Environ. Sci. Technol. 2009, 43, 5449–5454
Hydrodynamic Modeling of NOM Transport in UF: Effects of Charge Density and Ionic Strength on Effective Size and Sieving YANXIAO YUAN AND JAMES E. KILDUFF* Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180
Received February 4, 2009. Revised manuscript received May 9, 2009. Accepted May 11, 2009.
The transport behavior of natural organic matter (NOM) across polyethersulfone (PES) UF membranes having a range of nominal molecular weight cutoffs (MWCOs) was investigated and described with a hydrodynamic transport model. Transport of whole NOM and NOM fractionated on an anion exchange resin (IRA 958) was measured to investigate the impact of NOM size and charge density. It was found that the dominant transport mechanism, characterized by the membrane Peclet number, depended on the membrane MWCO, and transitioned from diffusion to convection at a MWCO of about 10 kDa. Increasing ionic strength significantly decreased the effective solute radius and decreased the observed rejection of charged NOM fractions, whereas no significant change was seen for neutral fractions. Using an available theoretical model for partitioning of charged solutes, the effect of ionic strength on the electrical double layer thickness can account for the observed changes in effective solute radius. These results provide insight into the role of solute charge and electrostatic interactions in NOM transport behavior.
Introduction Natural organic matter (NOM), an organic precursor of disinfection byproducts (DBPs), is a heterogeneous mixture of complex organic materials including humic substances, hydrophilic acids, proteins, lipids, carboxylic acids, amino acids, and hydrocarbons. Membrane processes (nanofiltration, NF, and ultrafiltration, UF) have been shown to be effective for removing NOM as a strategy to reduce the formation and risk of DBPs, and their economics are becoming increasingly competitive (1). NF membranes offer high NOM rejection, and concomitant divalent ion removal, whereas UF membranes may be appropriate when complete NOM removal is not necessary, and offers lower energy costs. In either case, understanding the factors that govern NOM rejection, and ultimately predicting process performance, is an important goal. Of particular interest are the effects of solution chemistry (pH and ionic composition) and process variables such as crossflow and filtration flux (or transmembrane pressure). Although these factors can also influence membrane fouling by NOM (2) the focus of this paper is on membrane transport phenomena. Rejection of NOM by NF and UF membranes generally decreases with decreasing pH and increasing ionic strength; explanations have included a * Corresponding author phone: 518.276.2042; fax: 518.276.4833; e-mail:
[email protected]. 10.1021/es900259r CCC: $40.75
Published on Web 06/08/2009
2009 American Chemical Society
decrease in solute-membrane repulsion (3), a shift to smaller apparent molecular size (3, 4) and an increase in the solute diffusion coefficient as refelcted in solute permeability (5). Transport models generally include both the transport across the membrane itself and transport upstream of the membrane in the boundary or concentration polarization layer. Solute transport in the concentration polarization layer is often described using the stagnant film model, as we do here. This model provides an estimate of the concentration at the membrane surface, which provides a boundary condition for transport across the membrane. Membrane transport has been described by solution-diffusion (1), hydrodynamic (6-8), and thermodynamic models (5, 9, 10) for NF and UF processes. Models based on the irreversible thermodynamic development of Kedem and Katchalsky (9), which consider the membrane as a “black box”, have been successfully used to evaluate NOM transport characteristics for UF and NF processes (5, 10). For example, Lee et al. (5) showed that NOM rejection by a NF membrane increased with both solution flux and crossflow velocity, and determined that transport across the membrane was primarily by diffusion. However, it is difficult to relate model parameters to solute properties. In contrast, hydrodynamic models evaluate solute flux by directly solving the governing hydrodynamic equations for the motion of a single solute in a well-defined pore (6-8). Although the thermodynamic and hydrodynamic approaches yield equivalent transport equations for the case of nonnegligible diffusive solute flux (8), hydrodynamic transport parameters are expressed directly in terms of the solute and pore characteristics. Sharma and Chellam (11) applied a hydrodynamic model to evaluate temperature effects on the morphology of several NF membranes; the model was able to accurately describe the effect of flux on the sieving of model solutes including sugars, alcohols, and glycols. In this work, we employed an approach similar to that of Sharma and Chellam (11) to describe quantitatively NOM transport characteristics in UF by combining the film model and a hydrodynamic model that accounts for hindered transport in liquid-filled pores. We then used fitted mass transport parameters to make estimates of NOM effective size. Because NOM is a polyelectrolyte containing charged functional groups (12, 13), its apparent size and configuration can change in response to solution chemistry when these groups are either shielded by neutral salts, neutralized by cation complexation, or protonated (4, 14). However, electrostatic interactions can play a large role in macromolecule transport in the absence of configuration changes, as demonstrated for the electrophoresis of humic substances (15) and the membrane transport of bovine serum albumin (BSA) (16). Based on these considerations, we treated the effective solute radius as a phenomenological parameter that combines conformation and electrostatic effects. The overall objective of this work was to demonstrate the efficacy of hydrodynamic models as a phenomenological approach to describe NOM transport in UF. By modeling the transport of whole NOM and ion exchange fractions, we provide insight into how molecular properties (size and charge density) and operating variables (flux) affect transport mechanisms (diffusion versus convection) and rejection.
