Experimental and Modeling Assessment of the Roles of

Article pubs.acs.org/IECR

Experimental and Modeling Assessment of the Roles of Hydrophobicity and Zeta Potential in Chemically Modified Poly(ether sulfone) Membrane Fouling Kinetics Wanyi Fu, Likun Hua, and Wen Zhang* John A. Reif, Jr. Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102, United States S Supporting Information *

ABSTRACT: This study investigated the roles of hydrophobicity and zeta potential of polymer membranes and foulants on membrane fouling during filtration. A series of chemically modified poly(ether sulfone) (PES) membranes were used to evaluate filtration performance with bovine serum albumin (BSA) and humic acid (HA) employed as model foulants. Hydrophobicity and zeta potential of both membranes and foulants were measured and incorporated in the surface interaction energy calculation by the extended Derjaguin−Landau−Verwey−Overbeek (EDLVO) theory analysis. Foulant deposition rate was then calculated based on particle transport equation and interaction energy. Membrane fouling rates, indicated by the decrease of permeate flux, were well correlated (R2 = 0.74−0.99) with the foulant deposition rates. This correlation indicates that both electrostatic interaction and hydrophobic interaction played decisive roles in membrane fouling. Our results have important implications for elucidation and prediction of the structure−property−performance relationship of diverse chemically modified membranes and may promote the rationale design and development of functional membrane filtration systems.

1. INTRODUCTION During the last few decades, membrane filtration has extensively been used in water and wastewater treatment,1,2 desalination,3 dairy production,4 biomass/water separation,5 and recovery of rare metals.6−8 Membrane fouling is still a major issue during the application of membrane filtration. Membrane fouling is commonly caused by cake formation, pore blocking, particle deposition, and concentration polarization, which results in the increase of membrane resistance, filtration failure, and high operational cost.9 Development of effective antifouling membrane materials is critical for economic viability and sustainability of membrane filtration processes. Membrane characteristics, such as hydrophobicity/hydrophilicity, surface charge, roughness, pore size, and porosity, etc., have been proven to impact on membrane filtration performance, especially on membrane fouling.10−13 Particularly, the impacts of hydrophobicity and surface charge on membrane fouling during filtration have largely been reported previously.10,13−17 In general, membrane fouling occurs more readily on hydrophobic membranes than on hydrophilic ones because of the hydrophobic interaction between foulants and membranes.18 As a result, hydrophobic membranes are commonly modified to relatively hydrophilic in order to mitigate membrane fouling.19,20 Several studies investigated the mechanisms and analyzed the contributions of different foulants to membrane fouling.21−23 It was reported that the hydrophobic fraction of natural organic matter (NOM) tends © 2017 American Chemical Society

to deposit more than the hydrophilic fraction of NOM on the membrane surface.22 Because water pollutants or foulants are often charged, membrane filtration performance and fouling behavior depend not only on hydrophobicity but also on the electrostatic interactions between membranes and foulants.22,24 Previous studies investigated the effects of hydrophobicity and surface charge of either membrane or foulants separately.25−28 Only a few reports considered two factors together on either membranes or foulants,23,29,30 but few of them analyzed these two interfacial properties of membranes and foulants at the same time.31 Further, the interfacial properties of membranes, though playing a pivotal role in solute−membrane and foulant−membrane interactions,32,33 have not been well correlated with the filtration flux and fouling kinetics. The extended Derjaguin−Landau−Verwey−Overbeek theory (EDLVO or XDLVO theory) is widely used to describe colloidal interactions and fouling potential of membranes.31,34,35 But few studies employed the EDLVO theory analysis to establish or interpret membrane fouling kinetics. Wang et al. found a positive correlation between the membrane−foulant adhesion force and the flux decline rate in the initial filtration stage.36 However, the results only showed Received: Revised: Accepted: Published: 8580

May 28, 2017 July 11, 2017 July 13, 2017 July 13, 2017 DOI: 10.1021/acs.iecr.7b02203 Ind. Eng. Chem. Res. 2017, 56, 8580−8589

