Electrokinetic characterization of poly(vinyl butyral) hollow fiber membranes by streaming potential and electroviscous effect

Journal of Membrane Science 425–426 (2013) 71–76

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Electrokinetic characterization of poly(vinyl butyral) hollow fiber membranes by streaming potential and electroviscous effect Yun-Ren Qiu n, Jing Qi School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China

a r t i c l e i n f o

abstract

Article history: Received 3 July 2012 Received in revised form 10 September 2012 Accepted 13 September 2012 Available online 23 September 2012

Streaming potentials and electroviscous effects were measured for two poly(vinyl butyral) (PVB) hollow fiber membrane modules with molecular weight cut off at 40 and 200 kDa (M40 and M200) in KCl and CaCl2 electrolyte solutions. The results show that the PVB membrane has a weak negative charge due to the specific adsorption of ions, and the streaming potential of the membrane depends strongly on the salt concentration, type and valence of ions. The iso-electric points (IEP) of membranes M40 and M200 are both around 3.0 in KCl electrolyte solution and 3.5 in CaCl2 electrolyte solution. The electroviscous effect increases with the increase of electrolyte concentration at low electrolyte concentration, it reaches a maximum at a certain concentration and then decreases with the increase of electrolyte concentration. The electroviscous effect is little greater for M40 than for the M200, and the electroviscous effect of KCl solution is greater than that of CaCl2 solution under the same concentration. The zeta potentials for M200 have been calculated by streaming potential and the electroviscous effect. The values of zeta potentials calculated from streaming potential are less negative than those from electroviscosity measurements. & 2012 Elsevier B.V. All rights reserved.

Keywords: Streaming potential Electroviscous effects Zeta potential Poly(vinyl butyral) Hollow fiber membrane

1. Introduction It has been increasingly recognized that electrokinetic phenomena can significantly affect the performance of membrane process [1], and which has been used to supplement the traditional membrane characteristics. Moreover, electrokinetic phenomena are of importance as they are often used for determining the membrane zeta potential. The most widely used technique is measuring the streaming potential across the membrane pores to determine electrical surface properties of membranes [2]. When a hydrostatic pressure is applied over a porous membrane with charged pore walls, the liquid in the pores will move, dragging the ions present in the pore with it, and there will be an excess of counter-ions inside the pore because of the presence of the double-layer. The transport of these ions by the flow causes a potential drop across the membrane, the potential drop causes a conduction current of co-ions in the direction of the liquid flow and of counter-ions in the opposite direction. The ions moving along the electric field will drag solvent molecules with them, thus changing the flow field of the liquid, resulting in the increase of apparent viscosity, the electroviscous effect. This effect is negligible at high salt concentrations but can cause viscosity increase over 25% at intermediate and low concentrations. The

n

Corresponding author. Tel./fax: þ 86 731 8879706. E-mail address: [email protected] (Y.-R. Qiu).

0376-7388/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2012.09.021

electroviscous effect method is based on measuring the water flux through the membrane at different salt concentrations. The variations in water flux with salt concentration can be related to zeta potential or surface charge density through the electrokinetic flow theory [3]. It has been shown that values of zeta potential obtained by the electroviscous method compare well with those obtained from streaming potential data [4]. The streaming potential coefficient is one of the important electrokinetic phenomena, it can be defined as the ratio of the measured electrical potential drop to the hydraulic pressure difference across a micro-porous membrane in zero current conditions. The streaming potential measurement has become a common experimental technique for electrokinetic characterization of a porous membrane because streaming potential is easily measured and is particularly sensitive to the change of salt concentration when a salt solution passes through a charged membrane by a hydraulic pressure difference [5–8]. The streaming potential shows strong dependence on the pore radius of the membrane when the pore radius is comparable to the Debye length determined by salt concentration [9]. Because the surface conductivity of the pores is high, the electrical double layer (EDL) is overlapping and the profiles of the ion concentration and electrical potential are superposing [9]. Zeta potential is a parameter indicative of the interactions between membranes and salt solutions as far as it is a very easily measurable magnitude and sensitive to changes in concentration [10], which is the potential at the shear plane between the compact layer

