Donnan Steric Partitioning Pore Model Research Articles

Comparative Analysis of Donnan Steric Partitioning Pore Model and Dielectric Exclusion Applied to the Fractionation of Aqueous Saline Solutions through Nanofiltration

The aim of this study was to analyze, both theoretically and experimentally, the material transport mechanisms governing the separation of ionic species in aqueous solutions using nanofiltration membranes. To interpret the experimental results, the Donnan Steric Partitioning Model (DSPM) and the Dielectric Exclusion Model (DSPM-DE) were applied and computationally simulated in Matlab. Experimental tests were conducted using a pilot-scale system with commercial NF90 membranes. The results indicate that the DSPM better describes the rejection of monovalent ions (sodium and chloride), while the DSPM-DE is more suitable for divalent ions (sulfate and magnesium). Additionally, both models were sensitized to explore the impact of hindrance factors on the rejection of different ionic species. For neutral molecules present in the solution, it was observed that the DSPM and DSPM-DE do not adequately interpret selectivity, suggesting that under such conditions, the electrostatic exclusion mechanism loses significance, with the steric mechanism prevailing.

The influence of feedwater pH on membrane charge ionization and ion rejection by reverse osmosis: An experimental and theoretical study

Modeling mass transport of ions across the polyamide active layer of a reverse osmosis (RO) membrane requires a comprehensive understanding of membrane structure and chemistry. For instance, membrane charge ionization and thus salt transport greatly depend on feedwater pH and composition, but these relations are not yet well understood. To address this gap in understanding, a one dimensional model is developed that couples transport of all ions using the extended Donnan steric partitioning pore model. The model includes membrane charge ionization as well as interaction with H+ and OH−-ions. The dependence of ion rejection and permeate pH is described as function of feedwater pH. Finally, model predictions are quantitatively compared with experimental data by adjusting a few fitting parameters using the Nelder-Mead algorithm. Contrary to other RO studies, we show that the polyamide is only weakly charged, but this small charge still plays a key role to determine membrane performance. These findings reveal the key role of local pH in the ionization of membrane functional groups, and how local charge affects overall membrane rejection of ions as well as permeate pH.

Multicomponent mass transport modeling of water desalination by reverse osmosis including ion pair formation.

Reverse Osmosis (RO) is one of the main membrane technologies currently used for the desalination of seawater and brackish water to produce freshwater. However, the mechanism of transport and separation of ions in RO membranes is not yet fully understood. Besides acid-base reactions (i.e., including the H+-ion), at high concentrations, the salt ions can associate and form ion pairs. In this study, we investigate how to include the formation of these ion pairs in the extended Donnan steric partitioning pore model. We study the desalination of a water source where three ion pairs can be formed (NaCl, MgCl+, and MgCl2) and also include water self-dissociation and the carbonate system. The model assumes infinitely fast reactions, which means that the participating ions are locally at chemical equilibrium with one another. A square stoichiometric reaction matrix composed of active species, moieties, and reactions is formulated. As the final constraint equation, we use the charge balance. The model predicts profiles in concentration, flux, and reaction rates across the membrane for all species and calculates the retention per group of ions. Ion pair formation has an influence on the fluxes of individual ions and therefore influences the retention of ions.

Modeling permeate pH in RO membranes by the extended Donnan steric partitioning pore model

We investigate permeate pH across an RO membrane by modeling transport of ions including protons and hydroxide ions using the extended Donnan steric partitioning pore model (ext-DSP model). We show that membrane charge density plays an important role in determining permeate pH, while the effect of flow rate and salt concentration are less significant. Depending on the polarity of the membrane charge, permeate pH may be lower or higher than feed pH, which indicates the necessity of a reliable membrane charging model. A general multi-site Langmuir charging model is formulated to characterize the membrane charging mechanism and constrain the model parameters. Besides, a simple formula of permeate pH based on the trans-membrane electrostatic potential difference is shown to be a good approximation to the full model prediction.

Ion Selectivity in Brackish Water Desalination by Reverse Osmosis: Theory, Measurements, and Implications

Reverse Osmosis (RO) is a membrane-based technology for water desalination. Of paramount importance is the understanding of ion selectivity in mixtures of salts, i.e., to what extent the membrane retains one ion more than another in a multicomponent salt solution. We apply continuum transport theory to describe a large set of data for the ion selectivity of RO membranes treating brackish groundwater with more than 10 different monovalent and divalent ions. The model is based on the Donnan steric partitioning pore model extended to include ions of multiple charge states, such as bicarbonate/carbonic acid, ammonia/ammonium, and hydroxyl/hydronium ions and the acid–base reactions between them and with the membrane charge. By adjusting for each ion the ratio of ion size over pore size, we can fit the model to the data. We note that the fitted ion sizes do not always follow a logical order based on the ionic or hydrated size of the ions and that rejection of divalent cations is overestimated in some cases. We ...

