Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling

A. Amirtharajah and S. C. Jones

Abstract

This paper is a summary of research on the role of mixing in the coagulation process. In particular, the optimal rapid mix G value and detention time were determined for coagulation using an organic, cationic polyelectrolyte. The optimal G value was in agreement with previous studies, but the optimal detention time was in seconds instead of several minutes. Studies on the use of static mixers are also summarized. Comparing the static mixer to a jar test for enhanced coagulation studies showed that the type of mixer is important in determining optimal coagulant doses for TOC removal. This conclusion has important implications for water treatment plants practicing enhanced coagulation. A computational fluid dynamics model of static mixers is also introduced that can provide detailed, quantitative information on the fluid flow and chemical dispersion in static mixers.

1. Introduction

Coagulation is the physicochemical alteration of the characteristics of turbidity, producing particles so that they can be subsequently removed. Coagulation oc­cupies a central role in the production of potable water - it is required for the success of sedimentation, filtration, and disinfection. Because coagulation involves adding a small volume of coagulant to a large volume of water (ratios of 1 : 50000 are typical [1]), the rapid (initial) mixing of coagulants has long been considered important in the design of water treatment facilities. Despite a fair amount of research on mixing and coagulation, there is little fundamental understanding of rapid mixing.

Amirtharajah and Mills [2] found that high intensities of mixing resulted in an improved settled water turbidity when coagulation was via charge neutraliza­tion. When sweep coagulation was the dominant mechanism, no effect of mixing intensity was observed. These results were explained on the basis of the kinet­ics of the reactions associated with each mechanism. The destabilizing species in charge neutralization are short lived and must be distributed throughout the flow quickly. In contrast, the voluminous aluminum hydroxide precipitate, result­ing from supersaturation, is the destabilizing species in sweep coagulation. This

H. H. Hahn et al. (eds.), Chemical Water and Wastewater Treatment IV© Springer-Verlag Berlin Heidelberg 1996

4 A. Amirtharajah and S. C. Jones

voluminous precipitate is the end product of the reactions and has a relatively long life span; therefore, quick and intense mixing should not be important. It is worth emphasizing that it is very important to consider both particle charge and particle number concentration when the mechanics of mixing is analyzed. 1\vo experimen­tal studies, one using polymers, the other with static mixers, are described in the following sections. The common theme of this paper is to evaluate the results of mixing studies in light of the mechanisms of coagulation.

2. Rapid Mixing of Polymers

When using organic polymers for coagulation, the mechanisms of coagulation are charge neutralization and polymer bridging [3]. Because the destabilizing species are not a product of fast hydrolysis reactions, high intensities of mixing should not be necessary. The potential for floc break-up and polymer scission [4], especially when polymer bridging is involved, should limit the optimal mixing intensity. Over the past two decades, several groups of researchers have attempted to deter­mine the optimal rapid mix parameters (i. e., the mean velocity gradient termed G value and detention time) when using organic polymers in coagulation. Although no consensus exists, optimal G values between 250 and 1000 s-1 have been suggested [5], where the optimal G value sometimes depends on the molecular weight of the polymer [6]. However, Leu and Ghosh [7] observed floc break-up at G values greater than 350 S-I. Detention times as low as 30 s [8] and as high as 8 minutes for a combined rapid mix-flocculation step have been suggested [9]. Nouvel and Amirtharajah [1993] determined optimal rapid mix parameters for an organic polymer used alone for coagUlation in a direct filtration scheme.

2.1 Methods and Materials

Nouvel and Amirtharajah [5] used a synthetic water made to three different tur­bidities (10-15 NTU, 30-35 NTU, and 45-50 NTU) using bentonite clay. Humic substances were added to the synthetic water from a solution concentrated from the Suwannee River in Georgia. The synthetic water was made to have a total organic carbon concentration (TOC) of 2.1 mg elL. The polymer used was Cat­Floc TL, a cationic polyelectrolyte with a molecular weight between 10" and UP atomic mass units (amu). A standard jar filtration procedure was used [10]. Rapid mixing occurred in an 8 L square, acrylic jar with a Cole-Palmer mixer. Slow mixing (flocculation) occurred in the standard Phipps and Bird six-station stirrer with 1 L square jars. 1\vo-stage tapered flocculation was used with G values of 60 and 40 s -1 and 8 minutes of total detention time. To simulate direct filtration, the flocculated water was filtered through a filter paper (Whatman No.1) and a 2-inch (51 mm) inner diameter column with 18 inches (457 mm) of anthracite coal.

Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling 5

2.2 Polymer Dose

By determining the optimal polymer dose for different suspensions, insight into the mechanisms of coagulation can be gained. Figure 1 shows filtered water turbidity (through Whatman No.1) versus different polymer doses from 0.5 to 6 mglL. The optimal dose of CatFloc TL was observed to be 4-5 mg/L. As Figure 1 shows, a stoichiometric relationship did not exist between the required dose and the concentration of particles in the suspension; thus, polymer bridging likely occurred. It needs to be emphasized that the TOC added was constant, and hence, higher doses of coagulant may have been necessary to create an adequate number of fiocs. In the 10-15 NTU suspension at a polymer dose of 4 mg/L, the zeta potential of the destabilized particles was -5.6 mV compared to -14 mV for the original, stable particles; thus, charge neutralization also occurred.

Raw Water Turbidity (NTUI

• 10-15 • 30-35

.. 45-50

23456 CatFloc TL Dose (mg/LI

2.3 G-value and Detention Time

Fig.I. Determination of the optimal polymer dosage for synthetic waters of various turbidity

In Figure 2, the detention time versus the filtered water turbidity is shown for the 30-35 NTU suspension using a CatFloc TL dose of 4.0 mglL. The two curves represent two different batches of synthetic water which were difficult to dupli­cate exactly. However, the general conclusion was consistent between batches. A minimum filtered water turbidity occurred at approximately 5 s. No additional benefit was gained from detention times greater than 5 s. The G value used for these tests was 274 S-I. Similar results were obtained for all suspensions tested and both types of filtration. The optimal detention time for mixing the suspensions tested was 5-10 s. These results were also confirmed in a pilot plant study, and the parameters were used for· the design of a large water treatment plant [50 million gallons per day (190 MUd)] which is currently under construction.

In Figure 3, the filtered water turbidity (anthracite coal filter) versus G value is shown for the 30-35 NTU suspension. The minimum filtered water turbidity occurred for G values between 400 and 600 S-I. The detention time was 5 s and the dose was 4 mglL. The optimal G values found in this study to agree, in general,

6

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A. Amirtharajah and S. C. Jones

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05 0 20 40 60 80 100

Detention Time (sl

0.30

0.25

0.20

0.15

0.10

0.05

0.00 200 400 600 800

G value (s"1

120

1000

Synthetic raw weter

Turbidity - 30·35 NTU

TOC - 2.1 mg CIl

CatFIoc Tl doH - 4.0 mgll -1

G value - 274 a

Fig.2. Detennination of the optimal rapid mix detention time for the synthetic water with turbidity of 30--35 NTU

Synthetic raw weter Turbidity = 30-35 NTU TOC = 2.1 mg CIl

CetFIoc Tl dOH - 4.0 mgll Detention time - 5 •

Fig. 3. Detennination of the optimal G value for the synthetic water with turbidity 30--35 NTU

with previous studies [7], but the optimal detention time is significantly smaller. However, previous studies focused on detention times of 1 minute and greater; apparently, detention times of 10 s or less were not studied. The upper limit on G value is likely due to polymer bridging being one of the dominant coagulation mechanisms. The detention time may be limited by floc break-up, which is a time dependent process [11].

2.4 ImpeDer Geometry

In a follow-up study to [5], Miller [12] studied the effect of impeller geometry for rapid mixing with CatFloc 1L. The studies described in [5] were duplicated except that three different impellers were used: a Rushton turbine, an axial fluid foil, and a marine propeller. For a description of these and other common impellers, refer to Oldshue and Trussell [13]. The optimal G values and detention times concurred with those found previously [5]. Miller [12] simulated both direct filtration with Whatman No. 40 filter paper and conventional treatment by settling for 16 minutes. Based on settled water turbidities, the axial fluid foil impeller performed the best

Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling 7

and the marine impeller the worst. However, filtered water turbidity showed no effect of impeller geometry. Laser doppler velocimetry measurements indicated that the axial fluid foil impeller had a lower turbulence intensity [12]; therefore, it may have been less likely to cause floc break-up. Daughter floes (those resulting from floc break-up) may have been large enough to filter but not settle.

