Natural organic matter diffusivity for transport characterizations in nanofiltration and ultrafiltration membranes

Journal of Membrane Science 315 (2008) 133–140

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Natural organic matter diffusivity for transport characterizations in nanofiltration and ultrafiltration membranes Noeon Park, Jaeweon Cho ∗ NOM ecology National Research Laboratory, Department of Environmental Science and Engineering, Gwangju Institute of Science and Technology (GIST), 1 Oryong-dong, Buk-gu, Gwangju 500-712, Republic of Korea

a r t i c l e

i n f o

Article history: Received 30 September 2007 Received in revised form 13 February 2008 Accepted 14 February 2008 Available online 19 February 2008 Keywords: Diffusivity NF/UF membrane Natural organic matter (NOM) Transport parameter Irreversible thermodynamic model

a b s t r a c t A diffusion cell was used to experimentally determine the diffusivity of natural organic matter (NOM). Various diffusivities were obtained for NOM with respect to both pH and the molecular weight cutoff (MWCO) of membranes. Values determined with the diffusion cell were compared to those estimated from flow field-flow fractionation (fl-FFF) and high-performance size exclusion (HP-SEC). Firstly, the diffusivities obtained with the diffusion cell were much lower than those from both fl-FFF and HP-SEC, which was due to the interference in NOM transmission through the membrane pores. Secondly, the diffusivity of NOM increased with decreasing pH due to both electrostatic interactions and double layer compaction. Thus, at lower pH, the mass transfer coefficient of NOM increased due to increases in the corresponding diffusivity. Thirdly, the diffusivity of NOM decreased as the MWCO of a membrane decreased, which was the result of the sieving effect between the NOM and the membrane. Along with the experimental identification of NOM diffusivity, the transport parameters (mass transfer coefficient (k), solute permeability (Pm ), and membrane selectivity ()) of NOM under different pH conditions were also investigated using irreversible thermodynamic models. The transport parameters of NOM in a membrane system depended on the permeability and surface charge. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The natural organic matter (NOM) produced in environmental systems may cause severe reductions in flux and removal during filtration through membranes. The transport phenomenon of NOM at the membrane surface and/or in pores is classified in terms of both convection and diffusion. The diffusivity of NOM provides useful information in the understanding of NOM transport phenomenon during filtration. The diffusivity calculated by the Stokes–Einstein equation, based on the thermodynamic and drag forces of a sphere solute, depends only on the molecular size. To evaluate the diffusivity of heterogeneous and complex NOM under different chemical conditions, including pH and ionic strength, the diffusivity of humic acids has previously been determined using diffusion cells equipped with a track-etched membrane [1]. The diffusivity of humic acids, with regard to the pH and calcium concentration, has been investigated; it was revealed that the diffusivity increased when pH and calcium concentration decreased and increased, respectively, which was resulted from the molecular compaction of humic acids. Park et al. [2] also determined the diffusivity of NOM at different pH to explain the removal mecha-

∗ Corresponding author. Tel.: +82 62 970 2443; fax: +82 62 970 2434. E-mail address: [email protected] (J. Cho). 0376-7388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2008.02.011

nisms of NOM by a UF membrane with respect to the J/k (ratio of water permeation to mass transfer coefficient) ratio. Mohammad and Ali [3] studied the removal efficiency of solutes having different MWCO with respect to the surface charge of membranes. However, explaining the transport of solutes as a function of the MWCO of membranes has proven to be quite difficult. The diffusivity of NOM across membrane pores depends on the chemical conditions of the feed solution as well as the membrane properties, such as the pore size distribution, roughness, and surface charge. Flow field-flow fractionation (fl-FFF) is another analytical tool able to determine the diffusivity and size of macromolecules, colloids, and particles, using classical FFF theory [4,5]. When either macromolecules or particles are injected into the FFF channel, they are influenced by two different flows: i.e., laminar and cross (or field) flows. The subsequent resulting forces, which include drag and diffusional forces, are able to separate the solutes for detection at the channel exit at different times. It has been revealed that NOM could be characterized using fl-FFF in terms of its molecular size distribution with a minimum detection limit of 390 Da [6–8]; the diffusivity of NOM (humic and fulvic acids) could be measured by fl-FFF [8]. The solute transport phenomenon in the concentration polarization (CP) layer near the membrane surface and across the membrane pores can be evaluated with transport parameters, including mass transfer coefficient (k), solute diffusive permeability (Pm ) and selectivity (), by irreversible thermodynamic models

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Thirdly, the diffusivity of NOM was determined using fl-FFF. Theories for the fl-FFF system, in terms of the retention parameter (), channel geometries (channel thickness w (=250 ␮m), channel volume V0 ), volumetric rate of cross-flow (Vc ), peak times ratio (R), and particle diffusivity (D), can be described as follows [4,5]: =

V 0D Vc w2

(3)



R = 6 coth

Fig. 1. Conceptual schematic of concentration polarization and thermodynamic solute transmission models.

