Effects of flocculation conditions on agglomerate structure

Effects of Flocculation Conditions on Agglomerate Structure R.

C.

K L I M P E L AND R . H O G G

Mineral Processing Section, Department of Mineral Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 Received August 28, 1985; accepted November 6, 1985 Direct experimental measurements of individual floc size and settling velocity allow the agglomerate density or porosity to be determined. Results indicate that density generally decreases with increasing floc size. The experimental data were fitted to an empirical model which was used in statistical testing for significant differences between measured floc density-size relationships in different systems. The effects of flocculation system variables such as agitation intensity, polymer concentration, mixing time, solids concentration, and primary particle size on resultant floc structures are presented and discussed. Based on these results, a simple multistage model is postulated. © 1986AcademicPress,Inc. INTRODUCTION

Polymeric flocculation of fine solid particles in liquid suspension is frequently used in industry to enhance settling rates and improve supernatant water quality. These flocculated particles typically exhibit loose porous structures with high internal surface area which reduce the effective floc density. Consequently, physical properties such as floc size and density may have a major impact on the effectiveness of subsequent processes. In particular, floc structure will determine the solids content and influence the dewatering characteristics of the sediment. Previous investigations of floc structure have included computer simulations of growing flocs (1-10) as well as experimental measurements on real systems (11-15). These studies have shown that porosity generally increases with increasing floc size and the results are consistent with a simple power-law relationship: 1 --e

=

structures can be scaled in terms of a fixed fractal dimension (10, 12). The fractal dimension d corresponding to Eq. [ 1] would be equal to 3 - ~. Strictly, for Eq. [ 1] to be valid under all conditions, the characteristic size xc should be equal to the size of the primary particles, for which E = 0. However, extrapolation of these relationships to an agglomerate containing only one primary particle show that experimental values are often significantly larger (16, 17), indicating that the relationship applies over a limited range of sizes. Unfortunately, many of the earlier measurements were performed on ill-defined and poorly characterized systems (precipitated metal hydroxides, for example) so that direct comparisons are difficult, if not impossible, to make and very little information is available on the effects of system variables on floc structure. The purpose of the work described in this paper was to evaluate floc densities in wellcharacterized suspensions flocculated under controlled conditions.

[1 l EXPERIMENTAL

where ~ is the porosity of an agglomerate of diameter x, xc is a characteristic floc size, and a is a constant (typically around unity). Several recent authors have pointed out that floc

Investigations of floc density were carried out on pure quartz, ground and air classified to give a fairly narrow particle size distribution in the 2- to 10-#m range. The flocculant

121 0021-9797/86 $3.00 Journal of Colloid and Interface Science, Vol. 113, No. 1, September 1986

Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.

122

KLIMPEL AND HOGG

form given by Eq. [ 1] is approximately valid over a limited range of floc sizes but the relationship "levels off" at small and large sizes. The experimental observations of this study were fitted to the following empirical expression: log(1 - El) l°g(1-e)=l+ (~ggl-X [2]

used was a nonionic polyacrylamide (less than 1% hydrolysis) of very high molecular weight (about 13 million). A "standard tank configuration" mixing unit described by Holland and Chapman (18), and applied to flocculation by Keys and Hogg (19, 20) was used to conduct the flocculation tests. Immediately upon conclusion of flocculation a sample of the suspension was placed into a settling tank. Photographic techniques were then used to make direct measurements of the size and settling velocity of individual flocs. These techniques and flocculation procedures have been described in detail elsewhere (16, 20). Floc densities were calculated using standard expressions (22) for free settling under the appropriate flow conditions. The measurement techniques have been evaluated statistically to establish the associated experimental error and reproducibility of the data (16,21).

where el is the limiting porosity for large flocs, Xg is a characteristic floc size, and X is a constant. This particular functional form was chosen for its ability to describe the general form of the data with appropriate limiting conditions. The solid line shown in Fig. 1 was obtained from a "best fit" of the data to this expression. Equation [2] was also used to test for statistical differences between sets of data using a parametric test procedure which allows 95% confidence regions to be placed on the optimal parameter values (23, 24). These confidence intervals were obtained by imposing stepwise changes (_+5, _+15, _+30%) in the value of one parameter and computing revised estimates of other parameters. The residual sum

RESULTS

Observed floc density-size relationships consistently have the general form illustrated in Fig. 1. It is clear that the simple power-law

