Journal of Membrane Science 215 (2003) 1–9

Streaming potential, electroviscous effect, poreconductivity and membrane potential for thedetermination of the surface potential of a

ceramic ultrafiltration membrane

M. Sbaı a, P. Fieveta,∗, A. Szymczyka, B. Aoubizab, A. Vidonnea, A. Foissya

a Laboratoire de Chimie des Matériaux et Interfaces, 16 route de Gray, 25030 Besançon Cedex, Franceb Laboratoire de Calcul Scientifique, 16 route de Gray, 25030 Besançon Cedex, France

Received 6 May 2002; received in revised form 14 November 2002; accepted 18 November 2002

Abstract

Streaming potential, electroviscous effect, pore conductivity and membrane potential were measured for a ceramic ultra-filtration membrane at various KCl concentrations. A space charge model was used to calculate the surface potentials fromthe experimental data. Surface potentials determined from the four experimental methods are in relatively good agreementalthough some discrepancies occur at low ionic concentrations. Pore conductivity and membrane potential methods lead tosimilar surface potentials on the whole range of concentrations studied but these latter are smaller than those obtained forboth streaming potential and electroviscous effect measurements.© 2002 Elsevier Science B.V. All rights reserved.

Keywords:Surface potential; Streaming potential; Electroviscous effect; Pore conductivity; Membrane potential; Space charge model

1. Introduction

The surface potential (ψs) is an important and reli-able indicator of the surface charge of membranes andits knowledge is of a great interest in the predictionand understanding of the filtration performances ofmembranes. The surface potential cannot be measureddirectly, but must be deduced from experiments bymeans of a model. Up to now, the most widely-usedprocedure for determining the surface potential ofmembranes has been the streaming potential (SP).However, alternative methods based on the electroos-motic effect [1–4], electroviscous effect (F) [5–8],

∗ Corresponding author. Fax:+33-3-81-66-20-33.E-mail address:patrick.fievet@univ-fcomte.fr (P. Fievet).

pore conductivity (λpore) [9], membrane potential(Em) [10] and salt retention measurements[11] havebeen recently proposed.

In this paper, three of these newly developed meth-ods have been used and compared to the traditionalstreaming potential method.

The first one, developed by Huisman and co-workers[5,8], is based on the electroviscous effect. The pres-ence of an electrical double-layer inside pores exerts aprofound influence on the behaviour of the fluid flow-ing through the membrane pores. When an electrolyteflows through charged pores under a pressure gradi-ent, a streaming potential is established. This potentialproduces a backflow of liquid by the electro-osmoticeffect, and the net effect is a diminished flow in theforward direction. The liquid appears to exhibit an

0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.doi:10.1016/S0376-7388(02)00553-7

2 M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9

Nomenclature

a effective pore radius (m)ci ion concentration in the pore

(mol m−3)C electrolyte concentration (mol m−3)CI , CII external concentrations of solutions

I and II in contact with themembrane (mol m−3)

Cm mean electrolyte concentration in themembrane (mol m−3)

Di ion diffusivity (m2 s−1)�E electrical potential difference (V)Ec concentration potential (V)Ecell cell potential (V)Em membrane potential (V)F Faraday constant (96,485 C mol−1)I electrical current (A)Ki ion mobility (m s−1 N−1 mol)Kij coupling coefficients�P hydrostatic pressure difference (N m−2)q solvent flow (m s−1)r radial co-ordinate (m)R universal gas constant

(8.31 J mol−1 K−1)Rcell electrical resistance of the measuring

cell (�)Rm electrical resistance of the electrolyte

inside pores (�)Rh

m electrical resistance of the electrolyteinside pores with high saltconcentration (�)

Rsol electrical resistance of the electrolytebetween the membrane and the twovoltage electrodes (�)

SP streaming potential (V N−1 m2)T temperature (K)x axial co-ordinate (m)z absolute value ofzizi charge number of the ionic species I

Greek letters�ϕ axial electrical potential difference (V)κ Debye parameter (m−1)κ−1 thickness of double-layer (m)λ0 conductivity of the bulk electrolyte

(�−1 m−1)

λh conductivity of the electrolyte at highsalt concentration (�−1 m−1)

λpore conductivity of the electrolyte in thepore (�−1 m−1)

µ viscosity of the electrolyte(0.001 kg m−1 s−1)

π standard dimensionless constant�Π osmotic pressure difference (N m−2)ψs surface potential (V)

enhanced viscosity (usually called apparent viscosity)if its flow rate is compared with the flow in absence ofdouble-layer effects (e.g. at high salt concentration)[12].

