Negative Rejection of NaCl in Ultrafiltration of Aqueous Solution of

Ind. Eng. Chem. Res. 2010, 49, 6539–6546

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Negative Rejection of NaCl in Ultrafiltration of Aqueous Solution of NaCl and KCl Using Sodalite Octahydrate Zeolite-Clay Charged Ultrafiltration Membrane Fasil Qayoom Mir and Anupam Shukla* Department of Chemical Engineering, Indian Institute of Technology Delhi Hauz Khas, New Delhi -110016 India

Permeation of mixed salt solution through charged membrane is a complex process, and depending upon electrostatic interaction among different types of ions and wall charges, complex separation behaviors such as negative rejection of a salt in the mixture have been observed for such systems. Negative rejection of a salt in an aqueous mixture of salts has been observed for nanofiltration membranes that have very small pores (pore diameter ∼1 nm). We report in this work studies on separation of mixed salt solutions of NaCl and KCl using a charge ultrafiltration membrane of large pore size (pore diameter 15-92 nm) whose preparation is described elsewhere [Workneh, S.; Shukla, A. J. Membr. Sci. 2008, 309, 189]. At a low total concentration of electrolytes in the feed (0.01 M), when the effective exclusion of co-ions occurs inside the membrane, negative rejection of NaCl is obtained. It is found that irrespective of the composition of the salt mixture used in this work, the magnitude of negative observed rejection increases with pressure initially but beyond a certain pressure its magnitude decreases by a small amount. It is also found that as the NaCl composition is increased the magnitude of negative observed rejection first increases but beyond a value of 60% NaCl it decreases for all the pressure differences used in this work. Simulated values of the intrinsic rejection coefficient, however, are found to increase monotonically with pressure, indicating that the maximum in magnitude of observed negative rejection is due to concentration polarization. With variation in feed composition the intrinsic rejection shows a trend similar to the observed rejection. 1. Introduction Ultrafiltration has been increasingly used for municipal and industrial wastewater treatment and also in effluent treatment in many industries.2,3 Relatively large pore size ultrafiltration membranes (pore diameter >5 nm) are being used for many interesting applications including the micellar enhanced ultrafiltration of nonbiodegradable and highly toxic inorganic micropollutants. Traditional techniques for their removal are incapable of reducing their concentrations to the required level (e.g., reduction process or lime precipitation).4 The advantages of using membranes for separations of inorganic pollutants include an easy inclusion in a given process, room temperature operation, and easy adjustment of modular membrane area according to the effluent load.4 Other membrane techniques used for this purpose include reverse osmosis (RO)5 and nanofiltration (NF).6 In the above-mentioned applications, ultrafiltration affords operation at low pressure and provides a low cost pretreatment or main separation step for clarification, removal of suspended solids, ions, etc. Invariably the applications involve treatment of solution containing a mixture of solutes including more than one electrolyte. It is therefore important to understand the separation characteristics of membranes for solutions containing a mixture of electrolytes. The separation of single electrolyte aqueous solution by charged ultrafiltration is well understood using the Donnan exclusion and/or space charge models.7,8 However, systems having mixed electrolyte solutions show complex behavior.9,10 Many studies on membrane-based separation of mixed electrolyte solutions have reported anomalous and even negative rejection of one of the solutes of the mixtures.11,12 Separation of an electrolyte mixture where the membrane shows negative rejection (i.e., concentration of the solute in permeate * To whom correspondence should be addressed. Tel.: +91 11 26596290. Fax: +91 11 26581120. E-mail: [email protected].

is more than its concentration in feed) for one of the electrolytes can also be used for selective separation of the electrolyte from the mixture. Most of the studies on negative rejection of electrolytes have been done using RO, NF, or ultrafiltration (UF) membranes of small pore size (∼2-4 nm).13–15 Negative rejection can occur because of different mechanisms including the presence of nonpermeating ions, a difference in charge of co-ion and counterion, a weakly charged membrane causing low filtration potential, and a difference in the mobility of counterions.13–15 Selective separation of ions of the same charge where one of the ions shows negative rejection can occur due to a difference in their mobility.12 This occurs because of decompensation of convective flux and electric migration at a moderate to high Peclet number regime. Such a regime is possible only with membranes of relatively large pore size. However, we have not found any study in the literature reporting negative rejection for charged UF membranes of pore size greater than 10 nm. The selective separation with negative rejection of one of the ions will be more if the difference in the mobility of the counterions is large. In the studies reported in the literature12 separation is performed between LiNO3 and CsNO3 and negative rejection of LiNO3 is reported to occur. It is also reported in the literature that selective separation of Na+ from K+ is very difficult and techniques such as the use of liquid membrane with costly crown ether have been tried.16 The sodium-potassium balance is important in body fluids of living organisms where it occurs via active transport in ion-selective channels.17 It is therefore important to study if some degree of selective separation between the two ions can be achieved by passive transport using synthetic membranes. In this work therefore ultrafiltration of aqueous solution containing NaCl and KCl is carried out to see if negative rejection of sodium (mobility lower than that of K+) can be obtained.

