Title: Physical aspects of mixing in coagulation control
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Title: Physical aspects of mixing in coagulation control
Physical Description: xvi, 232 leaves : ill. ; 28cm.
Language: English
Creator: Lai, Ruey Juen, 1945-
Copyright Date: 1975
 Subjects
Subject: Coagulation   ( lcsh )
Flocculation   ( lcsh )
Water treatment plants   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 173-175.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Ruey Juen Lai.
 Record Information
Bibliographic ID: UF00097529
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000161783
oclc - 02682695
notis - AAS8125

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PHYSICAL ASPECTS OF MIXING
IN COAGULATION CONTROL



By




RUEY JUEN LAI


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENTN
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY




UNIVERSITY OF FLORIDA


1975












ACKNOWLEDGMENTS


The author wishes to express his appreciation to his committee

chairman, Dr. J.E. Singley, for his assistance and guidance throughout

the course of this graduate research work. The author is most deeply

grateful for the learning experience derived from the association with

Professor H.E. Hudson, Jr., in Water and Air Research, Inc. His

inspirational enthusiasm and tireless assistance to a large degree

made this dissertation possible. Appreciation is extended to

Professor T. deS Furman, Dr. A.P. Black and Dr. H.E. Schweyer for

giving freely of their time and assistance.

The author is grateful to his parents for their support, either

spiritually or financially. The author also wishes to extend his

appreciation to his brother, Dr. Ron Juey-Rong Lai for his encouragement

throughout this research work.

To his wife, a special appreciation is extended for her understanding

and her time drawing all the figures in this dissertation.














TABLE OF CONTENTS


PAGE


ACKNOWLEDGMENTS ..............................................

LIST OF TABLES ...............................................

LIST OF FIGURES ..............................................

ABSTRACT .....................................................

CHAPTER

I INTRODUCTION .......................................

II LITERATURE REVIEW ..................................

Definitions .....................................

Theories of Destabilization .....................

Chemistry of Aqueous Aluminum ...................

Important Parameters in Particle Destabilization.

Transport of Colloidal Particles ................

Mixing--Theory and Application ..................

Coagulation Control in the Laboratory--
The Jar Test ....................................

Objectives ......................................

III EXPERIMENTAL MATERIALS AND METHODS .................

Chemical Preparations ...........................

Analytical Techniques ...........................

The Modified Jar Test Procedure ................


ii

v

vii

xiv



1

5

5

6

12

14

17

21


34

40

42

42

46

52







CHAPTER

IV


RESULTS AND DISCUSSION .............................

Velocity Gradient Calibration of Jar Test
Equipment ..................................... .

Floc Settling Characteristics Due to Different
Flow Pattern in Flocculation ....................

Effect of Rapid-Mix Time on Flocculation ........

The Effect of Total Gt Distribution on
Sedimentation ...................................


V SUAMARY AND CONCLUSIONS ............................

VI RECOMmENDATIONS ....................................

REFERENCES .. ...............................................

APPENDIX

A JAR TEST REPORTS ...................................

B SETTLING VELOCITY DISTRIBUTION CURVES ..............

C FIGURES OF EFFECT OF TIME OF FLOCCULATION ON
SEDIMENTATION ......................................

D FIGURES OF EFFECT OF G OF FLOCCULATION ON
SEDIMENTATION ......................................

BIOGRAPHICAL SKETCH ..........................................


PAGE

59


59


82

147


158

168

171


173



178

195


216


225

232













LIST OF TABLES


TABLE PAGE

1 Effect of Decreasing Size of Spheres ................. 2

2 Typical Chemical Analysis, Min-p-Sil 30 .............. 43

3 Impeller Characteristics ............................. 49

4 Comparison of G Value, All Models .................... 68

5 Jar Test Report of 200 ppm Silica with 35 ppm Alum
at g=25/sec .......................................... 86

6 Jar Test Report of 200 ppm Silica with 35 ppm Alum
at G=50/sec .......................................... 88

7 Jar Test Report of 200 ppm Silica with 35 ppm Alum
at G=75/sec ......................................... 90

8 Jar Test Report of 200 ppm Silica with 35 ppm Alum
at G=100/sec ......................................... 92

9 Jar Test Report of 20 ppm Silica with 35 ppm Alum
at G=25/sec ......................................... 120

10 Jar Test Report of 20 ppm Silica with 35 ppm Alum
at G=50/sec .......................................... 121

11 Jar Test Report of 20 ppm Silica with 35 ppm Alum
at G=75/sec .......................................... 123

12 Jar Test Report of 20 ppm Silica with 35 ppm Alum
at G=100/sec ........................................ 125

13 Jar Test Report of 20 ppm Silica with 70 ppm Alum
Using the P-B Paddle, Rapid-Mix Time Vary ............ 149

14 Jar Test Report of 20 ppm Silica with 70 ppm Alum
Using the Propeller, Rapid-Mix Time Vary ............. 155

15 Jar Test Report of 20 ppm Silica with 70 ppm Alum
Using the P-B Paddle, Total Gt=30,000 ................ 161







TABLE PAGE

16 Jar Test Report of 20 ppm Silica with 70 ppm Aliun
Using the Propeller, Total Gt=30,000 ................. 165

A-i Jar Test Report of 200 ppm Silica with 70' ppm Alum
at G=25/sec .......................................... 179

A-2 Jar Test Report of 200 ppm Silica with 70 ppm Alum
at G=50/sec .......................................... 180

A-3 Jar Test Report of 200 ppm Silica with 70 ppm Alum
at G=75/sec .......................................... 181

A-4 Jar Test Report of 200 ppm Silica with 70 ppm Alum
at G=100/sec ......................................... 182

A-5 Jar Test Report of 20 ppm Silica with 70 ppm Alum
at G=25/sec .......................................... 183

A-6 Jar Test Report of 20 ppm Silica with 70 ppm Alum
at G=50/sec .......................................... 184

A-7 Jar Test Report of 20 ppm Silica with 70 ppm Alum
at G=75/sec .......................................... 185

A-8 Jar Test Report of 20 ppm Silica with 70 ppm Alum
at G=100/sec ......................................... 186

A-9 Jar Test Report of 20 ppm Silica with 55 ppm Alum
Using the P-B Paddle, Rapid-Mix TimesVary ............ 187

A-10 Jar Test Report of 20 ppm Silica with 85 ppm Alum
Using the P-B Paddle, Rapid-Mix Times Vary ............ 189

A-ll Jar Test Report of 20 ppm Silica with 55 ppm Alum
Using the Propeller, Rapid-Mix Times Vary ............ 191

A-12 Jar Test Report of 20 ppm Silica with 85 ppm Alum
Using the Propeller, Rapid-Mix Times Vary ............ 193












LIST OF FIGURES


FIGURE PAGE

1 Potential Energy of Interaction of Colloidal
Particles ............................................ 8

2 Schematic Representation of the Bridging Model for
the Destabilization of Colloids by Polymers .......... 11

3 Al(III) Equilibria ................................... 13

4 (a) Flat-Blade Turbine. (b) Marine-Type Mixing
Propeller. (c) Pitched Paddle. (d) Typical Flow
Pattern in Baffled Tank with Turbine. (e) Typical
Flow Pattern in Baffled Tank with Propeller .......... 24

5 Characteristic Impeller Power Curves ................. 30

6 Schematic of a Prony Brake ........................... 38

7 Schematic of Cradled Dynamometer ..................... 38

8 Torque Measuring Set-Up .............................. 47

9 Sketches of Impellers Tested ......................... 50

10 Jar Test Apparatus ................................... 54

11 Velocity Gradients at Various Speeds, Series A ....... 60

12 Velocity Gradients at Various Speeds, Series B ....... 62

13 Configurations Used in Series C and D ................ 63

14 Speed Versus Velocity Gradient, Series of C and D .... 64

15 Calibration of Magnetic Stirring System, Series E
and F ............................................. 66

16 Summary of Relation Between Speed and Velocity
Gradient, All Series ................................. 67

17 Turbulent Drag Coefficients for Phipps-Bird Paddle
with and Without Baffles ............................. 69







FIGURE PAGE

18 Turbulent Drag Coefficients for Magnetic-Drive Jar
Testers .............................................. 70

19 Turbulent Drag Coefficients,for Various Impeller
Speeds ............................................... 71

20 Power Correlation for Phipps-Bird Paddle with and
without Baffles ...................................... 73

21 Power Correlation for Magnetic-Drive Jar Tester with
and without Baffles .................................. 74

22 Impeller Power Correlations .......................... 75

23 Floc Comparator for the Classification of Floc
Produced in Coagulation Tests ........................ 84

24 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=200 ppm, Alum=35 ppm, G=25/sec ...... 95

25 Settling Velocity Distribution Curve of Propeller
with Baffles. Silica=200 ppm, Alum=35 ppm, G=25/sec.. 96

26 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=200 ppm, Alum=35 ppm, G=50/sec ...... 97

27 Settling Velocity Distribution Curve of Propeller with
Baffles. Silica=200 ppm, Alum=35 ppm, G=50/sec ...... 98

28 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=200 ppm, Alum=35 ppm, G=75/sec ...... 99

29 Settling velocity Distribution Curve of Propeller with
Baffles. Silica=200 ppm, Alum=35 ppm, G=75/sec ...... 100

30 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=200 ppm, Alum=35 ppm, G=100/sec ..... 101

31 Settling Velocity Distribution Curve of Propeller with
Baffles. Silica=200 ppm, Alum=35 ppm, G=100/sec ..... 102

32 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=25/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ........... 103

33 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=50/sec,
Vs=3 crn/min. (Silica=200 ppm, Alum=35 ppm) ........... 104


vii









34 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=75/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ...........


35 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=100/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) .....


...... 106


36 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=10 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ........... 107

37 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=20 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ........... 108

38 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=30 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ........... 109

39 Comparison of Effect of G of Flocculation on -
Sedimentation at Constant t and Vs. t=40 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ........... 110

40 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=50 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) ........... 111


41 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=60 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=35 ppm) .....


..... 112


42 Photographic Comparison of the Floc Formed During
Flocculation. (Al by the Paddle, A2 by the Propeller). 115


43 Photographic Comparison of the Floc Formed During
Flocculation. (Bl, Cl and D1 by the Paddle, B2, C2
and D2 by the Propeller. Bl and B2 Have Long Baffles.
Cl and C2 Have Square Baffles. D1 and D2 Have
Rectangular Baffles.) ................................

44 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=20 ppm, Alum=35 ppm, G=25/sec .......


116


127


45 Settling Velocity Distribution Curve of Propeller with
Baffles. Silica=20 ppm, Alum=35 ppm, G=25/sec ....... 128


46 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=20 ppm, Alum=35 ppm, G=50/sec .......


