Yield stress of laterite suspensions

Yield Stress of Laterite Suspensions KOSTAS S. AVRAMIDIS 1 AND RAFFI M. TURIAN z Department of Chemical Engineering, University of Illinois, Chicago, Illinois 60680 Received June 7, 1990; accepted September 24, 1990 The yield stresses of aqueous laterite suspensions as functions of solids concentration and suspension pH, or ~ potential, were measured using the direct vane method. In addition, capillary rheometer shear stress-shear rate data were taken for the most concentrated test suspension, and these were used to estimate the yield stress by various extrapolations, and to compare them with the directly measured value using the vane geometry. Detailed characterizations of all test suspensions were carried out. The yield stress was found to depend strongly on suspension pH, attaining a m i n i m u m at the isoelectric point occurring at high pH. It was found to follow approximately a straight-line relationship with the square of the ~"potential, and its dependence on solids concentration is described by a two-parameter nonlinear relationship which gives the appropriate behavior in both the dilute limit and the concentrated limit near m a x i m u m packing. In situ particle size measurements by sedimentation suggest that the degree of flocculation is high under acidic conditions. The capillary rheometer data reflect strongly non-Newtonian, shear thinning behavior. © 1991AcademicPress,Inc. theoretical colloid science (1). Nonhydrodynamic effects play a predominant role in the rheological behavior as well as in the stability of suspensions consisting of particles with dimensions in the colloidal or near-colloidal range. According to the DerjaguinLandau-Verwey-Overbeek (DLVO) (2) theory of colloid stability these forces consist of Brownian motion associated with the random thermal motions of the molecules of the continuous phase, electrostatic surface forces arising from charges on the surface of the solid particles, and van der Waals attractions among the particles. The internal balance of charges in a colloidal suspension is incorporated into the concept of the electric double layer. The electric double layer consists of the particle charge and an equivalent amount of ionic charge which is accumulated in the liquid medium near the particle surface. The particle charge might have been created either by adsorption of ions from solution, in which case the surface potential could have been determined using the Nernst equation, or from interior lattice im- INTRODUCTION The general problem of relating rheological behavior to suspension microstructure is quite complex; it has many variables, which have wide ranges, and it is influenced by many effects. To establish relationships between rheological behavior and the constitutive nature of the suspension it is necessary to have adequate characterization of the suspension. This is not simple, especially for suepensions composed of many particles, of mixed sizes and complex shapes, and for suspensions of colloidal particles which are influenced by nonhydrodynamic forces. The complex rheological behavior of suspensions is not completely understood. Predictive theories based on basic principles are presently available only for dilute suspensions under idealized conditions. The behavior of aqueous colloidal dispersions of inorganic oxides continues to be an important problem in modern experimental and Present address: Dow Chemical USA, Designed Latex Research, Midland, MI 48674. 2 To w h o m correspondence should be addressed. 54 0021-9797/91 $3.00 Copyright© 199l by AcademicPress,Inc. All rightsof reproductionin any form reserved. Journalof Colloidand InterfaceScience,Vol. 143,No. l, April 1991 YIELD STRESS OF LATERITE SUSPENSIONS perfections (isomorphous substitutions), in which case the charge per unit surface area is a fixed quantity because it is determined from within the crystal and not from the surrounding liquid medium. It must be noted that for clays, the surface charge is created mainly by isomorphous substitutions in the lattice interior (3). For suspensions where the particle size and shape are ill-defined, and especially for oxide colloids, the electrophoretic mobility of the particles can be used to provide a reasonable description of the ~"potential (1, 4). Microelectrophoresis was used to determine the electrophoretic mobility and therefore the ~"potential of the laterite suspensions reported in this paper. Bird et al. (5) provide a comprehensive review of the literature on the rheology and flow ofviscoplastic materials. There are no general theories on the yield stress-concentration dependence of colloidal suspensions. We propose here a two-parameter nonlinear relationship for the yield stress-concentration dependence based on the solids concentration ratio (q~/ q~m), in which ~bis the volume fraction of solids a n d q~m is the volume fraction corresponding to maximum packing. In this relationship the numerator term, which is dominant in the limit ( ~ / q ~ ) ~ 1, is proportional to (4~/05~n)z in agreement with dilute limit theory', while the denominator term, which is dominant in the concentrated limit (qS/q~m) ~ 1, is proportional to [ 1 - (q~/ ~bm ) i / 31. This latter factor provides a measure of interparticle distance and vanishes at maximum packing. Laterite belongs to a broad class of claylike ores containing many mineral constituents. Laterites are generally apportioned as either ferrunginous or aluminus (bauxites) depending on whether it is the iron or the aluminum oxides that predominate. Extractive processes using such ores typically involve streams consisting of concentrated aqueous suspensions of these materials. Therefore, knowledge of the yield stress-concentration and the shear stressshear rate behaviors of such suspensions and their dependence on suspension chemistry is important. 