1.1603237

Rheological properties of concentrated aqueous silica suspensions: Effects of p H andions contentSaeid Savarmand, Pierre J. Carreau, Franois Bertrand, David J.-E. Vidal, and Michel Moan

Citation: Journal of Rheology (1978-present) 47, 1133 (2003); doi: 10.1122/1.1603237 View online: http://dx.doi.org/10.1122/1.1603237 View Table of Contents: http://scitation.aip.org/content/sor/journal/jor2/47/5?ver=pdfcov Published by the The Society of Rheology

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Redistribution subject to Rheological properties of concentrated aqueous silicasuspensions: Effects of pH and ions content

Saeid Savarmand, Pierre J. Carreau,a) Francois Bertrand, David J.-E. Vidal,

and Michel Moanb)

Center for Applied Research on Polymers (CRASP), Department of ChemicalEngineering, Ecole Polytechnique, P.O. Box 6079, Stn. Centre-Ville, Montreal, QC,

H3C 3A7, Canada

(Received 26 November 2002; final revision received 2 June 2003)

Synopsis

The rheological behavior of concentrated aqueous suspensions of nearly monodisperse submicron,spherical silica particles was studied in Couette and vane geometries. End corrections and walldepletion effects were found to be important. The apparent yield stress and shear viscosity wereinvestigated in the light of interactions between the charged silica particles. The effects of pH aswell as the addition of electrolyte were examined. The suspensions in de-ionized water withoutaddition of acid, base, or electrolyte gave the largest apparent yield stress and shear viscosity, whilethe addition of base, acid, and KCl resulted in significant decreases of the apparent yield stress aswell as of the viscosity. These effects have been interpreted in light of the DLVO theory and thecompression of the double layer around the solid particles ~Debye length!. 2003 The Society ofRheology. @DOI: 10.1122/1.1603237#

I. INTRODUCTIONConcentrated suspensions are encountered in many industrial applications in the paint,

ceramic, pharmaceutical, food industry, etc. The rheological characterization of thesematerials is of major concern to determine their processability and stability over time.Many attempts have been made to use physical and numerical models to study themicroscopic and macroscopic effects on the rheology of suspensions. The simplest one isthe Brownian hard sphere suspension model, which has been studied extensively bymany authors @Krieger and Dougherty ~1959!; Batchelor ~1977!; van der Werff and deKruif ~1989!; Jones et al. ~1991!; Bossis and Brady ~1989!; Brady ~1993!; Bilodeau andBousfield ~1998!#. In the Brownian hard sphere model, the balance between the hydro-dynamic forces and the Brownian diffusion forces determines the rheology of the sus-pension. This type of model, however, cannot fully explain the complex behavior ofsuspensions with strongly interacting particles. Aqueous suspensions of particles such assilica of known size @Zaman et al. ~1996!; Fagan and Zukoski ~1997!; Franks et al.~2000!# are good model suspensions of strongly interacting particles.

Interacting forces between particles, also called colloidal forces, include attractive andrepulsive forces. The former is composed of electrostatic forces between oppositely

a!Author to whom all correspondence should be addressed; electronic mail: [email protected]!On leave from: Laboratoire de Rheologie, Universite de Brest, France. 2003 by The Society of Rheology, Inc.J. Rheol. 47~5!, 1133-1149 September/October ~2003! 0148-6055/2003/47~5!/1133/17/$25.00 1133

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Redistribution subject to Scharged atoms on the particles and of the van der Waals forces originating from thespontaneous dipoles on the particle surfaces. The latter includes electrostatic forces be-tween similarly charged surfaces and steric forces due to the presence of adsorbed orgrafted polymer molecules on the particle surface. The range and relative magnitude ofthese forces determine the rheological behavior of these suspensions. If the van der Waalsforces dominate, aggregation or flocculation will take place, while the presence of suffi-ciently strong repulsive forces between particles leads to a stable colloidal system. pHand electrolyte concentration influence significantly the balance between attractive andrepulsive forces and cause divergent rheological phenomena such as thixotropy, yielding,shear thinning, and shear thickening.