129


47 Settling Velocity Distribution Curve of Propeller with
Baffles. Silica=20 ppm, Alum=35 ppm, G=50/sec ....... 130


105


FIGURE


PAGE










48 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=20 ppm, Alum=35 ppm, G=75/sec ....... 131

49 Settling Velocity Distribution Curve of Propeller with
Baffles. Silica=20 ppm, Alum=35 ppm, G=75/sec ....... 132

50 Settling Velocity Distribution Curve of Paddle with
Baffles. Silica=20 ppm, Alum=35 ppm, G=100/sec ...... 133

51 Settling Velocity Distribution Curve of Propeller with
Baffles. Silica=20 ppm, Alum=35 ppm, G=100/sec ...... 134

52 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=25/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 135

53 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=50/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 136

54 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=75/sec,
Vs-3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 137

55 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=100/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ........... 138

56 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=20 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 139

57 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=30 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 140

58 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=40 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 141

59 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. T=50 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=35 ppm) ............ 142

60 Assiumed Spatial Distribution of Velocity Gradients
For Various Impeller Types ........................... 146

61 Settling Velocity Distribution Curve of Paddle.
Silica=20 ppm, Alun=70 ppm, G (rapid-mix)=1000/sec ... 150


FIGURE


PAGE









62 Effect of Rapid-Mix Time on Sedimentation.
Flocculated with the Paddle. Silica=20 ppm,
Alum=70 ppm, G (rapid-mix)=1000/sec .................. 151

63 Effect of Rapid-Mix Time on Sedimentation.
Flocculated with the Paddle. Silica=20 ppm,
Alum=55 ppm, G (rapid-mix)=1000/sec ................. 153

64 Effect of Rapid-Mix Time on Sedimentation.
Flocculated with the Paddle. Silica=20 ppm,
Alum=85 ppm, G (rapid-mix)=1000/sec ................ 154

65 Settling Velocity Distribution Curves Using the
Propeller. Silica=20 ppm, Alum=70 ppm, G (rapid-mix)=
1000/sec ............................................. 156

66 Effect of Rapid-Mix Time on Sedimentation.
Flocculated Using the Propeller. Silica=20 ppm,
Alum=70 ppm, G (rapid-mix)=1000/sec .................. 157

67 Effect of Rapid-Mix Time on Sedimentation.
Flocculated Using the Propeller. Silica=20 ppm,
Alum=55 ppm, G (rapid-mix)=1000/sec ................ 159

68 Effect of Rapid-Mix Time on Sedimentation.
Flocculated Using the Propeller. Silica=20 ppm,
Alum=85 ppm, G (rapid-mix)=1000/sec .................. 160

69 Settling Velocity Distribution Curves of Various
Systems Using the Paddle at Constant Total Gt
(Gt=30,000). Curves A, B, C, D, E and F correspond
to Jars 1, 2, 3, 4, 5 and 6 in Table 15. Curves g
and H to Jars 1 and 2 in Table 15 (continued) ........ 163

70 Settling Velocity Distribution Curves of Various
Systems Using the Propeller at Constant Total Gt
(Gt=30,000). Curves A, B, C, D, E and F correspond
to Jars 1, 2, 3, 4, 5 and 6 in Table 16. Curves G
and H to Jars 1 and 2 in Table 16 (continued) ........ 167

B-l Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=200 ppm, Alum=70 ppm, G=25/sec .. 196

B-2 Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=200 ppm, Alum=70 ppm, G=50/sec .. 198

B-3 Settling Velocity Distribution Curves Using the
Propeller with Baffles. Silica=200 ppm, Alum=70 ppm,
G=50/sec ............................................. 199


FIGURE


PAGE








B-5 Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=200 ppm, Alum=70 ppm, G=75/sec .... 200

B-6 Settling Velocity Distribution Curves Using the Propeller
with Baffles. Silica=200 ppm, Alum=70 ppm, G=75/sec .... 201

B-7 Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=200 ppm, Alum=70 ppm, G=100/sec ... 202

B-8 Settling Velocity Distribution Curves Using the Propeller
with Baffles. Silica=200 ppm, Alum=70 ppm, G=100/sec ... 203

B-9 Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=20 ppm, Alum=70 ppm, G=25/sec ..... 204

B-10 Settling Velocity Distribution Curves Using the Propeller
with Baffles. Silica=20 ppm, Alum=70 ppm, G=25/sec ..... 205

B-ll Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=20 ppm, Alum=70 ppm, G=50/sec ..... 206

B-12 Settling Velocity Distribution Curves Using the Propeller
with Baffles. Silica=20 ppm, Alum=70 ppm, G=50/sec ..... 207

B-13 Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=20 ppm, Alum=70 ppm, G=75/sec ..... 208

B-14 Settling Velocity Distribution Curves Using the Propeller
with Baffles. Silica=20 ppm, Alum=70 ppm, G=75/sec ..... 209

B-15 Settling Velocity Distribution Curves Using the Paddle
with Baffles. Silica=20 ppm, Alum=70 ppm, G=100/sec .... 210

B-16 Settling Velocity Distribution Curves Using the Propeller
with Baffles. Silica=20 ppm, Alum=70 ppm, G=100/sec .... 211

B-17 Settling Velocity Distribution Curves Using the Paddle.
Silica=20 ppm, Alum=55 ppm, G (rapid-mix)=1000/sec ..... 212

B-18 Settling Velocity Distribution Curves Using the Paddle.
Silica=20 ppm, Alum=85 ppm, G (rapid-mix)=1000/sec ..... 213

B-19 Settling Velocity Distribution Curves Using the Propeller.
Silica=20 ppm, Alum=55 ppm, C (rapid-mix)=1000/sec ..... 214

B-20 Settling Velocity Distribution Curves Using the Propeller.
Silica=20 ppm, Alumn=85 ppm, G (rapid-mix)=1000/sec ..... 215

C-l Comparison of Effect of Time of Flocculation on
Sedimentation at Constant C and Vs. G=25/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) ............. 217


FIGURE


.PAGE









C-2 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=50/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) .......... 218

C-3 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=75/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) .......... 219

C-4 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=100/sec,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) .......... 220

C-5 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=25/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 221

C-6 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=50/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 222

C-7 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=75/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 223

C-8 Comparison of Effect of Time of Flocculation on
Sedimentation at Constant G and Vs. G=100/sec,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 224

D-1 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=10 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) .......... 226

D-2 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=30 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) .......... 227

D-3 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=50 min.,
Vs=3 cm/min. (Silica=200 ppm, Alum=70 ppm) .......... 228

D-4 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=10 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 229

D-5 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=30 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 230

D-6 Comparison of Effect of G of Flocculation on
Sedimentation at Constant t and Vs. t=50 min.,
Vs=3 cm/min. (Silica=20 ppm, Alum=70 ppm) ........... 231


xiii


PAGE


FIGURE










Abstract of Dissertation Presented to the
Graduate Council of the University of Florida
in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy


PHYSICAL ASPECTS OF MIXING
IN COAGULATION CONTROL

By

Ruey Juen Lai

June, 1975


Chairman: J.E. Singley
Major Department: Environmental Engineering


The application of mixing in coagulation control involves both

the rapid-mix and the slow-mix processes. This study deals with both

types of mixing.

The first part of the study involved the mean velocity gradient

(G) calibration of jar test equipment. Five groups of jar test systems

were studied, including a Phipps-Bird paddle, a marine-type propeller,

a two-blade pitched paddle and two magnetic-drive paddles. A new.

set-up has been applied to measure the torque in the jar test systems.

The torque is a function of the system geometry and impeller velocity (N).

Values of G, and turbulent drag coefficient (Ct), Reynolds number (NRe),

and Power number (N ) were determined. It was concluded that although

flow patterns may be different, impellers of different shapes produce

the same C values as long as their blade projected areas are the same.

The installation of baffles increased the energy input; however, all

fully baffled jars have the same energy input regardless of baffle size

or geometry.








The second part of the study investigated the similarity and

scale-up problems involved in water treatment plant design. Two scaling

equations relating N and power input (P) for a prototype and a model

were developed. For two geometrically similar systems, the power

consumption ratio is equal to the ratio of corresponding impeller

diameters to the cubic power. The impeller velocity ratio is equal

to the ratio of corresponding impeller diameters to the minus 2/3

power. Equal G values are a necessary but not a sufficient condition

for scale-up or scale-down.

The third part of the study focused on evaluating flocs produced

by a paddle and a propeller with the same projected area. From settling

velocity distribution curves with 4 types of solution and by visual

comparison from movies and pictures, it was concluded that the propeller

always produced much better settling floc (more than 10 times better

sometimes). The astonishing improvement made by the propeller results

from the flow pattern which manifests itself in two ways. First, the

flow pattern produced by the propeller is such that the floc may

contact gently with the floc already settled on the bottom and tend to

be adsorbed. The floc on the bottom then grows progressively and most

of the floc will be removed from the liquid before the flocculation is

stopped. This phenomenon could be termed "floc-layer adsorption."

Secondly, the spatial distribution of velocity gradient with the propeller

is much more uniformly distributed within the chamber than that with

the paddle.

The fourth part studied the effect of rapid-mix time on flocculation

performance as measured by settling velocity distribution curves. The

G value in the rapid-mix process of 1000 sec- was supplied by a high
G value in the rapid-mix process of 1000 sec was supplied by a high








speed portable laboratory mixer. The rapid-mix time was between 5 sec

and 180 sec. It was concluded that the shortest rapid-mix time tested

produced the best settling floc. The difference was greater when

the propeller was used for flocculation than that when the paddle was

used.

The fifth part studied the effect of the distribution of coagulation

Gt on sedimentation. The total Gt was maintained at a value of 30,000.

The test ranges from the extreme case of no rapid-mix to the opposite

extreme case of no flocculation. It was concluded that Gt is not a

useful design parameter since same Gt produces different settling floc.

The significance of the results includes a better technique for

running the jar tests, a better procedure for scaling-up (or scaling-down)

between bench-scale and full-scale data, and the upgrading of existing

or proposed full-scale plants by designing for the use of propellers

as flocculation agitators.














CHAPTER I

INTRODUCTION


Coagulation is a unit process of water engineering in which

chemicals are added to an aqueous system to combine finely dispersed

particles into larger agglomerates which can be removed in subsequent

operations such as sedimentation and/or filtration.

Matter in water may be broadly classified according to its

origin as inorganic (mineral) matter or organic (carbonaceous) matter.

Substances producing turbidity are often inorganic, while those causing

taste, odor, and color are generally organic compounds. The particles

producing turbidity may be further classified according to their size,

which may range from molecular dimensions to 50 or larger. The

fraction greater than ly in diameter is generally referred to as silt

and will settle out on standing. The smaller particles, which are

classified as colloidal, will remain suspended for very long times.

A distinguishing characteristic of particles of colloidal dimensions

is the ratio of the surface area to mass. This property is clearly

apparent from Table 1 [1]. Bacteria range from 1 to 5p while viruses

range from 0.01 to 0.10p .










TABLE 1 Effect of Decreasing Size of Spheres


Diam. of particle, Order of Size Total surface Time required
mm area* to settled


10 Gravel 0.487 sq in. 0.3 sec
1 Coarse sand 4.87 sq in. 3 sec
0.1 Fine sand 48.7 sq in. 38 sec
0.01 Silt 3.38 sq ft 33 min
0.001 (ip ) Bacteria 33.8 sq ft 55 hr
0.0001 Colloidal particles 3.8 sq yd 230 days
0.00001 Colloidal particles 0.7 acre 6.3 yr
0.000001 Colloidal particles 7.0 acres 63 yr minimum

* Area for particles of indicated size produced from a particle 10 mm
in diameter with a specific gravity of 2.65.
t Calculations based on sphere with a specific gravity of 2.65 to
settle 1 ft.
SOURCE: S.T. Powell, "Water Conditioning for Industry," McGraw-Hill,
New York, 1954.

Colloids, in addition to their characteristics of size and surface

area, have been further classified as hydrophobic (water-hating) and

hydrophilic (water-loving). A distinguishing property of hydrophilic

substances is their ability to react spontaneously with water to form

colloid suspensions which can be dehydrated to the original material

and then redispersed repeatedly. This class of compounds includes

substances such as starch, gums, and proteins. Dispersions of hydro-

phobic substances are generally prepared by physical or chemical means.

Clays and metal oxides are largely hydrophobic in nature.

The reason for turbidity removal from water supply is threefold.

From the public health standpoint, microorganisms fall in the colloidal

size range and may be either removed by coagulation directly or be

trapped in the Formation and settling of other coagulated colloids.

The second reason is one of aesthetics. The third reason is that








colloidal materials can severely impair the efficiency of ion

exchange, adsorption, and membrane processes used to remove soluble

substances [2] as well as provide protection for pathogens against

disinfectants.

The need for coagulation was recognized by the early Egyptians

in treatment of water from the Nile River. The Chinese were reported

to have added alum to Red River water to coagulate turbidity and

make it more drinkable [3]. By 1767, the common people of England

were successfully treating muddy water by adding 2 to 3 grains of

alum to a quart of water and allowing it to flocculate, after which

the supernatant was filtered. In 1884 the first patent on coagulation

was granted to Isaiah Smith Hyatt, who described the use of perchloride

of iron as a coagulant with his system of rapid-sand filtration in

the treatment of a turbid water. In 1885, Austin and Wilker of

Rutgers University published the results of the first scientifically

conducted American investigation of alum as a coagulant [4]. Since

then coagulants have been used popularly in water treatment plants.