Theory Mass Transport above the Membrane Surface. The transport of solutes in the boundary layer near the membrane surface is described by the stagnant film model, derived by integrating the one-dimensional steady state mass balance across the VOL. 43, NO. 14, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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concentration polarization (CP) layer to yield a steady state volumetric flux, Jv, in terms of a mass transport coefficient, k, and the concentration driving force across the membrane. Combining the film model with definitions of the observed (So ) Cp/Cb) and actual (Sa ) Cp/Cw) sieving coefficients, where Cw is the solute concentration in the feed boundary layer adjacent to the surface of the membrane (i.e., wall), Cb is the solute concentration in the bulk, and Cp is the permeate concentration, yields the relationship between So and Sa: Sa
So )
( )
Sa + (1 - Sa)exp -
Jv k
(1)
Mass Transport across the Membrane Layer. Local solute flux through a charged membrane can be expressed as the sum of the convective, diffusive, and eletrophoretic contributions (16). In this work, the electrophoretic contribution was neglected, because it is only important when the ionic strength is fairly low, and it is negligible when ionic strength is higher than 0.005 M (16). An expression for the actual membrane sieving coefficient was obtained in terms of the asymptotic sieving coefficient, S∞, and the pore Peclet number, NPe,m, by integrating the local convective and diffusive solute flux across the membrane, assuming that the solute flux does not vary with axial position in the pore (8). Defining boundary conditions within the pore in terms of external concentrations Cw and Cp by assuming equilibrium partitioning at the pore entrance (Cs ) φCw) and exit (Cs ) φCp), where φ is the partition coefficient, the actual sieving coefficient is expressed as follows: Sa )
Cp S∞exp(NPe,m) ) Cw S∞ + exp(NPe,m) - 1
(2)
The Peclet number is a measure of solute convection relative to diffusion: NPe,m )
φKcδm Jv φKdεm D∞
(3)
Where δm is the active layer thickness, and εm is the membrane porosity. Parameters Kc and Kd represent hindrance factors for convective and diffusive transport, respectively. The asymptotic value of the sieving coefficient, S∞, equal to the product of the hindrance factor for convection and the solute equilibrium partition coefficient,S∞ ) φ Kc, is attained as the pore Peclet number (NPe,m) increases to infinity and the contribution from diffusion becomes insignificant. The solute transport model is combined with the film model to predict solute transport behavior because concentration polarization near the membrane surface can affect the solute transport inside membrane pores (8). Combining eqs 1 and 2 yields the transport equation: ln(S o-1 - 1) ) -
Jv + ln{(1 - S ∞-1)[exp(-NPe,m) - 1]} k (4)
The asymptotic sieving coefficient S∞ ) φ Kc, and the diffusive hindrance parameter, φKd, are related to λ, the ratio of effective solute radius, reff, to membrane pore radius, rp (17): S∞ ) φKc ) (1 - λ)2[2 - (1 - λ)2]exp(-0.7146λ2)
(5)
φKd ) (1 - λ2)[1 - 2.848λ + 3.269λ2 - 1.361λ3]
(6)
The effective size accounts for the molecular size and electrostatic interactions between the solute and the pore 5450
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wall; two solutes having the same sieving coefficient have the same effective size. In this work, λ is expressed in terms of the specific pore area, s, using an approach shown to explicitly account for the membrane pore size distribution (8):
( )
λ ) 1 - exp -
reff 2s
(7)
The specific pore area, defined as the pore volume divided by the pore surface area, can be defined in terms of Lp, the membrane hydraulic permeability: s )
(
5µδmLp εm
)
1/2
(8)