In suspensions as well as in other multiphase systems, wall depletion at the solidsurface of a measuring device is frequently encountered leading to apparent slip effects.Cameron ~1989! studied nonhomogeneous flows in narrow-and wide-gap Couette geom-etries. He presented a model based on distinct fluid regions of different power-law indicesand considered the resultant apparent viscosity, avoiding the classical assumption of aslip velocity at the walls. One other option is to use a vane-in-cup geometry instead of theconventional bob-in-cup geometry. The vane geometry generally consists of 28 thinblades attached at equal angles around a small shaft. The vane was first used in soilmechanics @Skempton ~1948!; Cadling and Odenstad ~1950!; Flaate ~1966!; Matsui andAbe ~1981!#. A number of experimental @Nguyen and Boger ~1983, 1985!; Liddell andBoger ~1996!# and numerical studies @Barnes and Carnali ~1990!; Yan and James ~1997!#have been carried out on the application of the vane to determine the apparent yield stressand viscosity of fluids showing apparent slip at the solid walls. The vane has the advan-tage that the disturbance caused by the geometry is minimized, which is of great rel-evance with thixotropic suspensions. One key assumption is that the fluid within theblades moves with the vane as a solid body @Keentok ~1982!#. Thus, the cylindricalsurface generated by the motion of the vane blades is such that yielding occurs within thefluid itself @Nguyen and Boger ~1983!; James et al. ~1987!#. A thorough review on themethods and applications of the vane geometry is given by Barnes and Nguyen ~2001!.

Barnes and Carnali ~1990! reported results of a numerical simulation for power-lawfluids in bob-in-cup and vane-in-cup geometries. For power-law indices smaller than 0.5the fluid between the vane blades does not exchange with the fluid in the annular gapbetween the cup and the cylindrical surface defined by the vane. They also observed thatthe stresses at the cup wall were similar for both geometries. Their numerical resultspredict sharp peaks of stress at the vane tip @also reported in the calculations of Keentoket al. ~1985!#, and almost constant stress values in the gap between the vane peripheryand the cup ~in the bob-in-cup case the stress decreases with the radius!. Consequently,the migration of particles away from the solid walls was less important in a vane than ina Couette geometry, a phenomenon that was also observed by Gauthier et al. ~1971a,1971b!. In addition, the experimental results obtained by Barnes and Carnali ~1990! forone polymer solution and one suspension in both geometries gave similar results, sug-gesting that the vane geometry is appropriate for steady viscosity measurements.

The objective of this paper is to investigate the relationship between the rheology ofconcentrated aqueous silica suspensions and the particle interactions. The rheologicalcharacterization of these complex fluids requires an investigation of errors in the experi-mental measurements due to disturbances such as end effects and wall depletion effects.

1134 SAVARMAND ET AL.Hence, a preliminary study of these effects for various rheometers equipped with Couetteand vane geometries is presented in Sec. III. The particle interactions, which are essen-tially electrostatic repulsions, can be varied by changing the pH and/or by adding anelectrolyte. The main contribution in this work concerns the large range of pH investi-

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Redistribution subject to Sgated, from 2 to 11, and the various underlying microstructures. In this respect, a detailedphysicochemical characterization is presented in Sec. IV. Finally, measurements ofthe apparent yield stress and steady shear flow were made and are discussed in Sec. Vin terms of the range and magnitude of the colloidal forces and the resulting microstruc-tures.

II. MATERIALS AND APPARATUSThe silica micropowder used in this study ~Seahostar KE P30 from Nippon-Shokubai

Co. Ltd. of Japan! consisted of nearly monodisperse spherical particles of 0.29 mm~0.270.34 mm!, with a density of 1948 kg/m3 and a maximum moisture of 0.5%. Theaverage diameter was measured by a centrifugal particle size analyzer and the densitywas measured by nitrogen pycnometry. The silica was synthesized with the method ofsol-gel and manufactured using a vacuum drying process.

The suspensions were prepared using either de-ionized water or a 1022 M KCl solu-tion at a solids concentration of 40 vol %. All the suspensions were sonicated for 7 minwith a high intensity sonic probe ~Vibra Cell, model VCX 600, 20 kHz, 600 W! at a 40%amplitude and then put at rest for at least 24 h, after which the pH was adjusted byadding either 1 M NaOH or 1 M HCl. The suspensions were found to be stable ~nosedimentation! for a few days. Before the rheological tests, the volume fraction waschecked with the weight loss method. All the tests were carried out at 25 C.

Three stress-controlled rheometers, a Bohlin CVO 120, a Thermal Analysis AR 2000and a Rheometric Scientific SR 5000 with Couette and six-blade vane geometries wereused for the rheological measurements. The Couette and vane geometries covered a rangefrom 14 to 28 mm for the inner diameter, from 22 to 50 mm for the height, and from 1to 1.5 mm for the gap size.

A Zeta Potential Analyzer ~model Zeta Plus! from Brookhaven Instruments Corpora-tion was used for measuring the zeta potential. For the measurements, dilute suspensionsof volume fractions smaller than 0.08 vol % were used.