Efficient fitting of nanofiltration model parameters for a specified groundwater type by selecting suitable characterization data-sets

Nanofiltration (NF) models can be useful to perform optimal designs of membrane systems and to estimate membrane performance for waters. There is a special interest in obtaining NF models with parameters based on measurable properties of the membrane and independent from the feed and operating conditions. However, many times, from a practical point of view, NF parameters can be directly fitted from experiments performed with salts in a range of compositions. The aim of this study is to select the better combination of experiments to yield a suitable fitting for the NF model Donnan steric-partitioning pore model with dielectric exclusion (DSPM-DE). In our case, the best fitting for a specific group of waters is searched (groundwater belonging to a Mediterranean region with moderate salinity). The first part of the work is devoted to study which combinations of salts and concentrations lead to higher information. Using known values of NF parameters, permselective results were computationally generated using the NF model for a huge number of different combinations of compositions and random parameter sets. Performance factors for permeate flux and rejection based on the comparison between the characterization groups and a control group were defined. The second part of the work focused on the experimental validation of the selection procedure. The results showed that there are characterization sets (composition and operating conditions) that yield higher fitting performance. These combinations of experiments should be the preferred ones, when direct fitting from experiments is going to be performed.

Feed concentration and pH effect on arsenate and phosphate rejection via polyacrylonitrile ultrafiltration membrane

The aim of the present work was to study the retention properties of arsenate and phosphate at various feed concentrations and to investigate the effect of pH on the rejection of these ions through modified polyacrylonitrile (PAN) ultrafiltration membrane. In one component solution with feed concentration of 10ppm arsenate and phosphate separately showed ≥90% rejection at ≥pH 7 with PAN UF as well as nanofiltration membranes. Similarly, the mixture of arsenate and phosphate showed more than 90% rejection for feed concentration of 100ppm each. However, the arsenate rejection decreased to 55–60% for 10ppm arsenate and 100ppm phosphate mixture in the feed, while phosphate rejection remained ≥90%. The rejection of arsenate and phosphate reversed to ≥90% and ~60% respectively for 100ppm arsenate and 10ppm phosphate in the feed. The solution pH played an important role in changing the membrane surface properties. The rejection coefficient of arsenate and phosphate varied from 5% to 95% by changing pH between 3 to 10. Donnan steric-partitioning pore model incorporating dielectric exclusion used to investigate the arsenate rejection and good agreement was found between experimental and simulated data.

Effect of pH on the performance of polyamide/polyacrylonitrile based thin film composite membranes

In this study the effect of pH on the performance of thin film composite (TFC) nanofiltration (NF) membranes has been investigated at the relevant pH conditions, in the range of pH 1–13. TFC polyamide NF membranes have been fabricated on a polyacrylonitrile support via interfacial polymerization between piperazine in an aqueous phase and trimesoyl chloride in an organic phase. Membrane characterization has revealed that the produced membranes show a NaCl retention similar to NF-270 and Desal-5DK, a permeance in between those of NF-270 and Desal-5DK, and a slightly higher iso-electric point than NF-270 and Desal-5DK. The molecular weight cut-off of the membranes appeared to be practically constant in acidic and neutral conditions. At extremely alkaline conditions (pH > 11) an increase in molecular weight cut-off and a reduction in membrane flux has been observed. According to the Donnan steric partitioning pore model (DSPM) the change in performance in alkaline conditions originates from a larger effective average pore size and a larger effective membrane thickness as compared to the other pH conditions.

Comparison of the Volume Charge Density of Nanofiltration Membranes Obtained from Retention and Conductivity Experiments

A version of the Donnan steric-partitioning pore model with dielectrical exclusion (DSPM-DE) has been used to get information on the pore size and charge density of a commercial membrane, NF45 from FilmTec, from its retention of KCl solutions. The conductivity inside the pores has been measured by impedance spectroscopy, and the electric potential drop during retention experiments has also been measured. These experimental data on conductivity and electric potential are analyzed, by using the thermodynamics of irreversible processes and the space charge model, to obtain the pore charge density of the membrane. These two methods give results in fair accordance which probes that the sometimes controversial method of DSPM-DE can give accurate results for the charge as well as for the mean pore size of a nanofiltration membrane. Some clues to improve the way this model can be used are given as well.