Coagulation is not practiced exclusively in potable water

Treatment. Its application for waste treatment is becoming increasingly

attractive as, for example, an adjunct to phosphate precipitation.

The recent trend in pollution control is from the traditional biological

methods to chemical and physical waste treatment.

There are many different chemical coagulants and coagulant aids

used in water treatment. Babbitt, Doland, and Cleasby [5] list

aluminum sulfate (A2I(SO4)3*18 H120), ferric chloride, and seven others

as the most frequently used coagulants. Connercial aluminum sulfate,

known as "filter alum," contains a slightly higher percentage of









aluminum than Al2(SOQ4)318 H20 because it contains only about 14.3

waters of hydration. Because of its low cost, alum is the most

frequently used coagulant in this country; however, ferric salts

are often used because they form a denser, stronger floc. In the

past decade numerous polyelectrolytes have been added to the coagulant

list. They are generally more expensive than alum on a unit basis but

perform more effectively and more economically in many waters because

much lower dosages are required.














CHAPTER II

LITERATURE REVIEW


Definitions

The operational definition of coagulation is the reaction that

occurs upon the addition of a coagulant to water to collect the

suspended particles into agglomerates. Flocculation is the action

of bringing these small agglomerates together to build floc particles

that are large enough and heavy enough to settle from the water.

The physical-chemical or mechanistic definition was proposed by

LaMer [ 6]. By this usage, coagulation is the electrical

destabilization of the particle so that they may approach each other

closely enough to be attracted. Flocculation is the building of a

floc through an interparticle bridging mechanism to build a porous,

three dimensional network. Coagulation is derived from the Latin

"coagulare" meaning "to collect" and flocculation from "flocculus"

meaning "small tuft of wool". No distinct boundary between the

two steps can be observed easily in experimental work. Hahn and

Stumm [7 ] have elaborated on LaMer's definition of the coagulation

process. They state that the aggregation of particles in a colloidal

dispersion proceeds in two distinct reaction steps. Particle

transport leads to collisions between suspended colloids; particle

destabilization causes permanent bonds to form between them upon

collision. The rate of agglomeration, consequently, is the product








of the collision frequency resulting from particle transport and

the collision efficiency factor (the fraction of collisions resulting

in permanent contact), which is determined by the-destabilization

step. Particle transport of small colloidal particles is primarily

motivated by Brownian motion and called "perikinetic" transport;

whereas, transport of larger particles is primarily motivated by

velocity gradients, and is called "orthokinetic" transport. Many

authors commonly refer to the orthokinetic transport phenomenon as

the physical aspect of coagulation because the velocity gradients

in the suspending medium may be imposed by physical agitation or

mixing.

Theories of particle transport are based on fluid and particle

mechanics; theories of particle destabilization are based on colloid

and surface chemistry.

O'Melia [ 8] used the term coagulation to apply to the overall

process of particle aggregation, including both particle destabilization

and particle transport. The term flocculation is used herein to

describe only the particle transport step. This definition seems to

be a rational one and will be used throughout this dissertation.


Theories of Destabilization


Properties of Natural Colloids and Stabilizing Forces

Suspended particles found in natural waters are mkown to possess

electric charges. The majority of them are negatively charged.

O'MeJia [ 9] briefly summarizes the origin of these charges as

resulting from three distinct processes.









First, a particle charge may result from an imperfection within

the crystal lattice of a particle itself. A typical example of this

is the replacement of Si+4 atoms by Al+3 atoms in the layer structure

of a clay mineral, resulting in a net negative charge on the particle.

Second, many natural colloids contain surface active groups, such

as hydroxyl, carboxyl and amino groups. The ionized -from of these

groups gives rise to a net charge on the particle. Many proteinaceous

particles in nature, such as bacteria, contain groups of this type.

Third, the preferential adsorption of ions from solution may

result in a build-up of the charge of the adsorbed ions.

It is generally agreed that stability of colloidal particles is

due largely to the phenomenon of the electrical double layer consisting

of the charged-particle surface and a surrounding sheath of counter

ions. The layer adjacent to the particle is called the Stern fixed

layer. The outer layer of decreasing ionic concentration is named the

Gouy diffuse layer. When the bulk solution contains a high ionic

concentration (high ionic strength), the diffuse layer is compacted

so that it occupies a smaller volume. Due to the existence of the

primary charge, an electrostatic potential exists between the surface

of the particle and the bulk of the solution. When two similarly

charged colloidal particles approach each other their diffuse layers

begin to interact. This electrostatic interaction always produces a

repulsive force. This is illustrated in Fig. 1.

Attractive forces come mainly from van der Waals forces. These

are forces based on mutual attraction between any two structures that

have electrons that may be attracted by positive sites on another

entity to produce a dipole. These forces decay very rapidly with

















I I
S- Stern Laver
I I

-- Gouy Layer

I ---Plane of Shear


Repulsive Potential Energy Curve

SResultant Interaction Energy Curve





I -Distance From the
Surface of Colloidal
Particle

SVan der .Waals Attractive Energy Curve


FIGURE 1 Potential Energy of Interaction
of Colloidal Particles.


0.0




0-C
-r

0


(-)









increasing distance between the particles and are quite negligible

except when they are close together. These forces are responsible

for the aggregation of many colloidal systems. These forces are also

illustrated in Fig. 1.

The object of coagulation is to overcome these forces of repulsion

between particles.


Proposed Mechanism Models

Double-layer compression. This theory states that the destabilization

is accomplished by compressing the diffuse layer surrounding the

colloidal particles so that they may approach each other closely

enough (i.e., in van der Waals attraction force region) to be attracted.

High concentrations of electrolyte in the solution result in correspondingly

high concentrations of counter-ions in the diffuse layer. The volume

of the diffuse layer necessary to maintain electroneutrality is lowered

and consequently the thickness of the diffuse layer is reduced. However,

this theory has two major deficiencies in that it does not explain the

following:

(1) Anionic polyelectrolytes can destabilize negative charged

colloids [9].

(2) The optimum destabilization occurs around the zero ZETA

potential. According to the theory, the optimum destabilization

should occur at exactly zero ZETA potential [10].

Enmeshment in a precipitate. This theory describes a mechanism

of coagulation by which the coagulant reacts with water and OH to

form a precipitate which enmeshes colloidal particles. When a metal

salt such as A1(SO4,) or FeCL, is used as a coagulant in concentrations









sufficiently high to cause rapid precipitation of a metal hydroxide

(e.g., A1(OH)3(S), Fe(OH)3(S), Mg(OH)2(S) or metal carbonate

(e.g., CaCO3), colloid particles can be enmeshed 'in these precipitates

as they are formed [11]. The rate of precipitation is a function of

pH, metal ion concentration, and colloid concentration. The colloid

particles themselves can serve as nuclei for the formation of the

precipitate. This can result in an inverse relationship between the

optimum coagulant dose and the concentration of material to be

removed [11].

Langelier et al. [12,13] have shown that the coagulation of numerous

clay minerals with alum indicates that the clay minerals play an active

role in the mechanism.

Adsorption and bridging model. Within the last decade there

has been a rapid increase in the use of synthetic organic polymers

as destabilizing agents in the treatment of water and wastewater.

These polymer molecules contain chemical groups which can interact

with sites on the surface of the colloidal particle.

La\~er and Healy [ 6] have postulated a bridging theory which

states that reactive functional groups located along a long-chain

polyelectrolyte could form chemical bonds with reactive sites on solid

particle surfaces. Since the same polymer molecule could react with

several solid particles, it would act as a bridge connecting them to

form a settleable agglomerate. Postulated interactions in the bond

formation include ion exchange, hydrogen bonding, coordination

reactions, covalent bonding, van der I.aal's attraction, and repulsion

of the coagulant by the aqueous phase. The best illustration, shown

in Fig. 2, was based on LaMer and Healy's work [ 6] and given by O'Mclia [8].

























Po
Pol


React io: I
Initial Adsorption at the Opli uiim Polymer Dosoge



e PaDestobilized
lymer Parlicle Porlicle


Reaction 2
Floc Formotion
Flocculation

(perikinetic or
orthokinetic)


Deslobilizcd Porticles
Reocllon 3


Fl c Particle


Secondary Adsorption of Polymer


No cortoct with voconi sites
on another particle
Destobilized Porlicle Restabilized Porticle
Reaction '
Initoi l Adsorption Excess
Polymer Dosage (

+ 0
Stable Porlicle
EPcess Poalmers Particle (no vacant s tes)
Reaction 5
Rupture of Floc


Intense or FIoc
Prolonged Frgm nts
Floc Porticle Agitation Fr ments


Reaction 6
Secondary Adsorptionof Polymer


Reslcbil.zed Floc
Floc Frogment Frogment


FIGURE 2 Schematic Representation of the Bridging
Model for the Destabilization of Colloids
by Polymers. (After O'Melia [8])









Summary of models. In order to explain the coagulation mechanism

completely, it is found that three theories should be combined.

Adsorption, bridging and enmeshment'are each believed to predominate

in coagulation under certain conditions; the double-layer compression

appears to be secondary. In the moderate coagulant dosage and

moderate colloid concentration region, the adsorption and bridging

mechanism offer a reasonable explanation. At very low colloid

concentration (which needsvery high coagulant dosage to accomplish

destabilization) the enmeshment of colloidal particles in a "sweep

floc" is the best explanation.


Chemistry of Aqueous Aluminun

All metal cations are hydrated in water. Such simple species

as Fe 3+, Al 3+ Ca and H do not exist in a natural aqueous en-

vironment. Rather, these ions are present as aquocomplexes --

Fe(H20)6 Al(H 0)6, Ca(H 0) and H(H20) The solubility

equilibria of amorphous Al(OH)3(S) are shown in Fig. 3. Shaded areas

correspond to the approximate values of coagulant dosage and pH observed

in water treatment practice. When a quantity of Al(ITI) salt larger than

the solubility limit of AI(OH)3(S) is added to water, a series of

hydrolytic reactions occurs, proceeding from the production of simple

hydroxo complexes (e.g., A10H2+) through the formation of colloidal

hydroxometal polymers to the formation of a metal hydroxide precipitate.

This was reported by Stumm and Morgan [14] and Stumm and O'Melia [15].

Thus, Al(1II) coagulants are subject to hydroxo complex formation, poly-

merization, and aging reaction. A few typical reactions follow.






























0 ,

2 AI(OH)3 (S)
-2-



2+
AI(OH)
-6


-8

5+ +
-10 A13 (OH)3 Al


-12 I 1 \ \
0 2 4 6 8 10 12 14

PH

FIGURE 3 Al ( T1 ) 3quilibria










Al+ + 4 H20 = Al(OH)4 + 4H1

3+ 2+
Al (H20)6 + H20 = Al (H20) 5(OH)5 (OH) 2
21HO 6 225 5


2[A(H20) 50H]2+


OH 4+
= [(H20) 5A1OH' AIH20)
2 OH1 2


2+ AO\1 ]2+
2[Al(H20) 50H]2+ = [(H20)5A 0 Al(H20)5]
2 5 2 5 '\0/ 2


+
+ 2H30


The predominating reactions vary with pH. Black and Chen [16]

found out that, in the region pH<4, hydrated trivalent aluminum ion

predominates; in the range pH 4-6, hydrolyzed aluminum polynuclear
3+ 4+
cations predominate, (e.g., Al6(OH)5, Al8(OH)20) in the region

pH>6, insoluble aluminum hydroxide predominates.


Important Parameters in Particle Destabilization


Temperature

Little experimental information is available on the effect of

temperature on particle destabilization. Only two references can be

found on this aspect of coagulation.

Camp et al. [17] have shown that the optimum pH for Fe(III)

coagulation with low coagulant dosages increases with decreases in

water temperature. They concluded that the shift of optimum pH

probably is due to the temperature dependence of the equilibrium constants

involved in the chemical reactions of coagulation.