A shear preconditioning was applied for all tests so that measurements could be startedwith suspensions under similar conditions. No major differences were observed for dif-ferent preshearing and rest times. Hence, a preshearing of 10 min at 10 s21 followed bya 10 min rest period was applied for all tests. A thin layer of silicon oil with a viscosityof 0.06 Pa s was applied on the top of the sample to avoid the evaporation of water.

III. END EFFECTSIn order to convert torque values to stress values, the end effects associated to the flow

resistance between the bottom of the spindle and the fluid underneath were measured forall geometries. The method consisted of obtaining torque values for various angularvelocities and heights of the spindle immersed into the sample. Then, following Carreauet al. ~1997!:

T/Vn 5 ~L1Lc!, ~1!

where K is a constant, T, V, n, L, and Lc denote the torque, angular velocity, power-lawindex, height of the spindle immersed into the sample, and a corrected length to accountfor the end effects, respectively. As it was not possible to determine accurately the end

1135CONCENTRATED AQUEOUS SILICA SUSPENSIONSeffects on the silica suspensions due to the evaporation of the water content, xanthan gumaqueous solutions of concentrations ranging from 0.3 to 0.6 wt % were used. The power-law index of these solutions was less than 0.3, which is comparable with that of the silicasuspensions considered in this work. For each value of L, a number of angular velocities

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Redistribution subjecwere applied and the corresponding torques were measured. The curves of the appliedtorque versus the immersed length of the spindle into the fluid were then extrapolated tozero torque in order to determine the equivalent length, Lc , as shown in Fig. 1~a! for theSR 5000 equipped with a Couette geometry and in Fig. 1~b! for the AR 2000 rheometerequipped with a vane geometry.

The bobs of the CVO 120 and AR 2000 rheometers have conic ends and the followingequation can be derived using the geometric mean radius @Harris ~1977!#:

s

T5

12pRbRc~L11/3Rb!

, ~2!

where s, Rb , and Rc denote the shear stress, bob radius and cup radius. The value of Lcwas found to be 5.5 mm, which is in close agreement with the expected value of Lc 1/3 Rb 5 4.3 mm for a Mooney-type bob-in-cup geometry. However, there is no

equivalent expression for a bob-in-cup geometry with a recessed end used with the SR

FIG. 1. ~a! Measurement of the end effects for different angular velocities in the SR 5000 Couette geometryusing a xanthan gum solution. ~b! Measurement of the end effects for different angular velocities in the AR2000 vane geometry using a xanthan gum solution.t1136 SAVARMAND ET AL.5000. According to Fig. 1~a!, a value of 9.8 mm is obtained for Lc with the geometry ofthe SR 5000. This is 22% of the total height of the spindle so that the end correction hasto be taken into account when measuring the viscosity of highly shear-thinning fluids. It

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Redistribution subject tois worth noting that experiments carried out with a Newtonian fluid showed no endeffects. Consequently, it seems that the end effects and the corrected length depend uponshear thinning.

The end effects in the case of vane geometries were studied by Nguyen and Boger~1983, 1985! for yield stress measurements and by Barnes and Carnali ~1990! for steady-state viscosity measurements. Nguyen and Boger ~1985! verified different assumptionsfor the shear stress distribution at the vane ends. They concluded that the assumption ofa constant shear stress at both ends being equal to the shear stress along the cylindricalsurface defined by the blade tip was adequate for yield stress measurements. Conse-quently, they proposed the following equation:

s

T5

1

2pRv2~L12/3Rv!

, ~3!

where Rv is the radius of the vane. Barnes and Carnali ~1990! applied the extrapolationmethod discussed earlier to account for the end effects. They found a corrected length of2 mm for their vane-in-cup geometry for both Newtonian and non-Newtonian fluids.Since it represented only about 4% of the vane height, they ignored it. In the presentwork, the end effects were also measured by this same extrapolation method and com-pared with the values obtained assuming a constant stress on the end surfaces. Figure 1~b!shows the graph of the torque versus the immersed length of the vane in the xanthan gumsolution, from which we get a corrected length of 5.2 mm for the lower end. This iswithin one percent of the corrected value predicted by Eq. ~3!. Hence, Eq. ~3! was usedto determine yield stress and steady viscosity with the vane geometry.

The data obtained with the vane and Couette geometries of the AR 2000 and SR 5000rheometers for a 0.5 wt % xanthan gum aqueous solution are compared in Fig. 2~a!. Thedifferences between the data are within the experimental error ~smaller than 2%!. Sincethe power-law index of the xanthan gum solution is comparable to those of the suspen-sions used in this work, the agreement between the results confirms the suitability of thevane geometry for the rheological measurements presented in this work.