2.5 Summary of Results with Polymers

For relatively turbid suspensions (by direct filtration standards), CatFloc 'fL, a medium molecular weight cationic polyelectrolyte, destabilizes clay particles by both charge neutralization and polymer bridging for the suspensions studied. For these suspensions, the optimal rapid mix parameters for backmix reactors were G values of 400-600 S-1 and detention times of 5-10 s. The axial fluid foil impeller may prevent floc break-up, but the effect does not appear to be significant for direct filtration.

3. Static Mixers

Static mixers consist of stationary mixing elements mounted end-to-end along the direction of flow inside a pipe. Compared to a pipe without mixing elements (called an empty pipe), the static mixer causes an increase in turbulent mixing at the expense of increased head loss. This increase in mixing and head loss depends on the number and geometry of the mixing elements. Several geometries of elements are currently available: (a) an array of tabs that protrude into the flow, (b) corrugated metal sheets oriented at 90° to each other, and (c) counter-rotating helices also oriented at 90°. Pahl and Muschelknautz [14] compiled examples of mixer geometries, which represent several of the competing geometries available today.

A primary advantage of a static mixer is that it has no moving parts, and, thus, it is easy to maintain and inexpensive to operate. Further, since it occupies the same volume as a pipe, it requires no additional space, unlike a backmix reactor. This advantage makes the static mixer ideally suited for retrofitting existing facilities. However, before the static mixer can be recommended for a wide variety of water treatment installations, a rational design approach is needed that explicitly considers the coagulation reactions in such a mixing device.

3.1 Current Design Approach

One of the current design criteria for static mixers, as suggested by mixer suppliers, is that the variation coefficient should be 0.05 [15], The variation coefficient is the standard deviation divided by the mean of the instantaneous concentration of an inert tracer measured at some location downstream of the mixer. In most coagulation applications, 2-4 elements are required to achieve this level of bulk

8 A. Amirtharajah and S. C. Jones

mixing. Kawamura [1] recommends that the head loss in static mixers should not exceed 2 feet (0.6 m). For a given range of flow rates, the mixer supplier must be consulted to determine the expected head losses. Recent research has shown that such simple design criteria may not be adequate when mixing for competitive, consecutive chemical reactions where micromixing, i. e., molecular mixing, can affect the product distribution. Clark [16] suggested that aluminum hydrolysis and precipitation may consist of competitive, consecutive reactions; therefore, it is possible that this research may apply to rapid mixing for coagulation.

3.2 Micromixing in Static Mixers

Bourne et al. [17] compared two Sulzer static mixers (the SMV-4 and SMXL) for a competitive, consecutive reaction that was specifically developed to investigate micromixing in reactors [18]. Their results demonstrated that the mixer with the greatest head loss (the greatest G value) did not give the best mixing. Their research is described in the following. The head loss (.ap) in Pa across the mixer can be described as a function of the Newton number (Ne):

L ap = (Ne)eu2"d

where L is the mixer length in m, e is the fluid density in kglm3, d is the pipe diameter in m, and u is the superficial velocity in mls. The total energy dissipation (g» in W/kg is

g>= Qap , eVM

where VM is the liquid volume in m3 and Q is the flow rate in m3/s. The total dissipation consists of direct dissipation, due to mean velocity gradients near solid surfaces, and turbulent dissipation (c). Based on a micromixing model for this reaction, the mixing rate (or engulfment rate) depends on c. An efficient mixer for this type of reaction would have a high to c/g> ratio. In their experiments, g> was determined from measured head loss, and c was calculated from the micromixing model based on measured product distributions [17].