Recently Mohtadi and Rao [18] concluded that temperature (L-200C)

has no significant effect on the ZETA potential of a clay particle

dispersion. Using alan as a coagulant, they also determined that for


+ HO
3









coagulation carried out at optimum pH conditions, temperature had

no effect (10C-200C). When cationic polyelectrolytes were used, several

important parameters were all temperature independent.


/pH

The pH of the solution during coagulation is a very important

variable for two reasons. First, as shown in Fig. 3, it controls the

equilibrium composition of Al(III) or Fe(III) for any given coagulant

concentration. This also implies that the charges on the hydrolysis

product of Al(III) and Fe(III) vary with pH. Second, many colloids

in solution are amphoteric and will possess either a net negative or

positive charge, dependent on the pH (except at isoelectric point).


Alkalinity

The effect of alkalinity on buffer capacity has been studied by

several investigators [12,15]. Stumm and O'Melia [15] point out that

for waters with excessively high concentrations of bicarbonate, the

pH will be about 8.3 and will not be lowered by normal coagulant dosages.

Since Al(III) and Fe(III) salts are acidic in nature, it is essential

that the water have adequate buffer capacity to maintain the pH level

at a value suitable for coagulation.

Stenquist and Kaufman [19] observed that alkalinity has a strong

influence on the performance oF the initial mixing step, the effect

increases with increases in alkalinity.


Color

Natural color comes from complexes of poly-organic matter

with heavy metals (e.g., Fe, Zn and Cu). Black, Singley et al. [20]








have developed a method for the determination of the optimum conditions

for the removal of organic color from relatively soft, colored water

using ferric sulfate. The two variables that must be controlled are

coagulation pH and ferric sulfate dose. Babbitt et al. [5] state that

optimum color coagulation usually occurs at lower pH than for optimum

turbidity removal.


Colloid Concentration

In water treatment plants, water with a high colloid concentration

is not more difficult to coagulate than low colloid concentration water.

As a matter of fact, water with a low colloid concentration usually

gives more trouble to the operators than water with a high colloid

concentration. O'Melia [8] recently classified waters into four

classes and suggested explanations for their optimum treatment. First,

high colloid concentration, low alkalinity. This is the easiest system

to treat. Only one chemical parameter--the optimum dosage--must be

determined. Destabilization is achieved by adsorption of positively

charged hydroxometal polymers. Second, high colloid concentration,

high alkalinity. In this case, the engineer can either use a high

coagulant dosage or remove alkalinity first, and destabilize with a

lower dosage. Destabilization is achieved by adsorption and charge

neutralization at neutral and acid pH levels. Third, low colloid con-

centration, high alkalinity. Coagulation is readily accomplished here

with a relatively high coagulant dosage by enmeslhment of colloidal

particles in a 'weepi floc." Fourth, low colloid concentration, low

alkalinity. Coagulation is most difficult in such systems. Al(T1l)

and Fe(IlI) salts will he ineffective if used alone. Coagulation








aids might be needed to increase the rate of interparticle contacts

to a level suitable for coagulation.


Characteristic of Coagulants

Two types of coagulants exist: organic and inorganic. Organic

coagulants are polymeric compounds that can further be divided into

three classes according to their charges in solution: nonionic,

anionic and cationic.

The inorganic coagulants consist essentially of the salts of

multivalent metals. Of these the salts of Al(III) and Fe(III) are

most common. The preparation of inorganic coagulants for treatment

differs from plant to plant. These variations may include the type

and dosage of the coagulants, the strength (e.g., 1 mg/l, 10 mg/l or

50 mg/l) of the coagulant as applied [21], the aging of the coagulant

solution, and the sequence of addition of chemicals [21].


Transport of Colloidal Particles


Perikinetic and Orthokinetic Transport

Interparticle contacts, like particle destabilization, can be

accomplished in two ways. First, contacts by thermal motion, often

termed Brownian motion or Brownian diffusion. Seccnd, contact resulting

from bulk fluid motion.

The random motion of colloidal particles was first observed by

the English botanist Brown in 1827. Such motion results from the

rapid and random bombardment of the colloidal particles by molecules









of the fluid. When interparticle contacts are produced by Brownian

motion, the transport process is termed perikinetic flocculation [22].

Von Smoluchowski [23] derived the basic expression for the

collision frequencies under two different collision mechanisms. For

Brownian motion, the frequency of collisions was obtained by calculating

the diffusional flux of particles toward a single stationary particle.

The resulting relationship for the collision frequency is given by


M.. = 4rrD..R..n.n. (1)
ij iJ Ij i j

where M.. is the number of contacts made per unit time and unit volume

between particles of radius R. and R.; D.., the combined diffusivity,

D. + D.; R.. = R. + R.; and n. and n., the number concentration of
1 j 1j 1 j 1 J

particles of radius R. and R..
1 J

When contacts between particles are caused by fluid motion the

process is sometimes termed orthokinetic flocculation [22]. Smoluchowski

[23] also realized that the collision may be increased by the fluid

motion and derived the result under laminar flow condition:

4 3 dU
M- n.n.R (2)
ij 3 i j ij dZ

dU
where U is the velocity gradient and M.ij is the collision frequency.

The relative significance of perikinetic and orthokinetic transport

may be examined by considering the initial aggregation rates for a

monodisperse system of spherical particles of radius R. The ratio of

these rates can be found by dividing equation (2) by equation (1):

dU 2
M.i (orthokinetic) 1 R.
'2 dZ iM (3 ]
M.. (~erikinetic) 3 P D..
ij 1j









The combined diffusivity D.. may be defined for this system by the

Stokes-Einstein equation:


D.. K- (4)
ij 6TrrR (
-16
where K = Boltzmann's constant = 1.38x10 ergs/K

T = absolute temperature ('K)

p = absolute viscosity of fluid (gm/cm sec)

Assuming no particle breakup occurs, equation (3) becomes:

dU 3
M.. Corthokinetic) 2p dU R.-
13 dZ 13 (5)
IM.. (perikinetic) KT


In water at 25 C (p=0.01 gm/cm sec) containing colloidal particles

having a diameter of 1 (R. =2p), this ratio is unity when the velocity

gradient is approximately 1 sec For colloidal particles having

a diameter of 0.1p, a velocity of 1000 sec-I is necessary for orthokinetic

flocculation to be as rapid as perikinetic flocculation. Similarly,
-l
for particles 10p in diameter, a velocity gradient or 0.001 sec will

be sufficient to keep orthokinetic rate equal to the perikinetic rate.


Collision Kinetics of Small Particles in Turbulent Flow

In actual systems the velocity of the fluid varies both spatially

(from point to point) and temporally (from time to time). The instaneous

direction and quantity of the fluid velocity can not be measured.

Camp and Stein [24] applied Stoke's theory [25] to relate the

total energy input into the fluid to what they called a root-mean-square









velocity gradient. (Stoke's theory states that velocity gradient

equals to the square root of energy dissipation at a point divided by

the fluid absolute viscosity.) Thus,


G FIT dU
J P dZ
G --=


(6)


where W = energy input per unit time per unit volume of fluid

= "Dissipation Function" or power loss per unit volume of
-1 -3
fluid, g an sec
-l
G = rms velocity gradient, sec
-1 -1
u = absolute viscosity of fluid, g cm sec


Thus, under turbulent flow


4
.. = i n.n.R3 .G
1 1 3 i13


(7)


A diffusion model was also adopted by Levich [26]. The resulting

equation for turbulent flow is shown below


M.. = 12TB n.n.R 3
ij ,I i Ii


( 8)


where 8 is constant.

Fair and Gemmel [27] who took into account the possible elimination

of particles, arrived at the following equation:


k-1
I n.n.R..
i=1 1 3 13
=k-i


0O
0 V n3 dU
- 2n n.R.'-
k n ik dZ
1=1


dn 2
kd 3
dt 3


C 9)









The second tern inside the brackets indicates the elimination of

particles of size k due to their collision with all other particles.

The solution of the above equation with the appropriate boundary

conditions for different collision and break up mechanisms has been

the subject of several studies in recent years. By replacing the

summations by integrals an analytical solution was available in a

batch system. Hudson [28] simplified the equation by assuming that

the removal of primary particles occurs primarily by collisions with

flocs and arrived at the following equation


dnl 4 3 dU
= 3 nlnFRF dZ (10)


where RF is the radius of flocs, and nF is their number concentration.

Argaman and Kaufman [29] who considered the breakup of floc

derived a flocculation equation which is shoAwn below

O O
nI 1 + KFKSKpnlTG
-= (11)
n 1 + KBTG2

where KF and KB are the flocculation and breakup coefficients, KS and

Kp are the spectrum and stirrer performance coefficients, and T is the

residence time.


/ Mixing Theory and Application

/ Mixing is a widely practiced operation; it occurs whenever fluids

are moved in the conduits and vessels of laboratory and industrial-

processing equipment. Mixing is of interest not only when it results in

the dispersion of one component in another but also when it is an agency

for the promotion of heat transfer, mass transfer, solid suspension,

and reaction.








Although much has been published on the theory and practice of

mixing, these writings are spread throughout the literature [30].

Unfortunately little of this has been applied by water purification

engineers. The goal of this section, therefore, is to introduce some

fundamental concepts of mixing as well as concepts of power consumption,

similarity and scale-up.

For fluids the movement of material occurs by a combination of

these mechanisms: bulk flow in both laminar and turbulent regimes and

both eddy and molecular diffusion [30]. A very common and important

mixing operation is bringing different molecular species together to

obtain a chemical reaction; for instance, rapid mix in the coagulation

process. The inertia of fluids and viscous drag or fluid shear forces

provide two major resisting forces for mixing. For low viscosity fluids

like water in which turbulence is readily induced, the inertia of the

fluid provides not only the major resistance to stirring the fluid but

also the major method by which fluid movement is transmitted to parts

of the fluid which are remote from the stirrer. High fluid velocities

increase inertia and shear forces and particle agglomerates suspended in

liquids (for example, turbidity floc from coagulation) can be broken

up by these inertia and shear forces.

The basic types of equipment which are used for the mixing operations

are few. Essentially all types are modifications of vessel or

pipes [31]. In vessel-type equipment, there is a circulation or back

flow that moves fluid into all parts of the vessel or chamber.

Because the complex shapes of mixing vessels and the flow patterns

of contained fluids lead to differential equations which are impossible

to solve, the empirical approach employing dimensionless groups is most









frequently used for correlation of the process performance variables

in mixing equipment. The basic principles involved in this method

were developed by Johnstone and Thring [32].

The kinds of problems that arise in the design and use of mixing

equipment are selecting the type, size, and operating conditions which

will perform a desired service or obtain a desired production rate of

material with the desired properties. Keeping the combination of

capital and operating costs low is an important aspect of these

problems. Methods of predicting the process performance characteristics

of mixing equipment generally depend upon empirical methods involving

correlations of dimensionless groups and model relationships.


Impeller Characteristic and Major Flow Patterns

Impellers are divided into three major types: paddles, propellers,

and turbines (see Fig. 4) [31,33,34]. Each type includes many variations

which will not be considered here.

Paddles. They produce predominately a radial flow in the vessel.

They push the liquid radially and tangentially with almost no vertical

motion unless the blades are pitched. The currents generated travel

outward to the vessel wall and then upward or downward. Paddles are

usually larger and used in slower speed agitation than other types of

impellers. They are not effective for many process operations involving

high viscosity fluids.

Turbines. There are two basic forms of the turbine: the flat-

blade turbines which produce primarily radial and tangential Flow, and

pitch-blade turbines that produce axial flow. Turbines are usually

small and multibladed; however, the number of blades is not important [31].




















S0
*H -




0



1H 0
H H *H







OcJ













d -P
e-0














*H 0
C) d- P

























1 0
10 Q














I o -







-4












CLt
^ 0 P
S r- >

Es -r *^
E'O-

Tl3 ;,Q
~rc 3
r- "









Propellers. These are axial-flow, high speed impellers for liquids

of low viscosity. The modified three-blade marine-type propeller is

in almost universal use today.

The flow patterns produced by the turbine and the propeller are

shown in Fig. 4.