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attached to the pore wall and the mobile diffusion layer on the surface of the membrane pores. The traditional way of determining the zeta potential for ultrafiltration and microfiltration membranes is to measure the streaming potential, and then zeta potential could be estimated by the Helmholtz–Smoluchowski equation. However, zeta potentials may be calculated based on the electroviscous effect of the membrane [11]. The iso-electric point (IEP) of the membrane is the pH value at which the streaming potential is equal to zero regardless of the ionic strength [12]. Usually, the IEP of a neutral polymeric membrane is low as anions are more readily adsorbed than cations in a non acid solution, which also makes the membrane surface negatively charged [11]. For the charged membranes, besides the sieving effect, the surface charge also plays an important role in the performance of the membranes [12–14]; it can favor the antifouling of the membrane and benefit the separation of charged electrolyte due to the electrostatic interaction. The charging of a porous membrane surface in a solution usually comes about in two ways: one is the ionization or dissociation of the groups on the surface of the membrane pores, and the other is the adsorption of ions from solution onto the surface of the membrane pores. These lead to the formation of EDL that restores the electroneutrality in the solution. A microporous membrane can be regarded as a charged porous membrane to understand its separation performance better. It cannot be taken simply as a sieve that leads to the rejection of the solutes such as ions, molecules, clusters, aggregates, and even particles in solution [15]. The separation driving force of a charged membrane is hydraulic pressure difference. Therefore, charged membranes can reject inorganic salts of much smaller size than the membrane pore radius at a lower pressure. Reddy et al. [16] verified that a charged ultrafiltration membrane made of sulfonated polyethersulfone can reject inorganic salts like NaCl, Na2SO4, etc. due to the electrostatic repulsion even though it has pores much larger than the salts, and can separate amino acid or protein mixtures according to their iso-electric points. Huisman et al. [17] studied the effect of ion concentration on the salt retention for KCl solution of polysulphone ultrafiltration membranes, the salt retention vanished at very high salt concentrations, increased for decreasing salt concentrations. Poly(vinyl butyral) (PVB) hollow fiber membrane may have a wide application prospect because its hydroxyl groups can provide high hydrophilicity. It is important to obtain some direct knowledge of the membrane surface in actual applications and its dependence on the concentration and type of salts by using the streaming potential measurement. However, no work has been done with the aim of investigating the electrokinetic behavior of PVB hollow fiber membrane. Hence, the investigation on the electrokinetic properties of PVB hollow fiber membranes is necessary and important for their wide application. The electrokinetic properties of two PVB hollow fiber membrane modules (M40 and M200) were investigated by the streaming potential and electroviscous effect. The PVB hollow fiber membranes used in this research were prepared via the TIPS method [18]. To investigate the influence of the type of electrolyte and its concentration, KCl and CaCl2 electrolytes were used for the streaming potential and electroviscous effect, with the concentration ranging from 5.0  10  4 mol/L to 0.3 mol/L. The zeta potential for PVB hollow fiber membrane was calculated from streaming potential and electroviscous effect. The iso-electric points of the membranes in KCl and CaCl2 electrolytes were also measured respectively.

electrical current (j) can be generated according to the following equations [12]: JV ¼ L11 DP þ L12 DE

ð1Þ

j ¼ L21 DP þ L22 DE

ð2Þ

where L11, L12, L21, and L22 are coupling coefficients, these equations, from the linear theory of thermodynamics of irreversible processes, are applied to systems that are not very far from their equilibrium point. These equations are valid for any solute and solvent. Jv, DP and DE can be measured easily by experiments. When the electrical current (j) is zero, the streaming potential coefficient (n) is obtained for Eq. (2). When the electric current is set to zero

n ¼ ðDE=DPÞj ¼ 0 ¼ L21 =L22

ð3Þ

Using the streaming potential coefficient, apparent zeta potential can be calculated by the Helmoltz–Schmolukovski equation.

n¼

e0 er B mK

ð4Þ

where z is the zeta potential, V; e0er is the permittivity of the solution in the pore, C/(V m); m is the viscosity, Pa s; and K is the conductivity of the electrolyte solution, S/m. Moreover, Eq. (4) is restricted to the limit of rP/k  1 410 (rp is pore radius, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 k ¼ eRT=ð2F 2 cÞ, is Debye length, F is Faraday constant, c is the concentration in solution mol/m3, R is the molar gas constant, T is the absolute temperature). The electroviscous effect is defined as the increase in apparent viscosity over the bulk value ma/m0 [19], which equals the decrease in flux compared to the value in absence of a streaming potential [3]. The zeta potential of membranes can be calculated by the electroviscous effect [4]. Levine et al. [20] showed that for a 1–1 electrolyte solution, the apparent viscosity in a cylindrical pore is related to the zeta potential of the pore surface as !1 ma 8bðez=kTÞ2 ð1GÞF ¼ 1 ð5Þ 1 m0 ðr p =k Þ2 where ma is the apparent viscosity, m0 is the bulk viscosity of the electrolyte solution, z is the zeta potential of the capillary surface, k is the Boltzmann constant, G is a correction function for the overlapping double layers and F a correction function for high 1 zeta potentials; G and F can be calculated according to r p =k and 1 z [20]. For large values of rp =k , G E0 and FE1. Also, F¼1  G as z ¼0, b is a dimensionless parameter describing the properties of the electrolyte.

