Yielding of Suspensions in Compression - Industrial & Engineering

Nov 3, 1997 - There are several techniques available to determine the compression characteristics of a particular suspension. Three techniques are des...
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Ind. Eng. Chem. Res. 1997, 36, 4984-4992

Yielding of Suspensions in Compression Matthew D. Green and David V. Boger* Advanced Mineral Products Special Research Center, Department of Chemical Engineering, University of Melbourne, Parkville, 3052 Victoria, Australia

The compressive yield stress, Py(φ), is an important rheological parameter for the characterization of concentrated flocculated suspensions. It is a measure of the compressive strength of interparticle bonds in a strongly networked suspension structure and is used in the design of processes for the dewatering of fine particle suspensions. There are several techniques available to determine the compression characteristics of a particular suspension. Three techniques are described and compared: two based on centrifugal consolidation and one based on pressure filtration. Results for well-characterized ZrO2 and Al2O3 suspension systems are presented, showing the effect of flocculation conditions, sample preparation methods, and the initial suspension concentration on the compression rheology. The application of these findings to the design of a compression thickener for the concentration of bauxite residue or red mud for semidry disposal in the alumina industry is also explained. Introduction The use of compression to produce highly concentrated particle suspensions in large-scale industrial consolidation processes such as thickeners and pressure filters has become very important over the last few decades (e.g., Dixon, 1981; Chandler, 1983; Marunczyn and Laros, 1992; Eberl et al., 1995). Until recently, industry has often been reluctant to make use of compression for dewatering suspensions, fearing an inability to be able to handle the highly concentrated product from such a process. The innovative use of additives to reduce the viscosity or break down the structure of such a product under shear, however, can make pumping and handling of the product feasible (de Guingand, 1986; Green et al., 1992; Leong, 1994). An important application of highly concentrated mineral suspensions is in the rapidly expanding ceramics industry where the wet processing of concentrated suspensions has become prevalent (Lange, 1989; Horn, 1990; Ulrich, 1990). In this technique, a ceramic mold is filled with a suspension at the highest possible concentration. When the wet ceramic is fired, minimal shrinkage will then occur, which is the major cause of ceramic cracking and strength reduction. The objective then is to produce a suspension of the highest concentration that will still flow. This objective can be achieved by precisely controlling the surface chemistry of the particles (Horn, 1990; Leong, 1994) and by applying a compressive pressure until the suspension is sufficiently dewatered. A question of interest is, what is the compressive pressure required to produce a suspension of a certain concentration? At present, this question is answered empirically using a full-scale filter press or vacuum filter. With the techniques outlined in this paper, this question can be answered in the laboratory and other conditions and variables that affect dewatering may be evaluated without the costly interruption of an operating plant. The mining industry is another growing user of compression technology for the production of highly concentrated suspensions in tailings disposal. Traditionally, mine tailings are pumped into large settling ponds from which the supernatant is recycled back to * Author to whom correspondence should be addressed. E-mail: [email protected]. S0888-5885(97)00141-3 CCC: $14.00