Figure 2~b! shows the rheological data obtained from the AR 2000 and SR 5000rheometers with vane and Couette geometries for a 40 vol % silica suspension in de-ionized water. The corrected data obtained with the Couette geometry in both rheometersgave similar results. However, one can readily notice that the corrected data obtainedwith the vane of the AR 2000 rheometer are about 21% larger than those obtained withthe Couette geometries. These differences are attributed to an apparent slip at the walls ofthe Couette geometry. Wall depletion or lubrication effects are attributed to a reduction inthe concentration of the solid particles near the solid walls. According to Delime andMoan ~1991!, this phenomenon is enhanced in the case of very small particles ~smallerthan 1 mm! owing to an increase of the anisotropy of the Brownian motions near thewalls. A thorough review on apparent slip effects can be found elsewhere @Barnes~1995!#.

Efforts made to carry out rheological measurements using concentric disk geometrieswith rough plates did not alleviate this problem. The application of Yoshimura andPrudhomme ~1988! method to the concentric disk geometries also led to negative valuesfor the viscosity. It was further attempted to apply the method of Yoshimura and

1137CONCENTRATED AQUEOUS SILICA SUSPENSIONSPrudhomme ~1988! or Kiljanski ~1989! to the data obtained with two Couette geometriesof the strain-controlled ARES ~Rheometric Scientific! of two different gap sizes. Accord-ing to these methods, the slip velocity is a function of shear stress only and can beestimated from the viscosity values of the material measured with geometries of two


Redistribution subject different gap sizes at the same shear stress. Thus, two sets of steady viscosity measure-ments are required for the same set of imposed shear stresses. For the smaller gapgeometry of the ARES of 0.25 mm, the applied shear rate needed to be so large to providethe same shear stress as that obtained with the larger gap geometry of 1 mm. Theobtained shear stress at the outer cylinder had to be larger than the apparent yield stressto make sure that the material within the gap was in motion. The calculations, however,resulted in negative viscosities for the material. Therefore, among the aforementionedattempts for obtaining the material response, that of the vane method appears moresatisfactory and reliable. Consequently, all the rheological measurements in the creep andsteady state viscosity tests were carried out with the vane geometry.

IV. PHYSICOCHEMICAL CONDITIONS

FIG. 2. ~a! Comparison of the steady shear stress results obtained with the AR 2000 and SR 5000 vane andCouette geometries of a 0.5 wt. % xanthan gum solution in water. ~b! Comparison of the steady shear stressresults obtained with the AR 2000 and SR 5000 for a 40 vol % silica suspension in de-ionized water at naturalpH (pH 6.5).1138 SAVARMAND ET AL.A. Relationship between pH and ionic strengthThe pH and electrolyte effects can be studied by the measurement of zeta potential

and mobility of dilute suspensions, leading to the interparticle potential. The hydration ofsilanol groups on silica particles, SiOH, at small and large pH, creates positive


Redistribution subject to( SiOH21) and negative ( SiO2) sites on their surfaces, respectively. The pH at whichthe charge density is zero is known as the isoelectric point.

Figure 3~a! shows the results of the zeta potential as a function of pH in the range of211. The zeta potential is negative over the whole range, indicative of negative chargesites ( SiO2) on the particles. For the particles in de-ionized water, the zeta potentialapproaches zero as the pH is decreased to 2 which is the isoelectric point for silicaparticles. The natural value of the pH, which means the pH value without added acid orbase, is 6.560.1 and 5.560.1 for the silica suspensions in de-ionized water and a1022 M KCl solution, respectively. In de-ionized water, the zeta potential increasesrapidly as the pH decreases to the isoelectric point. The addition of an acid leads to theneutralization of some of the SiO2 groups with H3O1 and significant screening of theparticle charges. On the contrary, the addition of a base increases the negative chargedensity and the zeta potential becomes smaller and smaller with increasing pH.

In the case of silica suspensions in a 1022 M KCl solution, the variations of the zetapotential with respect to pH follows the same trend as that of the suspensions in de-ionized water. At low pH, the zeta potential is smaller than that of the suspensions inde-ionized water and it decreases with pH due to an increasing negative charge densityon the particles. Electrolyte mobility data can be used to estimate the equivalent concen-tration of the electrolyte, the ionic strength of the suspension, and eventually the doublelayer thickness. First, the equivalent conductivity can be obtained from the electrolytemobility as @Harned and Owen ~1943!#:

L 5 eNAu, ~4!

where L and u are the equivalent conductivity and electrolyte mobility, respectively; NAis the Avogadro number and e is the charge of an electron. The equivalent concentrationof the electrolyte can then be evaluated by using the Kohlrausch relationship

NL 5 (i

Nili ~5!

in which Ni and l i are the equivalent concentration ~normality! and equivalent conduc-tance of the ith ion, respectively, and N is the equivalent concentration of the electrolyte.The l is are taken from Harned and Owen ~1943!. The Debye length, k21, which is ameasure of the double layer thickness, can be expressed as @Hiemenz ~1977!#:

k21 5 S4pe2NA(izi2Mi10000kT D21/2

53.04310210

AN, ~6!

where zi and M i are the valence number and molar concentration of the ith ion, k is theBoltzmann constant, and T is the absolute temperature.