Similarity Considerations

Small-scale experiments are not always a reliable quide to large-

scale results. The aim of model theory is to predict the scale effects

and determine the conditions (if any) under which the performance of

a model gives a reliable forecast of prototype performance.

Similarity may be considered in two ways, by specifying the ratios

either of different measurements in the same body or of corresponding

measurement in different bodies [32]. The geometrical shape of a body is

determined by its intrinsic proportions, e.g., the ratio of height to

breadth. In geometrically similar bodies, all such ratios (shape

factors) are constant. Alternatively, when two geometrically similar

bodies are compared, there is a constant ratio between their respective

heights, breadths, and other corresponding measurements. This ratio

is termed the scale ratio.

Four similarity states are important in engineering, namely:

geometrical, mechanical, thermal and chemical similarity [32]. Two

bodies are geometrically similar when to every point in the one body there

exists a corresponding point in the other. Mechanical similarity

comprises static, cinematic and dynamic similarity. Each of these

can be regarded as an extension of the concept of geometrical similarity

to stationary or moving systems subjected to forces. Static similarity








is concerned with solid bodies or structures which are subject to

constant stresses. Kinematic similarity requires that velocities at

corresponding points be in the samneratio. Two systems are dynamically

similar when the ratios of all corresponding forces are equal. Thermal

similarity is concerned with systems in which there is a flow of heat.

Chemical similarity is concerned with chemically reacting systems in

which the composition varies from point to point and, in batch or

cyclic processes, from instant to instant.

Dimensional analysis is a technique for expressing the behavior

of a physical system in terms of the minimum number of independent

variables and in a form that is unaffected by changes in the magnitude

of the units of measurements [32]. The physical quantities are arranged

in dimensionless groups consisting of ratios of like quantities--lengths,

velocities, forces, etc.--which characterize the system. These groups

constitute the variables in the dimensionless equation of state (or

motion) of the system.


Power Theory

General Equation. The general dimensionless equation for agitator

power was derived by Rushton et al. [35] using dimensional analysis.


DNp DN2 Pg D D D D D D n 2
g pN3DS T Z C p T n 11
g pN D r 1

where D is impeller diameter, cm

T is tank diameter, cm

Z is liquid depth, cm

C is clearance of impeller off vessel bottom, cm

w is blade width, cm









p is pitch of blades, cm

n is number of blades,

Z is blade length, an
-3
p is density, gm an3
-1 -1
y is viscosity, g cm sec
-2
P is power, dyne cm sec2

N is impeller rotational speed, RPM (Note N=60S, where S is rps)
-2
g is gravitational acceleration, 980 cm sec-


The above equation applies to the metric system only. In the British

system, when P is expressed in ft.-lb.f min units, and density in
-3
Ib. ft to make the power number dimensionless, pound force is
-2
reduced to units of Ib. ft sec by multiplying P by gc instead of g

" (where gc is Newton's Law conversion).

Similarity. The types of similarity of interest here are geometric,

kinematic, and dynamic. The last seven ternns in Eq. (12) represent

the condition of geometric similarity. The reference dimension used

is the impeller diameter. Equation (12) assumes a single impeller

centered on the axis of a vertical cylindrical flat bottom tank. To

be fully inclusive, the equation would have to expand to include:

(1) off-center impeller positions, (2) multiple impellers, (3) baffle

width and number of baffles, and (4) tank shape. Thus, for geometrically

similar systems,

D2Np DN2 P1
S g D5N\


Equality of the groups in this expression insures dynamic and kinematic

similarity.








Physical significance of dimensionless groups. [31]

(1) Reynolds number, NRe. The first groups in Eq. (13) determine

the Reynolds number and represent the ratio of inertial forces to

viscous forces. This ratio determines whether the flow is laminar

or turbulent.

UL p(ND)D D2Np
NRe (14)


(2) Froude number, NFr. This number represents the ratio of

inertial force to gravitational force. When gravitational effects

are important, such as in an unbaffled tank, the Froude number can not

be disregarded.

2 2 2
U (D) DN2 (15
N (15)
Fr Lg Dg g

(3) Power number, N It can be shown that the power number is

analogous to drag coefficient for immersed bodies, and friction factor

in pipe flows.

N = (16)
SDN

Power equation in correlation form. [31]


Np= K(NR) (NFr ) D T j |


For geometric similarity, this reduces to


Np K(NRe )a (NFr)b

We define

Npr
P (Nr6= K1 (NRe) a

NFr








For a fully baffled tank, and in the laminar range, b generally

equals to 0, and p = Np [31]. For unbaffled tanks, there is dis-

agreement [31]. Typical curves of 0 vs. NRe are 'shown in Fig. 5

[31] for configurations often used in practice.

(1) Turbulent regime. At high Reynolds numbers in fully baffled

tanks, Np = constant. This is illustrated by curves DE and IJ in

Fig. 5. Thus

S= K' pN3D5
g


(2) Laminar regime. Lines A-B and H-B in Fig. 5 represent the

viscous range of flow and the slope shown is typical for all types of

impellers. Since Froude effects are important and the slope is -1,

then

Np = K"(NRe)

V1" 2 3
thus P =K" ND3


(3) Transition range. Early researchers generally assumed that

a critical value of Reynolds number must exist for mixing impellers

analogous to pipe flow. That a gradual change from laminar to fully

turbulent flow does exist--and in variable form for different system

geometries--is now well known. It is illustrated in Fig. 5 by line B-D.


Scale-Up and Scale-Down Considerations

It was shown by Johnstone and Thring [32] (see note,p.31) that in a

mixer which forms part of a pilot plant, the liquid is the same on the

small and the large scale, and similarity is impossible unless the effect

of the Froude number is eliminated. Thus, only a fully baffled mixer


























A
Laminar
H (tangential flow)

Turbulent baffled



to C
2 F
Turbulent unbaffled flow

G
Turbulent baf f led
(axial flow)

log NRe







FIGUPRE 5 Characteristic Impeller Power Curves.
(After Bates et al [311 )








or a very low Reynolds-nLumber laminar mixer, where Froude effects

are negligible, will be considered.

For preparing dispersions of solids in liquids, e.g., coagulation

and flocculation, the published evidence suggests that the most useful

criterion is power input per unit volume: i.e., in homologous* mixing

systems at equal values of W the degree of dispersion is equal.

The scale equations shown by Johnstone and Thring [32] are
-2/3
N prototype D prototype (17)
N model Dmodel ...


P prototype D prototype (1)
P model D model (18)

The upgrading of existing water and waste treatment plants

requires simulating plant operations on bench-scale studies. The

laboratory data can not be meaningful unless the similarity conditions

are maintained. This is where the scale-down comes in. The scale

equations (17,18) not only can be applied to scale-up problems, but also

can be applied to scale-down problems.

Homologous systems: Systems in which (1) the shapes of corresponding
solid members or of the solid envelops enclosing fluid masses are
geometrically similar; (2) chemical compositions and physical properties
at corresponding points are identical.
2 2
NOTE: 1. First condition, N' = N, i.e., SD
Re Re' p

Since, p' = p, p' = p, S'I2 = SD2, or S/S=(D/D')2

S2 D' S2D
2. Second condition, N' = N i.e., g-, -
Fr Fr g g

S' D 1/2
Which result in -= U)

where primed symbols relate always to the prototype and unprimed
symbols to corresponding quantities in the model.








Rapid-Mixing in Water Treatment

Rapid-mixing, as applied in the form of flash mixing, has been

used for a long time in water treatment plants to disperse coagulants

in water. It seems to water chemists or engineers that the sole purpose

of rapid-mixing is to spread the coagulants as uniformly as possible

in a short period of time.

Camp [36] measured the floc volume concentration and floc size

distribution for different values of G (mean velocity gradient) and

time. He observed that rapid mixing of sufficiently high velocity

gradients might delay formation of visible floc and disperse the floc

already formed to colloid size.

Argaman and Kaufman [29] assumed isotropic turbulence in a

flocculating vessel and made four assumptions. They measured effective

velocity and Eulerian type energy spectrum, which they substituted for

the Lagrangian type without justification. They concluded that the

1 2
assumptions 3(Rfloc -) and 4(u cG) were substantiated in the


research. However, their experimental jar with finger paddle design

had the tendency to break up the floc four times in each revolution.

Vrale and Jorden [37] measured the turbidity of water in a jar

after flocculation with various kinds of rapid-mixing devices. They

assumed the rate of decrease of supernatant turbidity was second order

in turbidity. However, Hudson [38] stated that the curve is better

fitted by first order instead. Vrale and Jorden observed that a backnix

reactor was a very inefficient way of accomplishing rapid mixing and

a tubular reactor appeared to be the most efficient type. They concluded

that points of application and the details of the turbulent scale and









intensity immediately at, and downstream of, the application point are

important design considerations. They suspected one reason for the

discrepancy between jar test results and plant operation to be due

to differences in the efficiency of rapid mixing. However, this

article did not have any data to support the suspicion.

Stenquist and Kaufman [19] applied flow-through grids with multiple

orifices in order to induce turbulence in a pipe flow. They measured the

concentration fluctuation of sodium chloride in various r and z

directions by using a single-electrode conductivity probe. However,

their data have limited use in practice because the grids and orifices

have a tendency to clog in large plants. They commented that the

alkalinity of the raw water had a strong influence on the importance

of the initial mixing step, the effect of rapid mixing increasing with

increasing alkalinity.

Halm and Stumm [39] studied the kinetics of coagulation with

hydrolyzed AlCIII) and postulated that the colloid transport step,

either due to Brownian motion or velocity gradient, was rate determining.

That is, the colloid transport step occurred most slowly and was the

most important step in coagulation.

Camp and Conklin [40] in studying jar test techniques developed

a gross drag coefficient for 2 liter beakers with and without stators.

With stators, they reported, the velocity gradients could reach very

high values, thus enabling the simulation of rapid mixing in jars.

In applying modified jar testing techniques at Phoenix, Arizona,

Griffith and Willimns [41] found out that the point of coagulation feed









and the intensity of flocculation agitation in plants had a

profound influence on the turbidity removal.

It was learned recently that adequate rapid mixing produced small,

dense flocs. These flocs could be filtered directly without prior

sedimentation and still maintain good water quality [38].


Coagulation Control in the Laboratory The Jar Test


Review of Procedures

The jar test procedure is widely used to simulate the water

treatment process in the laboratory and tc produce data for process

control, yet very few carefully controlled studies of jar test techniques

are found in the literature [42-45]. Conventionally, the procedure

consists of placing several samples of raw water in a series of vessels

which are stirred in a manner approximating that of the existing or

proposed plant. Varying dosages of coagulants and other chemicals used

in the related full scale process are added to each vessel. After an

appropriate period of mixing and flocculation, stirring is stopped and

the floc formed is allowed to settle for a specified time period. The

clarity of the supernatant is then used to evaluate the optimum chemical

dosages. Black et al. concluded that there is little or no uniformity

in methods used for conducting the jar test--that there are about as

many variations in procedures as there are individuals carrying out

the tests. Nickel [43] suggested that when performing a jar test,

a quantity of water no less than 1 liter should be used. A period of

rapid mixing at 100 revolutions per minute should be followed by a

flocculation period (slow mixing at 25 to 40 revolutions per minute)









of 20 minutes. Hannah, Cohen, and Robeck [44] used the following

technique: rapid mix for 3 minutes, slow mix for 25 minutes, then

allow 30 minutes for settling. Black and Chen [16] used the following

procedure in their studies: 2 minutes of rapid mixing at 100 revolutions

per minute, 10 minutes of slow mixing and 10 minutes of settling.

TeKippe and Ham [46] rapid mixed for 2 minutes prior to the addition

of lime and sodium hydroxide, then for 1 minute following their

addition. The slow mixing period lasted 20 minutes.