10.1021/ie901775v  2010 American Chemical Society Published on Web 06/21/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010

In this work, we report separation of a mixed electrolyte system consisting of aqueous solutions of NaCl and KCl using a sodalite octahydrate zeolite-clay composite, charged ultrafiltration membrane. The synthesis and characterization of the membrane have been described in an earlier work.1 In this work, by using the biliquid displacement method, the pore size range of the membrane has been determined to be 15-90 nm. The experimental protocol used for ultrafiltration ensured that the observations record separation due to membrane filtration only and the adsorption/ion-exchange effect is absent. Ultrafiltration experiments are done using aqueous solutions containing NaCl and KCl showing negative rejection of NaCl. Separation experiments are done with aqueous solutions of different NaCl to KCl composition ratios (total salt concentration of 0.01 M) and at different applied pressures to study their effect on the negative rejection value of NaCl. 2. Theory A simple model to simulate transport of a mixed electrolyte though a charged ultrafiltration membrane is based on three types of equations. One is the extended Nernst-Planck equation for transport of ion, the second is the condition of zero current flow, and the third is an equation to give the distribution of ions between the bulk and inside the pores of the membrane. In what follows we consider that the transport within pores of a membrane is unidirectional. Flux of an ion through a charge membrane consists of contributions from three different transport processes, which are convective transport, diffusive transport, and electromobility. In the limit of high flux where diffusive transport can be neglected, the Nernst-Planck equation for a system consisting of two binary salts with a common anion can be written as12

(

ji ) CmiΓi JV + ziDi

dφ dx

)

(1)

where ji is the ion flux, JV is the volume flux, Cmi is the ion concentration at the membrane surface, Γi is the ion distribution coefficient, Di is the diffusivity of the ion and zi is its valency, and dφ/dx is the streaming potential generated to give zero current flow. Concentration of an ion in the permeate solution can be written as CPi )

ji JV

(2)

where CPi is the concentration of ith ion in the permeate solution. The distribution coefficient is obtained by assuming equality of the electrochemical potential of the ions outside and inside the membrane (Donnan equilibrium):18

(

Γi ) exp -

zieψ kT

)

(3)

where ψ is the Donnan potential, k is the Boltzmann constant, and T is the temperature of the system. The zero current condition can be written as

∑z j

i i

)0

(4)

i

Using eqs 1 and 5 the concentration of an ion in permeate can be written as

(

CPi ) CmiΓi 1 + ziDi

1 dφ JV di

)

(6)

Using eqs 3, 5 and 6, concentration of ions in the permeate solution can be calculated. However, these equations require the concentration on the membrane surface while the measurements are taken for the concentration of ions in the bulk of the retentate (Cbi). Cmi is calculated from the values of Cbi using the procedure described in the literature.19–21 The membrane surface concentration is calculated using the osmotic pressure model, where the volume flux is calculated as22

∑ σ ∆π )

JV ) Lp(∆P -

i

i

(7)

where JV is the permeate flux, Lp is the hydraulic permeability of the membrane, ∆P is the applied pressure difference, σi is the membrane reflection coefficient, and ∆πi is the osmotic pressure difference for the ith salt. The osmotic pressure difference is calculated using the van’t Hoff equation for electrolytes. ∆πi ) νiRgT∆Ci

(8)

where Rg is the universal gas constant and ∆Ci is the difference in concentration of the salt in solution on the two sides of the membrane. The reflection coefficient of the ith salt is related to the intrinsic rejection (Ri) of the membrane through the equation given by Spiegler and Kedem.21,23 Ri ) 1 -

CPi Cmi

(9a)

and Ri ) σi

1 - Fi 1 - σiFi

(9b)

where Fi is given by

(

Fi ) exp -

1 - σi Pmi

)

(10)

Pmi is the solute permeability. Cmi, σi, and Pmi are calculated using eqs 7-10 following an iterative technique which is a slight modification of the one given in the literature.19–21 The technique involves assuming values of σ1 and σ2 and then calculating the values of Ri using eqs 6, 7, and 9b and measured values of CPi and JV. The Pmi values for the two salts are then calculated using eqs 9b and 10. The sum of the standard deviations in the two sets of Pmi values is then calculated and minimized by adjusting the σi value. The σi values obtained are used to calculate the surface concentration (Cmi) and the intrinsic rejection values. In the simulation the diffusivity values for Na+, K+, and Clions in water are taken to be 1.33 × 10-9, 1.96 × 10-9, and 2.03 × 10-9 m2/s, respectively.24 Simulations are carried with different values of the Donnan potential (ψ), and the one that gives the lowest value of the minimum standard deviations in Pmi values, calculated as described above, taken as the value of Donnan potential.