The results of the calculations are presented in Fig. 3~b!. For the suspensions inde-ionized water, the smallest electrolyte concentration occurs for a pH between 6.5 and

1139CONCENTRATED AQUEOUS SILICA SUSPENSIONS7, which corresponds to the natural pH. Moving away from this natural pH will raise theions content of the suspension and the electrolyte equivalent concentration as a result. Onthe other hand, for the suspensions in a 1022 M KCl solution, the electrolyte concentra-tion is not so sensitive to pH owing to the significant quantity of ions already present.


Redistribution subject B. Interaction potentialThe zeta potential and mobility data can be used to evaluate the particle interactions.

In the frame of the DLVO theory, the total interparticle potential energy is evaluated fromthe repulsion and dispersion ~Londonvan der Waals! contributions following Usui~1998! and Russel et al. ~1989!:

fDLVO 5 2p0ac02 ln@11e2k~r22a!#2

A6 F 2a2r224a2 1 2a2r2 1lnSr224a2r2 DG. ~7a!

In this expression, fDLVO is the total interparticle potential energy based on the DLVOtheory, 0 is the permittivity of the vacuum, is the relative permittivity of water, c0 isthe surface potential energy approximated by the zeta potential, A is the Hamaker con-stant which is 2 kT for silica particles @Bergstom ~1996!#, r is the center-to-center dis-tance between two particles, and a is the particle radius. To incorporate the short-rangerepulsion between the silica particles that contributes to the stability of silica suspensions

FIG. 3. ~a! Zeta potential as a function of pH for suspensions in de-ionized water and 1022 M KCl solution.~b! Equivalent concentration vs pH for silica suspensions in de-ionized water and 1022 M KCl solution.1140 SAVARMAND ET AL.near the isoelectric point, we have used the following empirical model proposed byChapel ~1994!:

fSR 5 a@A1d1e2~r22a !/d11A2d2e

2~r22a !/d2# , ~7b!


Redistribution subject towhere fSR is the short-range potential and A1 5 1.055531027 N/m, d1 5 5.63310210 m, A2 5 1.1671 5531026 N/m, d2 5 5.7310211 m are the parameters forthe silica particles. Thus, the total interparticle potential is obtained as

f 5 fDLVO1fSR . ~7c!The contribution of the short-range repulsion potential fSR was found to be less than

5% of the DLVO repulsive potential at the isoelectric point, at very short distances.Figure 4~a! displays results calculated at various pH in de-ionized water. It is observedthat the total potential energy is always repulsive. Consequently, the suspensions areelectrostatically stabilized in the range of pH studied here except in a region close to theisoelectric point (pH 2) where flocculation is expected to occur. It can be seen that asthe pH is increased from the natural pH value of 6.5, the total potential energy increasesto a maximum at about pH 7.2 while a further increase in the pH decreases the potentialenergy. The initial addition of the base changes some silanol groups on the particles tonegative groups according to the following reaction

SiOH1OH2 SiO21H2O. ~8!

The production of negative groups continues until the above equilibrium is reached.Further addition of the base at constant solids content acts similarly to the addition of anelectrolyte resulting in stronger screening effect. This is why the curve corresponding topH 8.0 is lower than that corresponding to pH 7.2.

The decrease in pH from its natural value of 6.5 has two effects. One is the increaseof the free ions in the suspension. The other effect is to neutralize some of the SiO2groups to silanol as follows:

SiO21H3O1 SiOH1H2O. ~9!

Both effects accentuate the reduction in the potential energy as evidenced by the curvesfor pH 5.5 and 3.6.

Figure 4~b! displays the variation of the total interparticle potential energy with re-spect to the interparticle distance for silica suspensions in a 1022 M KCl solution. Thetotal interaction potential is repulsive within the experimental pH range except in a zonenear the isoelectric point (pH 2.5). The mechanism for the variation of the potentialenergy is the same as explained before. The effect of the electrolyte can be assessed bycomparing the two silica suspensions at the same pH, one of which does not contain theadded electrolyte. The potential energy for the suspension in a 1022 M KCl solution atits natural pH, that is 5.5, falls sharply to zero at a dimensionless separation distance ofabout 0.6, while it remains larger at long distances in the case of the suspensions inde-ionized water.