55 EXPERIMENTAL General Description of Laterite The laterite suspension used in the studies reported in this paper was obtained from the AMAX Corporation as a 30.0 wt% slurry, which is very concentrated for these highly swelling solids. The weight percentage concentration corresponding to the maximum packing of the particles was found to be 47.4 (23.4 vol%). Properties of the solid powder are given in Table I. Laterite is a porous, indurated, concretionary claylike rock containing the minerals gothite, HFeO,, lepidocrosite, FeO(OH), and hematite, Fe203; hydrated oxides of aluminum, of which gibbsite is the most common and abundant; and perhaps titanium dioxide. Lateritic soils are red to reddish brown in color due to these minerals, and vary in type from a poorly graded sand to highly plastic clay. The probable clay structure in our laterite test material is montmoriltonite, which has a threelayer structure prone to swelling. The great instability of serpentine to weathering (the approach to equilibrium of a system composed of water, air, and soil) is one of the major reasons for nickeliferous laterite genesis (6). In the formation of nickel laterite the most important exchange reaction is the exchange of nickel for magnesium between soil water and serpentine with the result that magnesium in serpentine is substituted by nickel. The great disparity in surface area determined using nitrogen adsorption or mercury intrusion and that calculated from the Microtrac particle size data, which assumes the particles to be spherical and nonporous, is due in large measure to the significant particle porosity. Furthermore, the Leeds and Northrup Microtrac we have has a particle detection limit of 2 gm and therefore the contribution of smaller particles to the surface area is not included, and may be significant although certainly not of the order of the difference with the BET or porosimetry determinations. In Table I, dl0, ds0, and rig0 are the 10th, 50th (median), and 90th percentile diameters, and Yournal of Colloid and Interface Sczence, Vol. 143, No. 1, April 1991 56 AVRAMIDIS AND TURIAN TABLE I Properties of Laterite Powder Solid Density: 2.9452 g/cm 3 Particle size distribution Particle diameter (gm) Method d~o dso dgo d~ & Microtrac Elzone Sedigraph 2.14 3.06 0.60 3.48 3.44 4.20 13.70 7.04 21.40 -3.50 -- 5.69 4.81 -- Surface area Pore diameter (t,m) Method Specific area (m2/g) BET Porosimetry Microtrac 32.80 35.20 0.56 Volume median Surface median Average 0.428 0.023 0.084 (assuming nonporous spherical particles) Mineral content (wt%) Ni Co 1.63 -+ 0.02 0.044 -+ 0.001 Mg Mn 1.90 -+ 0.03 0.173 -+ 0.002 dn and dv, are the n u m b e r mean and the volume mean particle diameters, respectively. The clay structure in our test material is therefore highly porous, and the particles are subject to swelling and to isomorphous substitutions, with the surface adsorption of ions from solution existing, though to a limited extent. Summary of Tests Characterization experiments included m e a s u r e m e n t of particle and suspension densities, particle size distribution, BET particle surface area, mercury intrusion pore size distribution, suspended particle ~" potential using microelectrophoresis, suspension specific conductance, and sedimentation rate. O f the three methods used for particle size analysis (namely, the Microtrac, the Elzone, and the Sedigraph) which are based on different prinJournal of Colloid and Interface Science, Vol. 143, No. 1, April 1991 Fe 41.5 +- 0.7 AI 4.99 -+ 0.50 Si 4.35 -+ 0.05 Cr 1.55 + 0.01 ciples, the Sedigraph is based on particle sedimentation. Accordingly, particle size data taken using the Sedigraph under different p H conditions can be used to infer the state of particle aggregation. The primary particle size distribution using the Sedigraph required suspending the laterite particles, which have been previously repeatedly washed with doubly distilled water, in sodium hexametaphosphate (Calgon) dispersant solutions. The shear stress-shear rate behavior of the laterite suspension was determined using a suspension capillary rheometer. The yield stresses as functions of solids concentration and suspension pH, or ~"potential, were determined directly using the vaned apparatus. A supplementary set of p H - ~'potential measurements, at constant ionic strength using KNO3, were made to provide a more detailed examination of this dependence. All measurements of the 57 YIELD STRESS OF LATERITE SUSPENSIONS ~ potential were made using the Pen Kern Model 501 Lazer Zee-meter with a glass chamber. To ensure