Using eqs 1 and 4 we obtain12 z1Cm1Γ1 + z2Cm2Γ2 + z3Cm3Γ3 1 dφ )- 2 (5) JV dx z1 Cm1D1Γ1 + z22Cm2D2Γ2 + z32Cm3D3Γ3

3. Experimental Section 3.1. Membrane and Materials. A flat circular disk-shaped sodalite octahydrate zeolite-clay composite, charged ultrafil-


tration membrane is prepared using the procedure described in the earlier work.1 Distilled water has been used for preparation of all the solutions described in this work. NaCl and KCl of GR grade were procured from Merck India and used without further purification. 3.2. Characterization of the Membrane. Characterization with respect to the surface morphology, porosity, and separation of surfactant (sodium dodecyl sulfate, SDS) is described in the earlier work.1 In addition the pore size range of the membrane is determined using the biliquid displacement method. 3.2.1. Pore Size Range Using Biliquid Displacement Method. A continuous ultrafiltration setup is used for the biliquid displacement experiment. Water is used as the morewetting liquid, while 1-butanol is used as the less-wetting liquid. The measurements consist of two set of experiments. In the first set, membrane is dried at 110 °C for 6 h to ensure complete removal of water from its pores. Using the dried membrane, the flux of the 1-butanol (less wetting liquid) is determined at different applied pressure difference values of up to 272 kPa. The membrane is then taken out, dried in an oven, and immersed in hot distilled water for 1 h and then kept at distilled water at room temperature for 6 h to ensure that all the pores of the membrane are filled with water. After this the wet membrane is mounted on a continuous UF setup and the flux of the 1-butanol is again determined at different applied pressures. The experiments are carried out at increasing pressures until the flux of the 1-butanol through the wet membrane is same as that through the dry membrane. At each pressure the flux measurements are taken three times and the reported values are the average of the three measurements. 3.3. Separation Experiments. A cross-flow continuous ultrafiltration setup is used for separation experiments. The system has multiple ions, and the following measurements are done to determine the concentration of the two salts in retentate and permeate solutions. For all the experiments the pH of retentate and permeate solutions is measured to obtain the concentration of H+ and OH- ions. Also, for all the experiments the concentration of sodium ions is determined using an Orion sodium ion selective electrode (ISE). The ISE was calibrated using Orion standard solution for sodium ion selective electrodes and frequently checked against the standard solution in between measurements for permeate and retentate solutions, and if required the electrodes were recalibrated. Before measurements by the ISE, ionic strength adjustor supplied by Orion was added to the solution. Experiments are performed using solutions of four different compositions and eight transmembrane pressure difference values. For every composition of feed solution and four different transmembrane pressure differences, the Cl- ion concentration in both the retentate and permeate solutions is determined using ion chromatography (make, Thermo electron). The concentration of the K+ ion is calculated from the measured values of Na+ and Cl- concentrations and using the electroneutrality condition. For the remaining four transmembrane pressure differences, measurements of only sodium ions are carried out using the ISE. At first preliminary experiments are done to determine the time required to obtain steady state filtration readings. 3.3.1. Experiments To Determine Steady State and To Eliminate Other Effects. At initial times, apart from the filtration some other processes such as adsorption or ion exchanging of ions in the solution with membrane matrix may occur. In order to ensure that the measurements taken are at steady state and membrane filtration is the only mechanism causing change in the concentration of permeate, filtration

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Figure 1. Flux of 1-butanol through dry and wet (pores of membrane filled with water) membranes at different applied pressure differences.