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FIG. 1. Floc density/size relationships for 2 × 10-/zm quartz particles (x0 = 3.4 tzm) flocculated with various concentrations of nonionic polymer from suspensions containing 3% solids by weight, subjected to a mean shear rate G of 1031 s-t. Journal of Colloid and InterfaceScience, V oL 113, No. 1, September 1986

AGGLOMERATE

of squares (SSQ) corresponding to each stepwise change was compared to the original sum of squares and a standard F-test was employed to estimate the 95% confidence interval for each parameter. A detailed description of this parametric sensitivity procedure has been given elsewhere ( 16, 21). The effects of floceulation variables such as agitation intensity, polymer concentration, mixing time, original particle size, and solids concentration on resultant floc structures were investigated. This was accomplished by setting up a series of controlled changes in one variable while holding all remaining system variables constant in order to eliminate complexities due to interactions of more than one change in the system. The parametric sensitivity analysis was applied to each set of data. Differences between the parameter values obtained under different conditions were judged to be statistically significant only if there was no overlap of the 95% confidence intervals.

i. Polymer Concentration Density measurements were performed on flocs formed using various polymer concentrations ranging from 0.35 to approximately 6.00 ppm. Figure 1 illustrates the floc porositysize relationships as a function of polymer concentration. Statistical analysis of the data from each test indicated that there were no significant differences in the optimal parameter values over the range of polymer concentrations tested, for this specific mineral/polymer system. Table Ia gives the optimum parameter values along with the associated 95% confidence intervals for each test. It should be emphasized that the results presented here simply indicate that, for flocs of a given size, porosity is essentially independent of polymer dosage. The addition of polymer does, however, have a significant effect on floc growth with increased dosage generally leading to larger flocs (25, 26). Consequently, the average floc density may be expected to decrease with increased dosage due to an increase in the average floc size.

STRUCTURE

123

ii. Agitation Intensity The effect of agitation on floc structure was studied using four different impeller speeds: 500, 1000, 1500, and 2000 rpm, corresponding to mean shear rates G of 356, 1031, 1895, and 2917 s-X, respectively. Figure 2 illustrates the floc porosity-size relationships obtained as a function of impeller speed, and Table Ib summarizes the optimization results for each data set. From parametric sensitivity analysis, statistically significant differences between relationships were observed. For example, comparison of the optimal parameter values obtained at impeller speeds of 500 and 2000 rpm shows no overlap of the 95% confidence regions for any of the parameters. These differences are reflected by the data in Fig. 2 from which it can be seen that while the number of large flocs decreased with increased impeller speed, those flocs which did survive were typically less porous. This observation is in direct agreement with the concept of "mechanical syneresis," described by Yusa (27, 28) as the shrinkage and densification of loose bulky flocs by compaction and fluid shear.

iii. Excess Mixing Time The standard flocculation tests generally were performed utilizing a standard mixing time of 1 min. During this one minute the polymer was added continuously at a constant rate to give the final polymer concentration desired. In this series of tests the time of mixing was increased by specific intervals after conclusion of polymer addition. Three excess mixing times of 20, 40, and 60 s were used. As may be expected (25, 26), a decrease in maximum floc size with increased time of excess mixing was observed. This is roughly illustrated in Fig. 3 which shows data from each excess time interval tested. Although there is scatter in the data, it appears that the flocs become more compact as mixing time increases. Parametric sensitivity analysis revealed that there are statistically significant differences between relationships reflected primarily in the 95% confidence regions on Journal of Colloid and Interface Science, Vol. 113, No. 1, September 1986

124

KLIMPEL AND HOC~ TABLE I Effect of System Conditions on Floc Structure: Optimization Results (a) Polymerconcentration

Polymer concentration (ppm)

x, Numberof data points

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0.35 1.17 2.33 5.82 Combined