that the suspended laterite particles for the electrophoresis experiments encounter the same ionic strength as that in the suspension, the supernatant was used to suspend the particles for the mobility measurements. The pH of all the suspensions was varied using ammonium hydroxide (increase) of nitric acid (decrease), which are 1:1 electrolytes. Sedimentation experiments were carried out using a sedimentation column. The maximum packing concentration was determined using the Sorvall Model SS-3 centrifuge. A suspension sample was placed in the centrifuge for about 2 h at 3500 rpm (1019g). Subsequently the upper portion of the sediment was discarded as this was loosely packed, and the remaining cake was placed in a dish for drying until no weight change was observed. From the weight of the cake before and after drying the liquid weight was obtained by difference. Thus, with knowledge of the volumes of the solids and the liquid, the concentration at m a x i m u m packing could be determined. Well-mixed, representative suspension samples were used in all experiments. The pHadjusted supernatant was remixed with the sediment, and the dispersion was allowed to stand for 20 h when the pH was rechecked. It was usually found necessary to readjust the pH after the first 20-h interval, whereupon the pH was found to remain constant. Suspension samples having six different pH values were prepared and used in the experiments together with the original suspension as received. pension sample was prepared by mechanical shaking for 3 h using a paint shaker. Preshearing at high shear rate was carried out in the capillary rheometer until the shear stress-apparent shear rate data of at least three consecutive runs gave the same curve. To correct for end effects, and to check for possible wall effects, tubes of the same diameter but different length, as well as ones of the same length but different diameter, were used in the viscometric measurements using the capillary rheometer. The dimensions of the capillary tubes used in the measurements are given in Table II. The possible presence of wall effects was checked by plotting the measured wall shear stress against the apparent shear rate for capillary tubes of the same length but different diameter. It was found that to within experimental error such plots resulted in single curves, thereby suggesting that wall effects were negligible. Nondimensional equivalents of these plots, in which the friction factor is plotted against the generalized Reynolds number, were also made and gave the same results. Several methods were attempted for correcting the capillary rheometer data for end effects: the two-tube method proposed by Fredrickson (7), the single-tube method described by Skelland (8), and Bagley's method (9). The two-tube method requires that data with two different tube lengths, each long enough that fully developed flow is achieved, be taken for each tube diameter used. While this method is more tedious than the single-tube method, it is definitive. Bagley's method requires crossplotting the measured pressure drop against Rheological Measurements TABLE II The rheological experiments were carried out using a capillary rheometer designed and constructed in our laboratory. The laterite suspension as received was found to possess some time-dependent rheological behavior, i.e., thixotropy. All capillary rheometer data were obtained at 23.5 °C using presheared test samples of the laterite suspension. The sus- Dimensions of Capillary Tubes Used in Viscometric Measurements Diameter (cm) 0.4003 0.3155 0.2169 0.1453 Length (cm) LID Length (cm) LID 81.3 71.1 61.0 45.7 203 225 281 315 101.6 101,6 91.4 61.0 254 322 421 420 Journal of Colloid and Interface Science, Vol. 143,No. I, April 1991 58 AVRAMIDIS AND TURIAN the length-to-radius ratio with the apparent shear rate as a parameter. The method is tedious and the excessive manipulation of the data seems to magnify errors. Accordingly, the data were corrected for end effects by the twotube method. Measurements of the Yield Stress Using the Vane Geometry The direct method employed in this work for measurement of the yield stress of the laterite suspensions was the vane method (10, 11 ). The vaned geometry consists of four thin rectangular blades welded to a thin, rigid, central, cylindrical shaft at right angles to each other as shown in Fig. 1. The element is driven by the Brookfield viscometer motor. The dimensions of the vaned elements used in our experiments are given in Table III. The relationship for calculating the yield stress, r0, can be shown, using an approximate derivation due to Nguyen and Boger (10), to be given by ro - Jrnax K Jmax(L)~ - ro.