The second one uses pore conductivity measure-ments to determine the membrane surface potential.Indeed, the electrolyte conductivity within the poresreflects both the mobility of ions and their concentra-tions, which are dependent on the surface potential.

The third one is based on the membrane potentialmeasurements[13]. When the charge on the pore wallsof a membrane is high enough and the pore size suf-ficiently small, the diffusion of ionic species withinthe membrane may be significantly disturbed by theelectrostatic interaction between ions and the chargedsurface. The membrane potential may then reflect thecharge state of a membrane and can be related to thesurface potential by means of a model[10].

In a previous paper[14], the possibility of determin-ing the surface potential of porous membranes fromthe SP,Em andλpore methods was investigated in theframework of the space charge model. This theoreti-cal analysis allowed to evaluate the accuracy on thedetermination of the surface potential from the threecompared methods under various conditions of poreradius, surface potential and electrolyte concentration.Westermann-Clark et al.[15] have measured thesethree quantities (SP,Em and λpore) for charged mi-croporous membranes in order to test the quantitativeaccuracy of the space-charge model. They found thatthe model was quantitatively accurate for pores largerthan 3 nm in radius and for electrolyte concentrationsof 0.1 M or lower.

The aim of the present paper is to compare thesurface potential values determined from streamingpotential, electroviscous effect, pore conductivity and

M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9 3

membrane potential measurements for a range of saltconcentration. Surface potential values are numeri-cally calculated by considering a space charge model.

2. Theory

In previous papers[10,14,16], the electrokineticand electrochemical phenomena occurring in homoge-neous cylindrical pores were studied in the frameworkof the linear thermodynamics of irreversible processesand the space charge model outlined by Osterle andco-workers[17–19]. The local relations for transportthrough pores (Nernst–Planck and Navier–Stokesequations) and the non-linear Poisson–Boltzmannequation for the electrostatic condition of the porefluid were developed.

The influence of the surface potential on the stream-ing potential[14,20], the electroviscous effect[16],the pore conductivity[14] and the membrane potential[10,14] was examined. To this end, the integral ex-pressions of the phenomenological coefficients (Kij )coupling the solvent flow (q) and the electrical cur-rent (I) with both the hydrostatic pressure difference(�P), the osmotic pressure difference (�Π ) and theelectrical potential difference (�ϕ) were establishedand calculated numerically. The streaming potential,electroviscous effect, pore conductivity and membranepotential could then be expressed as:

SP=(�ϕ

�P

)I=0,�Π=0

= −K21

K23(1)

F =((q)�ϕ=0

(q)�ϕ �=0

)I=0,�Π=0

= 1

1 − (K13K21/K11K23)(2)

λpore = l

πa2

(I

�ϕ

)�P=0,�Π=0

= K23

πa2(3)

Em = (�ϕ)�P=0,I=0 = −2RTCm

K22

K23ln

(CII

CI

)(4)

wherea is the pore radius,Cm the mean solute con-centration in the membrane (bulk concentration),CIandCII the concentrations of both external solutionsin contact with the membrane.

The ratio of the pore conductivity (λpore) to the con-ductivity of the bulk electrolyte (λ0) can be written as

λpore

λ0= (K23)�ϕ �=0

(K23)�ϕ=0. (5)

The calculations presented in this paper are carried outusing the expressions forKij listed inAppendix A.

It should be noted that the approach adopted hereis only a valid approximation to the exact approachwhen the concentration gradient across the membraneis weak[15].

3. Experimental

3.1. Membrane and chemicals

The membrane used in this work is a non-commer-cial UF alumina membrane made at the InorganicMaterials Science group (Faculty of Chemical Tech-nology of Twente, The Netherlands) in the form ofa 39 mm diameter disc. The mean pore radius wasdetermined from coupled hydraulic and electrical re-sistance measurements (according to the proceduredescribed in[21]) and was found to be close to 27 nm.Membrane thickness is about 2 mm.

Electrolyte solutions are prepared from potassiumchloride of pure analytical grade and milli-Q qualitywater (conductivity less than 10−4�−1 m−1). For thewhole study, solutions at various concentrations in therange 0.0001–1 mol l−1 are studied at natural pH (nochemicals added), i.e. 5.6 ± 0.1. All electrolyte solu-tions are thermostated at 30± 0.5◦C.

