Flocculation and dewatering

Flocculation and dewatering

Int. J. Miner. Process. 58 Ž2000. 223–236 www.elsevier.nlrlocaterijminpro Flocculation and dewatering R. Hogg ) Mineral Processing Program, Departm...

169KB Sizes 0 Downloads 19 Views

Int. J. Miner. Process. 58 Ž2000. 223–236 www.elsevier.nlrlocaterijminpro

Flocculation and dewatering R. Hogg

)

Mineral Processing Program, Department of Energy and Geo-EnÕironmental Engineering, The PennsylÕania State UniÕersity, 115 Hosler Building, UniÕersity Park, PA 16802, USA Received 18 May 1999; accepted 27 May 1999

Abstract The design and operation of flocculation processes are discussed in the context of the specific requirements of dewatering systems such as sedimentation and filtration. Chemical conditions, reagent selection and process operating conditions are evaluated based on the fundamental mechanisms involved in particle destabilization and floc development. Opportunities for control of floc characteristics through appropriate process design are described. Specific requirements for different dewatering processes are discussed. q 2000 Elsevier Science B.V. All rights reserved. Keywords: flocculation; dewatering; sedimentation

1. Introduction Dewatering, of concentrates, tailings, etc., is an important ancillary process in most mineral processing operations. Improperly designed andror operated dewatering systems can become limiting factors in plant operation or capacity. Typically, final dewatering is accomplished by sedimentation or filtration and, in some cases, both. Flocculation is usually a necessary pretreatment step in dewatering streams containing significant quantities of very fine particles Že.g., - 5 mm.. For such systems, the effectiveness of the flocculation step may determine the performance and, ultimately, the capacity of the dewatering system. Flocculation is a complex process, normally carried out under conditions that are far removed from equilibrium. It follows that the effectiveness of the process depends not only on the use of appropriate chemical reagents Žcoagulants, flocculants, etc.. but also on how they are applied. The following discussion is intended to provide an overview of )

Tel.: q1-814-865-3802; Fax: q1-814-865-3248; E-mail: [email protected]

0301-7516r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 Ž 9 9 . 0 0 0 2 3 - X

224

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

the nature of the process and of how it can be controlled so as to achieve optimum performance in the context of dewatering operations such as sedimentation and filtration. 2. The flocculation process Flocculation is a process of aggregating dispersed fine particles into larger units Žflocs.. In general, the process involves three principal steps: Ø destabilization of the suspended fine particles, i.e., elimination of any interparticle repulsion, due to electrical charges, etc., that opposes aggregation; Ø floc formation and growth, i.e., the development of aggregates by particle–particle collision and adhesion; and Ø floc degradation, i.e., mechanical breakage of the aggregates due to shear, turbulence, etc., in the slurry. All three of these occur in any practical flocculation process. While the third step, degradation, is normally considered to be detrimental, it can also play a positive role in the redistribution of particles and reagents as flocs develop and grow. 2.1. Destabilization The fine-particle suspensions encountered in mineral processing often exhibit a significant degree of stability, tending to resist aggregation. Most commonly, this results from the electrical charge acquired by particles dispersed in aqueous media but it may be enhanced by solvation effects or by the presence of protective adsorbed films on particle surfaces. Destabilization can usually be accomplished by eliminating or shielding the charges. The charge on mineral particles dispersed in water typically arises from electrochemical interactions between the solid and the surrounding aqueous solution and can usually be controlled through the solution pH. At some pH, the so-called isoelectric point, the particles have no net charge and are unstable with respect to coagulation. Simple pH control is, therefore, often an effective means of destabilization, though it may be impractical if the isoelectric point occurs in an inconvenient pH range. As an alternative to eliminating the charge on particles, the charges on neighboring particles can be shielded from one another in the presence of relatively high concentrations of ions in solution. This effectively compresses the electrical double layers surrounding the particles permitting them to approach one another closely enough to fall into the range where attractive forces dominate. Multivalent ions are especially effective for this purpose and reagents such as lime, alum, etc., are widely used in practice. Destabilization by simple double-layer compression usually requires electrolyte concentrations of up to 0.05 molrl for monovalent and 10y4 molrl for divalent. For thoroughly characterized systems, destabilization by charge control or double-layer compression can be predicted using the well-known DLVO theory of colloid stability ŽKruyt, 1952.. Hydrolyzable cations such as Cu2q, Al 3q, Fe 3q can be highly effective in dispersion destabilization. In addition to causing double-layer compression, the hydrolyzed species are highly surface-active and can reverse the zeta potential Žattain an isoelectric point.. Close to this point of charge reversal, where the zeta potential lies in the range of "10 mV, the system is destabilized. These species can also promote aggregation by modify-

