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A method for the simultaneous determination of transport and structural parameters of forward osmosis membranes

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A method for the simultaneous determination of transport and structural parameters of forward osmosis membranes
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  A method for the simultaneous determination of transportand structural parameters of forward osmosis membranes Alberto Tiraferri, Ngai Yin Yip, Anthony P. Straub, Santiago Romero-Vargas Castrillon,Menachem Elimelech n Department of Chemical and Environmental Engineering, Yale University, New Haven, CT 06520-8286, United States a r t i c l e i n f o  Article history: Received 17 March 2013Received in revised form2 May 2013Accepted 6 May 2013Available online 23 May 2013 Keywords: Forward osmosisMembrane characterizationTransportStructural parameterActive layerPermeability a b s t r a c t We present a simple and rapid methodology to characterize the water and solute permeabilitycoef  fi cients (  A  and  B , respectively) and structural parameter ( S  ) of forward osmosis (FO) membranes.The methodology comprises a single FO experiment divided into four stages, each using a differentconcentration of draw solution. The experimental water and reverse salt  fl uxes measured in each stageare  fi tted to the corresponding FO transport equations by performing a least-squares non-linearregression, using  A ,  B , and  S   as regression parameters. Hand-cast thin- fi lm composite (TFC) FOmembranes and commercial TFC FO, TFC reverse osmosis (RO), and cellulose acetate-based asymmetricFO membranes are evaluated following this protocol. We compare the membrane properties obtainedwith our FO-based methodology with those derived from existing protocols based on an RO experimentfollowed byan FO experiment. Forall membranes, the FO-based protocol gives more accurate predictionsof the water and salt  fl uxes than the existing method. The numerical robustness of the method and thesensitivity of the regression parameters to random errors in the measured quantities are thoroughlyanalyzed. The assessment shows that con fi dence in the accuracy of the determined membraneparameters can be enhanced by simultaneously achieving close  fi tting of the predicted  fl uxes toexperimental measurements (i.e., high  R 2 values) and constant water to salt  fl ux ratios in each stage.Additionally, the existing and proposed approaches yield consistently dissimilar results for some of theanalyzed membranes, indicating a discrepancy that might be attributed to the different driving forcesutilized in RO and in FO that should be further investigated. &  2013 Elsevier B.V. All rights reserved. 1. Introduction Forward osmosis (FO) utilizes the osmotic pressure differencedeveloped across a semi-permeable membrane separating twosolutions of different concentrations to drive the permeation of water [1]. FO has shown promise in a variety of applications [1  –  7],and it is also attracting attention as a potential technology toaugment water supplies using seawater [1,8,9] and wastewater [10  –  12]. Where abundant and low value streams can be usedwithout the need for regeneration, such as seawater and waste-water, FO can be employed to concentrate the feed solution(osmotic concentration) or dilute the draw solution (osmoticdilution) [13].In recent years, a great deal of research has been directed at thefabrication of FO membranes [7,14  –  29]. These efforts have resultedin the development of substantially improved membranes tailoredfor the speci fi c needs of FO. Inparticular, thin- fi lm composite (TFC)FO membranes, consisting of a salt-rejecting, active layer and aporous support, have shown higher water  fl uxes, reduced saltpassage, and enhanced anti-fouling properties [22,29  –  31]. A con-venient and consistent methodology to characterize FO mem-branes is of critical importance to advance this technology onto itsmature phase, facilitating the sharing of data, their interpretation,and comparison.When describing membrane performance, the literature oftenreports values of water  fl uxes,  J  w , reverse solute  fl uxes,  J  s , theresistance to solute diffusion in the membrane support layer,  K  , orits inverse parameter, the mass transfer coef  fi cient,  k ¼ 1/K   [32].However, these quantities are not intrinsic properties of themembrane as they depend on the hydrodynamic conditions atthe membrane interface, the concentration and osmotic pressureof the draw and feed solutions, and the type and diffusivity of thesolutes. This approach therefore lacks generality, as direct compar-isons cannot be made unless the operating conditions areidentical.An alternative approach, adopted for  ‘ tight ’ , salt-rejecting FOmembranes, is based on three intrinsic parameters that fullydescribe membrane systems: the pure water permeabilityContents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/memsci  Journal of Membrane Science 0376-7388/$-see front matter  &  2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.memsci.2013.05.023 n Corresponding author. Tel.:  + 1 203 432 2789; fax:  + 1 203 432 4387. E-mail address:  menachem.elimelech@yale.edu (M. Elimelech). Journal of Membrane Science 444 (2013) 523  –  538  coef  fi cient,  A , and the solute permeability coef  fi cient,  B , whichdescribe the transport across the membrane active layer, and thestructural parameter,  S  , quantifying the mass transport lengthscale across the membrane support layer. These three parametersare univocal and can be used with the respective governingequations to accurately predict the water and salt  fl ux perfor-mance of a membrane sample in any laboratory-scale FO system.Therefore, the values of   A ,  B , and  S   represent common yardsticksfor describing membrane intrinsic characteristics and offer auniversal set of criteria for comparing performance, regardless of operating conditions.The existing approaches to measure  A ,  B , and  S   of an FOmembrane entail the use of at least two separate experiments.Initially, the parameters related to the active layer (  A  and  B ) aremeasured by applying a trans-membrane hydraulic pressure inreverse osmosis (RO) mode experiments. Subsequently, the mem-brane is tested using an osmotic driving force [7,15,17  –  29,33] to determine the support layer structural parameter,  S  . Experimentsin the pressure retarded osmosis (PRO) con fi guration (draw solu-tion facing the active side of the membrane) may also beconducted to complement [17  –  19,21,24  –  27] or substitute [14]measurements in FO con fi guration.These protocols are cumbersome and laborious, requiringmultiple experiments in different experimental setups. SubjectingFO membranes, intended foroperation near ambient conditions, tothe high pressures typical of RO tests, can result in mechanicaldamage to the membrane. Furthermore, current methodologiescombining RO and FO are based on the notion that transportparameters are universally valid and transferable, an assumptionthat warrants further examination in light of the fundamentallydifferent permeation driving forces in RO and FO: a  hydraulic  pressure difference applied on the RO membrane active layerversus the  osmotic   pressure difference across the membraneactive/support layer interface in FO. These fundamental differ-ences may result in dissimilar observed transport parametersbetween the RO and FO processes, a phenomenon also suggestedin recent studies [34]. It is therefore desirable to formulate a methodology for FO membrane characterization that evaluates themembrane performance under representative driving force andoperating conditions, and which, in addition, is both simple (i.e.,based on a minimum number of experiments) and reliable.In this study, we present a method to characterize the intrinsictransport and structural properties of FO membranes in a  single  FOexperiment. By changing the concentration of the draw solution ineach stage of the experiment, a set of FO water  fl ux and reversesalt  fl ux measurements are obtained. Membrane parameters aredetermined through non-linear regression, where  A ,  B , and  S   aretreated as adjustable parameters to  fi t the FO transport equationsto the experimental water and salt  fl uxes. To demonstrate thegenerality of the method, we characterized four sets of mem-branes exhibiting a wide range of transport and structural para-meters. Our results raise questions about the reliability of currentmembrane characterization protocols, and point towards furtherinvestigations in transport processes in osmotically driven mem-brane processes. 