Model Calibration. Two of the parameters in eq 4, the volumetric flux, Jv, and observed sieving coefficient, So, were measured directly. The remaining parameters, k, S∞, and NPe,m, were either estimated or treated as fitting parameters. The asymptotic sieving coefficient can be expressed in terms of λ (eq 5) and hence in terms of the effective solute radius and specific pore surface area (eq 7). Similarly, the pore Peclet number can be written in terms of the effective solute radius, specific pore surface area, and solute diffusivity. In the calibration step, the sieving properties of standard-grade dextrans, having narrow molecular weight (MW) distributions, were measured. The effective dextran radius was estimated from the Stokes-Einstein equation using a diffusion coefficient, D∞, from an available correlation, D∞ ) 1.76 × 10-8(MW)-0.552 (17), and both k and s were then treated as fitting parameters. Best fit values were determined by minimizing the sum of squared residuals between the observed dextran sieving coefficients as a function of permeate solution flux and the model calculations, using nonlinear regression software. Using sieving coefficient data for NOM, and the best fit value for s obtained from the calibration step, the average effective radius of NOM was estimated from eq 4 over a range of ionic strength values. In this step k and reff were treated as fitting parameters; their best fit values were determined as described above. A sensitivity analysis of the model is provided in the Supporting Information (SI).
Materials and Methods A brief description of experimental materials and methods follows; additional details can be found in the SI. Solutes. Dextrans (4 and 6 kDa molecular weight standards, American Polymer Standards Corporation, Mentor, OH) were used to estimate the specific pore surface area s of the 5 kDa MWCO membrane. Dextran sulfate sodium (10 kDa, Aldrich) was used for the 10 kDa MWCO membrane. The concentration of dextrans in solution was determined as total organic carbon (TOC). NOM was isolated from the Tomhannock (TMK) reservoir, NY; the Intercoastal Waterway, Myrtle Beach, SC (MB); and the Edisto River, Charleston, SC (CH). Selected experiments were also done using a commercial peat humic acid (PHA, International Humic Substances Society) as a model high molecular (104-105 Da) weight natural organic material. NOM materials were selected to represent different geographical areas, and to offer a range of properties; NOM size was important to provide appropriate ratios of solute size to membrane pore size for different membrane MWCOs. NOM was isolated and concentrated by a reverse osmosis (RO) system. Prior to each experiment, the concentrated samples were microfiltered and diluted to 10 mg C/L, pH was adjusted to 7.0, and ionic strength was adjusted to desired values using NaCl.
TABLE 1. NOM Characteristics NOM b
molecular weight Mw (g/mol) radius of gyration rgo (nm, eq 12) acidity (from pH 3 to 7, meq C g-1) acidity (from pH 7 to 10, meq C g-1) d charge density (C m-2) e SUVA (L mg-1 m-1) f humic substance content (%, pH 2) g effective size reduction ∆reff (nm) h effective size reduction ∆reff (nm) c
a
a
WTMK
589 0.56 8.8 11.1 -0.076 2.5 55.1 0.32 0.58
a
CTMK
WMB
541 0.54 14.0 0.1 -0.117 2.4 54.4 0.27 0.70
983 0.721 7.4 1.7 -0.076 4.5 74.1 0.63 1.24
a
CMB
539 0.534 9.9 0.1 -0.083 2.8 63.7 0.69 0.61
a
WCH
4212 1.490 10.1 11.8 -0.168 4.3 61.6 0.70 54.2
a
CCH
1610 0.923 14.7 0.3 -0.177 2.3 62.4 1.00 14.3
a W ) whole; C ) charged fraction; TMK ) Tomhannock Reservoir, Troy, NY; MB ) Intercoastal Waterway at Myrtle Beach, SC; CH ) Edisto River at Charleston, SC. b Determined by size exclusion chromatography, see Methods Section in the Supporting Information. c Radius of gyration from a correlation by Lin and Deen (20), used as an estimate of solute radius. d Calculated from the value of acidity titrated from pH 3 to 7 and the molecular weight measured by SEC, assuming a spherical molecule. e Specific ultraviolet absorbance, UV absorption per unit organic carbon. f Determined by XAD resin adsorption, for details see the Supporting Information. g Determined experimentally as described in the text and tabulated in Supporting Information Table S1; effective size reduction from IS 0.01 to 0.1 M, except for CTMK (0.02 to 0.1 M). h Estimated using eq 9.