( 1 + ~oKL DsL) 2 \ where K0 corresponds to zero length of immersion, i.e., L = 0 in Eq. [3]. For each suspension the yield stress is measured using vanes of different dimensions. For each vane element used, the torque measurements are repeated for different values of the immersion length L. According to Eq. [4] a plot of Jmax(L)/Ko versus L should yield a straight line with the L = 0 intercept equal to ro. A typical plot is given in Fig. 2 for the suspension with pH 10.11. Such a plot can be used as a check on the experimentally determined yield stress. It must be noted that in deriving Eq. [ 3 ] it was assumed that the stress distribution was uniform over the circular end surfaces. Therefore, in our experiments we have used [1] where Jmax is the m a x i m u m applied torque, and 7r 7rD3 K : -~D2H + -~ [2] in which D corresponds to the overall width of the vane and H is the vane height. As it stands Eq. [2] does not exclude the vane-top shearing surface area corresponding to the shaft radius; in addition we take measurements with the vane immersed at various depths into the suspension test sample, and thus allowance must be made for the extra shearing surface area IIDsL, where Ds is the shaft diameter and L is the excess immersed depth beyond the blade height H . Therefore, we define !! L 7r 7rD3 - 71" 3 71KL = -~ D 2H + -~ - ~ D s + "~ D 2sL . [3] Equations [ 1] - [ 3 ] can be combined to give Journal of Colloid and Interface Science, Vol. 143,No. 1, April1991 [4] FIG. 1. Schematic diagram of vane element. YIELD STRESS OF LATER1TE TABLE III Dimensions of Vanes Used in Yield Stress Measurements Vane (mm) H (mm) Kc (cm3) 8 9 10 !1 8.0 8.0 10.0 6.0 8.0 16.0 16.0 8.0 1.064 1.868 3.028 0.557 D several blade diameters to assess the magnitude of end effects. It is evident from the results in Fig. 2, and from the analogous results for the suspension corresponding to the other p H values, that to within experimental error the effect of the vane dimensions is accounted for adequately by this analysis. RESULTS AND 59 SUSPENSIONS shear stress-apparent shear rate data corrected for end effects were first fitted to logarithmic polynomials of first, second, and third order. The polynomial fit with the lowest standard deviation, that of third order, was chosen to represent the rR versus 8 V/D relationship. The wall shear rate, "YR, corresponding to the wall shear stress T~,, is calculated from the Rabinowitsch-Mooney relation (12). These data, expressed in the form of viscosity versus shear rate, are given in Fig. 3. The entire set of T versus -y capillary tube viscometer data were curve-fitted to a n u m b e r of empirical rheological models. These are the power-law model T = m~,n [5t the Bingham (Linear) plastic model T = TO + g0+ DISCUSSION Determination of the Shear Stress-Shear Rate Dependence To calculate the shear stress-shear rate dependence for the laterite suspension, the wall [6] the Casson model (4) ~_1/2 = r~/2 + #~/2,~1/2 [7] and the Herschel-Bulkley (4) model, with n arbitrary as well as n = ½ IJlllll I IIIIIH IIFHrl I Ilrlllr i If IHI i iiiiii i o J o o a + Vane: Vane: Vane: Vane: H=Smrn. H=lSmm. H=16mm. H=8ram, D=8mm D=Smm D=10mrn D=6mrn i i i r 10 20 30 40 50 L, (rnm) F I G . 2. J m ~ ( L ) / K o = 10.1 12. versus L: Laterite suspension pH i0° 10~ 102 10~ 10~ 10~ ~. (1/see) FIG. 3. Viscosity-shearrate data for 30.0 wt% laterite suspension at 23.5°C. Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991 60 AVRAMIDIS AND TURIAN = ~o + u0+ n, Determination of the Yield Stress [81 The results are listed in Table IV. The powerlaw and Bingham plastic models do not do a good job of representing the data over the whole measured range. The attempt to fit the data to the Herschel-Bulkley model with n = ½ was suggested by the results of the fit with the Casson model, and evidently results in an improved comparison with the data as shown in Table IV. The low value of the flow behavior index reflects a high degree of non-Newtonian behavior for the laterite suspensions, even in comparison to some relatively concentrated polymeric solutions. This industrial mineral slurry was tested as received, without washing nor any particular chemical treatment. The as-received concentration of 30.0 wt% of this slurry of highly swelling particles must be considered as extremely high in view of the fact that the concentration corresponding to maximum packing is only 47.4. The absolute average percentage deviation is defined by Abs. avg. % deviation = I ~ {(gexp-- 7"calc)/rexp}l X 100 N [9] where rexp is the actual stress corresponding to the value % rcalc is the calculated value for the value of'y using the appropriate equation, and N is the number of data points. To estimate the yield stress of the laterite suspension, the r versus 3' data over the lowest shear rate range from 7.8 to about 200 s -I were curve-fitted to various viscoplastic rheological models. These included the second- and third-order polynomial forms r = ro + #17 + U2"~'2 [10] -- 70 + u,+ + ~2+ 2 + ~3+ 3. Ill] In addition to the forms in Eqs. [10] and [11] we used the Bingham plastic model, Eq. [6 ], the Casson model, Eq. [ 7 ], and the HerschelBulkley model, Eq. [8], with n arbitrary as well as n = ½. The estimated values of r0 obtained by curve-fitting the experimental data over the range 7.8 to 200 s -1 to Eqs. [6] through [11 ] are listed in Table V. The absolute average percentage deviation is calculated from the individual percentage deviation between the experimental stress data point and the corresponding value calculated using the equation with the adjusted model parameters. Several comments should be made about the results in Table V. The value of the absolute average deviation alone cannot, in the present case, be used as