[9–11], as depicted in Fig. 1. The transport parameters determined by various thermodynamic models were affected by various factors, including the chemical conditions of the feed solution, membrane channel height, and cross-flow velocity. The diffusion versus convection terms were used to explain in detail the transport of NOM across membrane pores. In this study, the transport phenomena during filtration were evaluated with various parameters determined by thermodynamic models. Diffusion experiments were also performed to gain an understanding of the transport phenomenon of NOM during filtration. 2. Theories

The diffusivity of NOM was determined using three different systems: the Stokes–Einstein equation, and experimental methods with a diffusion cell and fl-FFF. Firstly, the diffusivity of the NOM was calculated using the Stokes–Einstein Equation (1) by measuring the molecular size of the NOM. This equation was devised by Einstein [12] by combining the hydrodynamic drag and thermodynamic forces.

(4)

where R = t0 /tr , with t0 and tr representing the retention times of the unretained (void) and retained peaks obtained from the FFF system, using UV detection at 254 nm, respectively. Equating Eqs. (3) and (4) gives Eq. (5), which can be used to estimate the diffusivity of particles, as follows:  = solution of Eq. (2) =

V 0D Vc w2

(5)

2.2. Transport parameters estimations The transport parameters of NOM in the CP layer and through the membrane pores were determined with two different irreversible thermodynamic models. Firstly, the Kedem–Katchalsky model, which was developed assuming the phenomenological transport coefficient to be a black box. Secondly, a modified Spiegler–Kedem model, which combined the concentration polarization onto the membrane surface [10].

JC − D

dc = JCp dx



Jv = k ln

Here, CL and CR are the NOM concentrations in the left and right chambers of the diffusion cell, respectively, and D, ˇ and t are the apparent diffusion coefficient (cm2 /s), a lumped cell constant (cm−2 ) and the specific time (s) during the diffusion experiments, respectively. The only difference between our method and that of Wang et al. was that on the right side of Eq. (2); they used the mass transfer coefficient (k), whereas, ours directly used the diffusion coefficient (D) was used.

Cm − Cp Cb − Cp



(7)

Where k, Cb , Cm , and Cp are the mass transfer coefficient, and the concentrations of the bulk solution, at the membrane surface, and of the permeate, respectively. With the observed (Robs ) and true (R) rejection expressions (see Eqs. (8) and (9)) of a membrane, the equation can be rewritten as follows, to finally give the following equation (Eq. (10)): Robs = R= ln

(2)

(6)

Integration of Eq. (6) provides a simple model for explaining the solute transport in the CP layer as follows:

(1)

where K is the Boltzmann constant,  is the viscosity of the eluent (i.e., liquid) phase, T is the absolute temperature of the solution and rp is the radius of the solute. The equation has two approximations; the solute is a sphere and no interaction exists between the solute and solvent. However, NOM are heterogeneous and complex compounds in aqueous systems, and possess various functional groups, including carboxylic acids, phenolics, etc. Secondly, the apparent diffusivity of NOM was estimated from diffusion experiments employing a diffusion cell, as suggested by Wang et al. [1]; based on Fick’s first law. The equation can be expressed as (CL − CR )0 = Dˇt ln (CL − CR )t

2



− 2

2.2.1. Film model An equation representing solvent flux (Jv ) was established by making the mass balance for the solutes, across membrane pores, and away from the membrane surface (Eq. (6)).

2.1. Diffusivity of NOM

KT D= 6rp

1

Cb − Cp Cb

Cm − Cp Cm

1 − R

obs

Robs

(8) (9)



= ln

1 − R R

+

Jv k

(10)

Both k and Cm can be determined from experimental data by plotting ln[(1 − Robs )/Robs ] versus the solvent flux (Jv ). The boundary thickness (ı) in the CP layer was calculated using k (k = D/ı) from Eq. (10). 2.2.2. Kedem–Katchalsky and Spiegler–Kedem models Kedem and Katchalsky developed a thermodynamic model to explain the transport characteristics assuming a membrane system to be a black box. They described both the solvent flux (Jv ) and solute