the process while the solids slowly settle and eventually fill the pond. Given the huge volumes of waste produced by mining operations, this disposal technique has numerous environmental and economic problems (Nguyen and Boger, 1986). An alternative disposal technique that is increasingly viable is to highly concentrate the tailings in a large thickener and then pump the slurry or paste to the disposal area in a “semidry” state (Robinsky, 1975; Cooling and Glenister, 1992). There are several compelling reasons for this trend in tailings disposal. As the ore yields from mining operations decrease, the volume of tailings generated from the extraction of the ore will increase. Adequate water supply and available land for disposal of these tailings are often scarce. There is also strong pressure on the industry to reduce the amount of waste expelled into the environment. A semidry disposal technique dramatically reduces the landfill area required and reduces the time required to reclaim the land and revegetate it. These arguments support the adoption in certain instances of a semidry disposal strategy in which mine tailings are pumped as a highly concentrated slurry or paste. The question considered here is how can compression be used to dewater fine particle suspensions to produce a material suitable for semidry disposal? This question can be answered using the laboratory techniques and results described in this paper. Materials and Methods Two metal oxide aqueous suspension systems were examined; zirconia, ZrO2, and alumina, Al2O3. The ZrO2 (mean volumetric particle diameter, d50 ≈ 0.47 µm, F ≈ 5.72 g/cm3) was supplied by ICI Advanced Ceramics, Australia. The Al2O3 was an AKP-30 alumina (d50 ≈ 0.40 µm, F ≈ 4.0 g/cm3) supplied by Sumitomo Chemical Co. Ltd., Japan. The metal oxide systems were chosen to represent “model” suspensions of polydisperse industrial particulate systems. The preparation of both metal oxide systems was carefully controlled to obtain reproducible suspensions. A procedure similar to that of Leong et al. (1993) was used. Appropriate amounts of the powder and additives were mixed with Milli-Q-filtered distilled water with 0.01 M salt (KNO3 and NaCl for ZrO2 and Al2O3, respectively). Poly(acrylic acid) (PAA) of 2000 MW (molecular weight), at 1.0 dwb % (dry weight base), was © 1997 American Chemical Society

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used in some samples as a dispersant (Aldrich Chemical Co.). All samples were prepared in the dispersed state using concentrated HNO3 or HCl to adjust the pH. Two methods for dispersal of the powder were used; small samples (less than 100 mL) were sonicated for 2 min using an ultrasonic horn (Branson Sonifier 450W, operated at 30-40% of the maximum power output), while larger samples (up to 400 mL) were mixed using a high shear mixer for 5 min (Janke and Kunkel, UltraTurrax operated at 10 000 rpm). Both methods of dispersion produced good suspensions exhibiting reproducible rheological results. The samples were adjusted to their correct pH using 1-5 M KOH or NaOH and then rested for at least 24 h. The shear yield stress, τy, was directly measured using the vane technique prior to any compression measurements. In the vane technique, a vane connected to a spring is placed in the sample, the spring is slowly tightened, the maximum torque corresponding to the point of yielding (the vane begins to move) is measured, and the shear yield stress is calculated (Nguyen and Boger, 1983, 1985). With the vane technique the stress at which the material begins to flow is measured. Compared to other shear yield stress techniques, the technique is relatively nondestructive and thus is a good measurement of the shear yield stress of highly concentrated and structured suspensions. Compressive Yield Stress, Py(O), Measurement The compressive yield stress, Py, quantifies the strength of a networked suspension structure that is subjected to compressive forces. If the applied stress exceeds the compressive yield stress for that particular concentration of suspension, φ, the suspension will irreversibly consolidate to a new equilibrium concentration corresponding to the new stress. The compressive yield stress is thus an intrinsic function of the local solids concentration of the suspension. The compressive yield stress is also a function of the structural state of the suspension. The suspension structure is determined, for example, by the surface chemistry of the particles, the initial conditions of the suspension, and the method of compression. Three techniques for measuring Py(φ) are described: two based on centrifugal consolidation and one based on pressure filtration. Multiple-Speed Equilibrium Sediment Height Technique. The multiple-speed equilibrium sediment height technique was developed by Buscall and White (1987). Preliminary experiments using a polystyrene latex were performed to demonstrate the technique (Buscall, 1983). It was first used in an industrial application by de Guingand (1986), who studied the compression characteristics of bauxite residue or red mud. In that work, an optimum flocculant dosage was found that significantly enhanced the compressibility of the red mud. The technique has also been successfully used at the University of Melbourne in the design of several thickening operations for the Australian mining industry (unpublished work). The compression dewatering of fine coal tailings containing a significant proportion of clay was investigated by de Kretser (1995; de Kretser et al., 1997). The clay in these tailings was found to control the rheology and dewatering characteristics of the system, and precise manipulation of the suspension chemistry enabled improved compression. Recent work on cement pastes and alumina suspensions by Miller et al. (1995) found a dependence of Py(φ) on the initial concentration of the sample and only a weak