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

225

ing dispersed particles through surface precipitation of colloidal hydroxides which lead to overall destabilization by mechanical entrapment or heterocoagulation ŽHealy and James, 1972.. In practice, these reagents probably play an important role in floc development as well as destabilization. Polymeric substances, especially polyelectrolytes, are also very effective for destabilizing fine-particle suspensions. To some extent, they function as highly charged ionic species but they are generally agreed to act primarily through a charge-patch mechanism in which individual molecules adsorb on oppositely charged surfaces forming localized regions of opposite charge to the surface ŽGregory, 1973.. Aggregation occurs by interaction of the patches with regions of bare surface on other particles. Because one polyelectrolyte molecule can, at most, provide a single particle–particle linkage, molecular concentration of the same order as particle Žnumber. concentrations is required for destabilization. Molecular weights of the order of 10 5 appear to provide the appropriate compromise between patch size and molecular concentration at reasonable Žppm. dosage levels. Lower molecular weight polymers Ž- 10 5 . function very well as dispersants. Higher molecular weight polymers Ž) 10 6 . are not generally effective for destabilization but play a very important role in floc development; hence, their widespread use as flocculants. The result of destabilization of a fine-particle dispersion by any of the above mechanisms is the formation of small flocs which may grow to larger sizes but are generally fragile and highly susceptible to breakage in the presence of turbulence or shear. Under conditions of vigorous agitation Žshear rates of about 1000 sy1 ., flocs typically reach an equilibrium size in the 5–10 mm range ŽRattanakawin, 1998.. For applications to dewatering by sedimentation or filtration, larger, stronger flocs are normally preferred and procedures to enhance floc growth are usually employed. 2.2. Floc deÕelopment Destabilization of a fine-particle suspension permits particles to adhere to one another on contact. Flocs can then grow as a result of collisions between particles moving relative to each other due to: Ø Brownian motion arising from thermal energy in the suspending fluid; Ø velocity gradients in mechanically agitated suspensions; and Ø differential settling of individual particles or flocs. Application of a population balance model to the floc growth process ŽKruyt, 1952. indicates that Brownian motion is the dominant mechanism for very small particles, i.e., in the initial formation of flocs following destabilization. Agitation effects begin to dominate in the later stages of growth where existing flocs aggregate to form larger units. Differential settling can become important during sedimentation, under quiescent conditions of a flocculated suspension. The population balance models can be used to obtain an approximate expression for the change in number concentration N of particles or flocs in suspension as flocculation proceeds. Thus: dN f yKN 2 , Ž 1. dt

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

226

where K is an effective flocculation rate constant which depends on the specific collision mechanismŽs. involved. In the case of Brownian motion above, K is approximately constant and can be estimated from ŽHogg, 1992.: 8 kT

Kf

3m

,

Ž 2.

where k is the Boltzmann constant, T is the absolute temperature and m is the fluid viscosity. In agitated suspensions, K is no longer constant but increases with the average volume V of the individual particles or flocs. In this case, ŽHogg, 1992.: 8VG

Kf

, Ž 3. p where G is the mean shear rate associated with the agitation. Obviously, the average floc volume V increases as flocculation proceeds. In fact, mass conservation requires that, neglecting porosity in the growing flocs,

f Vf

N

,

Ž 4.

where f is the overall solids concentration Žvolume fraction. in suspension. Substitution from Eqs. Ž3. and Ž4. in Eq. Ž1. reduces the latter from a second-order to a pseudo-first order expression: dN dt

s yK X N,

Ž 5.

in which: KXs

8Gf

. p The solutions to Eqs. Ž1. – Ž5. are, respectively, N0

Ns

Ž 6.