N. Park, J. Cho / Journal of Membrane Science 315 (2008) 133–140

flux (Js ) using the phenomenological transport coefficient, which can be described by the following equations:

135

3. Materials and methods 3.1. NOM samples

Jv = Lp (P −  )

(11)

Js = Pm (Cm − Cp ) + (1 − )Jv C ∗

(12)

where Lp , , , and Pm are the pure water permeability, osmotic pressure, and selectivity and solute diffusive permeability, respectively. The C* = ([(Cm − Cp )/ln(Cm /Cp )]) value is the average logarithm concentration between Cm and Cp . In Eq. (12), the solute flux (Js ) depends on the diffusion and convection in the membrane, which assumed the membrane system in a steady state. However, this assumption does not apply to NF/UF membranes due to variation in the calculation of C* value, thus, Spiegler and Kedem described the solute transport model based on the classical Kedem–Katchalsky model by assuming the existence of a local equilibrium, which has the form Jv = Lp (x)

 dp

Js = w(x)RT

dx

− RT

dc dx

 (13)

dc + (1 − (x))Jv C(x) dx

(14)

where w is the permeation coefficient. We assumed that the local transport coefficients (Lp (x), w(x), and  (x)) were constant within a given membrane, with the permeation coefficient (w(x)) equal to D/ı(x)RT. The corresponding equations are described as follows: Lp (x) = Lp ım

(15)

w(x) = wım =

D RT

(16)

(x) = 

(17)

The Spiegler and Kedem (S–K) model (i.e., Eqs. (13) and (14)) was integrated for distance (x) in the membrane system, as follows: 1 exp [Jv (1 − )/wRT ] −  = R {exp [Jv (1 − )/wRT ] − 1}

(18)

By substituting Eq. (18) into Eq. (10), a combination of the modified S–K model and CP concept was obtained. Robs = 1 − Robs

A concentrated NOM solution (NR-SW) was prepared from Nakdong River surface water using a reverse osmosis (RO) membrane (Saehan, Korea). During the concentration procedure, a portion of the NOM might be adsorbed onto the membrane surface; thus, this should be taken into consideration throughout the rest of this paper. The NOM were separated into colloidal (COM) and non-colloidal NOM (NCD) using a dialysis bag (Spectra/Por, USA) with a MWCO of 3500 Da. The NCD was then further fractionated into hydrophobic (NCD-HP), transphilic (NCD-TL) and hydrophilic (NCD-HL) NOM constituents using XAD-8/4 resins. A concentrated NOM solution from Dongbok lake (DL-SW), Korea, which was collected using an RO membrane, was also prepared, and its behaviors in the diffusion experiments were tested with different UF membranes (refer to Table 1). To assure constant experimental condition, the salt components (NaOH and HCl) were removed from the various XAD-8/4 resin fractionated NOM constituents, using an electro-dialysis apparatus, which was equipped with both anion and cation (CMX, Astom Corp., Japan) exchange membranes. The molecular weights of the NOM samples were measured by a high-performance size exclusion chromatography (HP-SEC) method using UV detection at 254 nm (FUTECS, Korea) [13]. The HP-SEC mobile phase was prepared from 0.096 M NaCl, with the use of phosphate buffer solution (0.0024 M NaH2 PO4 + 0.0016 M Na2 HPO4 ) to adjust the total ionic strength to 0.1 M. As expected, the COM showed a higher MW value than any of the other NOM constituents, with NR-NCD-HL exhibiting the lowest value. Also, the hydrophobic NOM fraction, as expected, showed a high SUVA (specific UV absorbance = UV absorbance at 254 nm/DOC) value.

   1−

 J (1 − )   v

1 − exp −

wRT

 J  v

exp −

k

(19)

The NOM transport parameters in a membrane were determined using different trans-membrane pressures (210, 280, 350, 420, 490, 550, 620, 695, 725, and 760 kPa) employing a non-linear parameter estimation method from the Statistica software.

3.2. Tested membranes Regenerated cellulose (RC) membranes, with MWCO of 12,000–14,000 Da (Spectra/Por), 10,000 Da (PLTK, Millipore, USA) and 5000 Da (PLCC, Millipore, USA), were prepared for the diffusion experiment. These membranes were chosen due to their virtually non-charged surfaces and significant hydrophilicity [2]. Both the electrostatic and hydrophobic interactions between the membrane and NOM might be eliminated due to the lesser charged and hydrophilic properties of the RC membranes. The NF membrane (HL) and two different tight-UF membranes (PW and GM) were also tested to evaluate the diffusivity and transport parameters of the NOM. As shown in Table 2, both the PW and GM membranes exhibited higher hydrophobicity (based on contact angles), zeta potential values and surface roughness than those of the HL membrane.