the sole criterion for selecting the 'best' equation from among the ones tested. Thus, although the third-de- TABLE IV Rheological Model Parameter for ,/-} Dependence of 30.0 wt% Laterite at 23.5°C a Model rn (g. s"-2/cm) Power law Bingham Casson Herschel-Bulkley Herschel-Bulkley (with n = 1/2) 93.11 n Absolute average percentage deviation 0.2549 10.9 ro (dyn/cm 2) #o (g/cm. s)b n Absolute average percentage deviation 447.7 284.6 145.0 0.0148 0.0189 32.3 --0.352 17.9 8.1 8.1 1/2 7.6 208.5 7.75 Shear rate range: 7.8 to 40,000 s-L b For the Herschel-Bulkley model it0 has units of g- sn-2/cm. a Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991 61 YIELD STRESS OF LATERITE SUSPENSIONS gree polynomial form, Eq. [ 11 ], results in the lowest percentage deviation, it is a poor choice; the relatively large number of adjustable constants and small number of data points, which also happen to have a large degree of scatter, results in a "fit" which "weaves" through the data points. This type of fit minimizes the deviation but is strongly affected by the inherent scatter and limitations of the data. The Bingham plastic model, Eq. [6], is inadequate because as a straight-line equation it is incapable of describing the nonlinear r versus 3/ dependence, which is almost invariably encountered with concentrated systems, in the low shear rate range. The Casson model, Eq. [7], seems to do the best job of describing these data. The estimated value o f t 0 = 141.9 d y n / cm z compares favorably with the directly measured value of 148.9 d y n / c m 2 given in Table V. Yield Stress-Concentration Dependence The yield stresses of all laterite suspensions were determined using the vane method. The results are given in Table VI. It is clear that the yield stress increases steeply with solids concentration. To describe the yield stress-concentration dependence we propose the equation r0 = {1 ~x(~/~m) ~ - (~9/~m)i/3} fl Estimated Yield Stress Obtained by Fitting Lower Range of Shear Stress-Shear Rate Data (30.0 wt% Laterite at 23.5°C) a Bingham Second degree Third degree Casson Herschel-Bulkley Herschel-Bulkley (n = 1/2) Direct m e a s u r e m e n t Yield Stress-Concentration Dependence of Laterite at 23.5 °C Concentration (vol%) Experimental yieldstress (dyn/cm2) Calculatedyield stress,Eq, (12) (dyn/crn2) Percentage deviation 3.60 5.70 8.30 12.65 15.26 18.86 20.74 6.5 25.8 92.6 148.9 405.0 1254.0 1974.0 7.9 23.8 62.6 213.0 409.0 1079.7 2097.1 -21.5 7.8 32.4 -43.0 - 1.1 13.9 -6.2 in which rx, o~, and fl are positive constants. The quantity in braces in the denominator provides a measure of the interparticle distance. The limiting forms of Eq. [12] in the dilute, (0/q~m) ~ 1, and the concentrated, (~b/ ~bm) ~ 1, limits are useful in demonstrating the roles played by the various coefficients. For (~b/qSm) ~ 1 the limiting form of Eq. [12] is given by the expansion ( 7 O / r x ) = (q~/qSm)~f 1 + f l ( O / ~ m ) 1/3 fl( fl- + 1) + - [12] TABLE V Equation TABLE VI Estimated r0 (dyn/cmz) Absoluteaverage percentage deviation 206.5 154.9 112.7 141.9 138.0 14.2 9.9 6.9 7.0 10.6 128.5 148.9 10.5 -- + 2 (~b/(bm) 2/3 O(qV0m)} (qS/0m)< 1. [13] It is clear from this that the term ( 0 / 0 m ) ~ in the numerator of Eq. [12] is the dominant term for (4~/~bm) ~ 1. Dilute limit theory ( 13 ) suggests that o~ = 2, which is the value we assume henceforth. In the concentrated limit, when (~b/~bm) --~ 1, the limiting form of Eq. [ 12 ] is given by the expansion (~O/Tx) _(1- 7m/{, _ (O X (1 -- ~b/q~m) @ O [ ( 1 -- ~b/q~m)2]} ) a Shear rate range: 7.8 to 200 s -1. (0/qSm)~ 1 [14] Journal of Colloid and Interface Science, VoL 143,No. 1, April 1991 62 AVRAMIDIS AND TURIAN from which it is clear that the term involving the parameter fl is the dominant term in the concentrated limit. The parameter rx is the value of the yield stress when the concentration-dependent factors in the numerator and the denominator in Eq. [12] are equal. We assume that ro = ~'x when q~ = ~h0, and Eq. [ 12 ] gives (qSO/qSm) = {1 -- (~O/49m) 1131~1~S [15] Accordingly, (4~0/qSm) is a function of ( f l / a ) only, and 40 corresponds to the solids concentration above which the denominator concentration factor becomes more important than the numerator. The values of the parameters rx and /3 obtained by the method of least squares were found equal to 176.2 d y n / c m 2 and 0.842, respectively, with the value of q~m equal to 0.234. The percentage deviation in Table VI is defined as % deviation = (~xp - ~l~) × I00 [16] Texp where reap is the measured yield stress and r~a~ is the yield stress using Eq. [121. The yield stress-concentration dependence is shown in Fig. 4. o 176.2 {~/~km)2 r - o 0.0 0.1 - 0.2 0.3 0.4 0.5 (~/%) 0.6 0.7 0.8 0.9 1.0 FIG. 4. Yield stress-concentrationdependence.Laterite suspension at 23.5°C. Journal of Colloid and InterfaceScience, ¥ o l . 1 4 3 , N o . 