,

t

Ž 7.

ž / 1q

t

and X

N s N0 eyt r t ,

Ž 8. X

where N0 is the initial number concentration and t and t are characteristic flocculation times defined by:

ts

1 N0 K

,

Ž 9.

and

tXs

1 KX

.

Ž 10 .

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

227

For a given mass concentration, the characteristic time for Brownian flocculation depends on the initial particle size, whereas that for agitated suspensions does not. If the initial size is 1 mm, the times are roughly comparable for shear rates of about 100 sy1 , corresponding to moderately gentle agitation. For larger sizes, the effects of agitation dominate even at very low shear rates. The flocculation time represents only a part of the difference between Brownian and shear flocculation. The change from a second-order ŽEq. Ž1.. to a pseudo-first order process ŽEq. Ž5.. has a significant effect on long-term floc growth. This can be seen more clearly in terms of the mean floc size x, which can be estimated from Eqs. Ž7. and Ž8. with substitution from Eq. Ž4., and recognizing that: V s V0

3

x

ž /

.

x0

Ž 11 .

These substitutions lead to: t

ž /

x s x0 1 q

t

1r3

,

Ž 12 .

and X

x s x 0 e t r3t .

Ž 13 .

A comparison of the variation in floc size with relative time Ži.e., for equal values of t and t X . is given in Fig. 1. The dramatic effect of agitation on long-term floc growth can readily be seen.

Fig. 1. Comparison of long-term floc growth for Brownian and shear coagulation with the same initial rate.

228

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

Since any practical application, including laboratory tests, involves some amount of agitation — for mixing reagents, etc. — flocculation behavior is essentially always dominated by the effects of agitation. According to Eq. Ž13., vigorous agitation Žat 1000 sy1 . of a suspension at 1% solids by volume would lead to a 5000-fold increase in the mean size in 1 s. This may be unrealistic, though there is no question that floc growth is extremely rapid ŽRattanakawin, 1998.. The simplified approach outlined above involves numerous assumptions regarding uniformity of velocity gradients, particle concentrations, etc., in agitated suspensions and neglects hydrodynamic and other interactions which may reduce actual growth rates. Most importantly, it neglects floc breakage in a turbulent environment. Rattanakawin Ž1998. has shown that destabilized alumina suspensions Žmass median particle size about 0.5 mm. agitated at high shear rates Žabout 1000 sy1 . coagulate very rapidly indeed, but the flocs reach a limiting Žmedian. size of between 5 and 10 mm. It appears that the limiting factor is floc breakage and that the limiting floc size occurs when growth and breakage rates are equal. Floc breakage has been studied quite extensively by direct measurement ŽGlasgow and Hsu, 1982., evaluation of limiting floc sizes ŽParker et al., 1972; Tomi and Bagster, 1978., and by analogy to emulsification processes ŽPandya and Spielman, 1982. or grinding processes ŽRay and Hogg, 1987.. While it is clear that breakage rates increase with floc size and agitation intensity and decrease with floc strength, specific relationships have yet to be established. High molecular weight polymer flocculants appear to play a significant role in the floc breakage process. It was noted previously that these reagents are relatively ineffective for suspension destabilization. However, the addition of small amounts of these polymers to a previously destabilized system can increase the limiting floc size to as much as 200–300 mm even in a highly turbulent environment ŽRattanakawin, 1998.. This observation clearly implies that the high molecular weight flocculants serve primarily as binding agents, enhancing floc strength and reducing breakage rates, thereby permitting growth to proceed to substantially larger sizes. It is well-established that high molecular weight polymers adsorb strongly and essentially irreversibly onto solid surfaces unless opposed by long-range repulsive forces ŽFleer et al., 1993.. The author has shown ŽHogg, 1999. that adsorption rates can be expected to be very high under the conditions encountered in flocculation processes. In order to take full advantage of the binding action of these polymers, it is necessary to ensure that the polymer is uniformly distributed within the flocs. Because of the high adsorption and floc growth rates, adsorption tends to occur preferentially on available external surfaces of the flocs, leaving the interior somewhat starved of polymer. Continuous, controlled addition of polymer can alleviate this problem by exploiting the continuous breakage and reformation of flocs to redistribute polymer from the external surfaces to the interior of the flocs. It has been shown conclusively that such controlled addition leads to a substantial increase in the limiting floc size Žand corresponding settling rate. ŽKeys and Hogg, 1979; Hogg et al., 1987, 1993.. In particular, it is found that prolonged mixing without further addition of polymer is generally detrimental to the process by causing irreversible floc breakage. The limiting floc size typically decreases as polymer additionrmixing time is increased at fixed total polymer dosage although