3.2. Experimental methods

The solution is firstly forced through the membraneunder a transmembrane pressure of 0.2 bar for 24 h.Next, the four methods are successively brought intooperation before equilibrating the membrane with asolution at different electrolyte concentration.

3.2.1. Streaming potentialThe experimental device is presented inFig. 1.

Streaming potential measurements are carried outby applying increasing pressure pulses ranging from0.2 to 0.4 bar. The range of pressure increments istaken sufficiently low to ensure identical electrolyte

4 M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9

Fig. 1. Experimental unit for streaming potential and permeate flow measurements.

concentrations from both parts of the membrane andto limit concentration polarisation effects.Fig. 2shows the variation of the electrical potential differ-ence between both sides of the membrane (�E) as afunction pressure increment (�P) for a 0.01 mol l−1

KCl solution. The electrical potential difference is

Fig. 2. Electrical potential difference (�E) on both sides of themembrane vs. the pressure increment (�P); 0.01 mol l−1 KCl;pH = 5.6 ± 0.1.

found to be a linear function of�P and the streamingpotential is deduced from the slope of�E = f (�P).

3.2.2. Electroviscous effectElectroviscous effect experiments are carried out

using the same experimental device as for streamingpotential. These experiments consist in measuring thepermeate flow with and without double-layer effectsin a range of transmembrane pressure ranging from0.2 to 0.4 bar. A 0.9 mol l−1 KCl solution is used todetermine the permeate flow without double-layer ef-fects (q(∆ϕ=0)/�P = 6.41 × 10−4 l m−2 s−1 bar−1).Indeed, the surface charge is so strongly screened atsuch an ionic strength that it has no influence on thebehaviour of the fluid flowing through the membrane.

3.2.3. Pore conductivityPore conductivity is determined from electrical re-

sistance measurements. These latter are carried outusing electrochemical impedance spectroscopy (theapparatus used in the present work is described in[14,20]). The galvanostatic four-electrodes mode isused to measure the electrical resistance within the

M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9 5

pores of the membrane (Rm). The resistance measure-ment is carried out with the membrane in the elec-trolyte solution (in order to obtain the resistance of themeasuring cell,Rcell) and with the lone solution (Rsol).Then, the membrane resistanceRm can be obtained bysubtracting the value ofRsol from Rcell. The electrolyteconductivity within pores (λpore) can be experimen-tally deduced from electrical resistance measurementsby using the following relation:

λpore = λhRhm

Rm(6)

whereλh is the conductivity of the solution at high saltconcentration (i.e. when the surface conduction effectscan be neglected, which means that the conductivity inpores can be assumed to be equal to the conductivityof the solution outside the membrane) andRh

m is theresistance across the pores when the cell is filled withthis solution. The termλhRh

m is a constant that dependsonly on the geometry of the porous space (equivalentto a “cell constant”).

3.2.4. Membrane potentialThe cell used for membrane potential measurements

was described in a previous work[22]. In the mem-brane potential process, the membrane is put betweentwo aqueous solutions at different electrolyte concen-trations which fill the following conditions:

CII

CI= 2 (7a)

lnCm = ln(CI)+ ln(CII )

2(7b)

whereCI andCII refer to the diluted and concentratedsolutions, respectively. The termCm denotes the meanconcentration in the membrane. This latter is identicalto the concentration used for streaming potential, elec-troviscous effect and pore conductivity experiments.

The electrical potential difference measured, calledthe cell potential (Ecell), is measured by means of a pairof Ag/AgCl electrodes. It is linked to the membranepotentialEm by the relation:

Em = Ecell − Ec (8)

whereEc denotes the concentration potential. This lat-ter can be written as

Ec = EII − EI (9)

where EI is the potential of the Ag/AgCl electrodeimmersed in the lower concentration solution againsta reference electrode (e.g. the saturated calomel elec-trode) andEII the potential of the other Ag/AgClelectrode immersed in higher concentration solutionagainst the same reference electrode.

4. Results and discussion

4.1. Measurements

Fig. 3presents the variation of the streaming poten-tial (SP) versus the salt concentration (C). As expected,the streaming potential decreases as the salt concentra-tion increases due to the phenomenon of double-layercompression: the double-layer thickness is reduceddue to a screening of the surface charge at a shorterdistance. Less counter-ions are present in the diffuselayer and then, less counter-ions can be displaced un-der the pressure difference. Furthermore, as shownby the well-known Helmholtz–Smoluchowski relation[23] a high ionic concentration makes the solution in-side pores more conductive leading to a smaller SP.

