Journal of Membrane Science 215 (2003) 19
Streaming potential, electroviscous effect, poreconductivity and membrane potential for the
determination of the surface potential of aceramic ultrafiltration membrane
M. Sba a, P. Fievet a,, A. Szymczyk a, B. Aoubiza b, A. Vidonne a, A. Foissy aa Laboratoire de Chimie des Matriaux et Interfaces, 16 route de Gray, 25030 Besanon Cedex, France
b Laboratoire de Calcul Scientifique, 16 route de Gray, 25030 Besanon Cedex, FranceReceived 6 May 2002; received in revised form 14 November 2002; accepted 18 November 2002
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
The surface potential ( s) 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 , electroviscous effect (F) ,
Corresponding author. Fax: +33-3-81-66-20-33.E-mail address: email@example.com (P. Fievet).
pore conductivity (pore) , membrane potential(Em)  and salt retention measurements  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. Sba et al. / Journal of Membrane Science 215 (2003) 19
a effective pore radius (m)ci ion concentration in the pore
(mol m3)C electrolyte concentration (mol m3)CI, CII external concentrations of solutions
I and II in contact with themembrane (mol m3)
Cm mean electrolyte concentration in themembrane (mol m3)
Di ion diffusivity (m2 s1)E electrical potential difference (V)Ec concentration potential (V)Ecell cell potential (V)Em membrane potential (V)F Faraday constant (96,485 C mol1)I electrical current (A)Ki ion mobility (m s1 N1 mol)Kij coupling coefficientsP hydrostatic pressure difference (N m2)q solvent flow (m s1)r radial co-ordinate (m)R universal gas constant
(8.31 J mol1 K1)Rcell electrical resistance of the measuring
cell ()Rm electrical resistance of the electrolyte
inside pores ()Rhm electrical resistance of the electrolyte
inside pores with high saltconcentration ()
Rsol electrical resistance of the electrolytebetween the membrane and the twovoltage electrodes ()
SP streaming potential (V N1 m2)T temperature (K)x axial co-ordinate (m)z absolute value of zizi charge number of the ionic species I
Greek letters axial electrical potential difference (V) Debye parameter (m1)1 thickness of double-layer (m)0 conductivity of the bulk electrolyte
h conductivity of the electrolyte at highsalt concentration (1 m1)
pore conductivity of the electrolyte in thepore (1 m1)
viscosity of the electrolyte(0.001 kg m1 s1)
standard dimensionless constant osmotic pressure difference (N m2) s 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).
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 . 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 .
In a previous paper , the possibility of determin-ing the surface potential of porous membranes fromthe SP, Em and pore 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.  have measured thesethree quantities (SP, Em and pore) 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. Sba et al. / Journal of Membrane Science 215 (2003) 19 3
membrane potential measurements for a range of saltconcentration. Surface potential values are numeri-cally calculated by considering a space charge model.
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 . The local relations for transportthrough pores (NernstPlanck and NavierStokesequations) and the non-linear PoissonBoltzmannequation 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 ,the pore conductivity  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 ( ) and theelectrical potential difference () were establishedand calculated numerically. The streaming potential,electroviscous effect, pore conductivity and membranepotential could then be expressed as:
F =((q)=0(q) =0
= 11 (K13K21/K11K23) (2)
pore = la2
Em = ()P=0,I=0 = 2RTCmK22K23
where a is the pore radius, Cm the mean solute con-centration in the membrane (bulk concentration), CIand CII the concentrations of both external solutionsin contact with the membrane.
The ratio of the pore conductivity (pore) to the con-ductivity of the bulk electrolyte (0) can be written aspore
0= (K23) =0
The calculations presented in this paper are carried outusing the expressions for Kij listed in Appendix 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 .
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 ) 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 104 1 m1). For thewhole study, solutions at various concentrations in therange 0.00011 mol l1 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 in Fig. 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. Sba et al. / Journal of Membrane Science 215 (2003) 19
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 l1KCl 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 l1 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 l1 KCl solution is used todetermine the permeate flow without double-layer ef-fects (q(=0)/P = 6.41 104 l m2 s1 bar1).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. Sba et al. / Journal of Membrane Science 215 (2003) 19 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 resistance Rm can be obtained bysubtracting the value of Rsol from Rcell. The electrolyteconductivity within pores (pore) can be experimen-tally deduced from electrical resistance measurementsby using the following relation:
pore = hRhmRm
where h 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) and Rhm is theresistance across the pores when the cell is filled withthis solution. The term hRhm 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 . 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)
where CI and CII refer to the diluted and concentratedsolutions, respectively. The term Cm 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 membranepotential Em by the relation:
Em = Ecell Ec (8)where Ec 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) and EII the potential of the other Ag/AgClelectrode immersed in higher concentration solutionagainst the same reference electrode.
4. Results and discussion
Fig. 3 presents 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 HelmholtzSmoluchowski relation 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 l1 KCl solution which indicatesthat the effect of the surface charge is negligible at thisconcentration.
Fig. 4 shows the electroviscous effect in terms ofratio (q)=0/(q) =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. Sba et al. / Journal of Membrane Science 215 (2003) 19
Fig. 4. Electroviscous effect q(=0)/q( =0) vs. salt concentration(C); KCl, pH = 5.6 0.1.
intermediate concentrations. A similar behaviour hasbeen reported by Huisman et al.  for a polysulphoneultrafiltration membrane (with a...