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

229

Fig. 2. Effect of mixing time Žwith continuous polymer addition. on flocculation of clay.

this appears to be offset by enhanced floc strength and resistance to subsequent degradation. Extremely short mixing times, on the other hand, also lead to reduced floc size and increased floc fragility. This effect has been attributed to limitation by the rate of polymer adsorption ŽHogg, 1999.. An example of the effect of the mixing time is given in Fig. 2, based on data from Hogg et al. Ž1987.. 2.3. Floc characteristics The performance of a flocculation process should properly be assessed in terms of floc size distribution and floc structure. In practice, however, it is common to use indirect measures such as settling rate, supernatant turbidity and sediment compressibility. Settling rate and turbidity are determined primarily by the floc size distribution, though the former may also be influenced by floc structure. High settling rate, accompanied by high turbidity, is usually associated with the bimodal floc size distributions obtained by ‘‘poor’’ flocculation, especially failure to provide adequate destabilization prior to the application of high molecular weight flocculants. Floc size distributions can generally be controlled by proper reagent selection and the appropriate use of reagent additionrmixing conditions as discussed above. Floc structure is more difficult to control. Detailed investigations of floc structure have been carried out by computer simulation using a variety of imposed conditions ŽVold, 1963; Sutherland, 1967; Sutherland and Goodarz-Nia, 1971; Meakin, 1984. and by measurement of floc density ŽKoglin, 1977; Tambo and Watanabe, 1979; Klimpel and Hogg,

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

230

1986.. These studies consistently show that floc density decreases with increasing floc size, roughly in accordance with a power–law relationship between porosity ´ and size x: 1y´sA

x0

ž / x

g

,

Ž 14 .

where x 0 is the primary particle size, A is a constant and the exponent g varies between 0.7 and 1.3. Eq. Ž14. is equivalent to the description of flocs as fractal systems with a fractal dimension d f between 1.7 and 2.3 Ž d f s 3 y g .. A fairly typical example, for flocculated 1 mm quartz particles, is given in Fig. 3. The simulation studies and also experimental measurements for submicron particles subject to Brownian coagulation give values of A close to unity. Measurements based on flocculation of larger Ž5–10 mm. particles with polymers under shear yield substantially larger values of A ŽKlimpel and Hogg, 1986, 1991., suggesting that such flocs may be subject to compaction under shear.

Fig. 3. Typical example of the relationship between floc size and the fractional solids content of the individual flocs. One-micrometer quartz particles flocculated with a non-ionic polymer ŽKlimpel, 1984..

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

231

2.4. Continuous flocculation processes The effects of system chemistry on flocculation, especially the destabilization step, apply equally to batch or continuous processes. Agitation and mixing are also important in both batch and continuous processes. An example of the effects of polymer dosage and mixing time Žresidence time. on flocculation in a continuous stirred tank is given in Fig. 4. The general result, that shorter mixing times lead to larger flocs for the same polymer dosage, is similar to that observed in batch processes. It should be noted, however, that there are inherent differences between the batch and continuous processes, and mixing conditions cannot be matched exactly. For example, continuous polymer addition to a batch system leads to a continuous increase in total polymer concentration, while in a continuous stirred tank at steady state, the concentration remains constant. In the batch system, all particles have the same residence timermixing time while there is a distribution of residence times in the continuous system. For industrial application, it is common to inject flocculants directly into a pipe. Injection at a single point corresponds approximately to the use, in a batch system, of very rapid addition followed by continued mixing. Continuous addition without subsequent mixing, which is typically more effective in batch systems, can be roughly approximated by multiple additions along the length of a pipe. Laboratory studies of continuous flocculation indicate that the general trends observed in batch processes are reproduced, but the magnitude of the effects tends to be less ŽSuharyono and Hogg, 1994, 1996.. This has been attributed to the differences noted above for stirred tanks and to scale-up problems for in-line mixing.