Figure 1. (a) Typical raw multiple-speed equilibrium sediment height data; ZrO2, pH 7.1, φ0 ) 0.150. Effect of tube diameter shown. (b) Corresponding compressive yield stress curves, Py(φ), determined from the raw data in part a. The symbols are determined using the approximate solution. The lines are determined from the full iterative solution.

dependence on the compressive history of the suspension. Miller et al. (1996) focused on evaluating the measurement of Py(φ) using alumina and zirconia suspensions. The technique has also been used by Eckert et al. (1996) to examine the consolidation of fine tailings from tar sands. Most of the results in this paper were determined using the multiple-speed equilibrium sediment height technique. The multiple-speed equilibrium sediment height technique is a method for the determination of the compressive yield stress function, Py(φ), for flocculated suspensions using a centrifuge. Suspension samples are placed in cylindrical, transparent, flat-bottomed, centrifuge tubes, and the equilibrium sediment height, Heq, is measured for various increasing values of the gravitational acceleration, g, at the bottom of the tube. Initially, the volume fraction solids concentration of the suspension is uniform throughout and equal to φ0. Raw data required are the initial height of the suspension, H0, the density difference between the solid and the fluid phases, ∆F, and the centrifuge radius from the center to the internal base of the tube, R. A typical plot of Heq(g) raw data is shown in Figure 1a (the effect of centrifuge tube diameter is discussed later). The data for the Heq(g) curves are exponentially decreasing with increasing g and are approximately linear when plotted on semilogarithmic coordinates. The conversion of the Heq versus g raw data to a Py(φ) curve is not trivial. The basic theory was developed by Buscall and White (1987). There are two available

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solution techniques: a full iterative algorithm and an approximate solution. An improved iterative algorithm has also been developed and evaluated by Green et al. (1996). It was shown there that the approximate solution is an acceptable technique if only limited data are available. The theory for these techniques is fully detailed in the above references and is not considered further. In Figure 1b are results comparing the full iterative solution with the approximate solution. The symbols on the Py(φ) curves were determined using the approximate solution on the raw data in Figure 1a; the lines were determined using the iterative solution. In all cases, the approximate solution gives slightly lower values of the concentration for a given Py but is adequate for most engineering purposes. Both solution methods are shown in the subsequent results of this paper. A certain minimum centrifuge tube diameter must be used to minimize any possible wall effects on the compression results. Figure 1b shows the effect of the centrifuge tube diameter on the results for a strongly flocculated ZrO2 suspension. These results show a significant shift of the Py(φ) curve to the right as the centrifuge tube diameter is increased. de Guingand (1986) observed a similar effect for bauxite residue. Narrow tubes thus apparently restrict the compressibility of the suspension and generate unrealistically low results. The minimum diameter required is related to the shear yield stress, τy, of the suspension. The greater the τy, the wider the centrifuge tube that must be used. Michaels and Bolger (1962) have theoretically computed for dilute suspensions the minimum diameter at which compression will occur for a suspension with a given τy. Applying their formulation to our results, however, give unrealistically high minimum centrifuge tube diameters. An additional effect to consider is that, as the suspension compresses, τy increases and wall effects thus become more important. Minimization of this effect would require even wider centrifuge tubes. The initial τy of the strongly flocculated ZrO2 used in Figure 1, with φ0 ) 0.15, was measured to be 198 Pa. The concentration of this suspension is near the maximum possible to prepare for strongly flocculated ZrO2 with no additives. Thus, the tube diameter effects seen in Figure 1b would be the greatest observed for the results presented herein. A tube diameter of 26.5 mm was used in all experiments, this being the widest practical tube diameter for the centrifugal measurements made here. The results do not indicate that the tube diameter effect is eliminated using this tube diameter, but possible wall effects on the compressive behavior of the suspensions are minimized. Concentration Profile Technique. The compressive yield stress function may be determined from the measurement of the concentration profile of a sample centrifuged to an equilibrium height at a given g. The measured concentration profile is integrated from the top of the sediment downward to determine the stress developed by the weight of the overlying sediment. This corresponds to the compressive yield stress at the concentration at that particular height, z. A complete Py(φ) curve is thus determined. This technique was first used by Bergstro¨m et al. (1992) and is a more direct method of determining Py(φ) than the multiple-speed equilibrium sediment height technique. The transmission of γ-rays through a suspension has been used to measure the equilibrium concentration