1, A p r i l 1 9 9 1 Yield Stress- ~ Potential Dependence Table VII summarizes the measurement of pH, ~"potential, particle size distribution, and yield stress for the laterite suspensions containing 30.0 wt% solids. The yield stress is highest at low pH and decreases progressively with increasing pH, with an approximately threefold decrease as pH is increased from 1.4 to 11.0. The rapid decrease in the yield stress with increasing pH is similar to the behavior of aqueous kaolinite dispersions in which the yield stress decreases with increasing pH and vanishes at pH 7.0 (14). With the laterite suspension studied in this work the yield stress remained quite high even at the highest pH. The monotonic pH dependence observed in this work is not universal; Thomas (15) reported that the yield stress of aqueous thorium oxide suspensions increased with pH up to pH 8.0 and then decreased slowly up to pH 12.0. Heath and Tadros (16) found that the yield stress of aqueous silica dispersions increased rapidly with pH up to pH 8.0, and then decreased rather steeply up to pH 10.0. A monotonic decrease in the yield stress of kaolinite clay with increasing pH has also been reported ( 17 ). The higher values of the yield stress of the laterite suspensions at the relatively higher flocculated conditions prevailing at the lower pH values and the lower values at the relatively less flocculated conditions corresponding to the higher pH range are in accord with the observations of Street (18). According to Street, when attractive forces are high (lower values of the ~" potential), the yield stress is high, and when repulsive forces are high (higher values of the ~'potential) the yield stress is low. Further, when repulsive forces predominate, the potential energy barrier which must be surpassed to achieve flocculation is higher, leading to enhanced stability, moderation of the degree of non-Newtonian behavior, and lowering of the yield stress value (19). When the f potential is equated to the Stern potential, as is usually done (20), the electrostatic repulsive energy will depend on the square of the ~"potential. Since the van der YIELD STRESS OF LATERITE SUSPENSIONS TABLE VII ~"Potential, Particle Size, and Yield Stress versus pH 30.0 wt% Laterite at 23.5°C) Particle diameter (.um) pH ~mV) dlo dso dgo ro (dyn/cm 2) 1.397 2.608 5.542 7.054* 8.608 10.112 11.011 -2.0 -1.4 -10.1 -13.6 -20.9 -29.1 -30.5 5.8 6.4 8.8 12.4 6.4 8.0 8.4 6.0 7.0 9.8 13.5 10.5 9.2 9.7 6.0 7.5 12.9 14.8 12.4 14.3 14.0 169.5 178.0 a 148.9 105.9 80.5 59.3 Test sample destroyed. bLaterite suspension as received,without additives. Waals energy of attraction is independent of surface potential, the total energy of interaction as well as the interactive force between the particles will vary as the square of the ~ potential (21 ). Hunter and Nicol (13) plotted r0 versus the square of ~"potential for kaolinite dispersions and found that a straight line resulted independently of the means by which the ~'potential was made to vary, i.e., whether by addition of a m m o n i u m or phosphate ions. Figure 5 is a plot of ro versus the square of the ~"potential for the laterite suspensions in this study. The straight line represents the least-squares fit to the data, and is given by r0 = 170.8 - 0.118~"2 63 A = Hamaker constant dp = particle diameter S = area of interaction between particles (red2/4) Xo = half-distance of closest approach of the planes of shear of the particles = volume fraction of solids e = dielectric constant of the medium K = Debye-Huckel parameter The r0 versus ~-2 dependence of laterite suspensions depicted in Fig. 5 is clearly consistent with Eq. [ 18 ]. The slope and intercept of the ro versus ~-2plot can be used to determine the parameters A, X0 and dp in Eq. [ 18 ], if one of them is known. The remaining variables in the equation can be either measured or estimated as in the case of K. Straightforward superposition of the yield stress-concentration dependence given by Eq. [ 12 ] and the yield stress- ~" potential dependence given by Eq. [17] can be achieved by assuming the parameter rx in Eq. [12] to have the form rx = rxo + rx, ~2. [ 19 ] g [17] in which r0 is in d y n / c m 2, and ~'is in mV. It was shown by Hunter and Nicol (13) for dilute suspensions exhibiting plasticity that the yield stress is related to interparticle forces by the relation ~~ o = . - o 24q52S { A " t o - rr2dp3 48rrX2 - e--5-~( 1 - tanh KX0)~'2I 4rr J [18] in which the first term in the braces accounts for the attractive energy, and the second for the repulsive energy. The definitions of the variables in Eq. [ 18] are as follows: i 200 4oo i 6oo ¢~,(mv)= [ BOO i000 FIG. 5. Yield stress-~"potential dependence. Laterite suspension at 23.5°C. Journal of Colloid and Interface Science, Vol. 143, No. i, April 199 l 64 AVRAMIDIS AND TURIAN Accordingly, superposition of Eqs. [ 12 ] and [ 17 ] gives the general relation (Txo q- TXl ~'2)(q~/q~m)2 r0 = {1 - (qS/qSm)l/3} ~ [201 The parameters rxo and rxl in Eq. [19] can be calculated from r0 vs. ¢ and ~"data using Eqs. [ 12 ] and [ 17 ]. Finally, Eq. [ 20 ] reduces to the form given by Hunter and Nicol (13) in the limit (q~/~bm) ~ 1. It should be noted that zeta potential measurements are carried out on an ore body and thus they represent an average value of the zeta potential of the various mineral constituents present in the laterite. For recent work on the zeta potential of mineral suspensions see (22-25). Sedimentation Rate and Dependence of in Situ Particle Size and ~ Potential on p H The rate of settling of solids of the laterite suspension as received (pH 7.054, ~"potential = - 1 3 . 