b¼

e2r e20 k2 T 2 1 16p2 mle2 ðk Þ2

ð6Þ

The apparent viscosity is easily obtained from water flux measurements at constant transmembrane pressure, the Debye length is calculated from the salt concentration, the conductivity can be measured, and the pore radius can either be measured. Thus all variables in Eq. (5) are known, except for z, as G and F depend on z for a certain electrolyte solution. The zeta potential can then be calculated from Eq. (5) by an iterative method.

3. Experimental 3.1. Membranes and chemicals

2. Theory When a difference of the electrical potential (DE) and pressure (DP) is applied across a membrane pore, a volume flux (Jv) and an

Two PVB hollow fiber membrane modules with molecular weight cut off (MWCO) at 40 and 200 kDa were used, and the other parameters of modules are given in Table 1. Before all experiments, the membranes were rinsed with distilled water to

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73

Table 1 Characteristic parameters of PVB hollow fiber membrane modules. Module number

MWCO of dextran (kDa)

Pore Inside radiusa(nm) diameter (mm)

Outside diameter (mm)

Membrane area (m2)

M40 M200

40 200

5.3 11.8

1.14 1.064

0.234 0.344

a

0.620 0.664

The hydraulic radius was estimated using the method of Hagel [21].

remove the diluent until the conductivity of the permeate stayed below 1 mS/cm. All reagents are analytical grade products. Various solutions were prepared with distilled water with conductivity less than 1 mS/cm. Background electrolytes for streaming potential, electroviscous effect were KCl and CaCl2. The electrolyte ionic strength of KCl electrolyte solution was varied from 5.0  10  4 mol/L to 0.15 mol/L, that of CaCl2 electrolyte solution was varied from 5.0  10  4 mol/L to 0.30 mol/L, pH values were adjusted by adding 1 mol/L HCl or NaOH. 3.2. Measurement equipment Measurements of streaming potential, permeability and salt retention across the membrane pores were performed, as shown in Fig. 1. The cell used for electrokinetic measurement contained two Ag/AgCl electrodes, one near the entrance at the feed side and the other at the permeate side. The potential difference between the electrodes could be measured using a high impedance digital voltmeter. The pressures at the entrance of the cell and at the outlet of the cell were measured using a mercury differential pressure meter. The amount of permeate was measured using an electronic balance (AUY220). The conductivities of feed and permeate were measured using a conductivity meter (DDSJ308A), and salt concentrations were calculated from these data using a calibration curve. The pH of the electrolyte bulk solution was measured by a pH meter (PHS-3C). 3.3. Methods The potential difference (DE) across the membrane was measured at various pressure drops across the membrane (DP), in order to calculate the streaming potential coefficient (DE/DP) across the pores. KCl and CaCl2 were selected as the electrolytes; the ionic strength of KCl electrolyte solution was varied from 5.0  10  4 mol/L to 0.15 mol/L, and that of CaCl2 electrolyte solution was varied from 5.0  10  4 mol/L to 0.30 mol/L. The streaming potentials were measured from low to high concentration. The pressure was varied in the range of 25–50 kPa, which was gradually increased with an interval of 5 kPa. All measurements were made at pH value from 2.5 to 9.0, and the temperature was maintained at 2571 1C. The corresponding electrical potential difference (DE) under each pressure difference (DP) was recorded, and then the streaming potential coefficients of membranes were determined from the slopes of the straight lines depicting the relation between DE and DP. Determination of electroviscous effect was performed for various ionic strengths in the range from 5.0  10  4 to 0.3 mol/L at constant pH 6.8 and a transmembrane pressure of 25 kPa. The electroviscous effect consists in measuring the permeate flux with and without double-layer effects, the apparent viscosity at high ionic strength (about 0.1 mol/L for KCl solution, and 0.15 mol/L for CaCl2 solution) equals the bulk viscosity, and the double-layer is almost totally screened. In addition, electroviscous effect was also performed for various pH values at a transmembrane pressure of 25 kPa, at the pH of iso-electric point, where the distributions of ions in the membrane

Fig. 1. Experimental setup for the determination of streaming potential and permeability.

pores are the same with those of the bulk electrolyte, and the permeability measured at the iso-electric point as a base value. Conductivity of feed and permeate were measured simultaneously.