Article

Industrial & Engineering Chemistry Research

Table 1. Surface Tension Properties (mJ m−2) of Probe Liquidsa

the prediction of fouling propensity by the EDLVO approach rather than a statistical correlation between the fouling rate and the interaction energies. The objective of this study is to investigate the hydrophobicity and zeta potential of membranes and foulants on membrane fouling during filtration. A series of PES membranes were used with bovine serum albumin (BSA) and humic acid (HA) employed as model foulants representative of proteins and natural organic matters, respectively. Hydrophobicity and zeta potential were measured by water contact angles and dynamic light scattering (DLS). The EDLVO theory and the particle transport equation were employed to develop a new particle deposition kinetic model that was used to compute the foulant deposition rates with considerations of colloidal interfacial forces as described by the EDLVO theory. The membrane flux decline rate was ultimately correlated with this foulant deposition rate. This correlation model holds paramount significance for characterization of the surface hydrophobicity and surface charges toward the prediction of membrane fouling.

a

probe liquids

γLW

γ+

γ−

γAB

γTOT

water formamide glycerol

21.8 39.0 34.0

25.5 2.3 3.9

25.5 39.6 57.4

51.0 19.0 30.0

72.8 58.0 64.0

Data taken from Van Oss.39

measured by a surface zeta potential cell equipped on a dynamic light scattering (DLS) instrument (Malvern Instruments ZetaSizer Nano ZS). The membrane samples were cut into 4 × 5 mm2 pieces and attached by double coated adhesive tapes (Tedpella) to the cell. The cell was placed in a standard 12 mm2 polystyrene cuvette (Fisher Scientific Co., Pittsburgh, PA) filled with the dispersant (i.e., 1 mM NaCl solution within the pH range 4−10)40 and tracer particles (300 nm carboxylated latex particles). The cuvette and cell were then placed in the temperature controlled ZetaSizer instrument at a temperature of 25 ± 1 °C. The pH was measured using a pHmeter (Orion model 420A, Boston, MA, U.S.A.) and adjusted by addition of NaOH and HCl solutions. 2.3.3. Characterization of BSA and HA as Model Foulants. The BSA stock solution (2 g L−1) was prepared by dissolving 2 g BSA into 1 L DI water. The HA stock solution (0.1 g L−1) was prepared by dissolving 0.1 g HA into 1 L DI water. Contact angles of the BSA and HA were measured using the same technique as described above. The BSA and HA coated surfaces were made by depositing the BSA solutions and HA solutions onto clean flat gold coated wafer. The samples were dried in the air at room temperature and transferred to a desiccator for later contact angle measurement. Zeta potential and mean size of BSA or HA were also determined by the DLS instrument.41 Each data value was an average of five measurements and all the measurements were performed at 25 ± 1 °C. 2.4. Cross-Flow Filtration Performance. Figure 1 illustrates the schematic diagram for the bench scale filtration device. The effective membrane area was approximately 9.6 cm2. All parts of the filtration cell are made from Teflon (PTFE), including the O-ring, screen, screws, and nuts. A crossflow filtration (CFF) mode was used in the study, in which the feed solution passes tangentially along the surface of the membrane. Pressures were monitored in the feed stream (PF), the retentate stream (PR) and the permeate stream (Pp) to calculate transmembrane pressure (TMP) in eq 1. The volume of the permeate was then measured and the flux was calculated using eq 2. P + PR TMP = F − PP (1) 2