The interpretation of jar test data must be founded on unvarying

and well-calibrated techniques if the data are to be quantitatively

meaningful. One of the important variables in the procedure is the

mixing intensity, which is related to the rotational speed and the

configuration of the agitator as well as the geometry of the mixing

vessel. As mentioned before, Camp and Stein [24] applied Stoke's

theory [25] and derived a mean velocity gradient, "G".

dU W
G = dZ (19)


The value of W depends upon the geometry of the stators, rotors,

and containers, and upon the speed of the rotors. Accurate values

of W can be determined best by measurement of the torque input to

the liquid at various speeds and liquid temperature:

2nsT
W = ...... (20)


in which s is the measured rotor speed in rps, T is the measured

torque input in dyne-cm, and V is the liquid volume in cm3. Note

that 1 gin force = 980 dyne so

2 (2sT1
2TrsTg (21)
Xr









when T is expressed in gm force-cm. (Where g is acceleration of

gravity and equals 980 cm sec-2)

By extensive experiments with hydrous ferric oxide floc, Camp [36]

demonstrated that the floc size and volume concentration may be varied

over a wide range by changing values of G and floc already formed

will redisperse with high G values. It is believed that G is an

important parameter in coagulation and flocculation processes.

Camp also defined two dimensionless gross drag coefficients in

mixing tanks [47]. For fully turbulent flow, the dissipation function
= 124paC t 3 (2 )3
W 124paCs where 124 is 2 p is the mass density of the liquid;

a is the projected area of the rotor blades, and Ct is turbulent gross

drag coefficient determined by the geometry of the system. For

laminar flow, W = 4.92 pC s2 where 4.92 is (2 )and C is the viscous
v 8 v
gross drag coefficient determined by the geometry of the system.

Since W = G2p in turbulent flow:

G2 = K Ct3 ........... [22] where K =124 Pa (22)


In laminar flow:

2 2
G2 = K2Cs ........... [23] where K2=4.92 (23)


Ct and C values can be calculated using G and s values from

G vs. s diagrams.


Torque Measurement

Torque, or moment, may be measured by observing the angular

defonnation of a bar or hollow cylinder [48]. Either the deflection

or the strain measurement may be taken as an indication of the applied

moment.









A rather old device for the measurement of torque and dissipation

of power from machines is the Prony brake. A schematic diagram is

shown in Fig. 6. Wooden blocks are mounted on a flexible band or

rope, which is connected to the arm. Some arrangement is provided to

tighten the rope to increase the frictional resistance between the

blocks and rotating flywheel of the machine. The torque exerted on

the Prony brake is given by


T = FL (24)


The force F may be measured by conventional platform scales or other

methods.

The power dissipated in the brake is calculated from


P N hp (25)
33,000

where the torque is ft-lbf and N is the rotational speed in revolutions

per minute.

The dc cradled dynamometer is perhaps the most widely used device

for power and torque measurements on internal-combustion engines, pumps,

small steam turbines, and other mechanical equipment. The basic

arrangement of this device is shown in Fig. 7. A dc motor generator

is mounted on bearings as shown, with a moment arm extending from the

body of the motor to a force-measurement device, which is usually

a pendulum scale. When the device is connected to a power-producing

machine, it acts as a dc generator whose output may be varied by

dissipating the power in resistance racks. The torque impressed on

the dynamometer is measured with the moment arm and the output power

calculated with Eq. [25]. The dynamometer may also be used as an





























FI~ ': 6 Schematic of a Prony Brake
Source: Hiolman, J. P. Ex-berimenta1l Lethods
for En:ineers, I.cGrawv.-ill, Inc., i'ew York,
Y. Second Edition [1971]


Bel I gii i -

\( '


I )-C Illotil


FI-'JR 7 Schematic of Cradled Dynamometer
Source: :olman, J. P., Ex'-erimnental
L.ethods for En;ineers, i.;cGrawv-.:ilJ.,
Ic. ;ev York:, ;. Y., Second Edition
[1971]









electric motor to drive some power absorbing device like a pump. In

this case, it furnishes a means for measurement of torque and power

input to the machine. Commercial dynamometers are equipped with controls

for precise variation of the load and speed of the machine and are

available with power ratings as high as 5,000 hp.

Camp [36] measured the torque in a jar "by supporting beakers

on a platform suspended on a piano wire and by direct connection of

the paddle shaft to a motor mounted on a thrust bearing." Without

more detailed information and a schematic diagram, it's rather hard

to imagine the apparatus.

Recently, the usage of commercial Torque Meters for measuring the

torque input in the jar has become popular. Nevertheless, for magnetic-

driven jar testers which have no shaft to mount the torque meter,

apparently some other methods have to be developed.


Settling Velocity Distribution Curves

The meaning and measurement of the settling velocity distribution

curves is explained clearly by Hudson [49]. The content in this section

comes directly from the corresponding section of that paper.

For many years, the most widely-accepted criterion for
settling basin design was nominal residence time, even though
as long as seventy years ago the concept of settling velocity
had been advanced as a basis for design [50]. About four
decades ago, principally in the treatment of wastewaters, the
concept of surface loading, usually expressed as gallons per
square foot per day of basin area, was brought into more common
use. To obtain this figure, the flow through a given basin or
plant was divided by the settling area of the basin or plant.
As standard reference books point our [4,51] this is equivalent
to a settling velocity measured in units of length per unit
of time, and the meaning of a stated surface loading (or
equivalent settling velocity) is that a well-designed basin
should be able to remove all particles that will settle at
such a velocity or faster.









Sometimes these loadings have been expressed in terms of
inches per minute or gallons per square foot per minute.
Some authors have preferred to express settling velocities
in centimeters per second, which usually leads to units
smaller than 0.1 centimeters per second. Others have used
feet per second or meters per day. British engineers use
feet per hour. The unit of centimeters per minute yields
values of 1 to 10 units in the normal design range. Four
centimeters per minute is approximately equal to one gmp/sf,
or 1440 gpd/sf. One centimeter per minute is almost exactly
equal to one furlong per fortnight, or 1.32 cubits per hour.

In this paper, settling velocities are expressed in
centimeters per minute because the time and distance spans
are such that one can readily visualize what is taking place.
It is customary [4 ,51] for settling velocity data to be
plotted against the per cent of the initial concentration
which settles at a rate equal to or greater than the stated
settled velocity. Most of the literature presents these
data as arithmetic plots of velocity against per cent
remaining, and the values have often been experimentally
determined by analysis of results in settling columns,
measuring the reduction in suspended matter at various depths
in the column after various time intervals.

Similar data can be produced from actual operating results
using the removal of turbidity during sedimentation, expressing
the result as per cent of raw water turbidity remaining,
plotted against the settling velocity, as determined for
a given plant by dividing the rate of flow by the settling
basin area. The data for each plant produce one point on
the settling velocity distribution curve. If it is possible
to regularly sample the settled water at a number of points
along the settling basin, several points on the curve can
be obtained. (p.I-7,I-9)


Objectives

(1) To determine the mixing intensity, expressed as the mean

velocity gradient "G", throughout the applicable speed range,

using various jar test configurations. This step needs a new

set-up to measure the torque in jar tests.

(2) To develop a procedure for scaling-up the laboratory jar

test data including power input, impeller speed, etc., to full-scale


plants.









(3) To determine the effect of flow patterns induced by

different impellers on flocculation and sedimentation measured by

settling velocity distribution curves.

(4) To determine the effect of rapid mix on subsequent

flocculation performance also measured by settling velocity distribution

curves.

(5) To determine if "Gt" or "G" or some other parameter is

needed for design of rapid mix and flocculation basins.















CLAPTER III

EXPERIMENTAL MATERIALS AND \,ETHODS


Chemical Preparations


Turbidity Suspensions

Colloidal silica (Si02) suspensions were prepared by appropriate

dilutions of stock suspensions of Min-p-Sil 5* which has an average

particle diameter of 1.1 microns. Silica dispersions have been

selected because specific physical and surface chemical properties

of the silica colloids are well defined and reproducible. SiO2

particles are approximately spherical in shape and have a specific

gravity of 2.65. Specifications accompanying the supply of Min-p-Sil 5

stated that it has a specific surface of 20,000 cm2/gm. The colloid

chemical properties of silica, as a first approximation, are similar

to those of clays and of other materials present in natural water [7,15].

The surface potential of silica colloids is negative within neutral pH

ranges and becomes increasingly negative with increases in pH. A

typical analysis of Min-p-Sil 30 is shown in Table 2 [52].

The silica particles were weighed on an accurate laboratory

balance and added to volumetric flasks partly filled with distilled

water and were then diluted to the proper slurry concentration.


A product of Pennsylvania Glass Sand Corp., Pittsburgh, Pa.









These stock suspensions were placed on a magnetic stirrer to keep

them well mixed. All slurries were mixed at least three days to

allow complete particle hydrolysis. (The slurry concentration was

kept constant at 10,000 mg per liter.) Colloidal dispersions were

then prepared by removing volumetric portions of the slurry for

further solutions.


TABLE 2


Typical Chemical Analysis
Min-p-Sil 30


Silicon Dioxide (Si02) 99.70%

Iron Oxide (Fe203) 0.023%

Aluminum Oxide (Al203) 0.101%

Titanium Dioxide (TiO2) 0.019%

Calcium Oxide (CaO) Trace

Magnesium Oxide (MgO) Trace


Physical Properties


Specific Gravity 2.650

Refractive Index 1.547

pH 7.0

Porosity Non-porous


Alum Solution

Reagent grade aluminum sulfate A12(SO4) 3181120 was used for the

preparation of stock alum solution. In order to eliminate hydroxo

complex formation and polymerization, the stock solution was maintained








at a concentration of 100 g aluminum sulfate per liter (1 ml=100 mg

aluminum sulfate).

The fresh alum reagent solution was diluted from the stock

solution with distilled water so that 1 ml=l mg of aluminum sulfate.

The problem of aging with alum solutions was recognized and avoided

by discarding all solutions aged for one week.


Alkalinity

The alkalinity of the samples was controlled by adding a specific

amount of NaHCO3 to the colloidal silica suspension. For a one-liter

sample 87.2 mg of NaHCO3 were added so that the initial alkalinity

of samples was exactly 50 ppm as CaCO3.


Hardness

The hardness of the samples was controlled by adding a specific

amount of CaC12 to the colloidal silica suspension. For a one-liter

sample 18.5 mg of CaC12 was added so that the initial hardness of

samples was exactly 20 ppm as CaCO,.


pH Control

In a jar test the pH control for a combination of variables

(e.g., alum dose, alkalinity) had to be determined by preliminary

titration. The amount of acid or base which had to be added along

with the alum to maintain the desired initial pH was measured-- that

amount of acids or bases as added prior to the addition of alum to the

jar. Concentrated acid or base was not suitable for this purpose.

Therefore. 0.1 N NaOH or 0.1 N H2SO4 was used. However, 0.1 N NaOH

can stand for one month without changing titer, and 0.1 N H2S04,








three months [45]. Beyond these times, the acid or base had to be

replaced with fresh stock.


Preparation of Synthetic Water

An adequate amount of silica stock solution was added to a 20 liter

carboy partially filled with distilled water. Distilled water was

then added to the final desired volume (usually 16 liters). Proper

amounts of NaHCO3 and CaC12 were then added.

Before sampling, the carboys were vigorously shaken for 5 minutes

to insure uniformity of the colloidal silica suspension. It was found

that despite this precaution the turbidity on each two-liter sample

was sometimes different, therefore it was decided to measure the

turbidity of each jar in the experiment. Alkalinity, hardness and

pH did not vary for each sample.

Typical analysis of synthetic water was


Type A. Silica (Min-p-Sil 5): 200 ml/l

Alkalinity: 50 ppm as CaCO3

Hardness: 20 ppm as CaCO3

Turbidity: 100 ftu

Type B. Silica (Min-p-Sil 5): 20 mg/l

Alkalinity: 50 ppm as CaCO3

Hardness: 20 ppm as CaCO3

Turbidity: 10 ftu








Analytical Techniques


Alkalinity

The alkalinity titrations were performed using 0.02 N H2SO4 with

bromcresol green-methyl red mixed indicator as described in Standard

Methods [53]. The sulfuric acid was standardized using standard

0.02 N sodium carbonate, also as described in Standard Methods.


Hardness

Total hardness was determined by titration with carefully

standardized EDTA, following the procedures as described in Standard

Methods.


pH Measurement

All pH measurements were made using a Corning Model 7 pH Meter*

with a Corning Combination glass and Ag/AgC1 electrode. The pH

meter was calibrated daily using standard buffer solutions.