4. Results and discussion 4.1. Effect of ionic strength on the streaming potential The streaming potentials for M40 and M200 at different ionic strengths changed from 5.0  10  4 mol/L to 0.3 mol/L at pH 6.8 were measured. The streaming potential coefficients (n) across the membrane were calculated from the slopes of the straight lines depicting the relation between DE and DP; the experimental results are shown in Fig. 2. It can be seen from Fig. 2 that the absolute value of streaming potential across the porous membrane both in KCl and CaCl2 solution decreases with the increase of ionic strength, which can be explained from the point of the electrical double layer. When the ionic concentration increases, the counter-ion concentration in the solution will also increase, this would result in compressed diffuse layer , and more counterions are extruded into the shear plane. Thus, the streaming potential is decreased [22]. If the ionic concentration is large enough, the streaming potential will be as little as zero. For both M40 and M200, it seems to be reasonable to assume that the main source for charge at the membrane surface was due to anion adsorption, where resulting charge at the membrane surface is negative. In Fig. 2, we notice a weaker streaming potential coefficient in nominal value in CaCl2 solution than that in KCl solutions for both M40 and M200, which is due to the higher valence of cation for the negatively charged membrane. According to Eq. (4), with other parameters fixed, the streaming potential coefficient of the membrane is inversely proportional to the conductivity of the solution in the membrane pores. For membranes with large pores, it can be approximately considered that the conductivity of the solution in the membrane pores is equal to that of the solutions. Therefore, the larger the conductivity of the CaCl2 solution, the lower the streaming potential coefficient of the porous membrane. In addition, the streaming potential coefficient of the M200 is always more negative than that of the M40 at the same ionic strength. The reason might be that there is less double-layer overlapping in the M200. This result is in good agreement with Ricq et al.’s report [23] and Pontie´ et al.’s result [24]; a similar

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can be explained by the adsorption of Ca2 þ ions on the membrane surface, as Ca2 þ is a high valence cation and has a higher affinity to the negatively charged membrane surface than K þ , and this makes the IEP move to a higher pH, which is similar to the previous researches [22,23,27]. The iso-electric point of M40 is close to that of M200 in the same solution indicating that the IEP of PVB hollow fiber membrane is independent on MWCO. The probably reason might be that the stable natures, chemical compositions and good thermal properties of PVB membranes ensure the same IEP of the two modules in the same electrolyte.

0.2 0.0

ν/(mV.kPa-1)

-0.2 -0.4 CaCl2 for M40 CaCl2 for M200 KCl for M40 KCl for M200

-0.6 -0.8 -1.0

4.3. Electroviscous effect

-1.2 1

10

100

I/(10-3mol.L-1) Fig. 2. Streaming potential vs. ionic strength for M40 and M200, using KCl and CaCl2 electrolytes at pH 6.8.

0.6 0.4

CaCl2 for M40 CaCl2 for M200 KCl for M40 KCl for M200

ν/(mV.kPa-1)

0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0

2

3

4

5

6 pH

7

8

9

10

Fig. 3. Streaming potential for M40 and M200 vs. pH (I¼ 1.0  10  3 mol/L).

¨ m et al. [25] and Soffer phenomenon has been observed by NystrO et al. [26]. A higher MWCO and higher permeate flux generate a greater charge displacement. In addition, the streaming potential value depends on solution and surface conductivities. The smaller the pore radius, the higher the surface conductivity contribution in the pore, and high conductivity leads to a smaller streaming potential coefficient.