The SMV-4, with a Ne of 2.4, was originally designed for turbulent flow. The SMXL, with a Ne of 1.2, was designed for laminar flow. Therefore, one could naively expect the SMV -4 to perform better given that it will have a greater head loss at a given flow rate. However, in their experiments, the SMV-4 had a cliP of 32%; while the SMXL had a c/g> of 67%. Furthermore, the SMXL had a greater absolute c than the SMV -4. Based on these results, Bourne et al. [17] recommended that mixing elements which occupy only a small portion of the total pipe volume are likely to be preferred for reactions where micromixing is important. In addition, these experiments indicated that the reaction took place in a fraction of the total mixer length. Therefore, the location of chemical injection is also likely to be important.

Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling 9

3.3 Bench-Scale Coagulation Experiments

3.3.1 Suspension with No Organics (TOC = 0 mgCIL). Schulgen [19] con­ducted semi-batch tests using a Komax motionless mixer of 0.5-inch (12.5 mm) inner diameter and 8 mixing elements. A synthetic water similar to that used in the polymer experiments [5], with no organic matter added and an initial turbidity of 13 NTU, was tested. Direct filtration was simulated using a 2 inch (51 mm) inner diameter glass column with 18 inches (457 mm) of anthracite coal. Con­ventional treatment was simulated by measuring turbidity after 20 and 35 minutes of settling. Results are shown in Figure 4 where filtered water turbidity is plotted against flow rate for five different chemical conditions, i. e., alum dose and pH. The alum doses of 20 mgIL likely represent sweep coagulation with the pH of 7.1 being optimum and the pH of 6.2 SUb-optimum. Optimal chemical conditions were chosen based on standard jar tests with different alum doses and plotting these results on the alum coagulation diagram [2].

The lower three alum doses likely represent charge neutralization with the dose of 12.5 mgIL being optimum and the dose of 5 mg/L sub-optimum. Zeta potential measurements, given in the legend of Figure 4, indicate that these mechanistic explanations are probable. The solid lines in Figure 4 represent a linear regres­sion through the data for each chemical condition. Although the data are widely scattered about the regression lines, they emphasize the general trend of turbidity with flow rate. For optimal chemical conditions, mixing had no effect on filtered water turbidity. However, for sub-optimal chemical conditions, either in pH or coagulant dose, higher mixing intensity was detrimental to filtered water turbidity. The trends shown in Figure 4 were also observed for settled water turbidity after 20 and 35 minutes.

3.3.2 Particles with Organics (TOC = 4.0 mg CIL). In a companion study, Burke [20], with the same experimental apparatus, added approximately 4.0 mgCIL to

1.5

1.2

0.9

0.6

0.3

0.0

Synthetic raw water Turbidity = 13 NTU Zeta potential - ·12.5 mV TOC - 0.0 RIg C/l added

~ ...

0 10 20 30 40 Flow Rate (mUs)

1" I I I I I I I I I I I I I I I I I I I

o 2000 4000 6000 8000 tStatic Mixer G value (s-',

Alum Dose Zeta Potential (mVI Symbol (mglll pH ~±(J

• • ... ... •

12.5 7.2 -4.1 ± 1.7 8.0 7.2 -7.6 ± 0.8 5.0 7.2 -10.4 ± 1.3

20.0 7.1 +8.9 ± 0.5 20.0 6.2 +9.1 ± 0.7

Fig.4. Performance of static mixer at differ­ent flow rates for five different chemical con­ditions. The synthetic raw water had no added TOC. tThe static mixer G value axis is approx­imate and for illustration only

10 A. Amirtharajah and S. C. Jones

the synthetic water while keeping the turbidity at 13 NTU. The organic carbon was obtained from the Suwannee River as mentioned previously. Conventional treatment was simulated by filtering the water after 30 minutes of settling. The static mixer was compared to an empty pipe at two different chemical conditions, i. e., alum doses of 50 mgIL and 30 mgIL both with pH 6.2. The 50 mglL is optimum, based on jar tests at different alum doses, and 30 mglL is sub-optimum.

Figure 5 shows the results for both mixers at both chemical conditions for TOC and turbidity removal. For sub-optimal chemical conditions (30 mglL) , an increase in mixing intensity was detrimental to both filtered water turbidity and TOC removal. Note that a detrimental response for TOC removal has an opposite slope to that for filtered water turbidity. Unlike the relatively flat response shown in Figure 4, in Figure 5 under optimal chemical conditions (50 mglL), an increase in mixing intensity was favorable to both filtered water turbidity and TOC removal. Figure 5 also compares the performance of the static mixer to the empty pipe. However, no consistent trend is observed.

