A combined osmotic pressure and cake filtration model for crossflow nanofiltration of natural organic matter

A combined osmotic pressure and cake filtration model for crossflow nanofiltration of natural organic matter (NOM) was developed and successfully used to determine model parameters (i.e. permeability reduction factor (η) and specific cake resistance (α_cake)) for salt concentrations, NOM concentrations, and ionic strength of salt species (Na⁺ and Ca⁺⁺). In the absence of NOM, with increasing salt concentration from 0.004 to 0.1 M, permeability reduction factor (η)) decreased from 0.99 to 0.72 and 0.94 to 0.44 for monovalent cation (Na⁺) and divalent cation (Ca⁺⁺), respectively. This reduced membrane permeability was due to salt concentrations and salt species. In the presence of NOM, specific cake resistance tended to increase with increasing NOM concentration and ionic strength in the range of 0.85 × 10¹⁵–3.66 × 10¹⁵ m kg⁻¹. Solutions containing divalent cation exhibited higher normalized flux decline (J_v/J_vo = 0.685–0.632) and specific cake resistance (α_cake = 2.89 × 10¹⁵–6.24 × 10¹⁵ m kg⁻¹) than those containing monovalent cation, indicating a highly compacted NOM accumulation, thus increased permeate flow resistance during NF filtration experiments. After membrane cleaning, divalent cation exhibited lower water flux recovery than monovalent cation, suggesting higher non-recoverable (R_non-rec) resistance than monovalent cation.     

Ion transport modelling through nanofiltration membranes

The aim of this work is to study the transport mechanism of ions through nanofiltration membranes. A model based on extended Nernst–Planck and film theory equations is reported. This model can be characterized by three transport parameters: the water permeability L_p, the salt transmittance Φ and the effective salt transfer coefficient K_eff. The knowledge of the feed and permeate concentration and of the permeate volumetric flux enable us to calculate these transport parameters. The model is used to estimate cadmium salts rejection by a NANOMAX 50 membrane. Experimental and calculated results are shown to be in good agreement. The model is then successfully extended to experimental data reported in the literature.     

Determination of concentration-dependent transport coefficients in nanofiltration: Experimental evaluation of coefficients

To characterize solute transport in nanofiltration (NF) the Spiegler–Kedem equation requires that two coefficients be determined for two-component solutions (a solute in water), solute permeability ω and reflection coefficient σ. For salts both coefficients strongly and in a complex way depend on concentration, which greatly complicates their evaluation from experiments. For this reason, the parameters are usually assumed constant for a given feed and the concentration dependence is assessed from flux–rejection curves for several feeds. This procedure however ignores the fact that the solute concentration and hence the coefficients significantly vary across the membrane. One way to overcome this inconsistency and address concentration dependence is to use physical models explicitly introducing exclusion mechanism(s) and fitting relevant membrane-specific parameters, such as fixed charge or dielectric properties. This procedure often fails to produce unique values of parameters for a given membrane and different salts. In the present study a new phenomenological approach is proposed and critically analyzed, based on the assumption of a similar concentration dependence of ω and 1 − σ, previously shown to be valid under fairly general conditions, thereby the Peclét coefficient A = (1 − σ)/ω may be assumed to be independent of concentration. The coefficients and their concentration dependence for a given solute may be directly and consistently evaluated by fitting flux–rejection data for several feeds and fluxes to numeric solution of the modified transport equations without the need to invoke specific physical models. The values of transport parameters deduced in this way for representative membranes and salts allow important conclusions regarding the transport mechanism. In particular, the roles of different mechanisms in overall salt exclusion could be addressed directly from the variation of ω or 1 − σ with concentration. On the other hand, the value of the Peclét coefficient, free of the effect of salt partitioning, may be analyzed in terms of hindered transport. Using the proposed method, this value was found to be very small for studied thin-film composite membranes, which may significantly simplify the transport equations.     