2. EXPERIMENTAL SECTION 2.1. Materials. The following chemicals were used asreceived: glycerol (Fisher Scientific, CAS No. 56−81−5), formamide (Sigma−Aldrich, CAS No. 75−12−7), humic acid (HA) (Sigma-Aldrich, CAS No. 1415−93−6), bovine serum albumin (BSA) (Sigma-Aldrich, Fraction V, CAS No. 9048− 46−8), sodium chloride (CAS No. 1310−73−2, Fisher Scientific), hydrochloric acid (Catalog No. A144C-212, Fisher Scientific), sodium hydroxide (CAS No. 7647−14−5, Fisher Scientific) and carboxylated latex particles with mean diameter of 300 nm (Catalog No. 3060A, Thermo Scientific). Deionized water (18.2 MΩ cm at 25 °C) were prepared using a Direct-Q UV3 System (EMD Millipore, Bedford, MA, U.S.A.). 2.2. Preparation of Chemically Modified Membranes. Three kinds of flat sheet PES membranes were provided by Pall Corporation: (1) pristine PES membrane; (2) PES membrane blended with 10% (w/w) PVP; (3) PES membrane cross-linked with 8% (w/w) PEG. These membranes were prepared following the reported procedure by Wu et al.37 Four other kinds of PES membranes were provided by EMD Millipore Corporation: The pristine PES membrane and chemically modified PES/PVP membranes were both prepared by the phase inversion method.38 PEG solutions were prepared by dissolving different amounts (2, 3, and 4 wt %) of PEG powder into deionized water. Then the PES membranes were dipped into the PEG solutions for certain times, exposed to an electron beam to cross-link the PEG, and dried in air. The surface modification process details are proprietary. The reported pore size of the tested membranes is 200 nm. 2.3. Characterization Methods. 2.3.1. Contact Angle Measurement. The contact angle measurements were performed using three probe liquids with well-known surface tension properties as shown in Table 1. The probe liquids selected are deionized (DI) water, glycerol, and formamide. A drop of probe liquid (∼5 μL) was placed on a dry flat membrane surface. At least three measurements of liquid drops at different locations were averaged to obtain the contact angles for each membrane sample. The image of the liquid drop was taken within 10 s to determine the air−liquid−surface contact angles with the ImageJ software. 2.3.2. Measurement of Membrane Surface Zeta Potential. The membrane surface charge or surface zeta potential was

V (2) A·t −2 −1 where J is the flux (L m h , LMH), V is the permeate volume (L), A is the effective membrane filtration area (m2), and t is the filtration time (h). In this study, the membrane compaction was achieved by 30 min filtration of DI water at a constant pressure 5 psi (34.5 kPa) before the BSA or HA fitration experiments, to achieve a steady flux state and to minimize the compaction effect.42,43 The pure water state flux (Table S1) were obtained for tested membranes. The foulant solution (200 mg L−1 BSA solution J=

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DOI: 10.1021/acs.iecr.7b02203 Ind. Eng. Chem. Res. 2017, 56, 8580−8589

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Figure 1. Schematic of the cross-flow filtration setup.

Table 2. Average Contact Angles of Membranes and Two Model Foulantsa contact angle (deg) materials Pall membranes

Millipore membranes

foulants

water PES PES/PVP PES/PEG PES/0% PEG PES/2% PEG PES/3% PEG PES/4% PEG bovine serum albumin humic acid

61.4 0 7.5 71.3 39.3 42.7 27.4 23.0 31.5

± ± ± ± ± ± ± ± ±

formamide

4.3 0 0.6 12.3 6.9 8.5 2.9 2.4 2.2

33.3 28.43 26.9 12.1 15.0 12.1 0 31.8 30.0

± ± ± ± ± ± ± ± ±

glycerol

3.2 5.9 6.3 3.5 6.4 4.9 0 0.6 2.7

37.5 33.6 47.9 42.4 38.8 43.9 52.5 50.4 60.8

± ± ± ± ± ± ± ± ±

4.4 7.4 10.5 7.4 9.6 9.8 14.5 0.4 4.1

a

The pristine PES membranes from Pall and Millipore companies had different formamide contact angles (33° and 12°, respectively). This difference might be attributed to the fact that fabrication procedures adopted by these two companies were not exactly the same, which resulted in different surface properties.

and 10 mg L−1 HA solution) was subjected to the membrane cell under a TMP of 34.5 kPa and a cross-flow rate of 25 mL min−1 to observe the fouling kinetics. The flux were recorded every 5 min for 120 min at a constant TMP. Normalized membrane flux was calculated using the equation:44,45 J normalized flux = × 100 J0

In this study, the fouling process by the deposition of BSA or HA was assumed to be the “particle” accumulation at the initial filtration stage. Therefore, a membrane fouling kinetics model was developed based on the particle transport equation:50,51 Jx = −Dx

(3)