6 mV) was determined using a sedimentation column. The sedimentation data are presented in Fig. 6. It is clear that the suspension had a tendency to settle relatively fast, attaining virtually complete settling in about 50 h. These observations are compatible with the stability characteristics of Riddick (26). Accordingly, the suspension was at the threshold of agglomeration and the rapid settling occurred because of the larger size of aggregates. The final sediment which was formed was loosely packed, was easy to resuspend, and had a sediment porosity of 0.819. This corresponds to a sediment volume fraction of solids of 0.181 as compared to a maximum packing volume fraction of 0.234. These findings are in accord with the sediment Characteristics of flocculated suspensions (3, 4). A comprehensive preliminary set of experiments was performed at constant ionic strength to establish the dependence of the ~" potential on pH for the laterite suspension. It should be noted that the same value of the ~ potential was obtained regardless of whether the desired p H value was attained from a higher or lower point. The results of these measurements are given in Table VIII, and they are plotted in Fig. 7. It is evident from Fig. 7 that at very low pH values the ~"potential starts out at low positive values. Positive f-potential values are also ob- Volume C o n c e n t r a t i o n = 12.7% Solids Density = 2.9452 g / c e S e d i m e n t Porosity = 0.{319 ~o e~ i too 200 300 400 Time (hours) FIG. 6. Sedimentation data for 30.0 wt%laterite suspension at 23.5°C. Journal of Colloid and Interface Science, Val. 143,No. 1, April 1991 500 YIELD STRESS OF LATERITE SUSPENSIONS 65 (28) reported a charge reversal phenomenon at a pH of 11.8 for red m u d suspensions. Dependence of ~ Potential on pH Stannic oxide exhibited two isoelectric points (Laterite Suspension at 25°Cy (22), and aqueous graphite suspensions ex~" P o t e n t i a l Specific c o n d u c t a n c e hibited three isoelectric points (29). The ~'popH (mV) (rnmho/cm) tential attains zero values at pH values of ap0.640 +2.00 58.5 proximately 1.08 and 11.12. The monotonic 1.084 +0.08 47.3 increase in negative value of the ~" potential 1.426 -3.40 9.4 over the pH range of approximately 1. l to 11.1 2.578 -4.40 25.3 could be explained by the following argument. 3.793 -8.t0 23.8 At low pH values a relatively larger number 4.208 -9.30 30.7 6.430 - 12.00 34.7 of hydrogen ions are in the proximity of the 7.022 - 13.30 1.1 suspended particles, thus reducing the net 7.520 -19.0 26.9 negative charge and therefore leading to pos9.011 -24.00 25.8 itive or low negative values of the ~ potential. 9.589 -28.00 23.0 Also, it is believed that ionization of ampho10.052 -28.70 23.6 11.057 -31.10 14.3 teric surface groups occurs widely in clay sys11.102 -8.60" 26.1 tems. 11.132 +4.60 14.9 Aging is an important phenomenon with 11.426 +8.10 15.1 suspensions exhibiting yield stress (30, 31 ). 12.236 +11.60 1.6 For the laterite suspensions studied in this 12.357 +10.40 1.5 work, however, the ~'potential-pH data shown a To correct for temperature effects use the equation in Fig. 7 and taken a year apart suggest no ~co, = ~'me~(l-0.02AT), where AT = T - 20 and tem- aging effects. peratures are in °C. TABLE VllI served at very high pH. The very low and very high pH limits are, therefore, in the ranges where the ~'-potential curve crosses the ~"= 0 axis, and consequently these are pH values where agglomeration and settling effects are strong. Over the range of pH from 0.64 to about 11.06 the ~" versus pH curve is nearly linear with ~', decreasing from +2.0 to about - 3 1 . 0 mV. In this range of pH the straight line obtained by the method of least squares is given by the equation o Data taken one year apart o .06(p~) % ~T ° D ~"= 3.71 - 3.06(pH). [21] In Eq. [21] ~"is in millivolts. Above a pH of 11.06 the ~"potential increases very abruptly, resulting in virtually instantaneous reversal from negative to positive ~" potential values. The p h e n o m e n o n of charge reversal is quite c o m m o n a m o n g suspensions of clay particles (27). It is clear from the data that the ~"potential is quite sensitive to pH. Hirosue et al. ? ? i 2 4 i 6 pH i 8 10 12 FIG. 7. ~ Potential versus pH for laterite suspension at 23.5o C. Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991 66 AVRAMIDIS From Table VIII it is seen that the specific conductance attains its m a x i m u m values at the lowest pH values and its minimum values at the highest p H values. The m i n i m u m value of the specific conductance occurs at pH 7.0221 which corresponds to the suspension with no added electrolyte. The presence of added electrolyte causes hydrogen ions to be available to contribute to the conductivity. With no added electrolyte, for the suspension as received, most hydrogen counterions are associated with the particles and are not free to contribute to the conductivity of the laterite suspension. In addition, counterions inherent to clay, possible ion-exchange mechanisms, and conduction mechanisms in interacting clay systems can affect suspension conductivity. However, it is difficult to infer the intrinsic