Table 1 The characteristics of various NOM samples

NR-SW NR-COM NR-NCD-HP NR-NCD-TL NR-NCD-HL DL-SW

DOC (mg/L)

UVA (cm−1 )

SUVA (L/mg m)

Molecular weighta (g/mol)

Conductivity (mS/cm)

Ds b (10−6 cm2 /s)

20.5 20.5 19.5 20.0 5.0 6.5

0.720 0.480 0.923 0.544 0.069 0.124

3.51 2.34 4.73 2.72 1.38 1.91

1270 2120 1210 1135 350 1050

4.0 4.0 4.0 4.0 4.0 0.1

4.571 3.855 4.645 4.744 7.011 4.868

Here, NR-SW (concentrated NOM solution obtained from Nakdong River surface water in Korea), NR-COM (colloidal NOM isolated from NR-SW), NR-NCD-HP (hydrophobic NOM fractionated from non-colloidal NOM), NR-NCD-TL (transphilic NOM fractionated from non-colloidal NOM), NR-NCD-HL (hydrophilic NOM fractionated from noncolloidal NOM), and DL-SW (concentrated NOM solution obtained from Dongbok lake in Korea). a Weight-average molecular weight value. b Ds was calculated by the Stokes–Einstein equation, estimated by Eq. (1).

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Table 2 Membrane properties

PW GM HL a b c

Materials/nominal MWCO, provided by manufacturers

Contact anglea (◦ )

Zeta potentialb (at pH 8)

Roughnessc (nm)

Polysulfones/10,000 Polyamide/8000 Polyamide/150–300

62 ( ± 2.0) 46 ( ± 0.6) 15 ( ± 1.0)

−16.4 −29.9 7.8

10.3 46.0 5.2

´ Contact angle was measured using the sessile drop method with a goniometer (rame-hart, Inc., US). Zeta potential of the membrane surface was estimated by the electrophoretic method with a light scattering electrophoresis apparatus (ELS-8000, OTSUKA, Japan) [14]. Mean average roughness value of the membrane surface was measured by atomic force microscope (SPM 9500j2, Shimadzu, Japan).

3.3. Experimentally determined NOM diffusivity using diffusion cell and fl-FFF apparatus The diffusion cell was composed of two chambers, with water circulated to maintain a constant solution temperature using a refrigerated circulator (25 ◦ C). Pure water (230 mL of blank solution) was poured into the right-hand side of the chamber for 1 h, after which the NOM (230 mL of sample) solution was injected into the left-hand side of the chamber. The ionic strength of the pure water in the right side of chamber was adjusted to that of the NOM samples using NaCl. The UV absorbances on both sides of the chamber were measured at 400 rpm for every 30 min. The diffusion cell constant (ˇ) was determined using materials with known diffusivity values, which for our system was determined using 0.01 M KCl and phenol solutions. From plots of ln[(CL − CR )0 /(CL − CR )t ] versus time, the diffusivities of various NOM samples were obtained. All experiments were conducted under identical conditions (4 mS/cm, 25 ◦ C and 20 mg/L), with the exception of the NR-NCD-HL constituent. The NOM diffusivity was investigated under various pH and MWCO conditions, and those of the various constituents were also compared using a symmetric fl-FFF apparatus (F-1000, FFF Fractionation LLC, US), with channel and cross-flows of 1.0 and 3.5 mL/min, respectively. A regenerated cellulose membrane, with a MWCO of 1000 Da (PLAC, Millipore, US), was used to eliminate the interaction between the membrane and NOM. The wavelength of the UV detector and the temperature were 254 nm and 25 ± 2 ◦ C, respectively. Polystyrene sulfonates (Polysciences, Inc., Warrington, PA, US), with molecular weight cutoffs (MWCOs) of 1800, 4600, 8000, and 18000 g/mol, were used as standard compounds. The mobile phase was the same as that used for the HP-SEC method. The diffusivities of various NOM constituents were determined using classical FFF theory [6–8]. For all used methods employed, including HP-SEC, fl-FFF, and diffusion cell, the NOM were identified with UV detection; therefore, some NOM constituents (especially non-aromatic/hydrophilic NOM) were unable to be recognized by the detector. This limitation could have been overcome with the use of an on-line DOC detector; however, this type of detector was not available for this study. It should also be noted that this study aimed to provide quick and easy estimation protocol, instead of rigorous characterization of NOM, for the rapid prediction of membrane performance and fouling with respect to various NOM, employing an UV detector, as this method of detection is currently available to most researchers.