Figure 2. Plot comparing each technique for determining Py(φ); ZrO2, pH 7.6, φ0 ) 0.15.

profile (Bergstro¨m, 1992; Bergstro¨m et al., 1992). A destructive testing method used here and by Miller et al. (1995, 1996) involves taking multiple sections from the sediment (typical spacing 0.5-2.0 mm). The solids concentration of each section is measured by mass loss on drying. The value determined by drying is taken as the concentration at the midpoint height of the section. A similar technique has been used on filter cakes by Sherwood et al. (1991) and Meeten (1993). To determine Py(φ), the raw concentration profile data may be integrated using trapezoidal constructions; otherwise, curves may be fitted to the raw data which are then integrated either analytically or numerically. The difference between the solution methods is small and largely dependent on the curve fitting of the raw φ(z) data. Filtration Technique. Filtration of a suspension through a membrane by a piston operated at constant pressure is a direct measure of the compressive yield stress at the final concentration of the filter cake after equilibrium is attained (Landman and White, 1994). By operation of the filtration device at a range of pressures on separate samples for each pressure, a complete Py(φ) curve is generated. This technique was successfully used by Miller et al. (1996). Miller’s apparatus was used to obtain the results that are part of Figure 2; the reader is referred to Miller et al. for details of the apparatus and its operation. Comparison of Measurement Techniques. Combined results from all three measurement techniques are compared in Figure 2. The results are for ZrO2 in the strongly flocculated state (pH 7.6). The results span a substantial range of solids concentration (φ ) 0.100.45) and compressive yield stress (4 orders of magnitude). Three centrifuges were used to obtain results over this large range using the multiple-speed equilibrium sediment height technique. These are referenced in Figure 2 as the low-, medium-, and high-speed centrifuges (LSC, MSC, and HSC). Concentration profiles were determined from the high- and low-speed centrifuged samples, and the resulting Py(φ) curves agree well with those from the multiple-speed equilibrium sediment height technique. The pressure filtration

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4987 Table 1. Comparison of Py(O) Measurement Techniques (Times Are per Sample)a technique

samples per run conc. accuracy (%) pressure accuracy (%) measurement time (min) equipment time analysis time (min) no. of data pointsb

multiple speed

concentration profile

pressure filtration

2-28a (4 (2 30 4-5 weeks 10 5-6

2-8a (0.5 (5 60 1 week 15 15-30

1 (1 (2 5 1 day 5 5-6

a Dependent on centrifuge size. b Minimum data points requiredsgreater accuracy achieved with more points, but times increase proportionally.