contribution of the laterite to the conductivity. A summary of the results of the particle size distribution measurements obtained by gravity sedimentation is given in Table IX. These results provide a view of the approximate in situ size distribution of particle aggregates as a function of pH. The laterite suspension as received had a p H value of 7.054 which demarcates the low and high p H ranges in Table IX. The median diameter, ds0, increases with pH up to a pH of 7.054, and it decreases again as the pH is increased above the value 7.054. The 10th, 50th (median), and 90th percentile diameters (i.e., dl0, ds0, and d9o) listed in Table IX suggest that the in situ particle aggregate size distributions are rather narrow, especially in the acidic range, although the mean particle aggregate size does depend on pH. These percentile values were read from the cumulative size distribution curves. The other diameter values in Table IX, i.e., dn, ds, dr, dsv and dw, are the number mean, the surface mean, the volume mean, the surface-volume mean, and the mass mean diameters, respectively. It is possible to infer the relative significance of the rate of flocculation from the values of the 10th, 50th, and 90th percentile diameters. The onset of flocculation is marked by a sudden rise in the cumulative mass percentage value, folJournal of Colloid and Interface Science, VoL 143, No. 1, April 1991 AND TURIAN lowed by a steep drop. Thus the rate of flocculation is higher when the values of dl0 and d9o are close to each other and it diminishes with the difference in these two values progressively higher. Accordingly, it can be inferred that the rate of flocculation for the suspension with pH 1.397 ( ~"= - 2 . 0 m V ) is high and diminishes as the pH increases to the value 7.054 corresponding to the suspension as received. This behavior is in accord with the stability characteristics cited by Riddick (26). Finally, flocculation is absent for the suspensions with pH higher than 7.054. The rate of flocculation decreases with increasing particle size for the laterite suspensions in acidic environments. This result agrees with the fact that small and large particles, with identical double layers, present identical repulsive potential curves for the interaction of unit surface areas. However, the total particle repulsion will be smaller for the small particles (3), and consequently flocculation is more pronounced for the suspension of smaller particles. As the pH increases above the value of 7.054 for the suspension as received, the rate of flocculation diminishes as the suspension approaches more stable states (negative of ~-increases). The last two rows of Table IX contain the particle size data obtained using sodium hexametaphosphate (Calgon) solution as a dispersant. The median diameter dso obtained using the Sedigraph with the laterite particles suspended in a 0.005 wt% Calgon solution as a dispersant is equal to 4.2 #m, which compares well with the values of 3.44 and 3.48 t~m in Table I. SUMMARY Colloidal, shear-dependent, concentrated aqueous laterite suspensions were characterized and their theological behavior described. From the results obtained in this work the following conclusions are drawn: 1. The laterite suspension is strongly nonNewtonian. The flow behavior index scarcely attained a value greater than 0.5 over the entire range of shear rate studied, from 7.8 to 40,000 s -1 . 67 YIELD STRESS OF LATERITE SUSPENSIONS TABLE IX Particle Size Data for Laterite Using the Sedigraph Panicle size (gm) pH (mV) dw dso dgo dn d~ dv d~v dw 1.397 2.608 5.542 7.054 a 8.608 10.112 11.011 b c -2.0 -1.4 - 10.1 -13.6 -20.9 -29.1 -30.5 --- 5.8 6.4 8.8 12.4 6.4 8.0 8.4 0.6 -- 6.0 7.0 9.8 13.5 10.5 9.2 9.7 4.2 0.7 6.0 7.5 12.9 14.8 12.4 14.3 14.8 21.4 11.7 5.8 6.6 9.8 1.1 10.6 0.4 7.4 . . 5.9 6.7 9.9 2.2 10.7 0.8 8.1 6.0 6.8 10.0 3.8 10.8 1.6 8.6 . . 6.1 7.1 10.3 11.8 11.1 6.6 9.8 6.7 7.8 11. I 14.0 11.7 10.5 11.0 . . . . . . Suspension as received. b Suspending medium: 0.005% Calgon solution. c Suspending medium: 0.05% Calgon solution. 2. The modified Herschel-Bulkley model seemed to give the best overall fit of the shear stress-shear rate dependence over the entire range of shear. 3. Estimates of the yield stress obtained indirectly by various extrapolations using shear stress-shear rate data gave values which were of the same order as the value determined directly using the vane geometry. The yield stress was correlated with concentration using a twoparameter nonlinear model possessing the appropriate low- and high-concentration behavior, and was found to possess a straight-line dependence on the square of the ~"potential. 4. In the pH range 0.64 to about 11.0 the relationship between pH and ~"potential is linear. The in situ particle size distribution over the entire pH range examined was rather narrow. The degree of flocculation was found to be high for acidic environments. 5. Suspended particle size distribution, suspended particle ~ potential, extent of flocculation, and suspension yield stress depend strongly on pH. ACKNOWLEDGMENTS This work was supported by the International Fine Particle Research Institute, Inc. 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