Turbidity

Turbidity measurements were made using Hach Analytical Nephelometer

Model 2424.** Four turbidity standards were supplied by the company,

i.e., 0.61, 10, 100 and 1000 NTU.


Torque Measurement and G Calculations

A torque-measurement device for the jar tester was developed and

tested. It is depicted in Figure 8. A two-liter beaker was hung by

a 0.3 cm O.D. copper wire attached to a fixed point on the ceiling.

Corning Glass Works, Philadelphia, Pennsylvania.
** Hach Chemical Company, Ames, Iowa.


































LL.






-P
C)
U







C)
o*


co



CS

H


F_








Two long steel wires. 0.05 cm O.D., were attached to the beaker at

points A and B from points E and F, respectively, in order to keep

the beaker from vibrating. A short, thin, strong cotton thread

BC perpendicular to the steel wire BF was attached to point B. A

second thread which formed a 45-degree angle to thread BC was attached

to point C at one end and to a stand on the other. The 45 degree

angle was convenient for the force balance at point C. During each

measurement the angle tended to change slightly due to the tension

in the threads. This was corrected by a fine adjusting screw H on

the bottom on one side of the stand. The difference between two

weights which maintained the balance on the scale pans was the force

(in gm-force) of the torque resulting from the rotation of the rotor.

The torque arm. R, was measured between AE and BC and found to be

constant at 7.0 cm. The temperature of the water was determined at

the time of each torque measurement. The initial force without any

rotor rotation was close to zero and was kept constant at 1 gram by

adjusting the screw H. This value was subtracted from every force

measured thereafter. Force values measured in this study ranged from

1 to 120 grams. The revolution of the rotor was measured by a tachometer

at low speed and by a stroboscopic light (STROBOTAC)" at high speed.

Once the torque was measured, W was calculated according to

equation (21). From known values for the viscosity of water at the

temperature of the experiment and the value of W, G values were

calculated. Values of Ct and C were calculated using equations (22)

and (23). Reynolds number and Power numbers were calculated by

equations (14) and (16). Note that power P equals 'dissipation

SA product of General Radio Company, Concord, Massachusetts.



















Blade Model


Phipps & Bird


Marine Type





Florida 1


Florida 2


TABLE 3

IMPELLER CHARACTERISTICS


Blade Type Diameter,
D, cm


2-blade 7.6
paddle

3-blade 5.0
propeller

2-blade 5.0
pitched paddle

2-blade 7.2
paddle

2-blade 7.2
paddle


Projected Area,
a,cm2


17.5


4.5


2.8


28.8


18.4


--












7-{]

c-i

!_ -L
-> ?--K-,Z' ~


CfI3


I-

N:


f-









IC)L


7 -


-A 5s




51













































LIU'
0
O



o
E 0







function' W times the volume of the liquid (2000 cm3). The model,

type, diameter and projected area of blades are shown in Table 3 and

Figure 9.


The Modified Jar Test Procedures


Some 20 different techniques [46] have been used for the design

and control of coagulation processes. They are: (1) the jar test,

(2) speed of floc formation, (3) visual floc size comparisons,

(4) floc density, (5) settled floc volume, (6) floc volume concentration,

(7) residual coagulant concentration, (8) silting index, (9) filterability

number, (10) membrane refiltration, (11) inverted gauze filter,

(12) cation exchange capacity, (13) surface area concentration,

(14) conductivity, (15) ZETA potential, (16) streaming current de-

tection, (17) colloid titration, (18) pilot column filtration,

(19) filtration parameters, (20) cotton-plug filters, and (21) electronic

particle counting.

The modified jar test was chosen for this study because it is

the most economical, most flexible, and most practically used technique.

The data generated are as useful as data derived from any of the other

techniques above [46].


Equipment

Laboratory multiple stirring machine. This machine* has six

places with a rheostat for controlling the rotational speed. However,

the tachometer attached to the machine with a zero to 100 RPM scale

is not accurate. The actual speed range for this machine is from 0


Product of Phipps and Bird. Inc., Richmond, Virginia.








to about 165 RPM. Correct RPM readings, hence, had to be checked

by another tachometer. At low speed, the RPM can be counted by eye

or by touching the rotating screw with a fingertip during a one-

minute or 30-second period.

Portable laboratory mixer. This mixer* has a range of from zero

to 1750 RPM. This mLxer was used as a rapid-mix device throughout the

modified jar tests. The small propeller shown in Fig. 9 was the

impeller used for this purpose.

Impellers. Two types of impellers were used:

(1) Paddles which were supplied with a Phipps-Bird (P-B) Jar

Tester. Dimensions of the paddle are shown in Fig. 9 and

also in Table 3.

(2) Lightning** laboratory 316 stainless, 3.1 in. (7.9 cm) diameter

propeller. This propeller is a marine-type with three blades.

This propeller has the same projected area as the P-B paddle.

The dimensions of the propeller are shown in Fig. 9(f).

Timers. A GRA LAB Universal Timer Model 1711 was used. The

timer allowed control of the modified jar tester with easy-to-read

scales. The timer can also turn-on or turn-off the jar test machine

automatically, when used properly. A small Heuertt timer with manual

control was also used for timing the rapid-mix process.

Glass tubing. The glass tubings were used in syphoning off

samples for a turbidity reading. The shape of the tubing is shown

on Fig. 10. Since each sampling syphoned off about 45 ml (40 ml for

* Product of Precision Scientific Co., Chicago, Illinois.
** Product of Mixing Equipment Co., Inc., Rochester, New York.
.Product of Dimco-Gray Company, Dayton, Ohio.
TT




















0 0
I o

Ln4
Or' u,

tz
I IMPELLER



-- I
I





FRONT VIEW
BAFFLE









IMPELLER










TOP VIEW

PINCH CLAMP
SIPHON TUBE


FIGUR 10 Jar Test Apparatus.








turbidity reading, 5 ml flush-out water) of the sample, in order

to maintain the sampling depth as exactly 10 cm means one had to

change the tubing each time with a longer (the immersed part) glass

tube after each sampling theoretically. Any movement of the tubing

disturbs the settling of the floc. When sampling times are close

(e.g.. 1 min, 2.5 min and 4 min), this disturbance can be serious and

will result in a distrotion of the data. After preliminary tests,

it was found that changing the tubing once during the middle of the

sampling period (e.g., between 4 to 8 minutes) with a new tubing

1 cm longer (in immersed depth) provided good compensation for both

sampling depth and sampling-tube-change disturbance. For the research,

then, two sets of tubes were used. The only difference between the

two sets was the length of the immersed part. The lengths of the

tubes were designed such that under the experimental conditions. the

sampling depth was very close to 10 cm. The total lengths were 13.5

and 14.5 respectively.


Operations

The jar test procedures were very similar for the later three

phases of work. The procedure will be outlined below.

Preliminary determinations. Since pH is known to have a considerable

effect on coagulation, it was the purpose of this preliminary test

to determine the optimum pH ranges for the coagulation of the

colloidal silica suspensions. The procedure was: Conventional

coagulation tests were performed (e.g., rapid-mix at 160 RPMI for

1 min.. slow-mix at 20 RPM for 15 min., allowed to stand for 15 min.

and then the supernatant was sampled for turbidity measurement) on








the prepared synthetic water to determine the coagulant demand with

special steps taken for pH control. This determined the optimum

coagulant dose under these circumstances. This coagulant dosage was

then added to six 2-liter samples of synthetic water and the amount

of acid or alkali required to cover a range of pH values was determined

by titration (0.1 N NaOH and 0.1 N H2SO4 were used). The pH range

of 5.0 to 8.5 was covered in steps of 0.5 pH units. These conventional

jar tests were conducted using the coagulant dose determined above

and the pH was varied by adding the quantities of acid or alkali as

determined above. Note that the acid or alkali must be added prior

to the addition of the coagulant. The final turbidity was plotted against

pH to determine the optimum pH range.

Flocculation (slow-mix) study. Six jars (2-liter beakers) of

synthetic turbid water at the same silica concentration were prepared

from the stock solution. To each jar the same amounts of acid or

alkali determined from the preliminary tests was added in order to

keep the pH in each jar at optimum conditions. Rapid-mix was performed

using a high speed (1750 RPM) portable mixer with a small marine-

type propeller. The rapid-mix time was 30 seconds. Before the

addition of coagulant, the jars were stirred for at least 10 seconds.

The coagulant was poured onto the water surface using a small graduated

cylinder. As soon as the rapid-mix process was completed, the modified

P-B jar tester which employed paddles on Jar No.'s 1,3, and 5, and

propellers on Jar No.'s 2,4, and 6 was started with the slow-mix at

the RPM. The problem of the delay between rapid-mix and slow-mLx,

especially for jar no. 1 (about 3 min.) was recognized. This problem








was partially compensated by repeating the jar test starting with

jar no. 6 using the same procedure and the average values taken.

From the first part of the research, the relationship of G

(mean velocity gradient, sec-1) vs. N (impeller speed, RPM) were

available. Those data allow the control of the G value as desired

with different configurations; however, the 2-liter beaker with four

1 cm x 17 cm baffles was chosen for this part of the research. The

advantages of using this configuration are (1) reduction of the

rotation of the water in the jars during the settling period after

stirring was stopped, (2) the jar-testing equipment operated at a

higher velocity gradient for the same rotary speed than when no

baffles were used, and (3) it was more convenient than other baffling

systems for the rapid-mix process in that the propeller did not

collide with the baffles during rotation and was easier to conduct.

After the stated slow-mix time, mixing was stopped by pulling up the

impeller shafts so that the impellers were not in contact with water.

One minute before mixing was stopped, 40 ml of samples was syphoned

from each jar for the initial turbidity measurement. Those turbidity

values tw.ere recorded on the jar test report as the turbidity of the

sample at zero time. After the mixing was stopped, 40 ml of samples

was syphoned from each jar at 1, 2.5, 4, 8 and 16 minutes for

turbidity measurement. The final supernatant was removed using a

100 ml pipette. This 100 ml sample was used for measuring the pH,

the alkalinity and the hardness.

The advantages of using six jars simultaneously for the slow-mix

step are (1) it permits the comparison of the floc formation, flow

pattern, and floc settling characteristics due to different impellers








side-by-side and allowed pictures or motion pictures to be taken

for later comparative studies, and (2) it saved about 80% of time

compared to the one-jar-each-time method. (For conventional jar

tests where only the final supernatants are considered, six jars

can be done simultaneously.) For settling studies to be made, at

least two persons are needed if six modified jar tests are studied

simultaneously.

Rapid-mix study. In this study the rapid-mix was performed using

the high speed portable laboratory mixer with a marine-type propeller.

The jar test procedure was similar to the flocculation study except

that each jar was run individually in order to eliminate the idle time

between rapid-mix and slow-mix processes. The flocculation process

was performed using either P-B paddles or marine-type propellers with

the same projected area. The flocculation G and t (time, min.) were

kept constant throughout this study.

Gt distribution study. In this study the jar test procedure was

similar to that of the rapid-mix study except that for each jar the

total Gt value (i.e., rapid-mix Gt plus slow-mix Gt) was kept

constant throughout the experiment.














CHAPTER IV

RESULTS AND DISCUSSION


Velocity Gradient Calibration of Jar Test Equipment


Mean Velocity Gradient Calibrations

The first set-up tested (Series A) made use of a 2-liter beaker

without baffles. The rotors used were: a Phipps and Bird (P-B)

paddle (Model A-l): a small three-blade marine-type mixing propeller

(Model A-2); and small pitched two-blade paddles (Models A-3 and A-4).

The only other difference was the distance of the paddle from the

vessel bottom. The impeller dimensions, distance of impeller above

the vessel bottom together with their G values are shown in Figure 11.

All curves had slopes of 3/2 at RPM greater than 60. It can be seen

that Model A-1 had higher G values than either A-2 or A-3. However,

the G values were slightly lower than those obtained by Camp [36;

Figure 1]. It was observed also that the distance of the pitched

blade (Models A-3 and A-4) above the beaker bottom did not change the

G value in the test range for clearances of 4.1 cm and 8.76 cm.