experiments are carried out for long times starting with 6 L of feed solution. The applied pressure difference is maintained at 68 kPa, and aqueous feed solution with a total NaCl + KCl concentration of 0.01 M is used. The time taken to collect 50 mL of permeate is measured along with its conductivity and concentration of sodium ion (using ISE) in the permeate. Ten measurements (passage of 500 mL of solution through membrane) are taken. 3.3.2. Experiments on Selective Separation in Aqueous Solution of NaCl and KCl. Experiments are carried in a continuous cross-flow ultrafiltration setup with high recirculation rates (300 mL/min, active membrane area 1.25 × 10-3 m2). The time taken to collect 50 mL of permeate is measured to determine the permeate flux. The first 50 mL of permeate is recycled back to the feed tank, and the values reported are the values obtained for the second 50 mL of permeate. After conducting an experiment at a pressure, the membrane is cleaned by passing distilled water through it at the same pressure or 68 kPa higher than the pressure used for the experiment until the water flux is regained within 5% of the original value. Experiments are performed with aqueous solutions of 0.01 M total salt concentration and different compositions of NaCl and KCl. Four different solutions with NaCl and KCl molar percentages of 20:80, 40:60, 60:40, and 80:20 are used. For each of the four types of solutions, separation experiments are performed at different applied pressure differences of up to 238 kPa. The reservoir is filled with 5 L of the solution, and three readings are taken for each pressure. 4. Result and Discussion 4.1. Membrane Synthesis and Characterization. As reported in the earlier work, the membrane used for the separation is a charged inorganic ultrafiltration membrane of high hydraulic permeability.1 The biliquid displacement method is used to further characterize the pore size distribution of the membrane. The method has the advantage that the sizes of only the through pores, which are available for permeation, are measured.25,26 Moreover, the value measured corresponds to the throat pore size that strongly determines the separation characteristic of the pores. Figure 1 shows the flux of 1-butanol through the dry and wet membranes (pores of membrane filled with water, the more-wetting liquid). The flux of 1-butanol through the dry membrane is found to vary linearly with the applied pressure

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difference. In the wet membrane the flow of 1-butanol is resisted by the presence of water, the more-wetting liquid, inside the pores of the membrane. The excess pressure required to displace water from the pore is given by the Laplace equation: ∆P )

2σ cos θ r

(11)

where σ is interfacial tension between the two liquids (1.8 mN/m for our system),27 θ is the contact angle, and r is the pore radius. It may be seen from Figure 1 that the wet membrane starts to permeate only when the applied pressure is about 41 kPa (corresponds to largest pores becoming available for permeation). It may also be seen from Figure 1 that the flux of the wet membrane at 41 kPa is less than the flux of the dry membrane at same pressure, indicating that not all pores are available for permeation. As the pressure is increased the flux of the wet membrane increases but remains less than that of the dry membrane at corresponding pressures up to 238 kPa. Beyond 238 kPa (corresponds to the lowest pore size) fluxes of both the dry and wet membranes are the same. Using eq 1, the largest and smallest pore diameters of the membrane are calculated to be about 92 and 15 nm. The value 58.5°, reported in the literature26 for the three-phase contact angle of 1-butanol, water, and silica, is used in the above calculations. 4.2. Selective Separation of Electrolytes. 4.2.1. Mechanism. Negative rejection of an ion in an aqueous solution containing two electrolytes offers the possibility of selective separation of ions. Negative rejection has been reported for RO, NF, and even neutral membranes, and different reasons have been assigned for each type of system.13–15,28 In ultrafiltration, theoretical analysis shows that negative rejection of one of the two (or more) salts in the feed can be obtained if the following two conditions are met. One is that the permeate volume flux is high enough that the contribution of diffusion to the net flux of ions through the pores can be neglected. The other is that effective co-ion exclusion from the membrane phase occurs. A large permeate flux requires a relatively larger pore size (theoretical analysis predicts 12 nm as the optimum size for a centinormal solution),29 and co-ion exclusion with large pore size requires a high surface charge density on the pore walls. For feed containing a single salt, as the pressure is applied initially the flux of the counterions is more than that of the coions (since the concentration of counterions in the pores of the membrane is higher than that of the co-ions) and results in the development of streaming potential. Streaming potential causes electromigration such that the net flux of the co-ions increases while that of the counterion decreases. The streaming potential rises until the net fluxes (convective and electromigration) of the counterions and co-ions become the same (zero current flow). Consider the case where a second binary salt is introduced in the feed. Both salts have the same anion, which is also the co-ion (ion having the same type of charge as the membrane), and the mobility of the co-ion ion is highest among the three ions. Introduction of the second salt reduces the concentration of the counterions of the first salt as the counterions of the second salt replace some of these in the membrane phase. This causes a change in the convective flux of the counterions. Also, the conductivity of the pores changes and thus a different value of the streaming potential is generated to bring the net current flow to zero. The change in the flux due to convection and electromigration may not be the same for different counterions (decompensation), and an undercompensation of change in the convective flux may result in negative rejection of the ion. The change in the streaming potential value depends upon the