4.3.1. Effect of ionic strength Fig. 4 shows the measured electroviscous effect (relative viscosity increase over its bulk value) result at ionic strengths between 5.0  10  4 and 0.30 mol/L and pH 6.8 for the membranes M40 and M200, using KCl and CaCl2 electrolytes. It is clearly seen that the electroviscous effect increases with increasing ionic strength at low ionic strength, it reaches a maximum at 1.0  10  3 mol/L for KCl solution while 1.5  10  3 mol/L for CaCl2 solution and then decreases with the increase of electrolyte concentration. A similar behavior has been reported by Huisman et al. [28] for a polysulphone ultrafiltration membrane (with a nominal cut-off value of 100 kDa) in KCl solutions at concentrations between 2  10  5 and 2  10  2 mol/L. The value of the electroviscous effect depends on the type of salt; the electroviscous effect of KCl electrolyte is higher than that of CaCl2 electrolyte at the same ionic strength. The minimum ionic strength for KCl electrolyte is about 0.1 mol/L, and CaCl2 electrolyte is about 0.15 mol/L. The electroviscous effect value is larger for the membrane M40 than for the M200 at the same electrolyte concentration. 4.3.2. Effect of pH The effect of pH on the electroviscous effect is shown in Fig. 5 using electrolyte ionic strength 1.0  10  3 mol/L for the M40 and M200 membranes. The electroviscous effect was calculated using the permeability measured at the iso-electric point as a base value. Fig. 5 indicates the iso-electric point pH 3.0 for KCl and pH 3.5 for CaCl2, this corresponds well with the results obtained by the streaming potential method. A minimum in the viscosity ratio is expected at the iso-electric point as this is where the distributions of ions in the region near the surface and the bulk electrolyte are the same, and viscosity within the pores and in the bulk electrolyte is the same. It can be seen in Fig. 5 that the electroviscous effect increases upon changing the pH away from the iso-

4.2. Iso-electricpoint measurements

1.18 1.16

KCl for M40 KCl for M200 CaCl2 for M40 CaCl2 for M200

1.14 1.12 1.10 μa/μ0

The streaming potentials variation with pH values have been experimentally determined at a given ionic strength 0.001 mol/L in KCl and CaCl2 solutions. The variations of streaming potential coefficients and zeta potentials with different pH values in different solutions for M40 and M200 are presented in Fig. 3. As can be seen in Fig. 3, the membrane is positively charged at low pH and negatively charged at pH values above the iso-electric point, and the streaming potential coefficients become more negative as the pH increases. The IEPs of M40 and M200 in KCl and CaCl2 solutions can easily be deduced from the graphs at the intersection of the curves, respectively. The curves lead to very close iso-electric points of M40 and M200 with respect to the same ionic strength. With careful observation of Fig. 3, we can easily conclude that the iso-electric point (IEP) in KCl solution for both modules is about 3.0, and which is close to 3.5 in CaCl2 solution. The significant shifting of the iso-electric point as the cation valence increases

1.08 1.06 1.04 1.02 1.00 0.98

1

10

100

I/(10-3mol.L-1) Fig. 4. Electroviscous effect vs. ionic strength for M40 and M200, using KCl and CaCl2 electrolytes at pH 6.8.

1.24 1.22 1.20 1.18 1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98

KCl for M40 KCl for M200 CaCl2 for M40 CaCl2 for M200 ζ/(mV)

μa/μ0

Y.-R. Qiu, J. Qi / Journal of Membrane Science 425–426 (2013) 71–76

2

3

4

5

6 pH

7

8

9

10

Fig. 5. Electroviscous effect vs. pH for M40 and M200 at I¼ 1.0  10  3 mol/L.

electric point. For the same electrolyte ionic strength, the electroviscous effect of M40 is greater than that of M200 at the same pH other than iso-electric point, and the electroviscous effect of KCl electrolyte is greater than that of CaCl2 electrolyte at the same ionic strength. 4.4. Comparison of the calculated zeta potentials The zeta potentials were calculated by the measured streaming potential method using Eq.(4) and the observed electroviscous effects using Eqs.(5) and (6). Also it is clear that the Eqs. (4) and (5) used to calculate zeta potential in the streaming potential method and electroviscous method give more realistic results for the M200 membrane (higher value of rp/k  1) than for the M40 membrane (lower value of rp/k  1). Therefore, calculated zeta potentials of M200 from both streaming potential measurements and electroviscosity measurements are shown in Fig. 6. It is found that the absolute value of zeta potential determined by both streaming potential and electroviscous method decreases with increasing ionic strength. The calculated values of zeta potentials from electroviscosity measurements are more negative than those from the streaming potential, and the calculated zeta potential values are more negative in KCl electrolyte solution those in CaCl2 electrolyte solution. This result agrees with the results earlier obtained for measurements on microfiltration membranes, where electroviscous measurements always resulted in higher values of zeta potential than streaming potential measurements did [4,28]. However, the trends predicted by the two methods are very similar, the zeta potential first increases with ionic strength, reaches a maximum and then decreases. With the increase of ionic strength, the decrease of the zeta potential may be explained by a decrease in the effective thickness of the diffuse layer as the ionic strength increases. More counter-ions can penetrate the compact layer because the increase of ionic strength leads to a compression of the diffuse layer, resulting in a lower charge density in the diffuse layer. The zeta potential in CaCl2 solution is less negative than that in KCl solution at the same ionic strength, it is probably due to the fact that Ca2 þ is a high valence cation and has a higher affinity to the membrane surface than K þ , and this makes the zeta potential in CaCl2 solution less negative. Compared with the streaming potential method, combining the electroviscosity theory with water flux measurements at different salt concentrations provides a simple and fast method of determining zeta potentials for membranes [3]. But the electroviscous method results in more negative zeta potentials than the streaming potential method. The great advantage of the electroviscous method to calculate zeta potential is that no