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• •

static static

empty pipa empty pipe

50 30 50 30

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Fig. Sa, b. Perfonnance of static mixer and empty pipe at different flow rates for two different chemical conditions measured by (a) TOe re­moval and (b) filtered water turbidity. The syn­thetic raw water had a TOC of 4 mgC/L. tThe G value axes are approximate and for illustration only

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Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling 11

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Enhanced Coagulation Requirement

• Synthetic raw water

Turbidity - 13 NTU • TOC II 4.0 mil CIL

(b) • Jar t •• t

o •

•

o Static mixer a Empty pipe

20 40 60 80 100

Alum Dose (mg/l)

Fig. 6a, b. Detennination of alumn dose re­quired to meet enhanced coagulation require­ments (a) and turbidity requirements (b) us­ing static mixer, empty pipe and jar test for rapid mixing

3.3.3 Removal Efficiency with Jar Tests. A second important result of Burke's research [20] was that the static mixer and empty pipe performed better than the jar test for TOe removal at all alum doses tested. Figure 6a shows TOe removal against flow rate for the standard jar test, static mixer, and empty pipe. The points at 30 and 50 mgIL of alum for the two in-line mixers represent the mean of 13 and 6 experiments, respectively. Figure 6b, shown for completeness, compares the different bench-scale tests for turbidity removal. Figure 6a shows that the in-line mixers performed better than the jar test for all alum doses tested. The proposed DisinfectantlDisinfection By-Products rule of the US Environmental Protection Agency requires that conventional treatment plants practice enhanced coagulation if their source water has TOe greater than 2 mgIL. In enhanced coagulation, the standard jar test is used to determine coagulant doses for optimal TOe removal [21]. For the water used in these studies, a TOe removal of 45 % is required [21]. Figure 6a demonstrates that if a static mixer was used in the bench-scale tests, an alum dose of 25 mgIL would be required; whereas, the standard jar test indicates that a dose of 35 mgIL is required. The rapid mix G value for all jar tests was 110 S-I; whereas, the G value for the in-line mixers varied from approximately 200 to 6000 S-1 for the in-line mixers. However, this difference in G value may not explain the difference in performance, because the empty pipe performed about the same as the static mixer even though its G value was smaller by a factor of

12 A. Amirtharajah and S. C. Jones

ten. The types of mixing devices are very different. The jar test has significant back-mixing with a rapid mix detention time of 30 s while the in-line mixers have a short detention time of less than 2 s. Based on several studies of different types of mixers, Clark et al. [22] showed that backmix reactors can require significantly higher alum doses than in-line mixers. Based on these results, for jar tests to give comparable results to full-scale treatment facilities, the same type of mixer (in-line versus back-mix) should be used at both scales.

3.4 Summary of Static Mixer Results

A Komax static mixer was used in bench-scale coagulation experiments for a syn­thetic water both with and without organics. As expected, the water with organics required a higher alum dose (50 versus 12.5 mg/L) for comparable treatment. For both synthetic waters under sub-optimal chemical conditions, the turbidity removal and TOC removal decreased with increasing mixing intensity. A comparison of these in-line mixers with the standard jar test showed that the in-line mixers per­formed better for TOC removal. This result has important implications for water treatment facilities that use in-line mixers and must meet enhanced coagUlation requirements.

4. Computational Fluid Dynamics Modeling

4.1 Definition

Computational fluid dynamics (CFD) is a relatively new approach to fluid me­chanics research with several advantages over the traditional theoretical and ex­perimental approaches. In CFD, the governing equations of fluid mechanics (in case of turbulent mixing, the Reynolds Averaged Navier-Stokes (RANS) equa­tions) are solved using very few simplifying assumptions. Complex geometries can be modeled, and changes in design can be evaluated quickly and inexpen­sively. CFD has been developed primarily for the aerospace industry, but it is increasingly being used in other industries where fluid mechanics is important such as the automotive, electronics, chemical, and biomedical industries [23]. The following is a description of the ongoing research that uses CFD to model static mixers in water treatment. The goal is to provide detailed, quantitative information of the flow field and chemical dispersion both within and downstream of static mixers.