coefficient (R2 ) from the linear curve fitting between the DOC and UV was 0.999, indicating a good correlation between the DOC and UV values for NR-SW. The UV value, rather than the DOC, was measured for every NOM sample throughout the correlation experiment. As shown in Fig. 2, a good linear relationship of the slope was obtained from plotting ln[(CL − CR )0 /(CL − CR )t ] versus time when a regenerated cellulose membrane, with MWCOs ranging from 12,000 to 14,000 Da, were employed. The combined cell constant of the diffusion system for the regenerated cellulose membranes was calculated using KCl solution. The effect of pH on the diffusion coefficient of NR-SW was also investigated; the corresponding results are shown in Fig. 2. As hypothesized, with decreases in the pH, the diffusivity of NR-SW increased, which can be explained by the change in the shape of the molecules (from linear to coil type) [14]. The diffusivity of NOM for the RC membrane was not influenced by the adsorption and electrostatic interactions between a membrane and NOM, as RC membrane is virtually non-charged and relatively hydrophilic. The molecular weight distributions of the diffused NOM on the right-hand side of the chamber (originally filled with pure water) were measured using the HP-SEC method. At lower pH range, the relatively large molecules of NR-SW could easily diffuse to the right-hand side chamber due to a reduction in the electrostatic interaction, which showed good agreement with the results of Wang et al. [1]. The bulk diffusivity of various NOM constituents, as determined from the RC membrane with MWCOs ranging between 12 and 14 kDa, are summarized in Table 3. The NR-COM did not favor kinetic behaviors over time due to their large molecular size, but the transmission of the NR-NCD-HL was most favored due to their lower molecular size. With the exception of the NR-NCD-HL, all the NOM samples exhibited lower NOM diffusivities than those calculated by the Stokes–Einstein equation; NOM diffusivity increases in the order: NR-NCD-HL > NR-NCD-TL > NR-SW > NR-COM, and all increased with decreasing pH due to the change in their molecular shape. With help of this method, the diffusivity of solutes in an aquatic system was revealed to be experimentally determined, in terms of pH, solute concentration, and ionic strength. However, the

4. Results and discussion 4.1. Regenerated cellulose membranes 4.1.1. Bulk diffusivity For the determination of the diffusivity of various NOM, experiments investigating the correlation between the DOC and UV254 were performed with NR-SW, as DOC measurements for the calculation of the diffusivity require large solution volumes. Various concentrations of NOM solution were prepared, with the UV values of each solution then measured. The value of the correlation

Fig. 2. Diffusion experiments with the RC membrane (12,000–14,000 Da): Both CL and CR are the concentrations of a KCl at left and right chamber in diffusion cell, respectively.

N. Park, J. Cho / Journal of Membrane Science 315 (2008) 133–140

137

Table 3 Diffusivities of the different NOM determined with the RC membrane at various pHs

NR-SW NR-COM NR-NCD-TL NR-NCD-HL

Conductivity (mS/cm)

MWHP-SEC a (g/mol, nm)

MWfl-FFF c (nm)

4.0( ± 0.1) 4.0( ± 0.1) 4.0( ± 0.1) 4.0( ± 0.1)

1270, 1.08 2120, 1.28 1135, 1.04 350, 0.70

0.93 1.13 0.81 –

Dcell b pH 2.4

pH 7.2

pH 10.0

3.02 0.61 3.21 12.89

1.97 0.40 1.77 9.10

1.67 0.09 1.37 –

Dfl-FFF c

Ds a

5.62 4.53 6.41 –

4.57 3.86 4.74 7.01

‘–’: not measured. a MWHP-SEC and Ds (×106 cm2 /s): molecular weight and diffusivity of various NOM constituents were estimated by HP-SEC and the Stokes–Einstein equation using the MW values from HP-SEC, respectively. b Dcell : diffusivities estimated with the diffusion cell using the regenerated cellulose and dialysis type membrane with MWCO ranging 12–14 kDa. c MWfl-FFF and Dfl-FFF (×106 cm2 /s): mean molecular weight and diffusivity of various NOM constituents, estimated using the fl-FFF apparatus.

solute diffusivity calculation based on the Stokes–Einstein equation has limitation as the molecular size of a solute should be additionally measured. The MW values of the various NOM constituents from the fl-FFF apparatus were lower than those found from the HP-SEC method. Correspondingly, higher diffusivity values for the NOM were obtained from fl-FFF than from the HP-SEC method, as a larger size will provide a lower diffusivity. This difference between the fl-FFF and HP-SEC methods was resulted from a difference in the separation mechanisms: two crossing flows for fl-FFF versus column resin type for HP-SEC. In addition, the accumulation membrane inside the fl-FFF can interact with NOM as a result of electrostatic repulsion, which provides smaller sized molecules (i.e., effective size) than are actually found. The diffusivities determined with diffusion cells were lower than those determined by both the fl-FFF and HP-SEC, which can be easily envisioned, as NOM should penetrate the pores of membranes positioned between the two diffusion cells. At lower, compared to higher pH ranges, the interference due to the electrostatic interactions between NOM and the membrane was minimized, which resulted in higher diffusivities for the former.