38 40 33 44 155

46.0-64.2 38.0-82.2 49.2-89.1 46.2-110.9 47.3-83.2

54.3 53.4 63.4 61.6 60.5

1.08-1.47 0.95-1.45 1.00-1.50 0.91-1.50 0.99-1.40

1.23 1.18 1.24 1.19 1.19

0.0283-0.0394 0.0162-0.0433 0.0143-0.0340 0.0079-0.0398 0.0166-0.0351

0.0338 0.0290 0.0244 0.0258 0.0264

0.96 1.34 1.49 1.53 1.28

0.0083-0.0268 0.0230-0.0408 0.0484-0.0612 0.0569-0.0706 0.0221-0.0513

0.0229 0.0329 0.0543 0.0630 0.0375

1.34 1.56 1.50 2.95 1.40

0.0230-0.0408 0.0365-0.0457 0.0439-0.0543 0.0676-0.0938 0.0132-0.0525

0.0329 0.0409 0.0488 0.0800 0.0394

1.09 0.99 1.26 1.27 1.06 1.01

0.0011-0.0219 0.0183-0.0230 0.0373-0.0446 0.0403-0.0494 0.0331-0.0432 0.0014-0.0437

0.0190 0.0205 0.04t5 0.0444 0.0377 0.0223

1,34 0,88 1,15 1,15

0.0230-0.0409 0.0039-0.0319 0.0204-0.0538 0.0100-0.0479

0.0329 0.0145 0.0384 0.0337

(b) Agitationintensity Impellerspeed (tom) 500 1000 1500 2000 Combined

56 62 50 57 225

42.2-109.6 39.5-61.0 35.5-45.6 31.0-38.5 36.3-70.0

58.2 47.4 40.6 34.6 47.3

0.68-1.29 1.10-1.61 1.30-1.72 1.36-1.78 1.02-1.60

(c) Excessmixingtime Excessmixing time (s) 0 20 40 60 Combined

62 82 65 51 260

39.5-61.0 46.2-60.0 46.1-55.6 37.9-48.1 42.7-93.3

47.4 53.2 50.5 42.8 54.4

1.10-1.61 1.35-1.82 1.34-1.69 1.28-3.90 1.13-2.07

(d) Solidparticle size Particle size fraction I II III IV V Combined

36 68 61 59 47 271

144-794 131-251 128-172 193-237 209-277 126-1586

188 178 150 214 240 244

0.48-1.77 0.90-1.11 1.11-1.42 1.13-1.42 0.92-1.22 0.62-1.60

(e) Solidsconcentration Weightpercentage solids

3 5 10 Combined

62 62 63 187

39.5-61.0 70.0-224 50.9-110 39.8-132

47.2 110 68.4 57.8

Journal of Colloid and Interface Science, Vol. 113,No. 1, September1986

1.10-1.61 0.68-1.21 0.86-1.49 0.75-1.77

AGGLOMERATE STRUCTURE 1.0

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n a r r o w size d i s t r i b u t i o n s s h o w n in Fig. 4, referred to as size fractions I t h r o u g h V f r o m finest to coarsest. T h e c o r r e s p o n d i n g floc d e n sity/size relationships are shown in Fig. 5, f r o m which it can be seen t h a t floc p o r o s i t y at a given size generally decreases with increasing p r i m a r y p a n i c l e size.

p a r a m e t e r el as shown in T a b l e Ic. A n u n u s u ally high value o f X was also o b s e r v e d for the 60-s excess m i x i n g t i m e test.

iv. Primary Particle Size A p u r e q u a r t z s a m p l e was classified using a D o n a l d s o n A c u c u t A i r Classifier into the five

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FIG. 3. Floc density/size relationships as a function of excess mixing time for 2 × 1 0 - # m quartz particles (xo = 3.4 ~zm)flocculated with 0.9 ppm of a nonionic polymer from suspensions containing 3% sofids by weight, subjected to a mean shear rate G of 1031 s-1. Journal of Colloid and Interface Science, Vol. 113, No, 1, September 1986

126

KLIMPEL AND HOGG

simulation studies (1-10), for example, give predicted densities which depend only on the number of primary particles in the floc. At a given porosity, the number of primary particles per floc is determined entirely by the size of the floc relative to that of the primary particles. The relationship between porosity and relative floc size might therefore be expected to be independent of the size of the primary particles. Consequently, replotting the data in Fig. 5 with respect to the relative rather than the absolute floc size should reduce all of the points to a single curve. In fact, this was found to overcompensate for the differences in the original relationships so that flocs formed from fine particles appeared to be less porous than those containing larger particles. In other words, a floc grown from small particles is denser than one continuing the same number of larger particles. It therefore appears that the density or porosity of a floc is not solely dependent on the number of particles which it contains. This may reflect complex interactions between system turbulence, binding forces between particles, and possible differences in the extent to which the flocs can be compacted.