2. A single FO experiment to characterize osmotic membranes A single and facile FO experiment is proposed to characterizethe intrinsic transport parameters,  A  and  B , and the structuralparameter,  S  , of an FO membrane by measuring the water andreverse solute  fl ux across the membrane under different drawsolution concentrations. As depicted schematically in Fig.1, the FOexperiment is divided into a discrete number of stages.The in fl uence of the adopted number of stages on the robustnessand accuracy of the methodology will be discussed in Section 5. Inour study, the experiments were carried out in four stages.In the  fi rst stage of the experiment, a draw solution concentra-tion  c  D,1  and a feed solution of deionized (DI) water were utilizedto measure the FO water  fl ux,  J  w,1 , and the reverse solute  fl ux,  J  s,1 .At the end of the  fi rst stage, a known volume of concentrated draw Fig.1.  Protocol of the single FO experiment. Experimental solutions and measured quantities are schematically represented as lines across the time scale for each of the fourstages of the experiment. Draw solution concentration (blue),  c  D , and feed solution concentration (red),  c  F , are represented as single lines in the top plot. Experimental water fl ux (green),  J  w , and experimental reverse solute  fl ux (purple),  J  s , are depicted as double lines in the bottom plot. The four stages are separated by a vertical dotted line.The stages allow the calculation of   A ,  B , and  S  . (For interpretation of the references to color in this  fi gure legend, the reader is referred to the web version of this article.)  A. Tiraferri et al. / Journal of Membrane Science 444 (2013) 523 – 538 524  solution was added to increase the draw solution concentrationfrom  c  D,1  to  c  D,2 . The osmotic pressure and salt concentrationdifference across the membrane increased and, as a result, boththe FO water  fl ux and the reverse solute  fl ux augmented to reachvalues  J  w,2  and  J  s,2 , respectively, in stage 2. A third and a fourthstage were then performed in a similar fashion. Values of water fl ux and reverse solute  fl ux were experimentally measured atevery stage. For each stage, addition of solute to the draw solutiongives rise to an initial transient state before the solute concentra-tion pro fi les on both sides of the membrane reach steady state.Allowing the system to attain steady state is necessary beforereliable values of water and reverse salt  fl uxes can be recorded. 3. Determining the intrinsic transport and structuralproperties of the membrane  3.1. Water and salt   fl ux governing equations in FO The mass transport across a membrane in FO can be expressedin terms of the membrane characteristic properties, the hydro-dynamics in the membrane  fl ow cell, and experimentally acces-sible parameters: the bulk solute concentration of the drawsolution,  c  D , feed solution concentration,  c  F , and the correspondingosmotic pressures,  π  D  and  π  F . The derivation of the FO water andsalt  fl ux equations presented in Appendix A follows the approachadopted to derive the governing equations in PRO in our previouspublication [35]. It should be noted that salt and draw solute areused interchangeably in the manuscript. The derivation yields thefollowing expressions for the water  fl ux,  J  w , and the reverse salt fl ux,  J  s , in FO:  J  w ¼  A π  D  exp  −  J  w S D   − π  F   exp  J  w k   1 þ  B J  w exp  J  w k   − exp  −  J  w S D  h i8<:9=; ð 1 Þ  J  s ¼ Bc  D  exp  −  J  w S D   − c  F   exp  J  w k   1 þ  B J  w exp  J  w k   − exp  −  J  w S D  h i8<:9=; ð 2 Þ where  k  is the feed solute mass transfer coef  fi cient and  D  is the bulkdiffusion coef  fi cient of the draw salt. The water permeabilitycoef  fi cient,  A , and salt permeability coef  fi cient,  B , are intrinsicpropertiesof themembraneactivelayer.Thesupportlayerstructuralparameter,  S  , is de fi ned as  t  s τ  = ε , with  t  s  being the thickness of thesupport layer,  τ   its tortuosity, and  ε  its porosity. In these equations,the terms exp ð  J  w = k Þ  and exp ð −  J  w S  = D Þ  account for concentrativeexternal concentration polarization (ECP) and dilutive internal con-centration polarization (ICP), respectively. The membrane character-istic parameters can be determined numerically by solving a systemof equations if all the other variables, water and salt  fl ux, feedchannel mass transfer coef  fi cient, salt diffusivity, and concentrationsor osmotic pressures of the solutions, are known.  