75

10 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100

CaCl2 by streaming potential KCl by streaming potential KCl by electroviscous effect

1

10

100

I/(10-3mol.L-1) Fig. 6. Zeta potential vs. electrolyte concentration for M200, using KCl and CaCl2 electrolytes at pH 6.8, calculated from the measured streaming potential and from the measured electroviscous effect.

special equipment is needed other than a membrane rig that allows measurements of transmembrane pressure and flux. For electroviscosity measurements precise data of permeabilities and pressures are needed. Temperature needs to be controlled accurately and the method is very sensitive to membrane fouling. A clear disadvantage of the electroviscous method is that the knowledge of the membrane pore size is necessary for a quantitative calculation of zeta potential, and the inhomogeneous pore size may cause great deviation as only the mean pore radius is used to calculate zeta potential. Furthermore, the membrane pore is not the cylindrical pore with the same diameter, and the measured pore size is just that of the skin layer of the porous membrane, which is much different from the cross-section. In addition, another disadvantage of the method is the low sensitivity at low values of zeta potential because of the non-linear relationship between the apparent viscosity and the zeta potential. The calculations from the electroviscous theory depends strongly on the assumed pore size [3], and the electroviscous effect is known to decrease with increasing width of pore-size distribution [29]. However, the streaming potential is hardly influenced by the pore-size distribution, as it is mainly determined by the mean flow pore size [30]. Hence, the streaming potential method is a rather easy technique as well.

5. Conclusions Two PVB hollow fiber membrane modules with molecular weight cut off at 40 and 200 kDa (M40 and M200) were characterized with streaming potential measurements in KCl and CaCl2 electrolyte solutions. The results show that the PVB membrane is negatively charged due to the adsorption of ions, and the valences of the electrolyte have an important influence on the streaming potential of the membrane. The effect of pH on the electroviscous has been investigated using electrolyte ionic strength 1.0  10  3 mol/L for the M40 and M200 membranes. The electroviscous effect indicates almost the same iso-electric points with the results obtained by streaming potential method. For the same electrolyte ionic strength, the electroviscous effect of M40 is greater than that of M200 at the same pH other than iso-electric point, and the electroviscous effect of KCl electrolyte is greater than that of CaCl2 electrolyte at the same ionic strength. The electroviscous effect results for M40 and M200 indicate that the electroviscous effect increases with increasing ionic strength at low ionic strength, it reaches a maximum at a certain

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concentration and then decreases with further increase of ionic strength. Zeta potentials for M200 have been calculated from streaming potential and electroviscosity. The trends predicted by the two methods are very similar, but the calculated zeta potentials from electroviscosity are more negative than those obtained with streaming potential measurements.

Nomenclature Roman letters The electrolyte concentration (mol m  3) Faraday constant, a correction function for high zeta potential G a correction function for the overlapping double layers I ionic strength (mol L  1) Jv volume flux (m s  1) j Electrical current (A) K the conductivity of the electrolyte solution (S m  1) k Boltzmann constant L11, L12, L21, and L22 coupling coefficients R retention rate, the molar gas constant (8.314 J mol  1 K  1) rp Pore radius (m) T the absolute temperature (K) c F

Greek letters

DE DP

e0 er Z k1

r ma m0 n z

difference of the electrical potential (V) hydrostatic pressure difference (Pa) vacuum permittivity (8.854  10  12 F m  1) relative dielectric constant of the solvent dynamic viscosity of the solution (kg m  1 s  1) Debye length (m) density (kg m  3) the apparent viscosity (Pa s) the bulk viscosity of the electrolyte solution (Pa s) streaming potential coefficient (V/kPa) zeta potential (V)

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