Donnan Steric Pore Model Research Articles

Effect of Ion Sizes on Separation Characteristics of Nanofiltration Membrane Systems

Abstract. The effect of the ion size on salt rejection is investigated using the Donnan steric pore model (DSPM). This model accounts for the transport phenomena occurring inside the membrane through the appropriate ion sizes. Four hydrated ions (Na+, Mg2+, C1−, S042−) are considered. The ion radius is determined from Stokes-Einstein relationship (Stokes radius), the Born’s theory (Born’s effective radius), and the strength of hydration (Pauling radius). Experimental data validate predictions of ion rejections. It was found that ionic hydration has strong influence on the diffusion properties of ions, which affects significantly the ion rejections. The charge density across the surface of the membrane varies according to the choice of radius of solute, causes remarkable variations in the model prediction. It was also found that the charge density should be predicted accurately to obtain the surface potential which will aid in the improvement of membrane performance and also give approximate index for fabrication of thin film composite layer membrane.

Optimization of composite nanofiltration membrane through pH control: Application in CuSO 4 removal

An approach to optimize the membrane performance by controlling the acidity or basicity of the diamine solution containing bifunctional piperazine, trifunctional 3,5-diaminobenzoic acid and acidic/basic additive is introduced. It was found that with the addition of sulphuric acid (H 2SO 4), pore radius becomes bigger and the skin layer becomes thinner. On the other hand, the membrane thickness was found to increase with the addition of triethylamine (TEA) whereas the pore radius was not affected by the addition of TEA. The membrane flux increased when the membrane was prepared under acidic condition, however, the mechanical strength of the membrane pores was poor and subjected to severe compaction problem. CuSO 4 rejection under different pore radius was simulated using Donnan steric pore model (DSPM). The simulation result shows that the optimum pore radius to separate CuSO 4 should be as close as possible to the size of hydrated Cu 2+ ion which is around 0.53 nm. The experimental rejections for membrane with different pore radius were compared to the simulated result. It was found that the trend of rejection agreed well with the simulated data which indicated that optimized CuSO 4 removal could be achieved using membrane prepared with the addition of 0.5% sulphuric acid.

The role of pH and concentration on the ion rejection in polyamide nanofiltration membranes

The role of pH and concentration is studied on the ion rejection of Desal5-DK polyamide NF membranes. Various samples are used taken from two different batches (DK99 and DK02). Extensive experimentation at room temperature on HCl–water (0.001–1 mol/m 3) as well as on NaCl–water (1–50 mol/m 3) solutions is presented to characterize the membrane as a function of electrolyte concentration, at feed pH values in the range from 3 to 6.5. The applied pressure in the feed side is varied from 3 to 30 bar. The effect of feed pH is studied both on salt rejection and on total volume flux, and general trends are obtained. DK02 membranes are less pH sensitive than DK99's. Na + and H + rejections are greatly affected by pH. Na + rejection goes through a minimum value as the feed acidity increases, and correspondingly H + rejection goes through a maximum value. Minima are approximately located at pH values in the range between 4.5 and 5. Volumetric membrane charge values corresponding to each operative condition investigated are calculated through the Donnan Steric Pore Model and Dielectric Exclusion. Membrane charge is obtained as an increasing function both with pH and with electrolyte concentration in the feed side. A Langmuir-type behaviour is apparent at constant pH values; amphoteric behaviour is re-confirmed. The points of zero charge approximately correspond to the pH values at which NaCl rejections approach their minimum values.

Calculation of the salt separation by negatively charged gel-filled membranes

The salt separations of negatively charged gel-filled membranes composed of poly(2-acrylamido-2-methylpropanesulfonic acid) gels anchored within a polypropylene microporous substrate have been determined experimentally and modeled theoretically. The separation of these membranes were calculated by both the Teorell, Meyer and Sievers (TMS) model and the Donnan–Steric Pore (DSP) model coupled with the extended Nernst–Planck equation. For modeling, the membrane effective thickness, effective charge density, and pore radius were either directly measured or calculated from theories without the use of fitting procedures. Good agreement between the experimental measurements and the theoretical calculations of salt separation was observed. For the theoretical calculations, the TMS model is suitable for membranes with moderate gel polymer volume fractions, while the DSP model is more suitable for membranes with high gel polymer volume fractions. Moreover, with a calculated constant effective charge density, the salt separation with different salt concentrations could be accurately predicted. The separation of various other salts could also be predicted with good accuracy.