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The observed decrease in floc porosity with increasing solid particle size may be expected due to differences in the number of particles contained by a floc of a given size. The floc

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FIG. 5. Floc density/size relationships as a function of primary particle size distribution for quartz particles flocculated with 0.9 ppm of a nonionic polymer from suspensions containing 3% solids by weight, subjected to a mean shear rate G of 1031 s-I. Journal of Colloidand InterfaceScience,Vol. 113, No. 1, September 1986

127

AGGLOMERATE STRUCTURE

v. Solids Concentration

The concentration of solids in a colloidal suspension directly determines the frequency of interparticle collisions in a system subjected to constant agitation. The effect of solids concentration on floc structure was investigated by varying the weight percentage of solids in suspension at values 3, 5, and 10%. The results seem to indicate a decrease in floc porosity with increased weight percentage of solids as illustrated in Fig. 6. However, considerable scatter in the measurements, especially at large floc sizes, led to somewhat inconclusive results from the parametric sensitivity analysis. The curve fitting results are summarized in Table Ie, and show the extremely broad 95% parameter confidence regions which were obtained. DISCUSSION

The relationships between floc porosity and size found throughout this study are consistent with a multistage growth model in which primary particles aggregate to form microflocs which, in turn, combine to form larger flocs. Similar models have been proposed by other workers (1, 3, 10, 12, 29) and, in fact, follow

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directly from the nature of flocculation as a random collision process. The addition of primary particles to a large floc causes almost imperceptible growth whereas very significant growth results from the association of two large flocs. In real systems, the process is further complicated by stresses resulting from agitation of the suspension. These can lead to compaction and breakage of the flocs. The porosity-size relationships can conveniently be split into three regions corresponding to small, intermediate, and large size flocs, referred to as Regions I, II, and III, respectively. These three regions of floc size and hence porosity or density are illustrated for a typical set of data in Fig. 7. Region I contains the small, low-porosity flocs (microtlocs) which exhibit porosities similar to those which would result from efficient solid packing. These small compact flocs may then act as the basic unit for the subsequent growth of larger flocs. The density/ size relationship in Region II can obviously be approximated by the power-law form given in Eq. [ 1] and is consistent with the theoretical treatments based on random collision processes (1-10). Recent computer simulations

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128

KLIMPEL AND HOCK] 1.0

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of random floc growth (10) have indicated an expected fractal dimensionality of about 1.75. A very similar value has been reported (12) from experimental measurements on colloidal gold particles following Brownian coagulation. The power-law slopes (a) obtained for the Region II flocs in the present study range from about 0.9 to about 1.3 and correspond to fractal dimensions between 1.7 and 2.1. It appears, therefore, that the flocs in Region II are formed, for the most part, by random aggregation of the dense microflocs of Region I. The transition from Region I to Region II probably reflects a change in the response of a floc to turbulence in the agitated suspension. Thomas (30) and others (31, 32) have pointed out that the stresses acting on a floc will result primarily from turbulent eddies of size comparable to that of the floc. For small flocs (in Region I) the stresses will generally be low but may contribute to compaction. The larger flocs, in Region II, will be subjected to higher stresses leading more to breakage than to compaction. The flocs in Region II may also be formed as a result of breakage of larger flocs. In this case, the porosity might have been expected to be approximately the same as that of the larger floc prior to breakage. However, Journal of Colloid and Interface Science, VoL 113, No. 1, September 1986

the results show that smaller flocs are generally less porous. This may be due to a combination of compaction of the fragmented floc due to fluid shear and preferential breakage of a large floc at points of contact between the smaller, denser flocs contained. The large highly porous agglomerates of Region III are those which are most likely to be affected by the prior history of growth. The porosity may depend on the number of small flocs contained, the densities and sizes of these smaller floes, and the degree of compaction and breakage which has occurred. Due to a wide variety of ways in which a large floc may be formed, an increased amount of scatter with increasing size should be expected, and is demonstrated by the data. In an agitated suspension, flocs are subject to continuous breakage and reformation. For large flocs, with a wide range of densities, it might be expected that those with the lowest density would break preferentially so that it is generally the denser, and presumably stronger floes which survive. This kind of selective breakage could be responsible for the leveling-off of the porositysize relationships at large sizes. Based on the concept of floc growth through random addition of microflocs rather than in-