Fig. 4. Effect of mixing time on continuous flocculation of clay suspensions Ždata of Suharyono, 1996..

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

232

3. Dewatering of fine-particle suspensions There are two basic requirements in the use of sedimentation for water clarification: 1. flocculation should be complete, in that all particles, especially the finest, should be incorporated into the flocs; and 2. flocs should be large enough to provide adequate settling rates. In principle, both of these can readily be satisfied with a properly designed and operated flocculation process. The completeness of flocculation is determined by the destabilization step as noted above; settling rates depend primarily on floc size and can be controlled through the appropriate application of high molecular weight polymer flocculants. Clarification problems encountered in industrial applications are most likely to arise from inadequate destabilization. The latter is particularly sensitive to water chemistry ŽpH, dissolved ionic species, etc.. so that, in certain circumstances, relatively minor fluctuations can drastically affect clarification. High molecular weight polymers are ineffective for clarification of stable suspensions although they do produce flocs which may settle at satisfactory rates. The remedy to clarification problems Žhigh effluent turbidity. mostly lies in the destabilization step, i.e., in water chemistry or the use of coagulants. Settling in sedimentation systems Žclarifiers, thickeners. generally involves three regimes ŽFitch, 1962.: 1. Free settling — individual flocs settle, more or less, independently; 2. Hindered settling — hydrodynamic interactions and significant return flow of water lead to reduced, concentration-dependent settling rates; and 3. Compression — flocs in permanent contact form a continuous network structure that has mechanical strength. The first two regimes are mostly involved in clarification and can be controlled through flocculation. The effect of polymer addition on settling rate can clearly be seen in Fig. 4. Floc structure is of secondary importance in these regimes. The third regime is dominated by floc structure and probably only indirectly affected by floc size Žthrough the floc size–floc density relationship, Eq. Ž14... The concentrations at the transitions between the settling regimes do depend on floc size. In the free and hindered settling regimes, the settling units are individual flocs and the effective concentration feff is given by:

feff s

fs

Ž1y´ .

.

Ž 15 .

Hindered settling becomes significant at concentrations of around 10% by volume. For large flocs with 90% porosity, this corresponds to a solids concentration of only 1% by volume. Similarly, compression dominates at concentrations above about 50% by volume which would correspond to about 5% actual solids in a highly flocculated suspension. The development of structure in a flocculated sediment causes a yield value to be established so that further settling occurs only when the stress acting, due to the self-weight of the sediment, exceeds this value ŽBuscall and White, 1987.. When settling

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

233

does occur, the rate is controlled by the extrusion of water from the inter- and intrafloc pores. The extent of flocculation appears not to be a major factor in this process ŽWeiland et al., 1994. since the structure of large flocs breaks down readily and water can be extruded from the pores quite rapidly. However, the process does appear to be limited by the small, relatively dense aggregates produced in the destabilization step. These ‘‘microflocs’’ require significant stress to overcome their yield strength, and the rate of water removal from the fine pores can be very low. Since destabilization is a necessary precursor to floc growth, and the microflocs formed in the process seem to be relatively unaffected by how the destabilization was achieved, chemical approaches to enhancing sediment compression have been met with very limited success. In order to achieve improved dewatering of fine-particle sediments, it is generally necessary to increase the applied stress, e.g., by increasing sediment depth as in deep-bed thickeners, by centrifugation, or mechanically, as in filter presses. 3.1. Filtration The performance of filtration processes is determined primarily by cake structure. In the case of flocculated suspensions, this depends, in turn, on the structure of the flocs and their modification due to liquid flow and applied pressure. Floc size, in itself, has only secondary effects but is important through its relationship to floc structure. Large, low-density flocs generally favor filtration rate through high permeability. If the open structure can be maintained through the filter cycle, the resulting cake should be amenable to dewatering by air displacement. Collapse of the structure under pressure

Fig. 5. Effects of flocculation on cake resistance and porosity in vacuum filtration of fine coal Ždata from Stroh, 1993..

