal instabilities (called Dean vortices) resulting from sufficient flow in composite polyamide–poly(ether sulfone) helical membrane tubes have been used to reduce concentration polarization during nanofiltration. These vortices enhance back-migration through convective flow away from the membrane–solution interface and increased shear at the membrane–solution interface and allow for increased membrane permeation rates. As a result, solute concentrations at the membrane–solution interface and resulting osmotic-driven back flow are reduced.The performance of two sets of modules (designated Set II and Set III), each set containing a prototype vortex generating helical tubular nanofiltration (NF) element and a conventional linear element was evaluated. Nanofiltration of aqueous solutions of inorganic salts (including KCl, K₂SO₄ and K₃PO₄) and amino acids of similar molecular weight (including glutamic acid, glutamine and lysine) was performed with Set II. These experiments, designed to evaluate the effects of solute type, were conducted at the same energy consumption and transmembrane pressures. Both membrane swelling and charge effects were evident as a function of varying the pH during membrane filtration of both inorganic salts and amino acids. Both flux and rejection were higher for the helical module than the linear module during amino acid nanofiltration.A new modified phenomenological model was shown to be effective for predictive purposes for cases of responsive concentration polarization. Its applicability is validated by performing nanofiltration of aqueous MgSO₄ solutions with a new set of modules designated as Set III. Modules of Set III contained dissimilar helical and linear elements. The model was then tested against the results obtained previously.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Caractérisation des propriétés électriques des parois de pores d’une membrane

The characterisation of the surface electrical properties of membrane materials is critical for understanding and predicting the filtration performances of membranes. In this paper, four simple experimental methods – streaming potential, electro-osmosis, pore conductivity and membrane potential –, allowing the characterisation of the charge state of membrane pore walls are presented. The four experimental parameters provide information about the sign of the electrical net charge. Examples illustrating the influence of the pH, electrolyte concentration and nature on the four experimental parameters are given. The zeta potential can be then deduced from these measurements by means of a model.     

The effect of gel layer thickness on the salt rejection performance of polyelectrolyte gel-filled nanofiltration membranes

The effect of gel layer thickness on salt separation of positively charged pore-filled nanofiltration membranes has been examined both theoretically and experimentally. The extended Nernst-Planck (ENP) equation coupled with the Teorell-Meyer-Sievers (TMS) model were used to calculate the pressure-driven sodium chloride rejections for membranes having gel densities in the range typically used in nanofiltration applications. It was found that salt rejection was dependent on membrane (gel-layer) thickness with salt rejections increasing rapidly with thickness up to 50–75 μm. Further increases in thickness beyond this point had a much smaller effect on salt rejection. The theoretical predictions were examined experimentally by preparing a series of membranes with cross-linked poly(3-acrylamidopropyl)-trimethylammonium chloride (PAPTAC) gels with varying densities within the pores of a thin microporous polyethylene (PE) support. The membranes were characterized by their polymer volume fractions (gel concentration), thicknesses and effective charge densities. The effect of membrane thickness was examined by using single and stacks of two membranes. The pure water fluxes and salt rejections of the membranes and membrane stacks were determined in the pressure range 50–550 kPa. The single salt rejections of the membranes which were very dependent on the thickness of the membrane or membrane stack, were fully in accord with the calculated salt rejections of the membranes.     

Potassium titanyl phosphate membranes: surface properties and application to ionic solution filtration

The relationship between the surface charge of potassium titanyl phosphate (KTP), studied on powder suspensions, and filtration properties of KTP nanofiltration membranes was studied. An experimental investigation of KTP powder characterization in different electrolytic solutions is presented: electrophoretic measurements show that the colloid particles are negatively charged whatever the solution pH, although they present a point of zero charge about 7.8. The selectivity of the membrane depends on the charge and size of ions. The interactions between the membrane and charged species have to be taken into account to explain the transfer through the membrane. With salts having the same cation, the rejection is higher for divalent anions than for monovalent anions. The best rejection rate is observed for applied pressure lower than 7 bar.     