3.2. Calculating A, B, and S numerically by minimization of a globalerror  We have developed an algorithm to calculate the membraneparameters,  A ,  B , and  S  , from experimental water and salt fl ux data.By following the four stage procedure outlined in Section 2, eightexperimental measurements were collected during a single FOexperiment, namely  J  w ,i  and  J  s ,i , where  i ¼ 1, 2, 3, 4 denotes thestage of the experiment (Fig. 1). The concentrations and corre-sponding osmotic pressures of the draw and feed solutions at eachstage were also recorded. The FO transport Eqs. (1) and (2) were fi tted to the experimental  fl uxes by least-squares non-linear fi tting, using  A ,  B , and  S   as regression parameters, and  c  D  ( π  D )and  c  F  ( π  F ) as independent experimental variables.  D , the bulkdiffusion coef  fi cient of aqueous NaCl, was treated as a knownparameter, its value being set to 1.48  10 − 9 m 2 /s [36]. The treat-ment of   k , the feed solute mass transfer coef  fi cient, is discussed inthe following section.The eight transport equations and three unknowns (  A ,  B  and  S  )constitute an over-determined system of non-linear equations,amenable for numerical solution by least-squares minimization of the global error in the calculated  fl uxes relative to the experi-mental values. Speci fi cally, the global error,  E  , is de fi ned as thenon-dimensional sum of the offsets in the water and salt  fl uxes E  ¼ E  w þ E  s ¼  ∑ ni ¼ 1  J  EXP w ; i  −  J  CALC w ; i  J  EXP  ; nw  ! 2 þ  ∑ ni ¼ 1  J  EXP s ; i  −  J  CALC s ; i  J  EXP  ; ns  ! 2 ð 3 Þ In this equation,  n  is the number of stages and had a value of 4 for the protocol described in this study, and the superscripts  EXP  and  CALC   indicate experimental and calculated (from Eqs. (1) and(2))  fl uxes, respectively. The quantity  J  EXP  ; nw  is the mean experi-mental water  fl ux over the four FO stages, i.e.,  J  EXP  ; nw  ¼  Σ ni ¼ 1  J  EXP w ; i   = n . The error at each stage was scaled by  J  EXP  ; nw  ,so that each term in Eq. (3) is weighed equally, avoiding spuriousbiasing of the global error due to the different orders of magnitudeof   J  EXP w ; i  . The same scaling was performed for the error relative tothe salt  fl uxes.Given that the water  fl ux equation is an implicit function of   J  CALC w ; i  , minimization of the objective function (Eq. (3)) is subject toclosure of Eq. (1). Mathematically, this implies that the minimiza-tion must be subjected to the non-linear equality constraint  J  CALC w ; i  −  A π  D ; i exp  −  J  CALC w ; i  S D   − π  F  ; i 1 þ  B J  CALC w ; i 1 − exp  −  J  CALC w ; i  S D   8>><>>:9>>=>>; ¼ 0  ð 4 Þ for  i ¼ 1,  … ,  n . Eq. (4) assumes that the effect of ECP is negligible (i.e., exp ð  J  w = k Þ¼ 1 in Eq. (1)). Justi fi cation of this assumption is givenin Section 3.3.Three different initial estimates were used to initiate theiterating calculations for  A ,  B , and  S  . The  fi rst set contained valuesthat were smaller than the expected results, namely0.1 L m − 2 h − 1 bar − 1 , 0.01 L m − 2 h − 1 , and 50  m m for  A ,  B , and  S  ,respectively. The third estimates had larger values of 5 L m − 2 h − 1 bar − 1 , 1 L m − 2 h − 1 , and 1000  m m for the three para-meters. The second set of 1.5 L m − 2 h − 1 bar − 1 , 0.3 L m − 2 h − 1 , and300  m m consisted of values that were assumed to be closer to theresults. The algorithm is implemented to accept the solutionassociated with the lowest  E   from the three possible solutionsrelated to each set of initial estimates.The goodness of the  fi t was assessed by computing thecoef  fi cient of determination, which for the water  fl ux is given by R 2 w ≡ 1 −  SS  err  ; w SS  TOT  ; w ¼ 1 −∑ ni ¼ 1 ð  J  EXP w ; i  −  J  CALC w ; i  Þ 2 ∑ ni ¼ 1 ð  J  EXP w ; i  −  J  EXP  ; nw  Þ 2 ð 5 Þ where  SS  err   is the residual sum of squares,  SS  TOT   is the total sum of squares, and  n  is equal to the number of stages, i.e.,  n ¼ 4 for theprotocol demonstrated here. The coef  fi cient of determination forthe salt  fl ux,  R 2 s , was calculated analogously.The algorithm was implemented in two different proprietarysoftware packages: Microsoft Visual Basic within Microsoft