Fig. 3. The removal trends (Robs ) against Jv (solvent flux)/k (mass transfer coefficient) ratio: RC membrane with MWCO of 5 kDa () and RC membrane with MWCO of 10 kDa ().

the difference in concentration and time. The slope of the RC membrane (PLTK, Millipore) with a MWCO of 10 kDa was steeper than that with the 5 kDa MWCO (PLCC, Millipore). Because the membrane pores acted as resistance toward the transport of NOM, the DL-SW NOM could not be easily transmitted through the PLCC compared to PLTK membrane; the Dcell ˇ values of the PLCC and PLTK membranes were 0.183 × 10−5 and 0.285 × 10−5 , respectively. Experiments were conducted to find the NOM transport parameters as a function of the J/k (i.e., water permeation/mass transfer coefficient) ratio. As shown in Fig. 3, the PLCC membrane, with a MWCO of 5 kDa, had a higher removal efficiency than that of the PLTK membrane, with MWCO of 10 kDa, with respect to the DL-SW

4.1.2. Effective diffusivity across membrane pores Regenerated cellulose membranes with MWCOs of 5 and 10 kDa were tested to investigate the effects of the MWCO. The RC membranes with greater hydrophilicity and a low surface charge were chosen for these experiments; the zeta potentials of the membranes, as measured by the electrophoresis method [15], ranged from 2.0 (at pH 2) to 6.0 (at pH 9). KCl solution was used to calibrate the membrane properties (hydrophilic and less charge). Experiments were conducted with DL-SW (6.5 mg/L), with Eq. (2) used for the calculations. The plots (similar to Fig. 2; not shown here) from the experimental data provided a good linear relationship between Table 4 Diffusivities and transport parameters of DL-SW NOM with different RC membranes Membranes

Nominal MWCO, provided by manufacturer

Classical K–K modela

(a) Transport parameters of DL-SW PLCC 5 kDa PLTK 10 kDa Membranes

Dcell (×106 cm2 /s)

Modified S–K modelb

k (×10 cm/s)

Pm (× 10 cm/s)



25.38 32.76

3.42 11.17

0.47 0.36

a

Membrane thickness (ım ) (cm)

3

a

c d e f

5

c

Classical K–K modele , Pm ım (×106 cm2 /s)

(b) Comparison between experimental diffusivity (Dcell ) and transport parameters (Pm ım d ) PLCC 0.79 0.014 0.48 PLTK 1.95 0.014 1.56 b

b

k: mass transfer coefficient (cm/s). Pm : solute diffusive permeability (cm/s). : membrane selectivity. ım : boundary thickness in the CP layer (nm). Classical K–K model does not combine the CP concept into the membrane system. Modified S–K model combines the CP concept evaluated from the film model.

k(×103 cm/s)

Pm (×105 cm/s)



– –

12.70 26.24

0.72 0.62

Modified S–K modelf , Pm ım (×106 cm2 /s)

1.78 0.37

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N. Park, J. Cho / Journal of Membrane Science 315 (2008) 133–140

Table 5 Diffusivity of NR-SW determined with the different charged membranes at various pHs (×106 cm2 /s) Conductivity (mS/cm) PW (10 k) GM (8 k) HL (150–300)