New type of nanofiltration membrane based on crosslinked hyperbranched polymers

Novel nanofiltration (NF) membrane was developed from hydroxyl-ended hyperbranched polyester (HPE) and trimesoyl chloride (TMC) by in situ interfacial polymerization process using ultrafiltration polysulfone membrane as porous support. Fourier transform infrared spectroscopy (FTIR-ATR), scanning electron microscopy (SEM), atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS) and water contact angle (CA) measurements were employed to characterize the resulting membranes. The results indicated that the crosslinked hyperbranched polyester produced a uniform, ultra-thin active layer atop polysulfone (PSf) membrane support. FTIR-ATR spectra indicated that TMC reacted sufficiently with HPE. Water permeability and salts rejection of the prepared NF membrane were measured under low trans-membrane pressures. The resulting NF membranes exhibited significantly enhanced water permeability while maintaining high rejection of salts. The salts rejection increase was accompanied with the flux decrease when TMC dosage was increased. The flux and rejection of NF 1 for Na₂SO₄ (1 g/L) reached to 79.1 l/m² h and 85.4% under 0.3 MPa. The results encourage further exploration of NF membrane preparation using hyperbranched polymers (HBPs) as the selective ultra-thin layer.     

Computer program for simulation of mass transport in nanofiltration membranes

A computer program, NanoFiltran, was developed to simulate the mass transport of multi-ionic aqueous solutions in charged nanofiltration (NF) membranes, based on the Donnan steric partitioning pore and dielectric exclusion (DSPM&DE) model, with incorporation of the non-ideality of electrolyte solutions and concentration polarization effects in the membrane/feed-solution interface. With this computer program, the extended Nernst–Planck (ENP) equations are discretized inside the membrane, using the finite-difference scheme. The discretized ENP equations together with the other model equations are linearized in order to obtain a system of equations that are solved simultaneously. The linearized system of equations is based on an initial guess for the electrical potential and ions concentrations profiles, which are updated iteratively. A robust method of under-relaxation of the electrical potential and ions concentrations ensures that the convergence is achieved even for NF systems that exhibit a very stiff numerical behaviour.     

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.     

Effect of operating variables on rejection of indium using nanofiltration membranes

Indium and its compounds exhibit excellent semiconductor properties however they are suspected carcinogenic to human beings. For the first time, we applied nanofiltration (NF) technology to the separation of indium from a synthetic wastewater as a literature review revealed little information on the treatment of such a waste. In this research, three types of nanofiltration membranes, NTR7450, ES10 and ES10C, were employed to compare their performances under various operating conditions. With increasing indium concentration in the feed solution, the rejection rates decreased in all the membranes, which could be ascribed to concentration polarization and ion-shielding effects. The changes of indium concentration in the permeate (C_p) were then correlated to the concentration factor (CF) during nanofiltration of the feed solution. The experimental results were well predicted by the theoretical analysis. Increase of operating pressure enhanced their rejection rates of indium, which might be attributed to the “dilute effect”. The real rejection (f_r) of indium by nanofiltration was found permeate flux dependent. Based on the results obtained, the nanofiltration mechanisms of multivalent cations such as In³⁺ were delineated and discussed. It was found that most of the models developed from nanofiltration of univalent and divalent cations were still valid for the nanofiltration process of trivalent cations. However, the strong chemical potential of trivalent cations to form complexes in the solution around neutral pH exerted a significant impact on indium rejection rates of the NF membranes. The experimental results suggest a stable performance of nanofiltration when applied to the semiconductor wastewater, however, acidic conditions should be avoided.     

Effect of membrane pretreatment on performance of solvent resistant nanofiltration membranes in methanol solutions

This paper reports the effect of membrane pretreatment using different organic solvents on the performance of polyamide, polyimide and polydimethylsiloxane (PDMS) membranes in methanol solutions. Membrane pretreatment using acetone, methanol and toluene results in significant changes of membrane flux and rejection for polyamide- and polyimide-based membranes (Desal-DK and STARMEM 228) due to membrane swelling. The Performance of a polydimethylsiloxane (PDMS)-based membrane (MPF-50) in methanol solutions was not significantly affected by membrane pretreatment.     

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.     