Excel(Microsoft Corporation, Redmond, WA) and Matlab (MathworksInc., Natick, MA). The input parameters included the average drawand feed solution concentrations in each stage, system tempera-ture, salt diffusion coef  fi cient in the bulk solution, measured waterand salt  fl uxes, and the initial guesses for the parameters to be  A. Tiraferri et al. / Journal of Membrane Science 444 (2013) 523 – 538  525  calculated. Both codes  fi nd estimates of   A ,  B , and  S   by minimizingEq. (3) subject to non-linear constraints (Eq. (4)). The two packages used different methods for the convergence of thenumerical solutions: Microsoft Excel adopted the generalizedreduced gradient method with forward differencing [37], whileMatlab employed the sequential quadratic programming (SQP)method. As shown in the Appendix, both implementations yieldidentical results. Details on the theory underlying each of thenumerical methods may be found in standard numerical methodstextbooks [38]. In the Matlab implementation, convergence wasreached when the relative change in the value of the  fi ttedparameters between successive iterations was less than a toler-ance, set here to 1  10 − 6 , and the maximum constraint violationwas less than 1  10 − 5 . More stringent tolerance values resulted inidentical results. The Excel spreadsheet and the Matlab  fi le areavailable for download, gratis for non-commercial use, from theSupplementary material of the online version of this paper (http://dx.doi.org/10.1016/j.memsci.2013.05.023).  3.3. Experimental and modeling assumptions In the derivation of Eqs. (1) and (2), the membrane re fl ectioncoef  fi cient,  s , was assumed to have a value of 1. That is, themembrane has a dense selective layer that is able to maintainvirtually the entire osmotic pressure difference across it (i.e.,  s approaches unity) [39]. Therefore, the proposed methodology isonly valid for tight salt-rejecting membranes.In FO, the membrane support layer faces the draw solution.Water permeating across the active layer dilutes the draw solutionin the support layer, resulting in dilutive ICP, the effect of which isto decrease the net osmotic driving force. ICP is partially mitigatedby transport of solute from the draw solution into the membranesupport layer. However, solute transport within the support layeroccurs almost exclusively by diffusion, process dependent on  D ,given that the support layer acts as an unstirred boundary layer[40]. It is important to note that, while the draw solute diffusivityis dependent on the local salt concentration  —  and therefore differsacross the membrane support layer  —  the mass transport modelfrom which Eqs. (1) and (2) were derived assumes a constant  D within the membrane support layer. This simpli fi cation is appro-priate for the range of concentrations of the sodium chloride drawsolution considered in this work, namely 0.05  –  2.0 M. Over thisrange,  D NaCl  varies by less than 3%, between 1.472 and1.519  10 − 9 m 2 /s [36].The osmotic pressure generated by the solute was assumed tobe related linearly to the solute concentration via the van ’ t Hoff equation,  π  ¼ υ cR  g  T  , where  υ  is the number of ionic species eachsolute molecule dissociates into,  R  g   is the ideal gas constant, and  T  is the absolute temperature (Appendix A). Although the sodiumchloride draw solution deviates from ideal behavior at highconcentrations, this relation was applicable for the procedureoutlined here because the solute concentration at the support/active layer interface was signi fi cantly lower than that of the bulksolutions, due to the effects of ICP. For example, a 1.5 M NaCl drawsolution in FO yields a support/active layer interface concentrationof   ∼ 0.3 and  ∼ 0.6 M for hand-cast TFC membranes and commercialasymmetric cellulose triacetate membranes, respectively [29].The low solute concentration at the support/active layerinterface means that the solution will not depart considerablyfrom ideality.From this assumption follows a linear relationship between theexperimental value of   J  w /  J  s  and the ratio  A / B , namely ð  J  w =  J  s Þ¼ð  A = B Þ υ R  g  T   [40]. Because this ratio only depends on intrin-sic membrane active layer characteristics,  A  and  B  (in addition to  υ and  T  ), it is always constant regardless of the concentrations in thedraw and feed solutions. The  