(5)

where Jx is the particle flux or the particle deposition rate (g m−2 s−1), Dx is the diffusion coefficient (cm2 s−1), C is the particle concentration (mg L−1), ux is the particle velocity components induced by the fluid flow (m s−1), Fx is the component of the external force vector (N). In our case, Fx is the colloidal interfacial force that can be computed by the EDLVO theory. T is the temperature (K), kB is the Boltzmann constant, 1.38 × 10−23 J K−1. For the particle dispersion component, the particle deposition rate or flux is expressed as follows: cb − cg cg − cb ∂C Jx(disp) = −Dx = −Dx = Dx (6) h h ∂x

where J is the flux measured every 5 min during the 2 h filtration; J0 is the flux measured at the beginning of filtration. 2.5. Modeling Analysis of Membrane Fouling with BSA and HA Solutions. 2.5.1. EDLVO Theory Analysis. The membrane−foulant interactions were modeled as surface− particle geometry.46 The total interaction energies,Utotal, between membrane and foulants (BSA and HA) are contributed by the Lifshitz−van der Waals (vdW), UvdW, electrostatic double-layer (EL), UEL and polar or Lewis acid− base (AB) energy, UAB, according to the EDLVO theory:35,47,48 Utotal = UvdW + UEL + UAB

DFC ∂C + uxC + x x ∂x kBT

(4)

Calculations of van der Waals, electrostatic and Lewis acid− base interaction energies are detailed in Section S2 in Supporting Information (SI). 2.5.2. Modeling Development of Membrane Fouling. Membrane fouling is commonly due to pore blocking, particle deposition, concentration polarization, and cake formation.9 Flux decline is a result of membrane fouling, and the effecting factors include the interactions between the particles and the membrane surface, the particles themselves, and other factors such as hydrodynamic forces.49

where cb and cg are the particle concentration (mg L−1) in the bulk (feed) solution, and the gel layer, respectively; h is the separation distance between the foulants and the membrane (nm). The particle deposition flux as a result of advection is expressed as follows:52,53 Jx(adve) = uxC = Jcb

(7)

where J is the water permeate flux, J = 8582

Q . A


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Industrial & Engineering Chemistry Research Table 3. Surface Energy Parameters (mJ m−2) of Seven Membranes, and Two Model Foulants γLW

materials Pall membrane

Millipore membrane

foulants

PES membranes PES/PVP membranes PES/PEG membranes PES/0%PEG PES/2%PEG PES/3%PEG PES/4%PEG bovine serum albumin humic acid

6.62 9.56 12.18 14.02 10.40 14.67 31.49 0.14 19.88

± ± ± ± ± ± ± ± ±

γ−

γ+

4.64 13.30 14.88 8.67 14.64 16.89 13.87 0.12 8.74

2.95 83.03 60.18 17.58 30.40 26.00 7.16 7.63 12.70

± ± ± ± ± ± ± ± ±

2.99 30.41 2.28 13.96 19.36 22.32 5.37 6.65 12.52

39.20 12.32 17.57 36.99 21.98 9.45 33.06 54.2 17.67

± ± ± ± ± ± ± ± ±

10.88 8.76 13.14 26.80 29.60 9.48 4.21 3.68 9.97

γAB

γTOT

21.51 63.97 61.57 51.00 51.70 31.35 30.78 40.67 29.96

28.13 73.53 73.75 65.02 62.10 46.02 62.27 40.81 49.84

Figure 2. Surface zeta potential of membrane samples under different pHs. (a) Pall membranes and (b) Millipore membranes.

The particle deposition flux driven by the interfacial force can be related to the interaction energy calcluated by the EDLVO theory: Jx(force) =

Dx FxC D c ∂U (h) = x b total kBT kBT ∂h

contact angle from 71° to 27°. This suggests that surface modification to make PES membranes hydrophilic was successfully achieved even with small amount of PEG or PVP additives. Table 3 shows the calculated surface tension parameters and the free energy component for each of the membranes and foulants by eq S6. The surface energy data show that pristine PES membranes have high electron donor components (γ−) and relatively low electron acceptor components (γ+). By contrast, PES/PVP and PES/PEG membranes have high electron acceptor monopolarity. These results agree with previous studies reporting that original polymeric membranes typically have a high electron donor monopolarity.54,55 Specifically, the PES membrane has a low AB component. A high γAB component value of PES/PVP and PES/PEG membranes means that there is a higher degree of hydration on the surface or high hydrophilicity.56 For Millipore membranes, the values of γAB did not increase proportionally with the increase of PEG ratio. As described in Section 2.2, the modification procedures were different for Pall and Millipore membranes. The Millipore PES membrane modified with PEG was obtained by dip-coating in PEG solutions. The weight percentage of PEG (2%−4% wt %) was the nominal weight ratio. In reality, the effective or true coating amount of PEG on PES may be less than the nominal ratio because PEG is water-soluble and dissolved during the membrane fabrication process. By contrast, the Pall membranes were modified by blending 10% PVP and 8% PEG into PES, which might give higher blend ratios of PVP and PEG than that in Millipore membranes. Therefore, the dependence of surface energy parameters on the coating ratios of PEG was not obvious and stable for Millipore membranes.