Electrochemical characterization of an asymmetric nanofiltration membrane with NaCl and KCl solutions: influence of membrane asymmetry on transport parameters

Electrochemical characterization of a nanofiltration asymmetric membrane was carried out by measuring membrane potential, salt diffusion, and electrical parameters (membrane electrical resistance and capacitance) with the membrane in contact with NaCl and KCl solutions at different concentrations (10(-3)< or =c(M)< or =5 x 10(-2)). From these experiments characteristic parameters such as the effective concentration of charge in the membrane, ionic transport numbers, and salt and ionic permeabilities across the membrane were determined. Membrane electrical resistance and capacitance were obtained from impedance spectroscopy (IS) measurements by using equivalent circuits as models. This technique allows the determination of the electrical contribution associated with each sublayer; then, assuming that the dense sublayer behaves as a plane capacitor, its thickness can be estimated from the capacitance value. The influence of membrane asymmetry on transport parameters have been studied by carrying out measurements for the two opposite external conditions. Results show that membrane asymmetry strongly affects membrane potential, which is attributed to the Donnan exclusion when the solutions in contact with the dense layer have concentrations lower than the membrane fixed charge (X(ef) approximately -0.004 M), but for the reversal experimental condition (high concentration in contact with the membrane dense sublayer) the membrane potential is practically similar to the solution diffusion potential. The comparison of results obtained for both electrolytes agrees with the higher conductivity of KCl solutions. On the other hand, the influence of diffusion layers at the membrane/solution interfaces in salt permeation was also studied by measuring salt diffusion at a given NaCl concentration gradient but at five different solutions stirring rates.     

Electroviscous Effects in Ceramic Nanofiltration Membranes

Membrane permeability and salt rejection of a γ‐alumina nanofiltration membrane were studied and modeled for different salt solutions. Salt rejection was predicted by using the Donnan‐steric pore model, in which the extended Nernst–Planck equation was applied to predict ion transport through the pores. The solvent flux was modeled by using the Hagen–Poiseuille equation by introducing electroviscosity instead of bulk viscosity. γ‐Alumina particles were used for ζ‐potential measurements. The ζ‐potential measurements show that monovalent ions did not adsorb on the γ‐alumina surface, whereas divalent ions were highly adsorbed. Thus, for divalent ions, the model was modified, owing to pore shrinkage caused by ion adsorption. The ζ‐potential lowered the membrane permeability, especially for membranes with a pore radius lower than 3 nm, a ζ‐potential higher than 20 mV, and an ionic strength lower than 0.01 m . The rejection model showed that, for a pore radius lower than 3 nm and for solutions with ionic strengths lower than 0.01 m , there is an optimum ζ‐potential for rejection, because of the concurrent effects of electromigration and convection. Hence, the model can be used as a prediction tool to optimize membrane perm‐selectivity by designing a specific pore size and surface charge for application at specific ionic strengths and pH levels.     

Influence of membrane fouling by (pretreated) surface water on rejection of pharmaceutically active compounds (PhACs) by nanofiltration membranes

The effects of surface water pretreatment on membrane fouling and the influence of these different fouling types on the rejection of 21 neutral, positively and negatively charged pharmaceuticals were investigated for two nanofiltration membranes. Untreated surface water was compared with surface water, pretreated with a fluidized anionic ion exchange and surface water, pretreated with ultrafiltration. Fouling the nanofiltration membranes with anionic ion exchange resin effluent, resulted in the deposition of a mainly colloidal fouling layer, with a rough morphology. Fouling the nanofiltration membranes with ultrafiltration permeate, resulted in the deposition of a smooth fouling layer, containing mainly natural organic matter. The fouling layer on the nanofiltration membranes, caused by the filtration of untreated surface water, was a combination of both colloids and natural organic matter.Rejection of pharmaceuticals varied the most for the membranes, fouled with the anionic ion exchange effluent, and variations in rejection were caused by a combination of cake-enhanced concentration polarisation and electrostatic (charge) effects. For the membranes, fouled with the other two water types, variations in rejection were smaller and were caused by a combination of steric and electrostatic effects.Changes in membrane surface hydrophobicity due to fouling, changed the extent of partitioning and thus the rejection of hydrophobic, as well as hydrophilic pharmaceuticals.     