J  w  /J  s  factor, termed the reverse  fl uxselectivity, can be regarded as a quality control parameter and itsnear constancy is a necessary condition for the successful use of the proposed methodology (see Sections 4.3 and 5.4). Lastly, we assumed the detrimental effect of ECP on the activeside to be negligible. This assumption is validated trivially by thenegligible feed solution concentration throughout the experimen-tal run (we use DI water as feed solution) and the very smallreverse draw salt  fl ux, both of which render ECP ineffectual. Inaddition, the approximation was justi fi ed by the hydrodynamicconditions maintained at the stirred boundary layer on the feedside, where typical values of the feed solution mass transfercoef  fi cient,  k , far exceed the permeating water  fl ux. Accordingly,this assumption was embedded in the algorithms by imposing k - ∞ , and, therefore, that the exponential term exp ð  J  w = k Þ appear-ing in Eqs. (1) and (2) had a value of 1. We also assumed that ECP in the draw solution is negligible because it is signi fi cantly lowerthan ICP within the support layer. 4. Implementation of the proposed methodology  4.1. FO membranes Both hand-cast TFC and commercial membranes were char-acterized. Hand-cast TFC FO membranes were fabricated adaptingthe procedure outlined in our previous publications [22,29]. Brie fl y, polysulfone (PSf, 9 wt%,  M  n : 22,000 Da, Sigma-Aldrich, St.Louis, MO) was dissolved in  N  - N  -dimethylformamide (DMF, anhy-drous, 99.8%, Sigma-Aldrich) by stirring at room temperature(23  1 C) for 6 h and then stored in a desiccator for at least 15 hprior to casting. To begin casting the membrane, a commercialpolyester non-woven fabric (PET, Grade 3249, Ahlstrom, Helsinki,Finland) was taped on a glass plate and was wet with 1-methyl-2-pyrrolidinone (NMP, anhydrous, 99.5%, Sigma-Aldrich). The PSf solution was then drawn down the PET fabric using a casting knife(Gardco, Pompano Beach, FL) with an adjustable gate height  fi xedat 375  μ m ( ∼ 15 mils). The whole composite was immediatelyimmersed in a precipitation bath containing 3 wt% DMF indeionized (DI) water at room temperature to initiate non-solventinduced phase separation [41,42]. The support membrane remained in the precipitation bath for 10 min before beingtransferred to a DI water bath for storage until polyamide (PA)formation. The PA active layer was formed on top of the hand-castPSf support layers via interfacial polymerization [22,29] between 1,3-phenylenediamine (MPD,  4 99%, Sigma-Aldrich) dissolved inDI water at 3.4 wt% and 1,3,5-benzenetricarbonyl trichloride (TMC,98%, Sigma-Aldrich) dissolved in Isopar G (Univar, Redmond, WA)at 0.15 wt%. Following this reaction, the membrane was cured in DIwater at 95 1  C for 120 s, rinsed with a 200 ppm NaOCl aqueoussolution for 120 s, then soaked in a 1000 ppm NaHSO 3  aqueoussolution for 30 s, before a  fi nal wet curing step at 95 1  C for 120 s.After fabrication, the TFC membranes were rinsed thoroughly andstored in DI water at 4 1  C.Commercial asymmetric cellulose triacetate membranes wereacquired from Hydration Technology Innovations (Albany, OR)(HTI-CTA, batch # 110610-ES-3). Thin- fi lm composite seawaterreverse osmosis membranes (SW30, Dow Chemical Company,Midland, MI) were also acquired and deployed. The PET fabriclayer on the support layer surface of these samples was removedaccording to procedures described in our previous study [43];these membrane samples are designated as  “ SW30 No PET ” .Additionally, prototype thin- fi lm composite FO membranes wereobtained from Oasys Water (Oasys Water Inc., Boston, MA). Allmembranes were thoroughly wet prior to the experiments byimmersing in 25% isopropanol solutions for 30 min. Three separatesamples for each membrane type were employed.  