Although the DLVO theory is strictly valid for dilute suspensions, it can also be usedto interpret qualitatively the behavior of interacting particles in more concentrated sys-tems. In the following, we will analyze the rheological behavior of the silica suspensionsas a function of pH or ionic strength in terms of electrostatic stabilization and floccula-tion.

V. RESULTS AND DISCUSSION

1141CONCENTRATED AQUEOUS SILICA SUSPENSIONSA. Step creep experimentsSeveral creep tests were performed and consisted of incrementing the shear stress

starting from very small values. The response of the material is reported in terms of thecreep viscosity as a function of the strain, following Citerne et al. ~2001!. As an example,


Redistribution subject totransient viscosity from creep data of a 40 vol % silica suspension at pH 6.5 are shown inFig. 5 as a function of strain. As can be seen, for stresses of 4.5 Pa and smaller not shownin this figure, the response is that of a linear elastic solid. For stresses larger than 5 Pa,there is a partial breakdown of the structure due to an extra stretch beyond the elasticlimits, which represents a viscoelastic characteristic. Above a critical stress value of 7.0Pa, a major breakdown of the structure occurs and the material begins to flow as a fluidleading to a steady-state rate of strain. In terms of time scale, for stress values of 6.8 andsmaller, no structure breakdown occurred even after a long time, while for 7.0 Pa andlarger stresses, the breakdown occurred within 100 s. It is worth noting that the 6.8 Pacase was done after the 7.0 Pa and before 7.2 Pa. It shows the reproducibility of theexperiments with identical preshearing conditions. The critical stress corresponding to the

FIG. 4. ~a! Total interparticle potential vs separation distance between particles for dilute silica suspension inde-ionized water at different pH. ~b! Total interparticle potential energy vs separation distance between particlesfor dilute silica suspension in 1022 M KCl solution at different pH.1142 SAVARMAND ET AL.transition between the fully elastic and viscoelastic behavior and the critical stress cor-responding to the transition between the viscoelastic and fully viscous behavior havebeen defined as static and dynamic yield stresses respectively by Zukoski and co-workers@Chen et al. ~1994!; Chow and Zukoski ~1995!; Liddell and Boger ~1996!#. The critical


suspension in de-ionized water is the largest at the natural pH, which is at pH 6.5. As

Redistribution subject toshown in Fig. 3~b! the electrolyte concentration is minimum at this pH; this correspondsto the largest characteristic interacting length between particles, L0 , calculated from thefollowing expression @Russel et al., ~1989!#:

L0 51k

lna

ln~a/ln a!, ~10!

a 5 4p0c02a2k exp~2ak!/kT, ~11!

L0 is several times the mean interparticle separation, 2a/f1/3, where here f is thevolumetric solids content. Hence, there are strong electrostatic interactions that prevailover the Brownian motion. The particles are then in an ordered microstructure, whichexplains the large apparent yield stress at this pH.

The addition of only a small amount of acid to the suspension ~small decrease in thepH) causes the apparent yield stress to drop drastically. The decrease can be explained bythe compression of the electric double layer around the silica particles due to the presenceof more free ions in the medium by the acid addition. This compression is such that theparticles behave as if they were smaller, which results in an apparent decrease in thevolume fraction and a strong reduction of the apparent yield stress. The addition of ionsscreens the charges at the surface so that the range of the interparticle repulsive forcesstress of 7.0 Pa shown in Fig. 5 corresponds to the transition from a viscoelastic solidbehavior to a fully viscous behavior and is referred to as the apparent yield stress of thesuspension, s0 .

Figure 6 and Table I report the apparent yield stress determined by the techniquediscussed above as a function of pH of the suspension. The apparent yield stress of the

FIG. 5. Creep results of a 40 vol % silica suspension in de-ionized water at pH 6.5 using the vane geometry.A 10 min preshearing of 10 s21 followed by a 10 min rest were applied for each test.

1143CONCENTRATED AQUEOUS SILICA SUSPENSIONSdiminishes significantly, as can be seen in Fig. 4~a! for low pH values. This causes therheology to resemble that of hard spheres leading to smaller values of the apparent yieldstress. As the pH is further decreased from 5 to 2 ~the isoelectric point of these silicasuspensions!, the net charge on the particle surface decreases to zero. The Londonvan


repulsions only comes from screening effect. Thus, the gradual decrease in the electro-