(8)

Thus, the overall particle deposition flux is expressed below: cb − cg D c ∂U (h) Jx = Dx + Jcb + x b total h kBT ∂h (9) ∂(J / J )

0 The rate of permeate flux changes was derived from ∂t the slope of the flux changes with the initial 60 min filtration time. This flux change rate was correlated with the particle deposition rate calculated by eq 9.

3. RESULTS AND DISCUSSION 3.1. Hydrophobicity and Hydrophilicity Analysis. The contact angles of three probe liquids on the membranes and the two model foulants (BSA and HA) were measured and shown in Table 2. The hydrophobic/hydrophilic properties of chemically modified PES membranes were expected to vary as compared with the pristine PES membranes due to the presence of the hydrophilic functional groups such as hydroxyl groups and amino groups in PVP and ether groups in PEG. Table 2 shows that the pristine PES membrane displayed a water contact angle of 61.4° ± 4.3°, indicative of the highly hydrophobic nature of PES. After blending with PVP, the water contact angle reduced to 0°, a superhydrophilic surface state. Similarly, the Pall PES membrane cross-linked with PEG showed a water contact angle of 7.5° ± 0.6°, also a highly hydrophilic surface property. Increasing the blending ratio of PEG from 0% to 4% in PES gradually reduced the water 8583


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Industrial & Engineering Chemistry Research Table 4. Characteristics of the BSA and HA Foulants foulant

pH value

colloid size (nm)

particle Zeta potential (mV)

bovine serum albumin humic acid

7.46 ± 0.18 6.57 ± 0.22

89.6 ± 2.4 122.3 ± 5.7

−20.6 ± 1.5 −45.8 ± 2.2

Figure 3. Normalized flux change in BSA filtration for PES, PES/PVP, and PES/PEG membranes from Pall Corporation (a), and PES membranes with different PEG amounts from EMD Millipore Corporation (b), 200 mg L−1 BSA solution, pH = 7.46. And flux change in HA filtration for PES, PES/PVP, and PES/PEG membranes from Pall Corporation (c), and PES membranes with different PEG amounts from EMD Millipore Corporation (d), 10 mg L−1 HA solution, pH = 6.57. Refer to Figure S1 for the non-normalized flux change graphs.

decline rates of flux compared to pristine PES membrane. This is because the water layer on hydrated membrane surface could hamper foulants adsorption and reduced membrane fouling. Figure 3b also indicates that when increasing PEG addition on PES, the fouling kinetics was significantly lowered. It indicated that hydrophilic membrane possessed lower membrane fouling potential than hydrophobic one, which was also reported in other literature.59−61 During the filtration of HA solutions, permeate flux also decreased with time for all membranes (Figure 3d). Unlike the BSA filtration results, the presence of hydrophilic macromolecular additives did not decreased the flux decline rates significantly other than the PES/4%PEG membrane. Figure 3 showed that the hydrophilic additives influenced the fouling kinetics of BSA and HA, but to different extent. Clearly, the impacts of hydrophilic additives depend on the interactions between foulant-membranes and the characteristics of both BSA or HA foulants and membranes. Therefore, the EDLVO theory was employed to analyze the interactions energy for the tested membrane-foulant systems in the following sections.