4.2 Governing Equations for Modeling Static Mixers

In a static mixer used for coagulation in a water treatment plant, the flow is incompressible and highly turbulent. To represent the instantaneous velocity U at any point in the flow field, it is decomposed into a mean and a fluctuating part:

Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling 13

u = u +u.

Using this definition, the nondimensional governing equations written in terms of mean velocity are the RANS equations:

v·u=o

au (- ) - 1 2-at + U: V U = - V15 + Re V U - (V . uu)

where t is time, V is the del operator, 15 is the mean pressure, Re is the Reynolds number, V 2 is the Laplacian, and uu are the Reynolds stresses. These equa­tions are unclosed, i. e., there are more unknowns than equations because of the Reynolds stresses uu. A turbulence model is required to solve these equations. The most widely used turbulence model is the k-c model of Jones and Launder [24]. In this model, two additional partial differential equations are solved: one for k, the turbulent kinetic energy, and the other for c, the turbulent energy dissipation. The Reynolds stresses uu are expressed in terms of k and c together with exper­imentally derived constants to close the RANS equations. The turbulence model provides an estimation of throughout the flow field. The micromixing models de­veloped by Bourne [17] and used to investigate chemical reactions in static mixers depend on c. Therefore, the output of the turbulence model can be directly used to make predictions about the efficiency of static mixers for fast competitive, consec­utive chemical reactions. However, the complex turbulent flows in static mixers may require a more complicated turbulence model with additional partial differen­tial equations. Mixing of coagulants in static mixers can also be modeled using an advection-diffusion equation combined with reaction terms. This approach results in additional closure terms which must be modeled [25].

4.3 Computational Methodology and Preliminary Results

The three dimensional RANS equations written for a typical static mixer geometry can require several hours to solve on today's fastest computers. Although com­mercial CFD codes are available, the approach taken in this research is to develop a new code specifically for this application to take advantage of state of the art computational methods [26, 27] that reduce the computational requirements. A de­tailed description of the computational methods used is given by Jones et al. [28]. In the development of this code, several test cases with analytical solutions are used to validate the code. An example is given in Figure 7 where the predicted velocity profile is shown for laminar, pressure-driven flow in a tube with a square cross-section. The predicted velocity profiles are in excellent agreement with the theoretical analytically-derived solution [29]. The code also successfully predicted the head loss in the tube. In this ongoing research, predictions for the fluid flow in a static mixer geometry should be available in 1997.

14 A. Amirtharajah and S. C. Jones

-- Exact solution 0 CFD prediction

1.0

)( III E

::> 0.5

::>

0.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0

y y y

Fig. 7. Comparison of a numerically predicted velocity profile to an analytical solution for pressure­driven flow in a tube with a square cross-section

5. Summary

This paper presents a summary of recent research to determine the appropriate G values and detention times when using organic polymers as the sole coagulant. The suggested G values agree with other research, but the optimal detention times for rapid mixing in a direct filtration mode were in seconds, much lower than previous studies had suggested. The paper also summarizes some recent research on the use of static mixers for coagulation for the removal of organics. However, no general conclusions can be drawn because of the complexity of the interaction between the hydrodynamics in a static mixer and the chemical reactions for coagulation. A computational fluid dynamics model was introduced that will provide a tool to study this interaction in future research.

Acknowledgments. This paper is a synthesis and summary of the research on mixing conducted by four graduate students at the Georgia Institute of Technology. Mark Nouvel, Dan Miller, Brad Schulgen, and Chris Burke have contributed significantly to our understanding of mixing with polymers and mixing in a static mixer. Their contributions are gratefully acknowledged.