Contribution of convection,diffusion and migration to electrolyte transport through nanofiltration membranes

Transport mechanisms through nanofiltration membranes are investigated in terms of contribution of convection, diffusion and migration to electrolyte transport. A Donnan steric pore model, based on the application of the extended Nernst-Planck equation and the assumption of a Donnan equilibrium at both membrane-solution interfaces, is used. The study is focused on the transport of symmetrical electrolytes (with symmetric or asymmetric diffusion coefficients). The influence of effective membrane charge density, permeate volume flux, pore radius and effective membrane thickness to porosity ratio on the contribution of the different transport mechanisms is investigated. Convection appears to be the dominant mechanism involved in electrolyte transport at low membrane charge and/or high permeate volume flux and effective membrane thickness to porosity ratio. Transport is mainly governed by diffusion when the membrane is strongly charged, particularly at low permeate volume flux and effective membrane thickness to porosity ratio. Electromigration is likely to be the dominant mechanism involved in electrolyte transport only if the diffusion coefficient of coions is greater than that of counterions.     

Evidence for shape-dependent deposition in crossflow microfiltration of microbial cells

Measurements of the mean cell volume and mean cell aspect ratio are reported for suspensions of the polymorphic yeast Kluyveromyces marxianus var. marxianus NRRLy2415 and for cakes of the same microorganism recovered after crossflow microfiltration with a tubular ceramic membrane at fixed trans-membrane pressure and crossflow velocity. The mean cell volume and the mean cell aspect ratio in the cake were determined using image analysis. The mean cell volume was found to be consistently smaller in the cake than in the suspension while tentative evidence was found that the mean cell aspect ratio was also smaller in the cake. Enhanced deposition of less elongated cells is likely to be a consequence of preferential deposition of small cells because, for the microorganism used in this study, the mean cell aspect ratio in a suspension increases with increasing mean cell volume. Close analysis of the data reveals that the mean cell aspect ratio is greater in the cake than would be expected based on the mean cell volume in the suspension, suggesting that the deposition of more elongated cells is favoured over less elongated cells of the same volume.     

Study on the thin-film composite nanofiltration membrane for the removal of sulfate from concentrated salt aqueous: Preparation and performance

Thin-film composite (TFC) nanofiltration (NF) membrane was prepared through the interfacial polymerization between piperazine (PIP) and trimesoyl chloride (TMC) on the polysulphone support membrane. The chemical structure of membrane surface was studied by attenuated total reflectance infrared (ATR-IR) and X-ray photoelectronic spectroscopy (XPS). Parametric studies were conducted by varying reaction time, curing temperature, curing time and additives in PIP solution for obtaining the optimum polymerization conditions. Systematic performance studies were conducted with different feed solutions, feed concentrations, feed pHs, operating temperatures and pressures. Continuous and comparative tests were also conducted to determine the performance stability and separation efficiency of the thin-film composite NF membrane prepared. High performance thin-film composite NF membrane for the selective sulfate removal from concentrated sodium chloride aqueous with the water permeability coefficient of 75 L/(m² h MPa) could be prepared under specific conditions. Experimental results on concentrated mixed solution of NaCl and Na₂SO₄ demonstrated that the NF membrane developed could be successfully used for the removal of sodium sulfate from the concentrated brine of chloralkali industry with high permeate flux, selectivity and performance stability.     

Removal of acidic dyestuffs in aqueous solution by nanofiltration

Separation of acidic dyestuffs, including Acid red 4, Acid orange 10, and Acid red 27, from aqueous solution by nanofiltration (NF) was shown to be a feasible process to accomplish an effective removal over a broad operational range. For most experiments conducted in this study, dyestuff rejections of greater than 98% were achieved. The permeate flux for experiments conducted with various dyestuffs was increased with increasing operating pressure and solution temperature. The permeability was increased and the rejection of dyestuffs was slightly decreased with increasing cross-flow velocity of solution. The effect of solution pH on the rejection of dyestuff was elucidated by the electrostatic characteristics between the species of dyestuff and the membrane surface. Maximum permeability was obtained for experiments operated in aqueous solution of pH 5, which was close to the isoelectric point of the membrane.     

Effect of solution chemistry on the surface charge of polymeric reverse osmosis and nanofiltration membranes

A streaming potential analyzer has been used to investigate the effect of solution chemistry on the surface charge of four commercial reverse osmosis and nanofiltration membranes. Zeta potentials of these membranes were analyzed for aqueous solutions of various chemical compositions over a pH range of 2 to 9. In the presence of an indifferent electrolyte (NaCl), the isoelectric points of these membranes range from 3.0 to 5.2. The curves of zeta potential versus solution pH for all membranes display a shape characteristic of amphoteric surfaces with acidic and basic functional groups. Results with salts containing divalent ions (CaCl₂, Na₂SO₄, and MgSO₄) indicate that divalent cations more readily adsorb to the membrane surface than divalent anions, especially in the higher pH range. Three sources of humic acid, Suwannee River humic acid, peat humic acid, and Aldrich humic acid, were used to investigate the effect of dissolved natural organic matter on membrane surface charge. Other solution chemistries involved in this investigation include an anionic surfactant (sodium dodecyl sulfate) and a cationic surfactant (dodecyltrimethylammonium bromide). Results show that humic substances and surfactants readily adsorb to the membrane surface and markedly influence the membrane surface charge.     