234

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

also promotes dewatering by reducing pore volume. However, the finer pores remaining in the compressed cake tend to increase the final cake moisture because of increased capillary pressure. Floc size and thereby, density can be controlled by the appropriate use of flocculants as discussed above. Some fairly typical results, for fine coal filtration, are shown in Fig. 5. Polymer addition clearly increases cake permeability as reflected in the increase in filtration rate. In this case, the effect on cake porosity is relatively small, which is commonly observed for mineral suspensions with broad size distributions. The data used in Fig. 5 were reported for a coal with a maximum particle size of 1.5 mm but with 35% by weight - 10 mm. For such systems, the coarsest particles form a rigid, relatively incompressible, network and flocculation of the fines primarily affects their distribution within the cake. Flocculation prevents fine particles from percolating through the cake and accumulating at the filter medium. In the absence of coarse material, flocculation tends to produce highly compressible cakes. In such cases, floc and ultimately, cake compressibility can be controlled to some extent through the amount of polymer added. Cake compressibility can be expected to decrease with increased polymer content. Large flocs with high compressibility can be obtained by rapid addition of a relatively small amount of polymer Žsee Fig. 2.. If high polymer dosage is used to reduce compressibility, relatively low rates of addition should help ensure uniform distribution of polymer within the cake. This condition may be advantageous when the integrity of the flocs is important as in filter presses or in reducing cake cracking in vacuum filtration. 4. Conclusions The necessary initial step in flocculation is destabilization of the dispersed particles. This can normally be accomplished by elimination of the surface change, by compression of the double layer, or by charge–patch interaction using polyelectrolytes. These different methods give similar results — relatively small flocs which incorporate essentially all of the dispersed particles. Polyelectrolytes produce slightly larger flocs. High molecular weight polymers are inappropriate for initial destabilization. They produce large flocs but require excessive dosage levels to ensure incorporation of all particles. High molecular weight polymers flocculants can be extremely effective in promoting floc growth in previously destabilized suspensions. Polymer additionrmixing conditions play a major role in determining flocculant performance. Floc growth rates seem to depend on the availability of polymer in solution, while breakage rates and floc integrity are determined by the internal polymer content in the flocs themselves. Agitation of the suspension with simultaneous polymer addition can be used to control the relative rates of floc growth and breakage. Dewatering processes such as sedimentation and filtration are profoundly affected by flocculation. The different processes and even different stages in the same process may impose different requirements on floc size and structure. Reagent selection is important but represents only part of flocculation process design. The reagent addition procedure is equally important but is frequently neglected in process design and operation.