Source water NOM was fractionated into charged and neutral fractions using an anion exchange resin (IRA 958, Polysciences, Inc., PA). The eluted fraction was designated as neutral whereas the adsorbed fraction, back-eluted using a 0.5-N sodium hydroxide solution, was designated as charged. NOM Transport Experiments. The membrane test apparatus used in this research, depicted schematically in SI Figure S1, was modified from a commercially available benchscale stainless steel crossflow membrane filtration (CFMF) unit (Sepa CF, Osmonics Inc., Minneatonka, MN). A recycle loop was used to provide crossflow independent of feed flow rate. Three commercially available poly (ether sulfone) (PES) ultrafiltration membranes, having nominal MWCOs of 5, 10 and 100 kDa and isoelectric pH of 4.6, were selected for transport experiments (Biomax, Millipore Corp., Bedford, MA). For each NOM sample, observed sieving coefficient (So)Cp/Cb) was measured under crossflow conditions as a function of ionic strength and filtrate flux, varied by changing TMP. Analytical Methods. All NOM and model compounds were quantified using a total organic carbon analyzer (Shimadzu TOC-VCSH). The hydrophobic (HPO) fraction of whole NOM was determined employing XAD resin adsorption based on the method developed by U.S. Geological Survey researchers (18). Organic acidity titrations were carried out using an auto titrator (DL55, Mettler Toledo, OH). High-pressure size exclusion chromatography (HPSEC) was employed to measure the molecular weight distribution of NOM solutions as described previously (13).
Results and Discussion NOM Characteristics. NOM from three surface water sources was selected to exhibit range of properties, which are tabulated in Table 1. They exhibit properties consistent with those typically reported for aquatic NOM: molecular weights ranging between 500 and 5000 Da, humic substance content between 40 and 80%, and charge density ranging from -2 to -11 meq g-1 at neutral pH (19). Estimation of the Specific Membrane Pore Area. The calculated average hydrodynamic (Stokes-Einstein) radii of the 4 and 6 kDa dextrans selected to estimate the specific pore surface area s of the 5 kDa PES membrane were 1.21 and 1.53 nm respectively. The effect of flux on the observed sieving coefficient for the two dextrans is shown in SI Figure S4; an average specific pore surface area of 4.62 × 10-10 m was found. An average hydraulic permeability of 1.23 × 10-10 m s-1 Pa-1 was measured, yielding a corresponding value of
3.65 × 10-7 m for δm/εm. The magnitude of this value appears reasonably consistent with other reports in the literature for PES UF membranes (16). The specific pore surface area for the 10 kDa PES membrane was estimated using 10 kDa dextran sulfate sodium salt (an appropriately sized neutral dextran was not available) having an average radius of 2.20 ( 0.005 nm determined using a scanning mobility particle sizer (TSI model 3936). Sieving data were collected using an ionic strength of 0.1 M to minimize charge interactions. The observed sieving coefficient data and model fit with s ) 9.07 × 10-10 m are shown in SI Figure S5. The hydraulic permeability for the 10 kDa membrane was 5.73 × 10-10 m s-1 Pa-1. Solute Sieving Coefficient: Whole Waters. Sieving coefficients were measured for NOM (as TOC) in three natural water samples (TMK, MB, and CH) and for their charged and neutral fractions. The TMK and MB waters were filtered through a 5 kDa (nominal MWCO) PES UF membrane, whereas the CH water was filtered through a 10 kDa PES membrane because it has a larger molecular size (Table 1). The reason for choosing membranes with different pore sizes for these three waters was to obtain λ values that would result in a wide range of transport behavior as ionic strength was varied. These waters exhibited low irreversible fouling over the duration of the experiment (>90% pure water flux recovery after 30 min hydraulic cleaning); therefore, the properties of the membrane were assumed constant. The observed sieving coefficients of the unfractionated whole TMK NOM during filtration by the 5 kDa Da PES membrane are plotted as a function of filtrate flux and ionic strength in Figure 1. Similar results are shown in SI Figure S6 for the MB water. Open and filled squares are experimental data at ionic strengths of 0.01 and 0.1 M, respectively, and solid