Determination of concentration-dependent transport coefficients in nanofiltration: Defining an optimal set of coefficients

The currently used equation for solute transport in nanofiltration contains two parameters (ω and 1 – σ) that may be concentration-dependent. A force balance equation allows interpretation of these parameters (as well as L_p) in terms of distribution and friction coefficients, as was demonstrated for a neutral solute and a single 1:1 salt. It is generally assumed in model calculations that it is the distribution coefficient that determines the concentration dependence of ω and 1 – σ. This suggests that a more practically convenient form of the equation may be proposed, in which only one concentration-dependent parameter, ω, appears, while the other is replaced with the ratio of the two, A, which has the meaning of the membrane Peclét number divided by the volume flux and may be assumed to be constant. This may facilitate the analysis of flux–rejection curves and parameter evaluation including concentration dependence, which is a crucial and unavoidable step towards predictive NF modeling. The direct connection between transport parameters and distribution coefficients also suggests that experimentally measured concentration dependence may help to discriminate between different exclusion mechanisms. An approximate analysis based on the connection between A and solute–water friction shows that for presently used NF membranes and realistic fluxes the expected contribution of convection to solute flow cannot become dominant so that the limiting value for salt rejection, R = σ, cannot be reached.     

Influence of operating conditions on the retention of phosphate in water by nanofiltration

The objective of this study was to investigate the retention of phosphate anions, H₂PO₄⁻ and HPO₄²⁻, by nanofiltration. The first part of this study deals with the characterisation of the NF200 membrane used in permeation experiments with aqueous solutions of neutral organic and charged inorganic solutes. In the second part the effects of feed pressure, ionic strength, concentration and pH on the retention of phosphate anions were investigated. Results show that the membrane is negatively charged, its pore radius is around 0.5 nm and the retention order for the salts tested was R(Na₂SO₄) > R(NaCl) > R(CaCl₂). The retentions of phosphate anions are in the order of 85% for H₂PO₄⁻ and 96% for HPO₄²⁻. They are relatively high when compared to retentions of other anions with the same charge. The retentions of phosphate anions, particularly the monovalent species, depend on the chemical parameters (feed concentration, ionic strength, and pH) and applied pressure. The experimental data were analysed using the Speigler–Kedem model and the transport parameters, i.e., the reflection coefficient (σ) and solute permeability (P_s) have been determined.     

Identification of dielectric effects in nanofiltration of metallic salts

Transport of four metallic salts (CuCl₂, ZnCl₂, NiCl₂ and CaCl₂) through a polyamide nanofiltration (NF) membrane has been investigated experimentally from rejection rate and tangential streaming potential measurements. Rejection rates have been further analyzed by means of the steric, electric and dielectric exclusion (SEDE) homogeneous model with the effective dielectric constant of the solution inside pores as the single adjustable parameter.     

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.     

Influence of inorganic electrolytes on the retention of polyethyleneglycol by a nanofiltration ceramic membrane

Retention properties of a nanofiltration ceramic membrane were investigated with single polyethyleneglycol (PEG) solutions and mixed PEG/inorganic electrolyte solutions. The rejection coefficient of PEGs was found to decrease in the presence of ions. It was shown that the effect of ions on the retention of neutral solutes increases with the electrolyte concentration. This phenomenon was ascribed to the partial dehydration of PEG molecules induced by the surrounding ions. This argument was confirmed by using various electrolytes (KCl, LiCl and MgCl₂). It was found that the lowering of the PEG rejection coefficients follows the Hofmeister series, i.e. Mg²⁺ > Li⁺ > K⁺. Experimental data were used to compute the resulting decrease in the Stokes radius of PEG molecules in the presence of the various electrolytes.