4.0( ± 0.1) 4.0( ± 0.1) 4.0( ± 0.1)

pH 2.4

pH 7.2

pH 10.0

Ds

2.377 1.441 1.360

2.390 1.667 1.716

2.557 2.782 1.650

4.571 4.571 4.571

NOM. The Robs for both membranes was also observed to decrease with increasing J/k ratio, suggesting the convectional transmission of NOM dominated diffusional transmission. The NOM transport parameters of both membranes are summarized in Table 4(a). The PLTK membrane having a higher MWCO value, exhibited a higher solute diffusive permeability (Pm ) and lower selectivity () than those of the PLCC membrane, which was in good agreement with the experimental diffusivity values of the DL-SW identified using the diffusion cell. The solute diffusive permeability (Pm ) could be considered as the experimental diffusivity through membrane pores, which can be estimated from membrane filtration experiments. By combining Eqs. (12), (14) and (16), the experimental diffusivities and transport parameters (Pm ım ) for both membranes can be compared, as summarized in Table 4(b). The diffusivities (i.e., Pm ım ) determined by the modified S–K models were higher and lower than those determined by the diffusion cell experiments (i.e., Dcell ) for the PLCC and PLTK membranes, respectively. The classical K–K models provided slightly lower (but similar) diffusivities than those determined by the diffusion cell. Note: the modified S–K model integrates the concentration polarization concept into the thermodynamic transport model (i.e., the classical K–K model (Eq. (12)); thus, the S–K model can consider both CP and concentration differences between the feed and permeate sides (i.e., Cm and Cp ). 4.2. Effects of surface charge and hydrophobicity of membrane on NOM diffusivity

Fig. 4. The plot of adsorbed NR-SW to different membranes.

As listed in Table 3, the NOM from the Nakdong River was characterized in terms of diffusivity, using the diffusion cell employing an RC membrane, fl-FFF, and HP-SEC. In this section, the same NOM was characterized with different membranes in terms of diffusion cell and membrane filtration experiments, with the aim of demonstrating the effects of membrane properties on NOM diffusivity.

4.2.1. NOM diffusivities determined using diffusion cell Three different charged membranes, as opposed to the RC membrane, were also tested to investigate the effects of the surface charge and MWCO values. In these experiments, the KCl was replaced with phenol for measurement of the cell constant to minimize the electrostatic repulsion between the ions and the charged

Table 6 Diffusivities and transport parameters of NOM determined with polyamide UF and NF membranes pH

Dcell (×106 cm2 /s)

Diffusion 3

k(×10 cm/s)

Convection 

5

Pm (×10 cm/s)

(a) Mass transfer coefficient (k) and membrane transport parameters, estimated using Eq. (16) GM 2.4 1.441 5.69 27.95 0.37 7.2 1.667 16.44 10.08 0.66 10.0 2.782 9.65 9.63 0.66 HL 2.4 7.2 10.0 Membranes

1.360 1.716 1.650 Dcell (×106 cm2 /s)

18.82 107.97 22.00

0.54 3.59 0.38

Membrane thickness (ım ) (cm)

0.81 0.90 0.85

Pm (×105 cm/s)



4.49 10.79 8.30

4.62 2.70 2.23

0.34 0.62 0.63

22.60 37.71 153.6

0.97 1.00 1.31

0.81 0.88 0.84

k(×103 cm/s)

Classical K–K model, Pm ım (×106 cm2 /s)

Modified S–K model, Pm ım (×106 cm2 /s)

(b) Comparison between Dcell and Pm ım with charged membranes in the convection system GM 2.4 1.441 0.019 4.71 7.2 1.667 0.019 4.12 10.0 2.782 0.019 4.71

0.88 0.51 0.42

HL 2.4 7.2 10.0

0.16 0.17 0.22

1.360 1.716 1.650

0.017 0.017 0.017

0.94 2.19 1.08

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(i.e., Pm )) of NOM away from the membrane surface. The corresponding transport parameters for both diffusion and convection behaviors are listed in Table 6(a). The Robs of the negatively charged GM membranes was lowest at pH 2.4, which can be explained by the relatively low back diffusive mass transfer coefficient (k) and relatively high-solute diffusive permeability (Pm ), as shown in Table 6. However, the GM membrane had similar Robs values at pHs 7.2 and 10.0, with respect to the NR-SW, as the membrane was negatively charged at both these pH values. The HL membrane was affected by pH changes, with respect to Robs and reflection coefficient, due to its very low MWCO. As shown in Table 6(b), the solute diffusive permeabilities (Pm ım ) for the GM membrane were lower than those determined using the diffusion cell, and decreased with increasing pH due to the membrane becoming negatively charged at higher pH ranges. However, the HL membrane exhibited no decreasing trends with respect to the solute diffusive permeability with increasing pH, which again was due to its very low MWCO. 5. Conclusions

Fig. 5. The removal trends of different membranes against Jv /k ratio.