Formation and characterization of asymmetric nanofiltration membrane: Effect of shear rate and polymer concentration

In this study, we report the effects of shear rates and polymer concentrations in the formation of asymmetric nanofiltration membrane using a simple dry/wet phase inversion technique. Employing the combination of irreversible thermodynamic model, solution-diffusion model (Spiegler–Kedem equation), steric-hindrance pore (SHP) model and Teorell–Meyers (TMS) model, the transport mechanisms and membrane structural properties were determined and have been characterized for different cases of those formation parameters. The experimental and modeling showed very promising results in terms of membrane performance with interesting structural details. The optimum shear rate (critical shear rate) was found to be at about 203.20 s⁻¹ and the best polymer concentration toward the formation of high performance nanofiltration membrane is in the range of 19.60–23.10%. The modeling results suggested that the pore radius of the membranes produced lies within the range of pore radius of 29 commercial available membranes. This study also proposed that the electrolytes transport through nanofiltration membrane was dominated by a convection factor which accounted approximately 30% more than a diffusion factor. This study also indicated that shear rate and polymer concentration were found to affect the membrane performance and structural properties by providing, to a certain extent, an oriented membrane skin layer which in turn exhibiting an improvement in membrane separation ability.     

Effect of temperature on the transport of water and neutral solutes across nanofiltration membranes

We carry out a detailed experimental and theoretical study of the influence of temperature on nanofiltration performance using the Desal5DK membrane. Experimental results for the permeate volume flux density and rejection of four neutral solutes (glycerin, arabinose, glucose, and sucrose) are presented for temperatures between 22 and 50 degrees C. Solute rejection is modeled using a hindered transport theory that allows us to unveil the crucial role played by changes in the membrane structural parameters (effective pore radius and membrane thickness) due to changes in temperature.     

Effects of membrane degradation on the removal of pharmaceutically active compounds (PhACs) by NF/RO filtration processes

The impacts of membrane degradation due to chlorine attack on the rejection of pharmaceutically active compounds (PhACs) by nanofiltration and reverse osmosis membranes were investigated in this study. Membrane degradation was simulated by soaking the membranes in a sodium hypochlorite solution of various concentrations over 18 h. Changes in membrane surface properties were characterised by contact angle measurement, atomic force microscopy analysis, and streaming potential measurement. The impacts of hypochlorite exposure to the membrane separation processes were ascertained by comparing the rejection of PhACs by virgin and chlorine-exposed membranes. Overall, the reverse osmosis BW30 membrane and the tight nanofiltration NF90 membrane were much more resilient to chlorine exposure than the larger pore size TFC-SR2 and NF270 nanofiltration membranes. In fact, rejection of all three PhACs selected in this study by the BW30 remained largely unchanged after hypochlorite exposure and further characterisation did not reveal any evidence of compromised separation capability. In contrast, the effects of chlorine exposure to the two loose nanofiltration membranes were quite profound. While chlorine exposure generally resulted in reduced rejection of PhACs, a small increase in rejection was observed when a more dilute hypochlorite solution was used. Changes in the membrane surface morphology as well as observed rejection of inorganic salts and PhACs were found to be consistent with mechanisms of chlorine oxidation of polyamide membranes reported in the literature. Chlorine oxidation consistently resulted in a more negative zeta potential of all four membranes investigated in this study. Conformational alterations of the membrane polyamide active skin layer were also evident as reflected by changes in surface roughness before and after chlorine exposure. Such alterations can either loosen or tighten the effective membrane pore size, leading to either a decrease or an increase in rejection. Both of these phenomena were observed in this study, although the decrease in the rejection of PhACs was overwhelming from exposure to highly concentrated hypochlorite solution.     

Influence of common ions during ultrafiltration of mixtures: Part I. Common anions mixtures

A lot of experiments were investigated to show the behaviour of an ultrafiltration membrane during the filtration of pure salt solutions. What happens when the filtered solution contains several ions?

In this paper, results are given concerning the filtration of mixtures of two salts solutions, salts with a common anion: NaCl + CaCl₂ and Na₂SO₄ + CaSO₄.

The surface charge of the membrane is characterized by streaming potential measurements and rejection rates by means of chromatography. These results confirm the adsorption of divalent ions on the surface and a good selectivity for divalent cations.     