results are also consistent with the two centrifuge techniques; however, only the upper range of pressures was accessed due to experimental constraints. The agreement between the three measurement techniques is good evidence that the compressive yield stress is a material property of a suspension. The two centrifuge techniques and the filtration technique compress by different consolidation mechanisms. In centrifugation, the expelled water from the suspension network is forced upward through the structure and hinders consolidation. However, in pressure filtration, the expelled water flows downward and contributes to the compression. In both cases, at equilibrium, it is the sediment structure that supports the applied stress. The agreement between the results thus suggests that the compressive yield stress is independent of the path taken to reach the final condition (that is, it is a material property). Which technique should be used? Given that all three techniques agree reasonably well, the accuracy of each technique, the ease of use, and the time to obtain results must be considered. A comparison of each technique is given in Table 1. The multiple-speed technique is time consumingsattainment of the equilibrium state for 5 or 6 speeds can require over a month for the mineral suspensions studied here. Measurement time per sample is low, but data analysis is moderately complex and accuracy is moderate. The concentration profile technique requires a suspension to reach an equilibrium height at a single centrifuge speedsabout a week. Sectioning of the sediment is laborioussrequiring about an hour per samplesbut the accuracy of the concentration profile and the resulting Py(φ) curve is good since many sections can be taken. Pressure filtration requires a custom-built apparatus, but results of moderate accuracy can be obtained in a day for a single sample of low volume. As an industrial engineer, the concentration profile technique is clearly the method of preference to use. Centrifuges are widely available, multiple samples can be tested simultaneously, data analysis is simple and straightforward, and results can be obtained in just over a week. The disadvantage is the laborious sectioning of each sample; this could be automated if necessary. If the number of samples is large and results are not urgent, then the multiple-speed technique should be used. Therefore, the technique to be applied is dictated by the particular circumstance. Results and Discussion Having ascertained that Py(φ) is a material property of concentrated suspensions, results are now presented showing how Py(φ) depends on the state of flocculation, the sample preparation, the initial concentration, and

Figure 3. (a) Effect of pH on compressive yield stress, Py(φ); ZrO2, φ0 ) 0.15. (b) Plot of Py vs pH for lines of constant concentrations taken from part a plus additional data.

the surface chemistry of the suspension. Model metal oxide suspensions are used to demonstrate these effects. Except where noted, the majority of the compressive yield stress results to be presented have been obtained using the multiple-speed equilibrium sediment height technique. Flocculation Effect. The compressive behavior of metal oxide suspension systems can be controlled by manipulating the degree of flocculation of the sample. The suspension pH fixes the surface charge on the particles, which, in turn, determines the magnitude of electrostatic repulsion between them. When the particles are electrically neutral, the repulsion is minimized and the suspension is strongly flocculated. This is the isoelectric point (iep) or point of zero charge. For pH’s not far removed from the iep, the suspension is weakly flocculated due to repulsive surface charges on the particles. Shown in Figure 3a is the effect on compression of varying the pH for ZrO2 suspensions. When the ZrO2 is strongly flocculated at pH 7.2, the suspension is the least compressible. When weakly flocculated, the suspension can be compressed to a higher concentration for the same applied stress. At pH’s far from the iep, suspensions are fully dispersed, which on settling (much slower than flocculated suspensions) form a hard, highly concentrated layer on the bottom. A sharp interface between the supernatant and the sediment also cannot be seen; thus, measurement of the compressibility of dispersed systems is not possible using both centrifuge techniques and, although not tried, pressure filtration would be difficult due to the formation of the hard layer. These same trends are also seen for Al2O3, although those results are not reported here.

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Figure 4. Effect of pH and φ on shear yield stress, τy, for ZrO2.

Figure 6. Effect of dilution on Py(φ); ZrO2 with 1.0 dwb % 2000 MW PAAsweakly flocculated: (b) base suspension Ultra-Turrax 5 min; (O) diluted by just stirring in water; (0) diluted and then sonicated for 2 min.

Figure 5. Effect of dispersion technique on Py(φ); ZrO2 with 1.0 dwb % 2000 MW PAA, pH 6.0, φ0 ) 0.263.

The effect of flocculation is better shown in Figure 3b by replotting the data of Figure 3a as Py versus pH for a series of constant concentrations. The least compressible condition is thus clearly at the iep (pH 7.2). Figure 3b may be compared with the corresponding plot of shear yield stress, τy, versus pH shown in Figure 4. In both plots, the pH’s of maximum Py and τy are identical. This suggests that the mechanism of breaking bonds between particles to cause motion by shear is related to that of the mechanism of breaking bonds in compression. A relationship between Py and τy is suggested later in the paper. Sample Preparation Effects. The method of suspension preparation for rheological and compressional study is extremely important. For suspensions both strongly and weakly flocculated by only electrostatic forces (pH and ionic strength), the measured Py(φ) was unaffected by the method used to prepare the samples (results not shown). Dilution of these suspensions after sonication or high shear mixing also had no effect on the measured Py(φ). In contrast, the Py(φ) measured for suspensions sterically stabilized by low molecular weight polymer was affected by the sample preparation method and by dilution before compression. In Figure 5, a concentrated stock suspension of ZrO2 (φ0 ) 0.26) sterically stabilized with 1.0 dwb % 2000 MW PAA was prepared in the weakly flocculated state (pH 6.0) using the high-shear Ultra-Turrax mixer (solid line). Subsamples of 50 mL were then sonicated for 1 min (dotted line). The Py(φ) curve is shifted to the right for the additionally sonicated sample, indicating that the structure of the suspension is further broken down