membranes, as phenol has a small MW (94 g/mol) and a neutral charge (pKa = 10) at pH 7. A good correlation was obtained between phenol and the HL membrane (similar to Fig. 2; not shown). The diffusivity of NR-SW was investigated using various charged polymeric membranes, the results of which are shown in Table 5. Both the PW and GM membranes exhibited opposing trends compared to the RC membrane in terms of their diffusive values with respect to pH, which was probably due to the adsorption of NOM onto the membrane surfaces (approximately 15% of initial condition at pH 2 was adsorbed based on mass balance calculation). Meanwhile, the HL membrane, which exhibited relative hydrophilicity and a slightly positive surface charge at neutral pH, had the highest diffusivity value at pH 7.2. This can be explained by the electrostatic interaction between the membrane and the NOM. The zeta potential values of the HL membrane were 20.9 and −28.3 mV at pHs 2 and 10, respectively. The transmission of the NOM across membrane pores was unfavored by electrostatic attraction at pH 2, but electrostatic repulsion occurred at pH 10 (see Fig. 4). 4.2.2. Determination of transport parameters The transport parameters of NR-SW across the membrane pores were estimated using the irreversible thermodynamic model (Eq. (19)). To investigate the transport characteristics of NR-SW with the membranes, transport experiments were performed to determine the observed removal efficiency (Robs ) with respect to the J/k ratio. As shown in Fig. 5, the NOM transmission behaviors of both the GM and HL membranes could be divided into diffusion (increasing of Robs as increasing J/k ratio) and convection (decreasing of Robs as increasing J/k ratio). The increases in Robs were believed to be affected by the back diffusion (as opposed to the diffusive transport

Firstly, the diffusivity of NOM was experimentally determined using various methods, including size measurement (by highperformance size exclusion chromatography) followed by the use of the Stokes–Einstein equation, flow field-flow-fraction (fl-FFF), and diffusion cells, for both virtually non-charged and charged membranes. Overall, the NOM diffusivities determined from the diffusion cell experiments with various different membranes (even with non-charged membranes) were all lower than those determined with fl-FFF and the Stokes–Einstein equation, and decreased with increasing pH values, as the diffusive transmission of NOM through the membrane pores in the diffusion cells was interfered with the membrane surfaces and pores. Secondly, membrane filtration experiments were also conducted to determine the NOM transport parameters, especially focusing on diffusive transmission through membrane pores; the diffusive transport parameters (i.e., solute diffusive permeability (Pm )) of NOM estimated by the thermodynamic models were compared to the diffusivities of NOM previously estimated using the diffusion cells. Thus, two different diffusivities, Pm ım (across membrane pores into permeate side) versus D (away from the membrane surface), could be determined from the perspectives of effective diffusivity estimations. In conclusion, the effective diffusivities of NOM were successfully determined using various methods, which can be used to predict membrane performance and fouling; if the diffusivity of NOM, in terms of either Dfl-LLL or Dcell , is higher than the NOM diffusive transmission parameter, in terms of Pm ım , relatively high-removal efficiency and relatively low fouling potential can be obtained with NOM for the membrane tested. Acknowledgment This research was supported by a grant from the National Research Laboratory Program by the Korea Science and Engineering Foundation (NOM ecology Lab: R0A-2007-000-20055-0).

Nomenclature C solute concentration (mg/L) Cb and Cp bulk and permeate concentration, respectively (mg/L) CL and CR NOM concentrations in the left and right chambers of the diffusion cell, respectively (mg/L) Cm solute concentration at the membrane surface (mg/L)

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References C* D Dcell Dfl-FFF

average logarithm concentration diffusion coefficient of a solute (cm2 /s) diffusivity estimated with the diffusion cell (cm2 /s) diffusivity estimated with the fl-FFF apparatus (cm2 /s) diffusivity estimated with the Stokes–Einstein Ds equation (cm2 /s) J flux (cm/s) Jv and Js solvent and Solute flux (cm/s) k mass transfer coefficient (cm/s) K Boltzmann constant (J/K) Lp pure water permeability (L/day m2 kPa) Pm solute diffusive permeability (cm/s) P trans-membrane pressure (psi or kPa) R gas constant, true rejection, and peak time ratio (t0 /tr , for fl-FFF) (J/K mol) Robs observed rejection radius of the solute (nm) rp t time (s) t0 and tR void time of the channel and emergence time of the solute (s) T absolute temperature (K) V0 and VC channel volume and volumetric rate of cross-flow in fl-FFF system (cm3 /s) w channel width (cm) x distance (cm) Greek letters ˇ lumped cell constant (cm−2 ) ı boundary thickness in the CP layer (nm) ım membrane thickness (cm)  osmotic pressure (atm)  retention parameter  viscosity of the liquid phase (g s/cm2 )  membrane selectivity ω permeation coefficient (g/s-atm-cm2 )

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