Potential use of nanofiltration membranes in treatment of industrial wastewater from Ni-P electroless plating

Nanofiltration (NF) membranes are a relatively new class of membranes which have properties in between those of ultrafiltration (UF) membranes and reverse-osmosis (RO) ones. Their separation mechanisms involve both steric (sieving) effects and electrical (Donnan) effects. The significance of this membrane, besides having small pores is the membrane's surface charges, which allows charged solutes that are smaller than the membrane pores to be rejected along with bigger neutral solutes and salts. Furthermore it is capable of rejecting multivalent ions effectively, and on the other hand lets the monovalent ions pass through. These are the characteristics that make the nanofiltration membrane a potential process to reject heavy metal ions, which in general are multivalent ions. In this study, the potential use of a nanofiltration membrane for rejection of heavy metal ions such as Ni 2+ from wastewater from Ni-P electroless plating industry was studied. A composite NF membrane designated as HL membrane was used. The characteristics of the membranes were analyzed using single salt rejection studies of NaCl, MgCl 2, Na 2SO 4, NiSO 4. The wastewater from the Ni-P electroless plating industry was found to contain various cations such as nickel, zinc and sodium. In order to ascertain the effect of ion rejection in a multicomponent system, the rejection behaviour of Ni 2+ ion in mixed solutions of Na 2SO 4 and NiSO 4 was tested and the rejections were then compared to those obtained using real solutions. The results show that in general the rejection of Ni is high regardless of the presence of other ions. The experimental data were also analyzed using two predictive models, namely Donnan steric pore model (DSPM) and ion transport model. The models are based on the extended Nerrnst-Planck equation but solved using different approaches and parameters. The results from the models were compared to find which model gives better agreement with the experimental findings.

Use of nanofiltration predictive model for membrane selection and system cost assessment

In this paper, a predictive model based on the Donnan–Steric–Pore model (DSPM) has been used to develop general criteria for selection of optimum nanofiltration (NF) membranes and to analyse the effect of various nanofiltration membrane characteristics on the cost of NF membrane system. By using an economic assessment model for NF processes, the two most important factors determining the performance of NF membranes which are λ (the ratio of solute radius and membrane pore radius) and ζ (the ratio of membrane charge effective density to bulk concentration) were examined. The optimal conditions for minimum operation cost and optimal operating pressure were also determined. Detailed cost analysis reveals both capital and operating cost were not affected by the variation of ζ. However, decreasing the membrane pore size will increase costs. It was found that up to 30% of the capital and operating costs in recovering sodium sulphate solution can be saved by using looser membrane compared to the tight membrane structure.

Predicting flux and rejection of multicomponent salts mixture in nanofiltration membranes

This paper presents a modified Donnan-Steric-Pore model (DSPM) to predict the rejection of mixture of NaCI:Na 2SO 4 in nanofiltration (NF) membrane based on the extended Nernst-Planck equation with the incorporation of charge and steric effects for the transport of ions inside the membrane and incorporation of concentration polarization effect for mixture of ions/solutes. With this approach, the permeate flux can be calculated based on the concentration of ions at the membrane surface. The membrane performance was modelled using three parameters namely; effective pore radius, r p , effective ratio of embrane thickness to porosity, Δx/ A k , and the effective charge density, X d . The simulation results shows that the model can predict the tendencies and patterns of rejection and flux reduction behaviour reasonably well for system containing NaCl:Na 2SO 4. The model can be used as a preliminary tool to assess the rejection capability as well as the flux behaviour of NF membranes in mixtures of solutions. For future works, the model can be improved further to account for non-ideal as well as real mixture solutions.