Demineralization of whey and milk ultrafiltration permeate by means of nanofiltration

In this work, the membrane technique of nanofiltration (NF) was used to carry out partial demineralization of whey and milk ultrafiltration permeate (MUP). The experiments were performed in a completely automated NF pilot plant. An aromatic polyamide spiral wound membrane supplied by Osmonics (USA) was selected (DK2540C model). Batch and discontinuous diafiltration (DF) configurations were compared. Permeate fluxes were higher for MUP due to the lower amount of proteins, which can cause severe membrane fouling. The degree of demineralization for the divalent cations was negligible for both feed streams. Protein and lactose permeation were also observed to be very low. Ion permeation was higher for MUP probably due to the lower amount of proteins. When discontinuous DF was performed, ion removal increased in the case of whey, but it did not significantly improve in the case of MUP. The degree of ion removal was higher than 30%. Finally, the Donnan Steric Partitioning pore Model was used to predict lactose and ion rejection. A good agreement between predicted and experimental data was observed.

Solute rejection by porous thin film composite nanofiltration membranes at high feed water recoveries

The authors developed a rigorous framework to model nanofiltration (NF) membrane selectivity at high feed water recoveries and verify it experimentally. The phenomenological model and the Donnan steric partitioning pore model (DSPM) were incorporated into a differential element approach for predicting removal of a variety of solutes from single salt solutions and natural water by NF membranes up to 90% feed water recovery in the temperature range 5–41 °C. In this approach, the entire membrane ensemble was divided into numerous sub-elements analogous to real-world full-scale NF installations, where concentrate (or reject) from one element feeds into the next element. Fundamental membrane properties (average pore radius, surface charge density, and ratio of thickness to porosity) and the reflection coefficient and permeability coefficient were first independently obtained for each solute–membrane–temperature combination using separate low recovery experiments with negligible concentration polarization and later used as model inputs to calculate solute removal in a purely predictive fashion for 5–90% recovery. This modeling approach accurately predicted removals from single salt solutions of NaCl and MgSO 4 as well as natural organic matter, disinfection by-product precursors, and several ions from pretreated Lake Houston water in a wide range of operating conditions demonstrating its use to simulate NF permeate water quality under real-world conditions of high feed water recovery.

Cleaning results of new and fouled nanofiltration membrane characterized by contact angle, updated DSPM, flux and salts rejection

In membrane process industries, membrane cleaning is one of the most important concerns from both economical and scientific points of view. Though cleaning is important to recover membrane performance, an inappropriate selection of cleaning agents may result into unsatisfactory cleaning or irreparable membrane. In this study the cleaning performance has been studied with measurements of membrane contact angle, Updated Donnan steric partitioning pore model (UDSPM) and salt rejection as well as flux measurement. Thin film nanofiltration (NF) membranes such as DK, HL and DL provided by GE Osmonics are used in this study. Tests were carried out with virgin DK, HL and DL as well as fouled DK membranes. Several cleaning agents were investigated; some of them were analytical grade such as HCl, NaOH and others such as SDS, mix agents were commercial grade agents that are already in use in commercial plants. Contact angle, DSPM and salt rejection as well as flux of virgin and fouled membranes before and after chemical cleaning were measured and compared. The contact angle measurements with and without chemical cleaning of different virgin and fouled membranes revealed very interesting results which may be used to characterise the membrane surface cleanliness. The contact angle results revealed that the cleaning agents are found to modify membrane surface properties (hydrophobicity/hydrophilicity) of the treated and untreated virgin and fouled membranes. The details of these results were also investigated and are reported in the paper. However, UDSPM method did not give any valuable information about pore size of the untreated and treated NF membranes. The salt rejection level of monovalent and divalent ions before and after cleaning by high and low pH cleaning agents is also investigated and is reported in the paper.