average conductivity of the pore that in turn depends strongly upon the mobility of the counterions, and the one (and the corresponding salt) with the lowest mobility may show negative rejection. 4.2.2. Selection of Feed Concentration. As discussed above, selective separation requires effective exclusion of the co-ion and increase in the concentration of the counterions. In the earlier work an indirect characterization of surface charge on the pores of the membrane using membrane potential experiments was reported. A membrane potential value of about -9.5 mV is reported (Figure 8, ref 1) for the membrane at an average concentration of 0.15 M NaCl and a concentration ratio of 2, corresponding to a cation transport number of ∼0.76. The transport number of sodium ion in aqueous solution of sodium chloride is ∼0.39, and thus the transport number value of 0.76 inside the membrane indicates good co-ion exclusion. The electric field generated by the surface charge determines the exclusion of co-ions (due to electrostatic repulsion). Counterions accumulate near the pore wall (due to electrostatic attraction) and cause reduction in the net electric field inside the pores, commonly known as screening of wall charge. The Debye length is a good measure of distance beyond which effective screening due to counterions occurs. The Debye length for the concentration of 0.15 M is ∼0.78 nm. The Debye length for solution of concentration 0.01 M is ∼3.1 nm, which is larger than that for the 0.15 M solution. Thus the exclusion of co-ions will be more effective for a solution of 0.01 M, the concentration at which the separation experiments are performed. 4.2.3. Design of Experimental Protocol. A particle filter is not used in the experimental setup; however, the entire setup is such that all the flow channels including the reservoir are covered and not exposed to the atmosphere. In addition, the water flux of the membrane is checked in between many of the separation experiments. These water flux measurements are found to be within 5% of the water flux for the fresh membrane. This indicates the absence of fouling of the membrane due to dust particles. To eliminate the possibility of errors due to adsorption/exchange of ions with membrane matrix, etc., filtration experiments are carried out until permeation of a total of 500 mL of salt solution at an applied pressure difference (∆P) of 68 kPa. It is found that the conductivity of permeate and also the concentration of sodium ion in the permeate solution determined using the ISE remains constant (within 2%) after passage of the first 50 mL of permeate. Even the sodium concentration in the first 50 mL of permeate is always found to be within 5% of the later measurements. This indicates that the adsorption/ion exchange of ions is negligible; the slight variation in the initial measurement could be because of unsteady condition at the beginning of the filtration. In light of the above, the first 50 mL of permeated solution is recycled back to the feed tank and measurements are taken for the next 50 mL of permeated solution. In all the experiments a feed solution of pH 7 was used. The pH of the retentate and permeate solutions is measured and is found to be 7 ( 0.3. The concentrations of both the H+ and OH- ions are therefore 4-5 orders of magnitude smaller than the concentrations of Na+, K+, and Clions. Thus, even though these two ions have very high diffusivity values as compared to the other three ions, they are not expected to play any role in the separation phenomenon reported in this work. The experiments are performed at high cross-flow rates to keep the concentration polarization at a minimum. 4.2.4. Results of Separation Experiments. In separate experiments using 0.01 M aqueous solution of NaCl, it is found


Figure 2. Variation of observed rejection values with pressure for a feed solution composition of 20% NaCl and 80% KCl.

that the membrane shows no rejection of sodium chloride. Similarly, the membrane also shows no rejection of KCl in 0.01 M aqueous solution containing only KCl. This is expected for a membrane of such large pore size as compared to the ionic size (hydrated ion diameter ∼0.4-0.5 nm).30 However, rejection of salt is observed in solution containing both salts. Figure 2a shows the observed rejection coefficients for Na+, Cl , and K+ ions for a feed composition of 20% NaCl and 80% KCl. For separations at four different pressure differences (68, 136, 204, and 272 kPa) the concentrations of both Na+ and Cl- ions in both the retentate and the permeate solutions are measured, while the concentration of K+ is determined using electroneutrality conditions. It can be seen from Figure 2a that moderately negative values of observed rejection (Robs ) 1 (CP/Cb)) for the Na+ ions is obtained. The values of the observed rejection coefficient of K+ ions have values close to zero. This clearly shows that separation gives negative values of observed rejection for NaCl and close to zero values of observed rejection