A. Tiraferri et al. / Journal of Membrane Science 444 (2013) 523 – 538 526  4.2. FO setup and experimental conditions FO water  fl uxes and reverse solute  fl uxes were determined inan experimental cross- fl ow FO system described in our previousstudies [22,35]. The custom-built cell had an effective membrane area of 20.02 cm 2 on both sides of the membrane. The unit wasoperated with co-current cross- fl ow without mesh spacers, andvariable speed gear pumps (Cole-Parmer, Vernon Hills, IL) wereused to circulate the solutions in closed loops at a cross- fl owvelocity of 17.1 cm/s. A water bath (Neslab, Newington, NH) keptthe temperature of both feed and draw solutions constant at25 7 0.5 1  C. All characterization tests were conducted with themembrane in FO con fi guration, i.e., porous support layer facing thedraw solution and active layer facing the feed solution. For FOcharacterization tests, a stock 5 M NaCl solution was preparedwith sodium chloride (NaCl) from J.T. Baker (Phillipsburg, NJ), bydissolving the appropriate amount of NaCl in DI water (Milli-Q,Millipore, Billerica, MA).In this study, NaCl was chosen as draw solute, because it ful fi llsa number of critical criteria. Speci fi cally, NaCl (i) is rejected to alarge extent ( 4  95%) by the membrane, (ii) is able to generate ahigh osmotic pressure, (iii) does not deviate signi fi cantly from thevan ’ t Hoff equation, (iv) has nearly constant  D  over the range of concentrations employed, and (v) is easily quanti fi able in the feedby conductivity measurements to determine  J  s .In the beginning of the experiment, DI water was circulated onboth the drawand feed side to equilibrate the system temperature.An appropriate volume of the NaCl stock solutionwas added to thedraw solution to obtain the desired concentration and initiate the fi rst stage. After attainment of steady state, the water  fl ux,  J  EXP w ; i  ,was determined by monitoring the rate of change in weight of thedraw solution, and the solute concentration in the feed wasmeasured at 1 min intervals with a calibrated conductivity meter(Oakton Instruments, Vernon Hills, IL). Once the water  fl ux hadstabilized, feed concentration and water  fl ux data were logged forat least 15 min. Appropriate amounts of the NaCl stock solutionwere then dosed into the draw solution to commence the secondstage and data collection was performed again. The procedure wasrepeated for the third and fourth stages. Tailored concentrations of NaCl draw solutions were chosen for different types of membranessince transport properties varied. Concentrations were selected toobtain a signi fi cant range in the magnitude of water and solute fl uxes throughout the stages, while avoiding overly low or high fl ux values. An appropriate range of   fl uxes is necessary to ensureinstrumental sensitivity during measurement and the validity of the assumptions stated in Section 3.3. The salt concentrations of the draw and feed solutions for all the characterization experi-ments are presented in Table B1 of the Appendix.NaCl reverse  fl ux during stage  i ,  J  EXP s ; i  , was calculated from themeasured change of concentration in the feed,  c  F,i . An NaCl molebalance in the feed solution yields  J  s ; i ¼ c  F  ; i ð V  F  0 ; i −  J  w ; i  A m t  Þ − c  F  0 ; i V  F  0 ; i  A m t   ð 6 Þ where  c  F,i  is the feed solute concentration,  V  F0  is the initial volumeof the feed solution,  A m  is the membrane area,  t   is the timeelapsed, and  c  F0  is the initial NaCl concentration. Due to both thepermeation of water and the salt leakage, the concentration of the 015304560750.000.080.160.240.320.40015304560750.000.080.160.240.32HTI-CTAHand-cast TFCSW30 No PETOasys TFC0.40015304560750.000.080.160.240.320.40015304560750.000.080.160.240.320.40       J   w    /       J   s    (   L   /  m  m  o   l   )       J   w    /       J   s    (   L   /  m  m  o   l   ) 3.8 %2.1 %  #A1 #A2 #A3 3.6 %5.5 %5.4 %4.1 %  #B2 #B3 #B1 2.5 %1.2 %2.2 %  #C2 #C3 #C1 3.5 %4.8 %5.3 %  #D3 #D1 #D2 Bulk osmotic pressure difference, ∆    (bar)Bulk osmotic pressure difference, ∆    (bar) Fig. 2.  Summary of experimental  J  w /  J  s  values plotted against the bulk osmotic pressure difference between the feed and the draw solution ( Δ π  ) for the different stages of each experiment. The plots show data for (A) Hand-cast TFC, (B) HTI-CTA, (C) SW30 No PET, and (D) Oasys TFC membranes. Three experiments for each membrane type arereported and represented by different symbols. Data points related to the various stages of the same experiment are connected by a solid line to guide the eyes only.Calculated values of the coef  fi cient of variation (%) of the  J  w /  J  s  values between the different stages of each experiment are also reported next to the related symbols.  A. Tiraferri et al. / Journal of Membrane Science 444 (2013) 523 – 538  527
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