Figure 7. Effect of dilution on Py(φ); ZrO2 with 1.0 dwb % 2000 MW PAAsstrongly flocculated; (b) base suspension Ultra-Turrax 5 min; (O) diluted by just stirring in water and adjusted pH; (0) diluted, adjusted pH, and then sonicated for 20 s.

by the sonication and has become more compressible. Samples of weakly flocculated, sterically stabilized suspensions thus should be sonicated separately before compression to separate the particles as much as possible. In Figure 6, 100 mL samples of the stock suspension were diluted to φ0 ) 0.10 in two ways: first, by stirring in water (dotted line); second, by stirring in water and then sonicating for 2 min (dashed line). The resulting curves lie significantly to the left of the original concentrated suspension (solid line). Dilution of the weakly flocculated suspension thus irreversibly alters the structure of the particle network in some way, becoming far less compressible than the original concentrated suspension. Sonication of the diluted suspension only partially recovers the original structure. In Figure 7, 50 mL samples of the stock suspension were diluted by stirring in water as before. The pH was then adjusted to the strongly flocculated state (pH 4.54.6 for this sterically stabilized sample containing PAA). One sample was subsequently sonicated for 20 s (dotted line), while the other sample was stirred (dashed line). The strongly flocculated suspensions are less compressible than the weakly flocculated suspension (solid line) in agreement with the previous section. The strongly flocculated structure also appears stable since the Py(φ) curve is unchanged by further sonication. The

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Figure 8. Effect of initial concentration on Py(φ) for strongly flocculated Al2O3 (iep pH 9.3-9.4).

Figure 9. Effect of initial concentration on Py(φ) for strongly flocculated ZrO2 (iep pH 6.8-7.2).

compression results of these strongly flocculated suspensions thus appear to be independent of their method of preparation. Consideration of the results in Figures 5-7 indicates that the compression rheology of sterically stabilized suspensions is sensitive to their preparation method. An important industrial problem is the optimization of the flocculation of mineral particles entering a thickener, which usually occurs in a feed-well at the thickener center. The flocculation efficiency in the feed-well determines the throughput (from the settling rate) and the underflow concentration (from the suspension compressibility) of the thickener (Landman et al., 1988). Samples for compression measurements for the optimization of an existing process thus should be taken from the thickener feed-well after flocculation. For the design of a new thickener, flocculation conditions of the suspension in the laboratory should closely match those in the plant. In these ways, the compression rheology measured will best represent the actual suspension used. Initial Concentration. It has been found here that the initial concentration, φ0, of the suspension is a determining factor in the final bottoms concentration achievable. A significant dependence of Py(φ) on φ0 is shown in Figure 8 for strongly flocculated Al2O3 at its iep; that is, when φ0 increases, the suspension becomes less compressible. The same effect of φ0 on Py(φ) is apparent for both strongly and weakly flocculated ZrO2 as seen in Figures 9 and 10. The initial concentration

Figure 10. Effect of initial concentration on Py(φ) for weakly flocculated ZrO2 (pH 5.6-5.7).