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for KCl. It also shows that the measurements of sodium ion concentration using the ISE alone can be used to obtain observed rejection coefficient values for Na+ ions. In view of this, for separation experiments conducted at four other pressure differences (34, 102, 170, and 238 kPa), values of the rejection coefficient determined using measurements of only Na+ ions correspond to the rejection of NaCl salt. Figure 2b shows the variation of rejection coefficient of NaCl for all eight transmembrane pressure differences. A similar set of experiments performed for feed solutions of three other compositions showed a similar trend. Figure 3 shows the observed rejection coefficients for the three ions for transmembrane pressure values where concentrations of both Na+ and Cl- are measured. Figure 4 shows the observed rejection coefficient for NaCl for all eight transmembrane pressures for all solution compositions used in this work. Negative observed rejection values of up to -40% are obtained. For a solution of a given composition, it is found that the magnitude of negative rejection increases initially with an increase in pressure, but beyond a certain applied pressure it starts to decrease with an increase in pressure. A similar trend is reported for negative rejection of Li+ ions in ultrafiltration of feed solution containing LiNO3 and CsNO3.12 The optimum pressure, at which maximum magnitude of negative rejection is obtained, is found to lie in the range 68-136 kPa for solutions of different compositions. It may also be seen from Figure 4 that at any given pressure the magnitude of negative observed rejection increases initially with an increase in the percentage of sodium chloride in the solution, and beyond a certain value, just as the trend with pressure, it starts to decrease, although the decrease in small. Irrespective of the applied pressure used in this work, the optimum composition of the solution is the one with 60% sodium chloride. Table 1 gives the values of characteristic membrane parameters: the reflection coefficients for the two salts and their solute permeabilities. These are calculated by simulating the model described in section 2, where the permeate flux, concentration of salts in permeate solution, and transmembrane pressure difference are given as input parameters. The Donnan potential value is calculated to be -12.5 mV and the reflection coefficient for KCl is found to be nearly constant irrespective of the composition of salts in feed solution with a value of about 0.32. The value of the reflection coefficient for NaCl is found to be negative for all four different feed solutions, but the magnitude is found to increase initially with the increase in percent of NaCl in the total salt from 20 to 60%. The magnitude of the reflection coefficient then decreases as the NaCl percent in the total salt is increased to 80%. The maximum magnitude of 0.289 is obtained at 60% NaCl in the total salt of the feed solution. The simulation takes into account the concentration polarization by introducing the osmotic pressure. Thus the simulation provides values of the intrinsic rejection coefficient (R ) 1 - (CP/Cm)), which is based on the (calculated value of) concentration of salt at the (upstream) membrane surface and is a true measure of rejection by the membrane. Figure 5 shows both the intrinsic and observed rejection values of the three ions for (0.01 M) feed solution containing 20% NaCl and 80% KCl at different transmembrane pressures. The intrinsic rejection for Na+ is a small negative value, and the magnitude increases slightly (from -6.84 to -6.97%) with an increase in pressure. For K+ it shows a positive value, and the value increases slightly (31.32 to 32.73%) with an increase in transmembrane pressure. It may be seen from Figure 5 that, for Na+ ions, the magnitude of intrinsic rejection is less than

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Figure 4. Variation of negative rejection of sodium chloride with applied pressure difference. Aqueous solutions containing NaCl and KCl of four different compositions were used. Table 1. Calculated Values of Characteristic Membrane Parameters for Separationa reflection coefficient solute permeability × 106 (m/s)

solution composition 20% 40% 60% 80% a

Figure 3. Variation of observed rejection values with pressure for feed solutions of compositions (a) 40% NaCl and 60% KCl, (b) 60% NaCl and 40% KCl, and (c) 80% NaCl and 20% KCl.

NaCl, NaCl, NaCl, NaCl,

80% 60% 84% 20%

KCl KCl KCl KCl

NaCl

KCl

NaCl

KCl

-0.070 -0.189 -0.289 -0.158

0.328 0.324 0.318 0.329

-2.35 -1.98 -2.14 -1.97

-2.20 -2.53 -1.60 -1.23

The total salt concentration is 0.01 M.

that of the observed rejection, showing depletion of the concentration of sodium ion at the membrane surface as compared to the bulk. This is expected as its concentration in permeate solution is more than the value in the bulk of the retentate. For K+ ions the magnitude of the intrinsic rejection is more than that of the observed rejection, showing accumulation of K+ ions at the membrane surface due to concentration polarization. Similarly, the intrinsic rejection value for Cl- ions is found to increase from 24.6% to 26.58% with an increase in pressure, and the magnitude is more than that of the observed rejection. It can also be seen from Figure 5 that the intrinsic rejection magnitude values for all the ions change monotonically with transmembrane pressure. Therefore, the maximum negative magnitude of the observed rejection for Na+ ions at intermediate transmembrane pressure is due to concentration polarization. Observed and intrinsic rejection values compare similarly for feed solution of other compositions also. Figure 6 shows the simulated values of intrinsic rejection coefficients of the three ions for feed of different compositions and at different transmembrane pressures. Figure 6a shows that the magnitude of the intrinsic rejection increases as the NaCl concentration in the feed solution increases from 20 to 60%, but decreases as the NaCl percentage is increased to 80% of the total salt concentration. The optimum negative rejection of Na+ ions with the composition of the feed solution is therefore an inherent property of the membrane and is not due to concentration polarization. Figure 6b shows that the intrinsic rejection of K+ ions remains nearly the same (between 31 and 33%) for all feed solution compositions used in this work. The rejection of Cl- ions is determined by the electroneutrality requirement. As the intrinsic rejection of K+ is larger than that of Na+ and remains constant with feed composition, so the intrinsic rejection of Cl- ions reduces as the NaCl in feed increases and turns negative for feed solution containing 80% NaCl as shown in Figure 6c.