Influence of steric, electric, and dielectric effects on membrane potential

The membrane potential arising through nanofiltration membranes separating two aqueous solutions of the same electrolyte at identical hydrostatic pressures but different concentrations is investigated within the scope of the steric, electric, and dielectric exclusion model. The influence of the ion size and the so-called dielectric exclusion on the membrane potential arising through both neutral and electrically charged membranes is investigated. Dielectric phenomena have no influence on the membrane potential through neutral membranes, unlike ion size effects which increase the membrane potential value. For charged membranes, both steric and dielectric effects increase the membrane potential at a given concentration but the diffusion potential (that is the high-concentration limit of the membrane potential) is affected only by steric effects. It is therefore proposed that membrane potential measurements carried out at high salt concentrations could be used to determine the mean pore size of nanofiltration membranes. In practical cases, the membrane volume charge density and the dielectric constant inside pores depend on the physicochemical properties of both the membrane and the surrounding solutions (pH, concentration, and chemical nature of ions). It is shown that the Donnan and dielectric exclusions affect the membrane potential of charged membranes similarly; namely, a higher salt concentration is needed to screen the membrane fixed charge. The membrane volume charge density and the pore dielectric constant cannot then be determined unambiguously by means of membrane potential experiments, and additional independent measurements are in need. It is suggested to carry out rejection rate measurements (together with membrane potential measurements).     

Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes

Tangential streaming potential (TSP) measurements have been carried out so as to assess the electrokinetic properties of the active layer of organic nanofiltration (NF) membranes. Due to the porous structure of NF membranes, cares must be taken to convert the experimental data into zeta potential. Indeed, an assumption that is implicitly made in Smoluchowski's theory (or in related approaches accounting for the surface conduction phenomenon) is that both streaming and conduction currents involved in the streaming potential process flow through an identical path. Such an assumption does not hold with porous membranes since the conduction current is expected to flow wherever the electric conductivity differs from zero. Consequently, a non-negligible share of the conduction current is likely to flow through the membrane body filled with the electrolyte solution. This phenomenon has been taken into account by carrying out a series of TSP measurements at various channel heights. Experiments have been conducted with various electrolyte solutions. The inferred zeta potentials have been further converted into membrane volume charge densities which have been used to predict the membrane performances in terms of rejection rates. The conventional NF theory, i.e. based on a steric/Donnan exclusion mechanism, has been found to be unable to describe the experimental rejection rates. Using the volume charge density of the membrane as an adjustable parameter, it has been shown that the conventional theory even predicts the opposite sign for the membrane charge. On the other hand, the experimental rejection rates have been well described by including dielectric effects in the exclusion mechanism. In this case, a noticeable lowering of the effective dielectric constant of the electrolyte solution inside pores has been predicted (with respect to the bulk value).     

纳滤膜对电解质溶液分离特性的理论研究(II): 混合电解质溶液

假定纳滤膜具有狭缝状孔, 使用纯水透过系数、膜孔径及膜表面电势来表征纳滤膜的分离特征, 用流体力学半径和无限稀释扩散系数表征了离子特性. 采用扩展Nernst-Planck方程、Donnan平衡模型和Poisson-Boltzmann理论描述了混合电解质溶液中离子在膜孔内的传递现象, 计算了三种商用纳滤膜(ESNA1-LF, ESNA1和LES90)对同阴离子、同阳离子和含四种离子的混合电解质体系中离子的截留率, 并与实验数据进行了比较. 计算结果表明, 电解质溶液中离子在纳滤膜孔内传递的主要机理是离子的扩散和电迁移, 纳滤膜对混合电解质溶液中离子的分离效果主要由空间位阻和静电效应决定. 该模型在低浓度时对含一价离子的混合电解质溶液通过纳滤膜的截留率计算结果比较准确, 但对高浓度或含高价离子的混合电解质溶液则偏差较大.     

A three mechanism model to describe fouling of microfiltration membranes

Mathematical modeling of flux decline during filtration plays an important role in both sizing membrane systems and in the understanding of membrane fouling. Protein fouling is traditionally modeled using one of three classical fouling mechanisms: pore blockage, pore constriction or cake filtration. Here, we have developed a mathematical model to describe flux decline behavior during microfiltration accounting for all three classical fouling mechanisms. Pore constriction was assumed to first reduce the size of internal pores. Pore blockage then occurs at the top of the membrane, preventing further fouling to the interior structure. Finally the foulants at the top of the membrane form a cake, which controls the late stages of the filtration. The model prediction shows excellent agreement with experimental data for 0.25 μm polystyrene microspheres filtered through 0.22 μm Isopore membranes (where pore constriction is expected to be minimal) as well as non-aggregated bovine serum albumin solution through hydrophobic Durapore membranes (where pore constriction is expected to dominate). The effects of different fouling mechanisms on the flux decline were characterized by the ratio of characteristic fouling times of the different mechanisms. In this way the model can provide additional insights into the relative importance of different fouling mechanisms as compared to an analysis by a single mechanism model or by derivative plots, and it can be used to provide important insights into the flux decline characteristics.