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

235

References Buscall, R., White, L.R., 1987. On the consolidation of concentrated suspensions: I. The theory of sedimentation. J. Chem. Soc., Faraday Trans. I 83, 873–891. Fitch, B., 1962. Sedimentation process fundamentals. Trans. AIME 223, 129–137. Fleer, G.J., Cohen-Stuart, M.A., Scheutjens, J.H.M.M., Cosgrove, F., Vincent, B., 1993. Polymers at Interfaces. Chapman & Hall, London. Glasgow, L.A., Hsu, J.P., 1982. An experimental study of floc strength. AIChE Journal 28, 779–785. Gregory, J., 1973. Rates of flocculation of latex particles by cationic polymers. J. Colloid Interface Sci. 42, 448–456. Healy, T.W., James, R.D., 1972. Adsorption of hydrolyzed metal ions at the oxide water interface. J. Colloid Interface Sci. 40, 42–52. Hogg, R., 1992. Agglomeration models for process design and control. Powder Technol. 69, 69–76. Hogg, R., 1999. The role of polymer adsorption kinetics in flocculation. Colloids and Surfaces A: Physicochemical and Engineering Aspects 146, 253–263. Hogg, R., Klimpel, R.C., Ray, D.C., 1987. Agglomerate structure in flocculated suspensions and its effects on sedimentation and dewatering. Minerals and Metallurgical Processing 4 Ž2., 108–113. Hogg, R., Bunnaul, P., Suharyono, H., 1993. Chemical and physical variables in polymer-induced flocculation. Minerals and Metallurgical Processing 10, 81–85. Keys, R.O., Hogg, R., 1979. Mixing problems in polymer flocculation. AIChE Symposium Series, Vol. 75, No. 190, pp. 63–72. Klimpel, R.C., 1984, The structure of agglomerates in flocculated suspensions. MS Thesis, The Pennsylvania State University, University Park, PA. Klimpel, R.C., Hogg, R., 1986. Effects of flocculation conditions on agglomerate structure. J. Colloid Interface Sci. 113, 121–131. Klimpel, R.C., Hogg, R., 1991. Evaluation of floc structures. Colloids and Surfaces 55, 279–288. Koglin, B., 1977. Assessment of the degree of aggregation in suspension. Powder Technol. 17, 219–227. Kruyt, H.R. ŽEd... Colloid Science I. Elsevier, Amsterdam, 1952. Meakin, P., 1984. Diffusion-limited aggregation in three dimensions: results from a new cluster–cluster aggregation model. J. Colloid Interface Sci. 102, 491–512. Pandya, J.D., Spielman, L.A., 1982. Floc breakage in agitated suspensions: theory and data processing strategy. J. Colloid Interface Sci. 90, 517–531. Parker, D.S., Kaufman, J., Jenkins, D., 1972. Floc breakup in turbulent flocculation processes. J. Sanit. Eng. Div., Am. Soc. Civ. Eng. 98, 79–99. Rattanakawin, C., 1998. Aggregate size distributions in flocculation. MS Thesis, The Pennsylvania State University, University Park, PA. Ray, D.T., Hogg, R., 1987. Agglomerate breakage in polymer-flocculated suspensions. J. Colloid Interface Sci. 116, 256–268. Stroh, G., 1993. The effect of coagulation and flocculation on the filtration properties of suspensions incorporating a high content of fines. In: Dobias, ´ˇ B. ŽEd.., Coagulation and Flocculation. Marcel Dekker, New York, pp. 653–695. Suharyono, H., 1996. Flocculation and consolidation in thickening processes. PhD Thesis, The Pennsylvania State University, University Park, PA. Suharyono, H., Hogg, R., 1994. Continuous flocculation processes. SME Preprint No. 94-231. Littleton, CO. Suharyono, H., Hogg, R., 1996. Flocculation in flow through pipes and in-line mixers. Minerals and Metallurgical Processing 13, 501–505. Sutherland, D.N., 1967. A theoretical model of floc structure. J. Colloid Interface Sci. 25, 373–380. Sutherland, D.N., Goodarz-Nia, I., 1971. Floc simulation: the effect of collision sequence. Chem. Eng. Sci. 26, 2071–2085. Tambo, N., Watanabe, Y., 1979. Physical characteristics of flocs: I. The floc density function and aluminium floc. Water Research 13, 409–419. Tomi, D.T., Bagster, D.F., 1978. The behavior of aggregates in stirred vessels: I. Theoretical considerations on

236

R. Hogg r Int. J. Miner. Process. 58 (2000) 223–236

the effects of agitation; II. An experimental study of the flocculation of galena in a stirred tank. Trans. Inst. Chem. Eng., Vol. 56, pp. 1–8; 9–18. Weiland, R.H., Bunnaul, P., Hogg, R., 1994. Centrifugal dewatering of flocculated clays. Minerals and Metallurgical Processing 11, 37–40. Vold, M.J., 1963. Computer simulation of floc formation in a colloidal suspension. J. Colloid Sci. 18, 684–695.