As can be seen, the streaming potential is close tozero for the 0.9 mol l−1 KCl solution which indicatesthat the effect of the surface charge is negligible at thisconcentration.

Fig. 4 shows the electroviscous effect in terms ofratio (q)�ϕ=0/(q)�ϕ �=0 versus salt concentration (C).It appears that this effect is negligible at low andhigh salt concentrations, but it reaches a maximum at

Fig. 3. Variation of the streaming potential (SP) vs. the electrolyteconcentration (C); KCl, pH = 5.6 ± 0.1.

6 M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9

Fig. 4. Electroviscous effectq(�ϕ=0)/q(�ϕ �=0) vs. salt concentration(C); KCl, pH = 5.6 ± 0.1.

intermediate concentrations. A similar behaviour hasbeen reported by Huisman et al.[7] for a polysulphoneultrafiltration membrane (with a nominal cut-off valueof 100 kDa) in KCl solutions at concentrations be-tween 2× 10−5 and 2× 10−2 mol l−1. This behaviouragrees with theory[24]. If the surface potential is in-dependent of salt concentration, then the maximumelectroviscous effect occurs forκmax a = 2.5. A valueof ∼7, close to 2.5, is obtained here (a = 27 nm andκmax ∼ 0.25 nm−1).

The variation of the ratioλpore/λ0 versus salt con-centration is shown inFig. 5. It can be seen that

Fig. 5. Variation of the ratioλpore/λ0 vs. salt concentration (C); KCl, pH = 5.6 ± 0.1.

the electrolyte conductivity within pores can substan-tially exceed the bulk conductivity (λ0). As expected,the influence of the charged pore walls on the poreconductivity decreases as the electrolyte concentra-tion increases. Indeed, when this latter increases, thedouble-layer thickness (κ−1) decreases and hence thebulk solution in the pore occupies a relatively largerand larger part of the pore. Consequently, the conduc-tivity inside pores (λpore) is less and less affected bythe surface charge due to greater and greater contri-bution of the bulk conductivity (λ0) compared to thesurface conductivity and then the electrolyte conduc-tivity inside pores (λpore) approaches closer the bulksolution (λpore/λ0 → 1).

Fig. 6 shows the concentration dependence of themembrane potential (Em). As can be seen,Em de-creases as the salt concentration increases.Em isclose to the highest limiting value of∼18 mV (Nernstpotential) which corresponds to the total exclusionof co-ions from the pore for the lowest salt concen-tration (0.00015 mol l−1), and to the lowest limitingvalue of ∼0 mV (diffusion potential) for the highestsalt concentration (0.9 mol l−1). Again, the decreaseof Em with increasing ionic strength is due to thephenomenon of double-layer compression. When theelectrokinetic radius (κa) is small (i.e. at low elec-trolyte concentration), the double-layer fills the entirepore and the number of co-ions in the pore is thereforelow. On the other hand, whenκa increases (i.e. the

M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9 7

Fig. 6. Membrane potential (Em) vs. mean salt concentration (Cm);KCl, pH = 5.6 ± 0.1.

electrolyte concentration increases), the double-layeris then confined to a small region near the porewall. Consequently, the relative abundance of co-ionswithin the whole pore increases due to the substan-tial contribution of the bulk solution in the poreand their electrostatic exclusion at the pore entrancedecreases. Fora � κ−1 (0.9 mol l−1), the pore con-tains almost as many co-ions as counter-ions and themembrane potential tends to the diffusion potentialvalue.

4.2. Comparison

The surface potential values are obtained from thetheoretical curves calculated by the Space Chargemodel. As shown in[14,16], a particular value ofλpore or Em can be associated with a single value ofψs whereas a particular SP orF value can be asso-ciated with two significantly different values ofψs.This ambiguity could be easily removed by plottingψs as a function of the electrolyte concentration. Theψs values for which a decrease with concentration isobserved correspond to the true values ofψs.

It must be mentioned that the use of the Helmholtz–Smoluchowski (HS) relation for calculating theψspotential led to aψs−C curve with a maximum. Thisresult is due to the fact that the membrane is stronglycharged. Thus, the HS relation that does not take intoaccount the surface conduction phenomenon, greatlyunderestimates the true surface potential particularlyat low concentration.