lines correspond to model fits using eq 4. The ability of the hydrodynamic model to describe the data is quite good, with regression coefficients (R2) generally higher than 0.80. Fitted and calculated model parameters are tabulated in SI Table S1. The measured (observed) sieving coefficients for the whole TMK and MB NOM decreased with increasing flux; the highest flux values measured correspond to sieving coefficients near the minimum value. Diffusive and convective fluxes were calculated from the concentration profile within the pore (see the Supporting Information for details). For the 5 kDa membrane, solute transport was primarily governed by diffusion (see SI Figure S10), even for fluxes greater than the flux corresponding to the minimum So, which is consistent VOL. 43, NO. 14, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Effects of ionic strength and filtrate flux on the observed sieving coefficient of whole TMK (WTMK) NOM. Membrane: PES MWCO 5 kDa; Experimental conditions: feed concentration 10 mg C/L, pH 7.0, crossflow velocity 0.3 m/s.
FIGURE 2. Effects of ionic strength and filtrate flux on the observed sieving coefficient of the whole CH (WCH) NOM. Membrane: PES 10 kDa; Experimental conditions: feed concentration 10 mg C/L, pH 7.0, crossflow velocity 0.3 m/s. with values of Npe,m less than 0.5 in most cases. The membrane Peclet number, NPe,m, is a measure of solute convection relative to diffusion averaged over the membrane thickness, δm. When Npe,m , 1, the transport process is dominated by diffusion, whereas when Npe,m . 1, transport is dominated by convection. Ionic strength had a large influence on solute transport, as illustrated in Figure 1 and SI Figure S6. As ionic strength was increased from 0.01 to 0.1 M, the minimum observed sieving coefficient (corresponding to Jv ) 1.30 × 10-5 m/s, TMP ) 20 psi) increased from 0.32 to 0.57 for TMK NOM and from 0.09 to 0.40 for MB NOM. This significant increase is consistent with the interpretation that the effective NOM molecular size, and hence λ ) reff/rp, became smaller with increasing ionic strength; this will be discussed in more detail in a subsequent section. The membrane Peclet number decreased as ionic strength increased and λ became smaller, because φKd increased to a greater extent than φKc; consequently, a larger fraction of solute flux was caused by diffusion. Concentration polarization was also reduced as ionic strength increased and λ became smaller, as a result of greater solute sieving (i.e., lower rejection). The observed sieving coefficients of the whole CH NOM are plotted as a function of filtrate flux and ionic strength (using the 10 kDa PES membrane) in Figure 2. Open and filled squares are experimental data at ionic strengths of 0.01 and 0.1 M, respectively, and solid lines are corresponding model fits using eq 4. Model parameters are tabulated in SI Table S1. The effect of flux on the observed sieving coefficient can again be seen clearly. In contrast to the TMK and MB water filtered on the 5 kDa membrane, the measured 5452
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FIGURE 3. Effects of ionic strength and filtrate flux on the observed sieving coefficient of NOM fraction. Membrane: PES MWCO 5 kDa; NTMK: neutral TMK NOM fraction; CTMK: charged TMK NOM fraction; Experimental conditions: feed concentration 10 mg C/L, pH 7.0, crossflow velocity 0.3 m/s. (observed) sieving coefficients for CH water filtered on the 10 kDa membrane increased with increasing flux; the lowest flux values measured now correspond to sieving coefficients near the minimum So value. Diffusive and convective fluxes were again calculated from the concentration profile within the pore. At the lowest values of flux measured, near the minimum sieving coefficient, diffusion and convection contributed nearly equally. As flux increased (and/or as ionic strength decreased) the contribution of convection increased further. The higher flux achieved with the 10 kDa membrane yielded a greater contribution of convection than observed for the TMK and MB waters filtered on the 5 kDa membrane. This is quantified by larger membrane Peclet numbers, ranging from 0.2 to 1.8 for the 10 kDa membrane, as compared to a range from 0.06 to 0.7 observed for TMK and MB filtration using the 5 kDa membrane. The observed sieving coefficients of a peat humic acid were