Effect of an acidic treatment on the chemical and charge properties of a nanofiltration membrane

In order to improve the performance of a nanofiltration membrane (DS5 DL from Osmonics ®) several pre-treatments have been tested. Specifically, the membrane has been immersed, for different times, in an aqueous solution of HF or H 3PO 4, or of a mixture of both these acids. The chemical and charge properties of the membranes, both pre-treated and untreated, have been studied. The chemical changes have been analyzed by ATR-IR and SEM-EDX. These changes can be interpreted in terms of a partial hydrolysis. Moreover, the charge of the nanofiltration membranes has been analyzed in terms of the Donnan steric partitioning pore model with dielectric exclusion, DSPM-DE. Results on the charges inside the pores (volume charge) are compared with those coming from streaming potential from tangential measurements and referred to the membrane surface, done as a function of salt concentration and pH. These results on charges allow an evaluation of the adsorption parameters and the proper charge that are interpreted in terms of the chemical modifications induced by a partial hydrolysis. These changes in chemical nature and charge enable proper interpretation of the performances of the membranes in the elimination of metallic impurities in industrial phosphoric acid solutions. The acidic pre-treatment can also be applied to improve the performance of the membrane in other applications.

Evaluation of the “DSPM” model on a titania membrane: measurements of charged and uncharged solute retention, electrokinetic charge, pore size, and water permeability

The DSPM (Donnan steric partitioning pore model) was evaluated in the case of a titania membrane with “nanofiltration properties” by measuring the electrokinetic charge, pore size, and water permeability of the membrane, along with charged and uncharged solute retention. The zeta potential values ( ζ) were determined from measurements of the electrophoretic mobility (EM) of titania powder forming the filtering layer of the membrane. Zeta potential values were converted into membrane volume charge ( X) by assuming two limiting cases: a constant surface charge ( σ s cst) and a constant surface potential ( ψ s cst). The mean pore radius and thickness/porosity ratio of the membrane were determined by permporometry and from water permeability measurements, respectively. Retention measurements were carried out as a function of the permeate volume flux for both neutral solutes (polyethylene glycol PEG of different size) and salts (KCl, MgSO 4, K 2SO 4, and MgCl 2) at various pH values. Ionic retentions showed minimum values near the IEP of the membrane. Retention data were analyzed using the DSPM. Very good agreement was found between the pore radius calculated by the model and that determined by permporometry. X values calculated from fitting retention data using the DSPM were also in satisfactorily agreement with X values calculated from EM measurements assuming a constant surface potential for a large pH range. Furthermore, the DSPM leads to X values ( X DSPM) between those calculated from EM ( X EM) using the two limiting bounds. In other words, X DSPM was higher than X EM assuming ψ s cst at pH values far from the isoelectric point (IEP) and lower than X EM assuming σ s cst. These results show that the DSPM is in qualitative agreement with the charge regulation theory (increase of the pore surface potential and decrease of the pore surface charge density with decreasing the pore size). On the other hand, the thickness/porosity ratio of the membrane calculated from solute retention data differed significantly from that determined from water permeability measurements. Moreover, a single value of Δ x/ A k could not be determined from PEG and salt retention data. This means that the Δ x/ A k parameter loses its physical meaning and includes physical phenomena which are not taken into account by the DSPM. Nevertheless, the model satisfactorily predicted the limiting retention, as this is not influenced by the Δ x/ A k parameter.

Analysis of the salt retention of a titania membrane using the “DSPM” model: effect of pH, salt concentration and nature

Retention measurements with single salt solutions of KCl, LiCl, K 2SO 4, MgCl 2 and MgSO 4 were carried out as a function of the permeate flux for a commercial titania membrane close to the nanofiltration (NF) range. The effect of both pH and salt concentration was studied. The membrane shows amphoteric behavior with an isoelectric point (iep) at pH 6.2 (in presence of an indifferent electrolyte: KCl or LiCl). The obtained results agree qualitatively with the Donnan exclusion principle, characteristic of electrically charged membranes: a higher co-ion valence leads to a higher retention, a higher counter-ion valence leads to lower retention and retention decreases with increasing concentration. The analysis of the retention data by the Donnan steric partitioning pore model (DSPM) allowed to evaluate the effective volume charge of the membrane. It was shown that the membrane volume charge depends not only on pH, but also salt and its concentration. At low pH values (when the membrane is positively charged), the membrane charge is higher for magnesium salts than for potassium salts and lower for sulfate salts than for chloride salts. Also, in the high pH range (when the membrane is negatively charged), the membrane charge is higher in absolute value for sulfate salts than for chloride salts and lower (in absolute value) for magnesium salts than for potassium salts. Moreover, it was shown that the membrane charge does not increase with concentration for sulfate salts unlike chloride salts, when the membrane is positively charged. Also, the membrane charge does not increase (in absolute value) with concentration for magnesium salts unlike potassium salts, when the membrane is negatively charged. These results have been attributed to specific adsorption of magnesium and sulfate ions on the membrane material.

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.

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 phenomenon was found for each of the membrane materials.