Redistribution subject to static forces manifests itself through a gradual decrease in the apparent yield stress.For the suspension in a 1022 M KCl solution at its natural pH, that is at 5.5, the

magnitude of the characteristic interacting length, L0 , is significantly decreased due tothe presence of more free ions. According to Fig. 3~b!, the electrolyte concentration of thesuspension with KCl is quite larger than that of the suspension in de-ionized water at thesame pH. Furthermore, Figs. 4~a! and 4~b! show that the interparticle potential is suchthat the range of interparticle forces is much smaller when KCl is present. In this case, thescreening effect of the free ions is so important that the dispersion forces between theparticles results in the formation of flocs. The much larger apparent yield stress of 1.0 Pafor the suspension with KCl is caused by the larger interparticle interaction forces. Uponapproaching the isoelectric point, the repulsion forces between the particles diminish dueto the screening effect and the neutralization of some of SiO2 groups. Consequently,flocculation is more important in this case and larger values of the yield stress areobserved.

A small increase in the pH from 5.5 has two effects. One is the increase of free ionsdue to the addition of a base and the other one is the production of more SiO2 groupson the particles according to Eq. ~8!. As can be seen in Fig. 4~b!, the net result is ander Waals attractive forces then become dominant leading to the formation of flocsresponsible for the gradual increase of the apparent yield stress. Due to flocculation nearthe isoelectric point, the yield stress values were observed to be strongly dependent onthe preshearing and rest time before the creep tests started. Reproducible data could notbe obtained in this region and no data are reported here.

The addition of a base also reduces the apparent yield stress due to the screening of theparticle charges but not as drastically as in the case of the addition of an acid. In the lattercase, the neutralization of more SiO2 groups significantly enhances the decrease of theinterparticle electrostatic forces as was discussed earlier. This leads to a sharp drop in theapparent yield stress. In the former case, the decrease in the interparticle electrostatic

FIG. 6. Apparent yield stress vs pH for 40 vol % silica suspensions in de-ionized water and 1022 M KClsolution using the vane geometry.

1144 SAVARMAND ET AL.increase of the interparticle potential energy and a decrease in the apparent yield stress.However, the addition of more base would increase the screening effect and eventuallywould result in flocculated suspensions and large apparent yield stress values. This casewas not considered in the present work.


B. SteaStead account

for end to 250 sto ensur asing anddecreasi ng resultsare show measure-ments a

In te Fig. 7~a!comply with de-ionized ent yieldstress v t pH 5.5correspo an indi-cation o about 2!increase culation.Due to onal par-ticulate apparentyield str

A sim ! and theapparen observedthat the spondingto the i ric point,the visc8. Thesstress.

8.0 0.04 0.71 0.04

Redistribution subject to SOR licensedy viscosity experimentsy viscosity data were obtained with the vane geometry and corrected toeffects, as explained before. The measurement time was varied from 50e that steady state was reached and the experiments consisted of increng the shear rate/shear stress in a well-defined manner. The correspondin in Figs. 7~a! and 7~b!. The standard deviations associated with these

re less than 4%.rms of the resistance of the suspension to shear, the viscosity results ofwith the apparent yield stress values of Fig. 6. The largest viscositywater was obtained at pH 6.5 and it corresponds to the largest apparalue. The very small ~almost zero! value of the apparent yield stress ands to the smallest viscosity. In this case, the low shear rate plateau isf a no-yield material. Reducing the pH down to the isoelectric point (pHs the viscosity as well as the apparent yield stress value because of flocthe net attractive interparticle interactions, a continuous three-dimensinetwork structure is formed, which is responsible for larger values of theess and viscosity.ilar correspondence can be seen between the viscosities of Fig. 7~b

t yield stress values for the suspensions in a 1022 M KCl solution. It isviscosity increases considerably as the pH approaches the value corresoelectric point. However, at pH far away from that of the isoelect

aParameters of the power-law expression: h 5 mugun21.TABLE I. Parameters for the power-law model obtained from steadyviscosity curves and the apparent yield stress of the step creep tests for 40vol % silica suspensions in de-ionized water and 1022 M KCl solutionsusing the vane geometry.

Medium pH m (Pa sn)a na s0 (Pa)De-ionized

H2O2.0 5.5 0.10 fl2.5 4.7 0.10 3.13.0 3.4 0.24 2.54.0 2.3 0.17 1.54.5 0.47 0.26 0.155.0 0.34 0.30 0.125.5 0.13 0.52 0.036.0 0.74 0.10 0.406.5 7.0 0.10 7.07.7 6.0 0.10 3.58.1 3.7 0.10 2.09.5 1.2 0.13 0.77

10.0 0.38 0.17 0.25

1022 M KCl 2.0 3.2 0.18 fl3.0 7.2 0.13 4.35.5 1.9 0.56 1.07.5 0.06 0.65 0.05

1145CONCENTRATED AQUEOUS SILICA SUSPENSIONSosity does not change significantly, as can be seen from the curves for pH 7.5 ande curves also exhibit low shear rate plateaus, suggesting the absence of a yield