Fig. 7. Salt concentration dependence of surface potential (ψs)calculated from streaming potential (�), electroviscous effect (�),pore conductivity ( ), and membrane potential (�) experiments.

This result clearly shows that it is necessary to usea model more realistic than the simple HS relation.

Fig. 7 shows the values of surface potential (ψs)calculated by means of space charge model fromstreaming potential, electroviscous effect, pore con-ductivity and membrane potential measurements ver-sus salt concentration (C). At first, it can be seenthat the surface potential is positive at natural pH(5.6 + 0.1), which means that the isoelectric point(iep, pH for which the membrane charge is zero) ofthe membrane is greater than this pH value. This re-sult is consistent with the iep reported in the literaturefor alumina membranes[6,25,26].

A good qualitative agreement is obtained for thefour experimental methods. As expected, the surfacepotential decreases with increasing salt concentrationsince the addition of electrolyte leads to a compressionof the double-layer. However, surface potential val-ues determined from the various experimental meth-ods show some discrepancies, especially at low saltconcentrations.

It clearly appears that the results obtained frompore conductivity and membrane potential measure-ments are in very good agreement in the whole rangeof salt concentrations. It can be noted that surfacepotential values inferred from membrane potentialmeasurements are very scattered for the lowest saltconcentration (0.00015 mol l−1). This is due to theshape of curvesEm −ψs which show thatEm greatlyincreases at low surface potential values and then

8 M. Sbaı et al. / Journal of Membrane Science 215 (2003) 1–9

levels off (at a value corresponding to the Nernstpotential) for small electrokinetic radii[14].

Both streaming potential and electroviscous effectmeasurements give higher surface potentials thanthose obtained from the two other methods. Somediscrepancies between streaming potential and poreconductivity results have already been reported in aprevious paper[9] and were attributed to a possi-ble ionic conduction behind the shear plane, whichis not taken into account by the classical theory ofelectrokinetics.

5. Conclusion

The surface potential of a ceramic ultrafitrationmembrane was determined at different salt concentra-tions using streaming potential, electroviscous effect,pore conductivity and membrane potential methods.As expected, the surface potential decreases withincreasing ionic strength due to the phenomenon ofdouble-layer compression. It was found that surfacepotentials determined from the four experimentalmethods are in relatively good agreement excepted forlow ionic concentrations. Similar surface potentialsare obtained by pore conductivity and membrane po-tential methods on the whole range of concentrationsstudied. Streaming potential and electroviscous effectmeasurements lead to higher surface potentials thanthose obtained from pore conductivity and membranepotential measurements.

Acknowledgements

The authors would like to thank A. Yaroshchuk forhelpful discussions. They would also like to thankDr. H.J.M. Bouwmeester of the University of Twente(Netherlands) for providing the membrane used in thiswork.

Appendix A

For a membrane separating two aqueous solutionsat the same temperature but different pressures andelectrical potentials and containing slightly differentconcentrations of the same electrolyte, the following

linear relations between flows and conjugated forcesfor a system near equilibrium are usually set up:

q = K11

(−dP

dx

)+K12

(−dΠ

dx

)+K13

(−dϕ

dx

)

I = K21

(−dP

dx

)+K22

(−dΠ

dx

)+K23

(−dϕ

dx

)

with

K11 = πa4

8µ

K12 = π

µC

∫ a

0r

∫ a

r

1

r

∫ r

0(c1 + c2)r dr dr dr − πa4

8µ

K13 = 2πzF

µ

∫ a

0r

∫ a

r

1

r

∫ r

0(c1 − c2)r dr dr dr

K21 = πzF

2µ

∫ a

0(c1 − c2)(a2 − r2)r dr

K22 = πzF

RTCm

∫ a

0(D1c1 −D2c2)r dr

+ πzF

Cmµ

∫ a

0r(c1 − c2)

∫ a

r

1

r

∫ r

0(c1 + c2)

× r dr dr dr − µzF

2µ

∫ a

0(c1 − c2)(a2 − r2)r dr

K23 = 2πz2F 2∫ a

0(K1c1 +K2c2)r dr

+ 2πz2F 2

µ

∫ a

0r(c1 − c2)

∫ a

r

1

r

∫ r

0(c1 − c2)

× r dr dr dr.

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