measured using a 100 kDa PES membrane under the hypothesis that NOM transport in this system would be dominated by convection because of the large membrane pore size. The observed sieving coefficients are plotted as a function of filtrate flux and ionic strength in SI Figure S7. The properties of the 100 kDa PES membrane were estimated from the literature (8). In this experiment, the dominance of convection in NOM transport is clearly evident; the measured (observed) sieving coefficients increased with increasing flux at all ionic strengths. The large contribution of convection is quantified by large membrane Peclet numbers ranging from 0.8 to 17.4. Solute Sieving Coefficient: Neutral and Charged NOM Fractions. The observed sieving coefficients for charged and neutral NOM fractions are shown in Figures 3 and 4 for TMK and MB water, respectively. The results for CH water were qualitatively similar to those for the TMK water, and are shown in SI Figure S8. Solid curves are corresponding model fits using eq 4, and model parameters are tabulated in SI Table S1. The minimum in the observed sieving coefficient of charged and neutral fractions were similar to those of the whole water NOM. In addition, the dominant transport mechanism for the fractions was similar to that of the whole waters; e.g., for the TMK and MB fractions, most of the experimental data for the fractions is near or below the flux corresponding to the minimum sieving coefficient, and solute transport was primarily governed by diffusion. As shown in Figures 3 and 4 and SI Figure S8, a different effect of ionic strength on the transport behavior of charged and neutral NOM fractions was observed, confirming the distinct characteristics of these two fractions as obtained from the anion exchange fractionation technique.
FIGURE 4. Effects of ionic strength and filtrate flux on the observed sieving coefficient of NOM fraction. Membrane: PES MWCO 5 kDa; NMB: neutral MB NOM fraction; CMB: charged MB NOM fraction; Experimental conditions: feed concentration 10 mg C/L, pH 7.0, crossflow velocity 0.3 m/s.
the reduction in effective radius was significant for the whole water samples and their charged fractions, ranging from about 21% for the Tomhannock NOM to a high of 52% for the charged fraction of the Charleston water. The reductions observed here are much larger than those reported by Hosse and Wilkinson (15) and Lee et al. (5) based on diffusion coefficient measurements. Changes in Effective NOM Size. If NOM can change its size and/or configuration in response to changes in solution chemistry, such phenomena would offer one possible explanation for the observed changes in the sieving coefficients with ionic strength. The data of Cornel et al. (14) provide support for this interpretation. However, the NOM used here is aquatic in origin and much lower molecular weight. Changes in sieving coefficients can also result from electrostatic interactions, as discussed previously. Pujar and Zydney (21) proposed a simplified model to estimate the effective radius of BSA during UF processes. Their development assumes that the energy of electrostatic interaction is dominated by the energy associated with the distortion of the double layer around the charged solute caused by the presence of the pore boundary; this assumption is good when the solute charge density is much greater than the pore charge density (21), which is the case here. The charge density on NOM used here is in the range of -0.08 to -0.2 C/m2 as compared to a charge density on PES UF membranes on the order of -0.001 to -0.0028 C/m2. The lack of any significant change in the observed sieving coefficient of the neural fractions with increasing ionic strength provides additional support for this assumption. The resulting relationship for the effective radius is equal to a constant true radius, rs, plus a term accounting for electrostatic interactions: reff ) rs +