References

[1] Kawamura, S.: Integrated Design of Water Treatment Facilities. John Wiley, New York 1991, pp.63,75

[2] Amirtharajah, A., Mills, K.M.: Rapid-mix Design for Mechanisms of Alum Coagulation. Journal AWWA 74 (4) (1982) 210

[3] Amirtharajah, A., O'Melia, C.R.: Coagulation Processes: Destabilization, Mixing, and Floccula­tion. In: Water Quality and Treatment, 4th edition, F. W. Pontius, (Ed.). McGraw-Hill, New York 1990, pp.269-365

[4] Horn, A. F., Merrill, B.W.: Midpoint Scission of Macromolecules in Dilute Solution in Turbulent Flow. Nature 312 (1984) 140,141

[5] Nouvel, M., Amirtharajah, A.: Rapid Mix of Organic Polymers in Direct Filtration. In: Proceedings AWWA Annual Conference, AWWA, Dallas, Texas 1993

[6] Stump, V.L., Novak, J.T.: Polyelectrolyte Selection for Direct Filtration. Journal AWWA 71 (1) (1979) 338

[7] Leu, R.J., Ghosh, M.M.: Polyelectrolyte Characteristics and Flocculation. Journal AWWA 80 (1) (1988) 159

Mixing for Coagulation: Organic Polymers, Static Mixers, and Modeling 15

[8] Keys, R.O., Hogg, R.: Mixing Problems in Polymer Flocculation. Water-1979 American Institute of Chemical Engineers Symposium Series 190 (75) (1978) 63

[9] Yeh, H.H., Ghosh, M.M.: Selecting Polymers for Direct Filtration. Journal AWWA 73 (1) (1981) 211

[10] Brink, D.R., Choi, S.I., AI-Ani, M., Hendricks, D.W.: Bench Scale Evaluation of Coagulants for Low Turbidity Water. Journal AWWA 80 (4) (1988) 199

[11] Amirtharajah, A., Tambo, N.: Mixing in Water Treatment. In: Mixing in Coagulation and Floc­culation, A. Amirtharajah, M.M. Clark, and R.R Trussell (Eds.). AWWA Research Foundation, Denver, Colorado 1991, pp.3-34

[12] Miller, D.C.: Comparison of Impellers for Rapid Mixing of Organic Polymer Coagulants. Un­published Masters Special Research Problem, Georgia Institute of Technology, Atlanta, Georgia 1992

[13] Oldshue, J.Y., Trussell, R.R.: Design of Impellers for Mixing. In: Mixing in Coagulation and Floc­culation, A. Amirtharajah, M. M. Clark, and R. R Trussell (Eds.). AWWA Research Foundation, Denver, Colorado 1991, pp. 309-342

[14] Pahl, M.E., Muschelknautz, E.: Static Mixers and Their Applications. International Chemical Engineering 22 (2) (1982) 197

[15] Mutsakis, M., Rader, R.: Static Mixers Bring Benefits to WaterlWastewater Operations. Wa­terlEngineering and Management 133 (11) (1986) 30

[16] Clark, M.M.: Scale-Up of Laboratory Flocculation Results. In: Proceedings AWWA Annual Con­ference, AWWA, Denver, Colorado 1986, pp.1239-1256

[17] Bourne, J.R., Lenzner, J., Petrozzi, S.: Micromixing in Static Mixers: An Experimental Study. Industrial Engineering Chemistry Research 31 (4) (1992) 1216

[18] Bourne, J.R., Maire, H.: Influence of the Kinetic Model on Simulating the Micromixing of 1-Naphthol and Diazotized Sulfanilic Acid. Industrial Engineering Chemistry Research 30 (6) (1991) 1385

[19] Schulgen, B.F.: Effectiveness of Static Mixers for Coagulation in Water Treatment. Unpublished Masters Thesis, Georgia Institute of Technology, Atlanta, Georgia 1995

[20] Burke, J.C.: Effectiveness of Static Mixers for Enhanced Coagulation. Unpublished Masters Spe­cial Research Problem, Georgia Institute of Technology, Atlanta, Georgia 1996

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[22] Clark, M.M., Srivastava, RM., Lang, 1.S., Trussell, R.R., McCollum, L.J., Bailey, D., Christie, J.D., Stolarik, G.: Selection and Design of Mixing Processes. AWWA Research Foundation, Denver, Colorado 1994

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Appiah Amirtharajah and S. Casey Jones School of Civil and Environmental Engineering Georgia Institute of Technology Atlanta, Georgia 30332 U.S.A.