Figure 5. Comparison of observed and intrinsic rejections of ions at different transmembrane pressures for feed composition of 20% NaCl and 80% KCl: (a) Na+, (b) K+, and (c) Cl- ion.

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Figure 6. Variation of calculated values of intrinsic rejection coefficients of three ions with transmembrane pressure for different feed solution of compositions for (a) Na+ ions, (b) K+ ions, and (c) Cl-.

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5. Conclusion Membrane separation of aqueous solutions containing more than one electrolyte, which is a common situation encountered in practice, is a complex phenomenon, and negative rejection of salts has been reported in many studies. Different reasons are cited for different types of membrane, magnitudes of charge of ions, etc. Negative rejection in a system of ions having the same sign and equal magnitude of charge but with different mobilities is possible at moderate to high Peclet numbers. This can be achieved at low to moderate applied pressures using a charged and large pore sized ultrafiltration membrane. However, few experimental studies have been reported. A large pore size (pore diameter 15-90 nm) ultrafiltration membrane, whose preparation is described elsewhere, is used for ultrafiltration of aqueous solutions containing both NaCl and KCl. A membrane of such a large pore size gives the requisite Peclet number even at a low applied pressure difference. The total concentration of electrolytes in the feed is kept at a low value (0.01 M) so that effective exclusion of co-ions occurs inside membrane pores as determined using membrane potential values reported elsewhere.2 It is found that no rejection is obtained if ultrafiltration of feed containing only one electrolyte is performed. However, for feed containing both electrolytes negative rejection of NaCl is obtained. It is found that, irrespective of the composition of salts used in this work, the magnitude of negative observed rejection increases with pressure initially, but beyond a certain pressure its magnitude decreases by a small amount. It is also found that as the NaCl percentage in the salt mixture is increased the magnitude of negative observed rejection first increases, but beyond 60% it decreases for all the pressure differences used in this work. Simulation of experimental data shows a negative value for the reflection coefficient of NaCl with magnitude increasing with the increase in NaCl amount in the feed. It also shows a positive value for KCl that remains constant with the composition of the feed solution. Simulated values of the intrinsic rejection of Na+ are found to increase with increase in pressure, and this suggests that the maximum in magnitude of observed rejection is due to concentration polarization. However, the intrinsic rejection value for Na+ shows a trend similar to that for observed rejection, showing that the maximum in rejection due to change in the composition of feed solution is an inherent property of the membrane and is not due to concentration polarization. Acknowledgment The authors acknowledge financial support (Grant No. SR/FTP/ ETA-24/2005) received from the Department of Science and Technology, Government of India, for carrying out this research work and also Prof. S. K. Gupta, Department of Chemical Engineering, IIT Delhi, for help with the ion chromatographic analysis of solutions. Literature Cited (1) Workneh, S.; Shukla, A. Synthesis of sodalite octahydrate zeoliteclay composite membrane and its use in separation of SDS. J. Membr. Sci. 2008, 309, 189. (2) Hankins, N.; Hilal, N.; Ogunbiyi, O.; Azzopardi, B. Inverted polarity micellar enhanced ultrafiltration for the treatment of heavy metal polluted wastewater. Desalination 2005, 185, 185. (3) Gomez, M.; Plaza, F.; Garralon, G.; Perez, J.; Gomez, M. A. A comparative study of tertiary wastewater treatment by physico-chemicalUV process and macrofiltration-ultrafiltration technologies. Desalination 2007, 202, 369. (4) Gzara, L.; Dhahbi, M. Removal of chromate anions by micellarenhanced ultrafiltration using cationic surfactants. Desalination 2001, 137, 241.