3.2. Membrane Surface Zeta Potential and Foulant Zeta Potential. Figure 2 shows the pH dependence of the surface zeta potentials (SZP) for different membranes. All membrane surfaces were negatively charged over the entire pH range 4−11. The absolute SZP values increased (more negatively charged) with the increasing pH, which is consistent with literature.57 The negative surface charges occur because anions can approach the hydrophobic surfaces (such as PES membrane).58 The addition of modifiers such as PVP and PEG to PES decrease the net surface charge of the PES membrane. By increasing the amount of PEG, the net surface charge of PES membrane was progressively reduced (Figure 2b). The characteristics of BSA and HA foulants are summarized in Table 4. 3.3. Membrane Fouling during Filtration of BSA Solution and HA Solution. The effect of additives on membrane fouling performance was investigated by filtration of 200 mg L−1 BSA and 10 mg L−1 HA solutions. The results of flux changes over the filtration time (Figure 3) show that flux decreased for all membranes due to fouling. The presence of hydrophilic macromolecular additives clearly slowed down the 8584


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Figure 4. EDLVO interaction energy profiles for the Pall membrane−foulants combinations tested. Refer to Figure S2 for the EDLVO interaction energy profiles of Millipore membrane-foulants combinations.

3.4. Interaction Energy for Different Membrane− Foulant Systems. Figure 4 shows the EDLVO interaction energy profiles for the two membrane−foulant interaction systems, which varied significantly with the specific membrane−foulant combination. The zeta potential affects exclusively the EL term, while hydrophobicity controls both vdW and AB components. The profiles showed that the EL and AB components were both main contributors to the total interaction energy for BSA−membrane system while the EL interaction energy was a main contributor for HA−membrane

system. Since EL interaction was strongly affected by surface zeta potential, it indicates that manipulating membrane surface charge could be more important than membrane surface hydrophilicity in the control and prevention of membrane fouling during HA filtration. For all the seven PES membranes, a strong electrostatic repulsion existed between foulants and membrane surfaces. And the repulsion between foulants and chemically modified membranes was larger in magnitude than that for the pristine PES membrane, which indicates that chemically modified PES 8585


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Figure 5. Positive correlation between the particle deposition rate and the flux decline rate during the filtration of BSA (a) and HA (b). Solid markers and line: Pall membranes; Hollow markers and dashed line: Millipore membranes.

magnitude of hydrophobic and electrostatic interactions and consequently membrane fouling kinetics, which deserves further examinations.

membranes are more resistant to membrane fouling. Figure 3 supports this finding and shows lower flux decline rates or less fouling on chemically modified PES membranes. Therefore, PEG or PVP modifications on PES membranes play a pivotal role in the membrane fouling behavior. 3.5. Contributions of three major components to membrane fouling. According to eq 9, the particle deposition rate is controlled by three components or fluxes (J): dispersion, advection, and deposition. The calculations of these three components (detailed in Section S5) showed that, compared with Jx(force), the former two components (Jx(disp) and Jx(adv)) were found to be substantially smaller by several orders of magnitude for both HA and BSA and thus could be negligible (see comparisons in Table S2). It is also interesting that these three transport components are all dependent on foulant concentration and Jx(force) is always greater than Jx(disp)and Jx(adv) under our experimental conditions. For instance, the diffusion coefficients (Dx) for BSA and HA range from 5 × 10−7 cm2 s−1 to 8 × 10−7 cm2 s−1.62,63 Our calculations show that only when the concentrations of BSA or HA reach above approximately 103 to 106 mg L−1, Jx(disp) and Jx(adv) can reach similar orders of magnitude as Jx(force) under normal filtration flux (40−100 LMH).64 However, typical BSA or HA concentrations commonly used as model fouling agents are between 2.5 mg L−1 to 300 mg L−1.65−69 3.6. Correlation between the Particle Deposition Rate and the Fouling Rate. To predict the fouling behavior of the PES membranes, a correlation between the particle deposition rate and the flux decline rate was developed. The flux decline rates,

∂(J / J0 ) ∂t

4. CONCLUSIONS The combined effects of hydrophobicity and surface charge of polymer membranes and foulants on membrane fouling was studied both experimentally and theoretically. Pristine PES membranes and their chemically modified forms were used for filtration experiments with BSA and HA as model foulants. The experimental results for different membrane−foulant systems showed that the hydrophilized membranes yielded smaller flux decline rates. Further, the EDLVO theory analysis indicated that the EL and AB components were both main contributors to the total interaction energy for BSA−membrane system, while the EL interaction energy was a primary contributor for HA−membrane system. Positive correlations (R2 = 0.74−0.99) were obtained between the fouling rates and the particle deposition rates on different membrane−foulant systems. This correlation could be further improved for developing predictive models of membrane fouling, which requires additional considerations of other factors such as membrane pore size, surface roughness, solute chemistry, and hydrodynamic conditions.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b02203. Pure water state flux for tested membranes, the calculations of interaction energies, non-normalized flux change graphs, EDLVO interaction energy profiles, and the calculation of particle deposition rate (PDF)