129

AGGLOMERATE STRUCTURE

dividual solid particles, normalization by the size of the primary panicles, as attempted earlier, may only be appropriate during the brief initial period of microfloc formation. After this initial growth stage, it is the microflocs which act as the basic unit for continuing growth. Consequently, the floc density-size relationships are probably determined more by the distribution of microfloc sizes and densities than by the primary panicle size. Since the size-density relationships shown in Fig. 5 are roughly parallel, it is clear that normalization is possible with respect to some arbitrary microfloc size and/or density. An example, based on microfloc size, is given in Fig. 8, which was obtained by determining, by trial and error, a characteristic microfloc size for each of the five sets of data shown in Fig. 5. For convenience, the microfloc size was arbitrarily chosen as the size corresponding to a porosity of 0.3 on the normalized composite curve. The values range from about 20 to 40 ~tm for the materials studied here. The corresponding numbers of primary panicles contained in these microflocs would range from about 30 for the coarsest material (size fraction V) to about 3000 for the finest (fraction I).

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Empirically, the apparent microfloc size increases with about the one-third power of the primary panicle size. An alternative normalization procedure, based on microfloc density, leads to very similar results and a similar relationship between microfloc density and primary panicle size. It is important to recognize that these microflocs are not unique, well-defined entities. The concept of a specific microfloc size is useful only as a means of representing the formation of large flocs from random associations of smaller, densified agglomerates whose size and density probably both decrease with decreasing primary particle size. The degree of compaction which can occur in a microfloc may depend on the number of primary partides contained in it. A small number of coarse particles, e.g., size fraction V, would be more easily compacted by rearrangement under stress than a large number of fine particles, as in size fraction I. The data presented in Fig. 6 suggest that the limiting porosity E1may be related to solids concentration in the suspension. Obviously, the average floc density must be limited by the solids concentration (unless gel formation leads to expansion of the whole system). Thus the maximum value that the average floc porosity could attain is

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where ~ is the volume fraction of solids in the suspension. It is possible, however, for individual flocs to have porosity greater than Emax since the development of structure could lead to lower packing densities than those in the dispersed state. A simple analogy is the formation of ice (structured) from liquid water ("dispersed"). On the other hand, as flocs grow and the average porosity approaches Emax,the flocs cease to act as independent entities and are in more-or-less permanent contact with one another. The concept of individual flocs is no longer meaningful and the suspension resembles a continuous network whose density varies about the mean value. Journal of Colloid and Interface Science, V o l .

113, N o . 1, S e p t e m b e r

1986

130

KLIMPEL AND HOGG CONCLUSIONS

As a result of the work described in this paper, the following conclusions can be made with regard to the structure of agglomerates in focculated suspensions:

ferred to as microflocs, rather than of primary particles, provides an explanation for the observed floc density-size relationships of this study. ACKNOWLEDGMENT

1. Floc density decreases (porosity increases) with increasing f o c size with an apparent leveling off of floc densities at small and large sizes. 2. Density determinations performed on flocs produced under a variety of system conditions all yield similar density-size relationships. However, statistically significant differences between relationships were detected. These differences were primarily reflected at large floc sizes. More specifically: (i) The effect of polymer dosage on floc porosity was found to be insignificant for the specific solid/polymer system investigated. It should be noted here that preliminary studies of the effect of flocculant type on floc structure have also shown an insignificant effect. However, since floc size is strongly affected by polymer type and dosage, the average floc density m a y be a function of these variables. (ii) The densities of large flocs generally increase slightly with excessive mixing beyond polymer addition and with high shear rates. However, this is accompanied by a significant decrease in the m a x i m u m floc size. (iii) Floc density generally appears to increase with increasing solids concentration, although this could not be demonstrated conclusively by statistical analysis due to the large a m o u n t of scatter in the data. (iv) As expected, differences in primary solid particle size demonstrate the most significant changes between density-size relationships and, for any given floc size, floc density increases with increasing initial particle size. It was also concluded that the variations in floc structure could not be explained entirely by differences in the n u m b e r of primary particles contained by the floc. 3. The concept of floe growth through rand o m addition of small dense agglomerates, reJournal of Colloid and Interface Science, Vol. 113, No. 1, September 1986

The research described in this paper was supported by the National Science Foundation under Grant CPE8121731.

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