FIGURE 5. Effective NOM molecular radius reff at ionic strength of 0.01 and 0.1 M as NaCl. A large effect of ionic strength was observed for all the charged fractions. The effect was most dramatic for the charged fraction of the MB water; the observed sieving coefficient increased from 0.15 to 0.63 with increasing ionic strength from 0.01 to 0.1 M, at a permeate flux of about 1.5 × 10-5 m/s. In contrast, no significant change in the observed sieving coefficient with increasing ionic strength occurred for any of the neutral fractions. This result implies that the membrane properties controlling transport did not significantly change with increasing ionic strength, and justifies the treatment of the specific pore surface area as constant. The distinctly different transport behavior of the charged and neutral fractions confirms that the negatively charged species were responsible for the effects of ionic strength observed for the whole NOM, and emphasizes the role of charged functional groups. The lack of any significant ionic strength effect for the neutral fractions confirms that these molecules carry little charge. Inspection of eq 4 reveals that the observed changes in the sieving coefficient with ionic strength correspond to changes in the asymptotic sieving coefficient and the membrane Peclet number. Such changes are governed primarily by λ, as this parameter affects the partition coefficient and the convective and diffusive hindrance factors. Because the membrane properties controlling transport did not significantly change with increasing ionic strength, changes in λ were mainly caused by changes in the effective solute radius. The values of effective radius for all waters and their fractions at the two ionic strengths investigated are shown in Figure 5. No significant effective radius change was observed for any of the three neutral NOM fractions, whereas
4rs3σs2 ′ λ (1 - λ′) εrε0kBTκ
(9)
where ε0 is the permittivity of free space, εr is the dielectric constant of the bulk solution, κ is the inverse of the Debye length, σs is the solute charge density, and λ′ is the ratio of the true molecular radius to membrane pore radius. Changes in the effective solute radius are equal to the changes in the electrostatic term, which is sensitive to molecular size and charge density; however, the dependence on λ′ is relatively weak (21). To estimate the electrostatic term, solute charge density was estimated from the acid-base titration data from pH 3 to 7. The “true” NOM molecular size, rs, was approximated by its radius in a fully coiled state at an ionic strength equal to 0.10 M using the correlation proposed by Lin and Deen (20):
( ) 2 rgo Mw
1/2
) 0.23
(10)
where r2go was used as an estimate of rs. The change in the effective solute radius as a function of ionic strength (equal to the change in the electrostatic term of eq 9) and the measured change in effective solute radius based on sieving coefficient data are tabulated in Table 1. Although the model predicts larger changes than those measured, especially for the large and highly charged CH water, the result of this analysis suggests that all of the observed changes in effective solute size can be accounted for by electrostatic interactions; it is not necessary to invoke conformation changes as a cause for the effective size reduction. While this analysis does not rule out such changes, it does illustrate the importance of electrostatic interactions. Implications for Ultrafiltration Design. The modeling results presented in this paper clearly show the effect of flux VOL. 43, NO. 14, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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on the observed sieving coefficient. Although the data presented was for one crossflow velocity, the model has great utility in optimizing the design and operation of membrane processes in terms of solute properties, membrane properties, solution flux, and crossflow. The scope of this study was on membrane transport phenomena; as such our findings would have the greatest direct relevance to a membrane process either operated below a critical flux condition to minimize fouling, or operated with frequent cleaning or backwashing to prevent the buildup of a fouling layer. However, our approach could be extended to conditions under which significant fouling occurred, modeling the fouling layer as a second resistance in series with the membrane. Therefore, the work reported in this paper would be one component of a model that incorporated both the membrane and the fouling layer. We are currently extending the model to address this situation.
Acknowledgments We acknowledge the U.S. Environmental Protection Agency (EPA grant RD83090901-0) and the U.S. National Science Foundation (BES-9984709) for financial support.