Nanofiltration modeling: the role of dielectric exclusion in membrane characterization

A general model is presented, called Donnan steric pore model & dielectric exclusion (DSPM&DE) to describe mass transfer of electrolytes and neutral solutes through nanofiltration membranes. The transport equations of ions through the membrane are based on the extended Nernst–Planck equation, accounting for ionic diffusion, electromigration and convection in the membrane pores; the hindered nature of diffusion and convection of the species inside the membrane is considered. Ionic partitioning at the interfaces between the membrane and the external phases takes into account of three separation mechanisms: steric hindrance, Donnan equilibrium and dielectric exclusion. The role of the difference existing between the dielectric constant of the aqueous solution in the pores and the dielectric constant of the membrane material is assumed dominant in determining the rejection mechanism related to the dielectric effects. The membrane is characterized through the use of adjustable parameters such as the average pore radius, the effective membrane thickness and the volumetric charge density. A general assessment is presented for membrane characterization. A new procedure is introduced for the membrane parameters calculation, based on a simple analytical relationship developed to describe rejection of single symmetric electrolytes. Two versions of the DSPM&DE model are presented, in which the “integral” model is a weak simplification of the general “differential” model. The validity of the models presented is fully demonstrated in the case of negatively charged membranes, through the comparison with experimental results performed in a wide range of operative conditions. The separation effect related to the dielectric exclusion is relevant with respect to Donnan equilibrium in determining bivalent counter-ions rejection, such as CaCl 2 as well as MgSO 4, whereas dielectric effects are not so remarkable in the case of mixtures containing various co-ions, such as NaCl+Na 2SO 4.

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.

A comparison of membrane charge of a low nanofiltration ceramic membrane determined from ionic retention and tangential streaming potential measurements

The retention of neutral solutes and ionic solutions on a NF ceramic membrane was measured. The Donnan Steric Pore Model (DSPM) was fitted to these observations yielding effective pore radius ( r p ) and thickness/porosity ratio (Δ x/ A k ) from neutral solutes data and the effective volume charge ( X) from electrolyte data. Effective volume charges were also directly determined using tangential streaming potential measurements. The DSPM gives X in good agreement with the values obtained by streaming potential. However, it overestimates Δ x/ A k compared to the value deduced from neutral solute retention.

Retention of mineral salts by a polyamide nanofiltration membrane

Retention measurements with single salt solutions (KCl, K 2 SO 4 , MgSO 4 and MgCl 2 ) were carried out with an AFC 30 organic membrane. The membrane showed high retentions for K 2 SO 4 and MgSO 4 solutions and moderate ones for MgCl 2 and KCl solutions. The effective pore radius and the effective thickness to the porosity ratio of the membrane were determined from the limiting retention of glucose and permeability measurements, respectively. The Donnan Steric Pore Model (DSPM), based on the extended Nernst-Planck equation and a modified Donnan equilibrium accounting for steric effects, was used to characterize the membrane in terms of effective membrane volume charge. It appears that the membrane is positively charged in presence of MgCl 2 and MgSO 4 solutions and negatively charged for KCl and K 2 SO 4 solutions. This was attributed to ionic adsorption at the interface membrane/solution.

A modified Donnan–steric-pore model for predicting flux and rejection of dye/NaCl mixture in nanofiltration membranes

This paper presents a modified Donnan–steric-pore model (DSPM) to predict the rejection of mixture of salts/charged organic in nanofiltration (NF) membranes, based on the extended Nernst–Planck equation with the incorporation of charge and steric effects for the transport of ions inside the membrane, and incorporation of concentration polarization effect for a mixture of charged ions/solutes. With this approach, the permeate flux can be calculated based on the concentration of ions/charged solutes at the membrane surface. The membrane performance was modeled using three parameters, namely: effective pore radius, r p; effective ratio of membrane thickness to porosity, Δx/A k; and the effective charge density, X d. Comparison of the calculation based on the model with published experimental data shows that the model can predict the tendencies and patterns of rejection and flux reduction behavior reasonably well for systems containing NaCl–dye–H2O. Effects on fluxes and NaCl rejections of system variables such as mass transfer film thickness, dye valence, dye diffusivity, and dye/salt concentration ratio were studied using this model. This model can be used as a preliminary tool to assess the rejection capability as well as the flux behavior of NF membranes towards binary solution and mixtures.