effect thus appears to be a universal property of these metal oxide suspensions. Several explanations are postulated for these initial concentration effects. First, if the initial state is a weakly structured, open network of particles with few connecting bonds, then under compression the particles would have room to move to a semiordered state of a high concentration. However, if the initial suspension is already highly concentrated, then a strong structure may be already present which may constrain the movement of particles under compression. The concentration achieved will thus be lower since the particles cannot pack as well compared with if they had started in the diluted state. Another possible mechanism that would describe these initial concentration effects is based on the suspension microstructure. Two suspensions of the same initial concentration may have very different microstructures. A suspension may consist of dense aggregates of particles joined by relatively few bonds and contain large void spaces between the aggregates. Compression of such a structure would involve the yielding of relatively few bonds. Conversely, a suspension that is a homogeneous structure of single particles would require the yielding of many more bonds for compression to occur. The compressive yield stress would thus be proportional to the number of bonds between either aggregates or particles depending on the structure of the suspension (Kapur et al., 1997). As the initial concentration of the suspension changes, the initial microstructure may change, which would directly affect the compression rheology. The effect of the initial concentration of the suspension used in compression tests has important ramifications when industrial processes are examined. For example, in the optimization or design of thickeners, samples for compression tests should be either taken from the thickener feed-well directly after flocculation or prepared at the concentration that is or will be used. The suspension sample to be tested under compression will thus have a representative structure of that in the actual process. It should be noted, however, that if the feed concentration is below the gel point, φg (the concentration at which particles form a continuous network), then the final compression height in the centrifuge or filter press will be low and hence measurement accuracy will suffer. Effect of Additives. Polymeric additives change the surface chemistry of suspended particles and dramatically affect the compression rheology. The addition of

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Figure 11. Effect of Py(φ) on pH for ZrO2 with and without 2000 MW poly(acrylic acid), φ0 ) 0.176; curves taken at constant concentration.

Figure 13. Comparison of shear and compressive yield stress curves (τy(φ) and Py(φ), respectively) for strongly (open symbols) and weakly (closed symbols) flocculated ZrO2: (O) τy(φ) pH 6.97.2; (b) τy(φ) pH 5.6-5.7; (0) Py(φ) pH 7.2; (9) Py(φ) pH 5.7. Table 2. Power Law Constants for Fit of Data in Figure 14 pH

A

7.2 5.7

7.4 × 1.1 × 107 106

m

B

n

5.6 6.3

6.3 × 4.7 × 108 108

6.7 6.9

coordinates for strongly and weakly flocculated ZrO2 with no additives. The data can be fitted to power laws of the forms

Figure 12. Effect of low- and high-MW poly(acrylic acid) (2000 and 750 000) on Py(φ) for ZrO2 at the iep, φ0 ) 0.159 (reproduced from Leong, 1994).

low MW PAA coats the particles with a thin layer of polymer that reduces the attractive forces between the particles by a steric separation (Leong et al., 1993). In Figure 11, 1.0 dwb % of 2000 MW PAA is added to a ZrO2 suspension and Py versus pH is plotted for a range of φ and compared with that of no additive. The effect on the compression behavior of the suspensions is to shift the pH of maximum flocculation and make them substantially more compressible. The shear yield stress is likewise reduced by such an addition (Leong, 1994). A longer-chained polymer has the effect of flocculating the particles through a bridging mechanism. The shear and compressive rheology of this system has been examined by Leong (1994). Figure 12 is reproduced here to illustrate the effect of adding a 750 000 MW, 1.0 dwb % PAA compared with the same suspension with no polymer. For comparison, the effect of the 2000 MW PAA is also shown. The long polymer chains induce a widely separated particle structure that restricts particle movement and hence is less compressible. In industry, long-chained polymer flocculants are commonly used to quickly settle mineral suspensions. Such treatment adversely affects the compression rheology of the system and should be avoided if high final concentrations are to be achieved. Compressive Yield Stress and Shear Yield Stress Correspondence. It is useful to compare the shape and order of magnitude of τy(φ) and Py(φ) curves. In Figure 13 are plots of τy(φ) and Py(φ) on log-log

τy(φ) ) Aφm

(1)