Supporting Information Available Additional experimental details, a sensitivity analysis of the transport model, additional sieving coefficient data, model parameters, and a description of how concentration profiles and fluxes were calculated are provided. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Chellam, S.; Taylor, J. Simplified analysis of contamination rejection during ground and surface water nanofiltration under the information collection rule. Water Res. 2000, 35, 2460–2474. (2) Kilduff, J. E.; Mattaraj, S.; Sensibaugh, J.; Pieracci, J. P.; Yuan, Y.; Belfort, G. Modeling flux decline during nanofiltration of NOM with poly(arylsulfone) membranes modified using UVassisted graft polymerization. Environ. Eng. Sci. 2002, 19, 477– 495. (3) Braghetta, A.; Digiano, F. A.; Ball, W. P. Nanofiltration of natural organic matter: pH and ionic strength effects. J. Environ. Eng. ASCE 1997, 123, 628–641. (4) Kilduff, J. E.; Weber, W. J. Transport and separation of organic macromolecules in ultrafiltration processes. Environ. Sci. Technol. 1992, 26, 569–577. (5) Lee, S.; Amy, G.; Cho, J. Application of Sherwood correlations for natural organic matter (NOM) transport in nanofiltration (NF) membranes. J. Membr. Sci. 2004, 240, 49–65.
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(6) Deen, W. M. Hindered transport of large molecules in liquidfilled pores. AIChE J. 1987, 33, 1409–1425. (7) Opong, W. S.; Zydney, A. L. Diffusive and convective protein transport through asymmetric membranes. AIChE J. 1991, 37, 1497–1510. (8) Zeman, L. J.; Zydney, A. L. Microfiltration and Ultrafiltration Principles and Applications; Marcel Dekker, Inc.: New York, 1996. (9) Kedem, O.; Katchalsky, A. Thermodynamic analysis of permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta 1958, 27, 229–246. (10) Park, N.; Cho, J. Natural organic matter diffusivity for transport characterizations in nanofiltration and ultrafiltration membranes. J. Membr. Sci. 2008, 315, 133–140. (11) Sharma, R.; Chellam, S. Temperature effects on the morphology of porous thin film composite nanofiltration membranes. Environ. Sci. Technol. 2005, 39, 5022–5030. (12) Chin, Y. P.; Aiken, G.; O’Laughlin, E. Molecular weight, polydispersity, and spectroscopic properties of aquatic humic substances. Environ. Sci. Technol. 1994, 28, 1853–1858. (13) Kilduff, J. E.; Karanfil, T.; Chin, Y. P.; Weber, W. J. Adsorption of natural organic polyelectrolytes by activated carbon: A sizeexclusion chromatography study. Environ. Sci. Technol. 1996, 30, 1336–1343. (14) Cornel, P.; Summers, R.; Roberts, P. Diffusion of humic acid in dilute aqueous solution. J. Colloid Interface Sci. 1986, 110, 149– 164. (15) Hosse, M.; Wilkinson, K. Determination of eletrophoretic mobilities and hydrodynamic radii of three humic substances as a function of pH and ionic strength. Environ. Sci. Technol. 2001, 35, 4301–4306. (16) Pujar, N. S.; Zydney, A. L. Electrostatic and electrokinetic interactions during protein transport through narrow pore membranes. Ind. Eng. Chem. Res. 1994, 33, 2473–2482. (17) Wolff, S. H.; Zydney, A. L. Effect of bleach on the transport characteristics of polysulfone hemodialyzers. J. Membr. Sci. 2004, 243, 389–399. (18) Kilduff, J. E.; Mattaraj, S.; Wigton, A.; Kitis, M.; Karanfil, T. Effects of reverse osmosis isolation on reactivity of naturally occurring dissolved organic matter in physicochemical processes. Water Res. 2004, 38, 1026–1036. (19) Wilkinson, K. J.; Reinhardt, A. Contrasting roles of natural organic matter on colloidal stabilization and flocculation in freshwaters. In Flocculation in Natural and Engineered Environmental System; Droppo, I. G., Leppard, G. G., Liss, S. N., Milligan, T., Eds.; CRC: Boca Raton, FL, 2005; pp143-170. (20) Lin, N. P.; Deen, W. M. Charge effects on the diffusion of polystyrene sulfonate through porous membranes. J. Colloid Interface Sci. 1992, 153, 483–492. (21) Pujar, N. S.; Zydney, A. L. Electrostatic effects on protein partitioning in size-exclusion chromatography and membrane ultrafiltration. J. Chromatogr., A 1998, 796, 229–238.
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