, during the filtration of BSA and HA, could be

derived from the data in Figure 3 and summarized in Table S3. ∂(J / J0 ) ∂t

ASSOCIATED CONTENT

and Jx(force), (the dominant contribution for foulant

■

deposition) for various membrane types were plotted in Figure 5, which elicits fairly satisfactory linear relationships (R2 = 0.7− 0.9). This linear relationship also suggests that Jx(force), or the interfacial forces between foulants and membrane surfaces play a decisive role in the membrane fouling kinetics, as opposed to diffusion or advection. Moreover, the linear correlation seems to shift from the two different membranes obtained from Pall Corporation and EMD Millipore Corporation. This shift implies that the different membrane fabrication procedures would greatly influence the correlation model. For example, molecular weight of polymers, membrane pore size, roughness, and other possible membrane properties could vary the

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (W.Z.). ORCID

Wanyi Fu: 0000-0001-9653-4012 Likun Hua: 0000-0002-1228-6128 Wen Zhang: 0000-0001-8413-0598 Notes

The authors declare no competing financial interest. 8586


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ACKNOWLEDGMENTS The authors gratefully acknowledge funding support from the NSF Industry/University Cooperative Research Center for Membrane Science, Engineering, and Technology [grant number IIP1034710]. The authors thank EMD Millipore Corporation and Pall Corporation for providing the membrane samples.

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ABBREVIATIONS PES, poly(ether sulfone) PVP, polyvinylpyrrolidone PEG, poly(ethylene glycol) DI, deionized NOM, natural organic matter TMP, transmembrane pressure BSA, bovine serum albumin HA, humic acid EDLVO, extended Derjaguin−Landau−Verwey−Overbeek vdW, Lifshitz−van der Waals EL, electrostatic AB, Lewis acid−base LMH, liters per m2 of membrane per hour (L m−2 h−1) AFM, atomic force microscope SEM, scanning electron microscope DLS, dynamic light scattering

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Jx, the particle flux (g m−2 s−1) that is related to the particle deposition rate Dx, diffusion coefficient [cm2 s−1] C, the concentrations of foulant/particle [mg L−1] P, pressure [kPa] J, filtration flux [L m−2 h−1] A, membrane area [m2] V, the permeate volume [L] ux, particle velocity components induced by the fluid flow [m s−1] Fx, component of the external force vector in eq 5 [N] cb, particle concentration in the bulk (feed) solution [mg L−1] cg, particle concentration in the gel layer [mg L−1]

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NOMENCLATURE θ, the water contact angle [degrees] a, the radius of foulant particle, [m] A132, Hamaker constant for interacting subject 1 and subject 2 in the medium 3 [J] h0, the minimum equilibrium distance due to the Born repulsion, 0.157 [nm] h, the separation distance between the membrane and the foulants [nm] NA, Avogadro’s number, 6.02 × 1023 [mol−1] e, electron charge, 1.6021 × 10−19[C] ci, the molar concentration of one species ions (i) [mol L−1] ε0, the dielectric permittivity of a vacuum, 8.854 × 10−12 [C V−1 m−1] ε, the dielectric constant of water, 78.5 zi, the valence of one species ions (i) κ−1, double layer thickness, [m], κ = NAe2∑cizi2/ε0εrkBT)1/2 λ, correlation length of molecules in a liquid, [m] kB, Boltzmann constant, 1.38 × 10−23 [J K−1] T, temperature [K] n, the molar concentration of ionic species in the medium [mol m−3] ξ1, membrane surface zeta potential [mV] ξ2, foulant zeta potential [mV] U, interaction energy [J] or [kBT] ΔG, free energy of interaction [J m−2] γ, surface tension [mJ m−2] γLW, apolar or Lifshitz-van der Waals component of the surface free energy, [mJ m−2] γAB, polar or acid−base component of the surface free energy, [mJ m−2] γ+, electron-accepting parameter of the acid−base component, [mJ m−2] γ−, electron-donating parameter of the acid−base component, [mJ m−2] γTOT, total free energy component, [mJ m−2] 8587


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