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Redistribution subject toIt is interesting to compare the properties of the two suspensions at the same pH valueof 5.5. The viscosity of the suspension with KCl is considerably larger than that of thesuspension in de-ionized water. The suspension in KCl also exhibits an apparent yieldstress. The values of the zeta potential are similar for these two cases @see Fig. 3~a!#.However, one may notice from Figs. 4~a! and 4~b! that the considerable difference be-tween the ionic strengths of the two suspensions results in remarkably different curves forthe interparticle potential energy, especially at long interparticle distances. Consequently,the suspensions with KCl are less stable than the suspensions in de-ionized water andflocculation is responsible for the larger viscosity and the apparent yield stress in thisformer case.

The effect of ions content and pH on the power-law parameters are presented in Table

FIG. 7. ~a! Viscosity vs shear rate for 40 vol % silica suspensions in de-ionized water at different values of pHusing the vane geometry. ~b! Viscosity vs shear rate for 40 vol % silica suspensions in 1022 M KCl solution atdifferent values of pH using the vane geometry.1146 SAVARMAND ET AL.1. The variation of the consistency factor, m, follows the same trend as that of theapparent yield stress for all the suspensions in de-ionized water as well as those in a1022 M KCl solution. The magnitudes of m and s0 are both measures of the strength ofthe suspension microstructure. Thus, the arguments given in the last section regarding the


Redistribution subject toeffects of the ionic strength and pH on apparent yield stress hold also for consistencyfactor. The power-law index, n, is a characteristic of the shear thinning. For most of thepH and ionic strength values of this work, the values of n are smaller than 0.3. It is onlylarger than 0.5 for a narrow domain about pH 5.5 for the suspensions in de-ionized water.For the suspensions with KCl, n is larger than 0.5 when 5.5 , pH , 8.5, that is faraway from the isoelectric point. These results show that, as expected, suspensions withlarger apparent yield stresses also exhibit more shear thinning. The initial interconnectednetwork of these suspensions is significantly broken down when subjected to increasinghydrodynamic forces, which leads to the formation of a shear-induced layer or liquid-likestructure of smaller viscosity.

VI. CONCLUSIONThe apparent yield stress measurements by the creep method of Citerne et al. ~2001!

clearly stressed the elastic, viscoelastic, and fluid stages of the yield process for theconcentrated aqueous silica suspensions. The apparent yield stress and the viscosity of anaqueous silica suspension in the absence of an additional electrolyte are maximum at itsnatural pH and any addition of free ions to the suspension by either changing pH oradding an electrolyte will result in a decrease of these rheological parameters. There aretwo maxima in the apparent yield stress versus pH curves in the absence of an additionalelectrolyte: one at the natural pH and the other at the isoelectric point. When an electro-lyte is added ~KCl in this work!, only one maximum exists and is located at the isoelec-tric point. The consistency factor of the power-law region of the steady viscosity curvesfollows the same trend as that of the apparent yield stress of the creep tests. It was alsoobserved that suspensions with larger values of apparent yield stress have smaller power-law indices and enhanced shear-thinning behavior.

The results presented in this work clearly demonstrate that, in the case of stronglyshear-thinning materials, the shear stress/shear rate data obtained from a Couette geom-etry with a recessed end at the bottom and a Mooney-type Couette system with a conicsection at the bottom do not match if the end effects are not considered. The measuredvalues of the so-called corrected length associated with the end effects for the Mooney-type Couette geometry is in good agreement with the common value for a conic section,i.e., 13Rb . For the Couette geometry with the recessed bottom, we showed that thecorrected length must be evaluated when dealing with strongly shear-thinning materialssuch as colloidal suspensions. For the vane geometry, the measurements of the correc-ted length confirmed that the constant stress assumption at the vane ends is valid forsteady-state viscosity measurements. Comparable results obtained for the Couette and thevane geometries using a xanthan gum aqueous solution suggests that the vane-in-cupgeometry is a suitable alternative for measuring the rheology of shear-thinning fluidsand suspensions. The data obtained in this work for concentrated aqueous silica suspen-sions using a vane geometry were 21% larger than those obtained with Couette geom-etries. This difference is attributed to the apparent slip or wall depletion effects at theinstrument walls.

1147CONCENTRATED AQUEOUS SILICA SUSPENSIONSACKNOWLEDGMENTThe financial support received from NSERC ~National Science Engineering Council

of Canada! is gratefully acknowledged.


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1149CONCENTRATED AQUEOUS SILICA SUSPENSIONS

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