Py(φ) ) Bφn

(2)

where A, B, m, and n are constants. For the data in Figure 13, the values for these constants are listed in Table 2. The exponents m and n are approximately equal (within fitting error) for both the τy(φ) and Py(φ) curves, as evidenced by their parallel nature in Figure 13. The preexponential factor for Py(φ), B, are between 40 and 90 times greater than that for τy(φ), A, as evidenced by the axis scales in Figure 13. From this information a relation between τy(φ) and Py(φ) may be written by the substitution of eq 1 into eq 2 to yield

( )

Py(φ) ) B

τy(φ) A

n/m

(3)

If m and n are equal, then a linear relation between Py and τy is obtained. The prediction of Py(φ) from τy(φ) measurements is extremely useful since the determination of Py(φ) can take many weeks using the commonly available centrifuge methods, whereas τy(φ) measurements can be completed in days. From the limited data in Figure 13 which show similar power law exponents for both strongly and weakly flocculated ZrO2, a relation dependent on the state of flocculation of the material could also be developed. Applications An extremely useful application of Py(φ) data is in the design and/or optimization of thickeners containing a compression zone. Using these curves, the thickener height, Hi, required to produce a certain bottom concentration, φb, from a given initial concentration, φi, in the thickener may be estimated (de Guingand, 1986). This is easily calculated for a batch thickener at

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of various pressure cycles on the filtration time may also be calculated. The optimization and design of filtration systems may thus be achieved without costly plant trials. The ideal type and amount of flocculant may be determined in the laboratory. At the design level, the optimal dewatering technology for the suspension system can also be found. Conclusions

Figure 14. Effect of flocculant on the compression behavior of bauxite residue, φ0 ) 0.060. The equivalent height for a batch thickener is also shown on the left axis.

equilibrium using the equation

Py(φb) ) ∆Fg0φiHi

(4)

where g0 is the gravitational acceleration. Equation 4 underestimates the height necessary for a continuous thickener since the compressive forces never reach equilibrium in continuous flow. To determine the thickener height required for a continuous thickener, a second parameter is required that quantifies the rate of compression. This parameter is the hindered settling function, r(φ). With it, the bed height and the concentration profile in the thickener may be exactly calculated (Landman and White, 1994). This technique is currently being trialed by Alcoa of Australia on a 75 m diameter superthickener used to concentrate bauxite residue for semidry disposal. In Figure 14 are compression data for bauxite residue or red mud with various amounts of added flocculant (Green et al., 1994). Also shown is the equivalent batch thickener height required for a typical feed concentration of φ ) 0.060. It can be seen that for unflocculated red mud, in a clarifier with no compression zone, the bottom concentration is φ ) 0.20 (43 wt %). A batch thickener height of 5 m yields a bottom concentration of about φ ) 0.27 (53 wt %). The optimum addition of 145 ppm flocculant can then further increase the bottom concentration to about φ ) 0.32 (59 wt %). The utilization of a compression zone in a thickener together with the correct dosage of flocculant can thus increase the bottom concentration from 0.20 to 0.32 or from 43 to 59 wt %. This represents significant dewatering and in this case is more than adequate for a semidry tailings disposal scheme (Glenister and Abbott, 1989; Ritcey, 1989; Cooling and Glenister, 1992). The material produced from the thickener possesses a shear yield stress but can still be pumped. In fact, pumping energy requirements can be lower since the pipeline is now operating in laminar flow. Problems such as erosion and settling in the pipeline and difficulties with startup are also minimized (Thomas, 1977). Compressive yield stress curves have also been used in the optimization of full-scale high-pressure filtration systems in the kaolin industry (Eberl et al., 1995). The pressure required to achieve a certain filter cake concentration may be directly determined from such a curve. In conjunction with filtration rate data and the subsequent determination of the hindered settling function, r(φ), the effect of filter cake thickness and the effect

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Received for review February 12, 1997 Revised manuscript received July 11, 1997 Accepted July 22, 1997X IE970141I

X Abstract published in Advance ACS Abstracts, September 15, 1997.