(5) Padilla, A. P.; Tavani, E. L. Treatment of an industrial effluent by reverse osmosis. Desalination 1999, 126, 219. (6) Hafiane, A.; Lemordant, D.; Dhahbi, M. Removal of hexavalent chromium by nanofiltration. Desalination 2000, 130, 305. (7) Lakshminarayanaiah, N. Transport phenomena in membrane; Academic Press: New York, 1969. (8) Gross, R. J.; Osterle, J. F. Membrane transport characteristics in ultrafine capillaries. J. Chem. Phys. 1968, 49, 228. (9) Condom, S.; Persin, M.; Larbot, A.; Prouzet, E. Influence of common ions during ultrafiltration of mixtures part I. Common anions mixtures. J. Membr. Sci. 2000, 300, 117. (10) Garcia-Aleman, J.; Dickson, J. M. Permeation of mixed-salts solutions with commercial and pore filled nanofiltration membranes: Charge inversion phenomena. J. Membr. Sci. 2004, 239, 163. (11) Pontie, M.; Diawara, C. K.; Rumeau, M. Streaming effect of single electrolytes mass transfer in nanofiltration: potential application to a selective defluorination of brackish drinking water. Desalination 2002, 151, 267. (12) Bardot, C.; Gaubert, E.; Yaroschuk, A. E. Unusual mutual influence of electrolytes during pressure-driven transport of their mixtures across charged porous membranes. J. Membr. Sci. 1995, 103, 11. (13) Levenstein, R.; Hasson, D.; Semiat, R. Utilization of the Donnan effect for improving electrolyte separation with nanofiltration membranes. J. Membr. Sci. 1996, 116, 77. (14) Gilron, J.; Gara, N.; Kedem, O. Experimental analysis of negative salt rejection in nanofiltration membranes. J. Membr. Sci. 2001, 185, 223. (15) Childress, A. E.; Elimelech, M. Relating Nanofiltration Membrane Performance to Membrane Charge (Electrokinetic) Characteristics. EnViron. Sci. Technol. 2004, 34, 3710. (16) Sata, T.; Tanimoto, M.; Kawamura, K.; Matsusaki, K. Electrodialytic separation of potassium ions from sodium ions in presence of crown ether using cation-exchange membrane. Colloid Polym. Sci. 2000, 278, 57. (17) Doyle, D. A.; Morais, C. J.; Pfuetzner, R. A.; Kuo, A.; Gulbis, J. M.; Cohen, S. L.; Chait, B. T.; Mackinnon, R. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 1998, 280, 69. (18) Yaroshchuk, A. E. Asymptotic behaviour in the pressure-driven separations of ions of different mobilities in charged porous membranes. J. Membr. Sci. 2000, 167, 163. (19) Ghose, S.; Bhattacharjee, C.; Datta, S. Simulation of unstirred batch ultrafiltration process based on reversible pore-plugging model. J. Membr. Sci. 2000, 169, 29. (20) Shukla, A.; Kumar, A. Characterization of chemically modified zeolite-clay composite membranes using separation of trivalent cations. Sep. Purif. Technol. 2005, 41, 83. (21) Shukla, A.; Kumar, A. Separation of Cr (VI) by zeolite-clay composite membranes modified by reaction with NOx. Sep. Purif. Technol. 2007, 52, 423. (22) Ahmad, A. L.; Chong, M. F.; Bhatia, S. Mathematical modeling and simulation of the multiple solutes system for nanofiltration process. J. Membr. Sci. 2005, 253, 103. (23) Spiegler, K. S.; Kedem, O. Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient membranes. Desalination 1966, 1, 311. (24) Cussler, E. L. Diffusion, Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: New York, 1997. (25) Jakobs, E.; Koros, W. J. Ceramic membrane characterization via the bubble point technique. J. Membr. Sci. 1997, 124, 149. (26) Potdar, A.; Shukla, A.; Kumar, A. Effect of Gas Phase Modification of Analcime Zeolite Composite Membrane on Separation of Surfactant by Ultrafiltration. J. Membr. Sci. 2002, 210, 209. (27) Vyazovkin, E. S.; Gabdrafikov, I. G.; Vishnevskii, A. V.; Potashnikov, G. L. Interfacial tension of the system raw material-solvent in selective treating process. Chem. Technol. Fuels Oils 1990, 26, 120. (28) Pontalier, P.-Y.; Ismail, A.; Ghoul, M. Mechanisms for the selective rejection of solutes in nanofiltration membranes. Sep. Purif. Technol 1997, 12, 175. (29) Yaroshchuk, A. E. Optimal charged membranes for the pressuredriven separations of ions of different mobilities: theoretical analysis. J. Membr. Sci. 2000, 167, 149–161. (30) Bockris, J. O’M.; Reddy, A. K. N. Modern Electrochemistry, 2nd ed.; Kluwer Academic Publishers: New York, 2002; Vol. 1.

ReceiVed for reView November 10, 2009 ReVised manuscript receiVed May 11, 2010 Accepted June 7, 2010 IE901775V

Negative Rejection of NaCl in Ultrafiltration of Aqueous Solution of

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