The second configurations tested (Series B) involved a beaker

with 4 long baffles, 1 cm x 17 cm, extended from top to bottom, separated

by 90 degrees each with the P-B paddle (Model B-l); the propeller

(Model B-2); and the pitched paddle (Model B-3). This type of baffling

is commonly used in the chemical industry. For the experiment,


















103
9
8
7
S6

.5

4

3


2
C,
-H





> 2
10

o 8
7
6
5


/

/O


10 2 3


5 6 7 8 9 10'


2 3 4 5 6 7 8 9 10


i, ( impeller speed, RPM )


FIGURE i1


Velocity Gradients at 'Various Speeds,
Series A.


A4
NC


Al


( A3

0 A4


Camp w/o
stators








the baffles were made of Plexiglas and attached to the beaker with

cement (see Figure 12). Results were shown in Figure 12. Again,

the paddle yielded higher values than the pitched blade impellers.

The slopes of the curves were 3/2 in the test range.

The third configurations tested (Series C) involved a 2-liter

beaker with 3 sets of twin rectangular baffles (3.8 x 1.9 cm). The

beaker configuration was identical to the one used by Camp [40, Figure 1]

except for the method of stator attachment. In Camp's experiments,

the stators were attached to a metal framework and placed in the

beaker. This left some void space between stators and the beaker.

As in the second configuration the stators were cemented directly to

the beaker.

The fourth configuration tested (Series D) used a 2-liter beaker

with six 3 x 3 cm baffles similar to those used by Camp [40, Figure 1].

Again, the baffles were attached by cementing. Figure 13 shows the

dimensions of the systems. Figure 14 shows the G values obtained.

The curves had slopes of 3/2 in the test range. The two different

shapes of baffles resulted in the G values shown for all three systems,

i.e., C-l = D-l, C-2 = D-2 and C-3 = D-3. However, the G values of

C-1 (or D-l) were much higher than those from the other two systems.

The data show that the quadruple and triple baffles had the same effect.

A comparison of Figures 12 and 14 also reveals that the G values for

B-I were the same as D-l. This means that the long baffles had the

same effect as either the rectangular or square baffles.

Camp found that the C value of P-B paddle with stators was higher

than that found in this study for rotor B-l (see Figure 14). This




























----
B\


10 1 L I i i I
10 2 3 4 5 6 7 8 9102


I I
2 3


4 5 6 7I 8 91
4 5 6 789103


N ( impeller speed, RPM )

FIGURE 12 Velocity Gradients at Various Speeds,
Series B.


B2


O 81

A B2

0 B3






















Fi9 8-4i -


~lalF~r~iLL -~~Eb tt-


i-~~






















A D2

D C3

S D3

stators (P-B paddle)

sEators ( Pitched paddle)


2 3 4 5 6 7 8 9 10 2 3 4

N ( impeller speed, RPM )

FIGURE: 14 Speed Versus Velocity Gradient,
Series C and ).


5 6 7 8 9103


O 0

S

0


C1

D1

C2

Camp

Camp


. .I I I A


I I I


r r I


I I









might have been due to the turbulence and vortex caused by small void

between the stators and the beaker.

The G values of 450 pitched paddles were found by Camp (3.2 cm

x 1.78 cm) to be lower than for P-B paddles. This is in agreement

with this study.

The last two set-ups tested were series E-l and F-l which

utilized a magnetic-drive Jar Tester.* Model E-l had no stators

while F-1 had three-blade stators.

Figure 15 shows the configuration and G value of these systems.

The curves have slopes of 3/2 at higher rpm. For Model F-l the slope

changed to 1 at 45 rpm and below. For Model E-1 the point of inflexion

occurred at 75 rpm.

Comparison of Figures 14 and 15 reveals that the G values for F-l

were almost as high as B-1 for the same impeller speed. Model E-,l

although it yielded lower C values than F-l, generated more mixing than

the small marine type and pitched-blade paddles with baffles. Above

75 rpm E-l values coincide with Camp's data for P-B paddles without

stator.

Figure 16 combines Figures 11, 12, 14, and 15. For comparison,

the G values at 100 rpm for each model have been listed in Table 4.

It is interesting to note that the marine-type propeller and

the pitched-blade propellers had the same G for three different baffle

configurations.

The temperature range for all torque measuring experiments was

from 22C to 240C.


Environmental Specialties, a division of Water and Air Research, Inc.,
Gainesville, Florida.




















/
/'


1 E1
"r r i -t

t -*| /'J'^.- I
El


Plan View


1-

m


-Ft 72c 4-
Fl


Camp w/ stators

-.-.- Camp w/o stators


2 4 5 I i7 102
2 3 4 5 6 7 8 9 102


2 3 4 5 6 7 8 9 103


N ( impeller speed, RP:: )


FIGURE 15


Calibration of magnetic Stirring System,
Series E and F.


O El

A F1




67














103
9
8
7
6
S5
04

3 -/ .


H 2




-f ^/ // /







3-


2 A2
S//




3 A2




10 1 7 I 3
10 2 3 4 5 6 7 8 910 2 3 4 5 6 8 9 10
N ( imoeller speed, RPM )

FIGURE 16 Summary of Relation Between SDeed and
Velocity Gradient, All Series.









TABLE 4

Comparison of G Value at 100 RPM


G Sec-I Model

140 B-1, C-l, D-1

120 F-i

70 E-1

54 A-i

21 B-2, C-2, D-2

17 B-3. C-3, D-3

16 A-2

13 A-3, A-4



Turbulent Drag Coefficient Ct


The Ct results were calculated and are shown on Figures 17,18,

and 19. They were similar in shape to those from Camp's data [47,

Figures 3 to 6]. The value of Ct was approximately constant in the

higher rpm range. For each set-up, there was a rotational speed below

which Ct increased as the speed was decreased. When Ct was constant,

from equation (22), then


G2 = Klls3 (26)


where K11 = K Ct, so that log G versus log s had a slope of 3/2.

Figures 17 and 18 also show that the installation of baffles

increased the turbulent drag coefficient. Figure 19 shows turbulent

drag coefficients for various impeller speeds.































With Baffles


thout Baffles


SB1,C1, D1


0 Al


2 3 4 5 6 7 8 910Z


N ( impeller speed, RPv )

FIGURE 17 Turbulent Drag Coefficients for
Phipps-Bird Paddle with &nd without
Bz-ffles.


1
10
9
-P 8
7
6
5


2 3 4 5 6 7 8 9103


I I I I f t 1 1 ( I
I I gp


I I I . .



























































O Fl

0 El


II I I I I I I


I I


2 3 4 5 6 7 3 910V


2 3 4 5 6 7 8 9103


S( impe1ller speed, :.. )

TFI 18 TLrbuulent Dir:' ': )ue ffi.cients for
: ne, ic-Dr-ive J:- t.rs


-1
-P 9
" 8
7
6























BI, Cl, D


C23,D3
C2,D2 B3

82


A3,A4
==~-=7A2-


2 3 4 5 6 7 8 9102


I I I I I I I I 1
2 3 4 5 6 7 8 9103


N (impeller speed, RPM)


FIGURE 1"


Turbulent Drag Coefficients for Various
Impeller Speeds.


-16
101
9
8
7
6
S5
4








The curves of C illustrated in Figures 17, 18, and 19 are based

on fully turbulent drag which is assumed to be proportional to the

square of velocity [47]. This proportionally does not hold except

where the curves are nearly horizontal. These figures also show that

a gradual change from laminar to fully turbulent flow existed and

was variable for different system geometries.

Plots of Cv are not necessary because the value of Cv may be

computed for any impeller speed from the corresponding value of Ct,

according to the following equation from Camp [47];


Cv = 25 paCts



Computations of Impeller Characteristics

If it were desired to find the projected area of a marine-type

propeller in order to achieve the same G values as C-l (Phipps and

Bird paddle) (see Figures 13 and 14), the definition of Ct and the

G and W correlations, G2 = 124 pCts3a, i.e., aCt = G2- could be
124 ps3

used. From Figure 14 (curve C-l), when rpm = 130, G = 200 sec-1,

assuming a water temperature of 25C then P = 1 cp = 1 x 10-2 gm cm-1 sec-1


and p = 1 gm cm-3 and aCt = G2 = 0.316 cm2. Now, since the C
124ps3

versus rpm curve for this "unknown" propeller is not available, the

C-2 and D-2 curves (3 blade marine-type propeller with 4.5 cm2 projected

area) can be utilized. Figure 19 (curve C-2 and D-2) shows that when

2
s = 130 min-1 = 13/6 sec-1, Ct = 1.8 x 10-2, a= 0.316 an2 = 17.6 cm2
1.8 x 10

This value corresponds very closely to the projected area of the Phipps

























With Baffles


"~^"^ -~A -_ __ /


Without Baffles


0 BI,C1,D1

0 Al


I I I .


2 3 4 5 6 7 8 910'


2 3 4 5 6 7 8 9 103


NRe sD2


FIGURE 20 Power Correlation for Phipps-Bird Paddle
with and without Baffles.


1


0


I I I I I I I I I I 1 J


I I i I i i I I





















































O Fl

0 El


I I II


2 3 4 5 6 7 8 9 102


NRe_- D2
A


FIGURE 21


Power Correlation for Miagnetic-Drive
Jar Tester with and without Baffles.


n
Lr)
a0


2 3 4 5 6 7 8 9103
































BI,C1,D1


A3,A4


2 3 4 5 6 7 89102


_I I 1I 1 I 1 I
2 3 4 5 6 7 8 9103


P sD2
NRe
,K


FIGURE 22 Impeller Power Correlations


101
9
8
7
6
5
u o 4

0- 3

II
2
z








and Bird paddle, 17.5 cm (see Table 3). This example verified Camp's

conclusion [47] that impellers produce the same mean-velocity-gradient

G as long as they have the same projected areas.


Energy Input into the Jar

The energy input at different rotational speeds in mixing is

usually expressed by plotting NRe versus N This plot for A-1 and

B-1 (i.e., C-1 or D-l) (Figure 20) shows that there is a constant

energy increase into the jar due to installation of baffles. Similarly

for magnetic-drive jar testers, F-l had higher energy input than E-l

even though F-l had a slightly smaller rotor (Figure 21). Figure 22

shows the impeller power correlations for various systems.

Another criterion of energy input into the jar is W (the dissipation

function). As a matter of fact, this is the criterion for reaching

the scaling equation for mixing vessels. Plots of W versus N are not

necessary because they may be computed for any impeller speed from the

corresponding value of G taken from the curve. Recall that

G ( 1/2


thus W = G2-


Scale-up and Scale-down Considerations

An example of scale-up is shown below:

Sample Problem -

A mixing tank in a treatment plant is going to be built (a) 10,

(b) 100, (c) 1,000. (d) 10.000 times larger than any model in this

research. Assume the laboratory results are available from the jar

test: what is the procedure for scaling-up so that we can be sure the

mixing condition in the prototype is similar to that in the jars?









Solution -

From the experiment, the following data are available: D, T,

Z, C, w, p, R, P, N, G and W.

(a) 10 times larger

D' T' 7' r' C, 1 I '
(1) Scale ratio T Z C w p 10
D T Z C w p 9

where primed symbols relate to the prototype and unprimed symbols

to corresponding quantities in the model.

Hence, D' = 10D, T' = 10T, Z' = 10Z, C' = 10C, w' = 1w, p' = 10p,

' = 10 Z.

This is the requirement for geometrical similarity.

(2) Impeller speed

TN' D' -2/3 -2/3 1
Scaling equation N= ()-23 = (10)-2/ 4 65 0.215

Hence N' = 21.5% N.

(3) Power consumption

P' D' 3 3
Scaling equation -p- = 10
p = 10

Hence P' = 103P = 103WV.

(b) 100 times larger

(1) Scale ratio = 100

Hence D' = 100D,...,' = 100 9.

(2) Impeller speed


N' D' 3 3 6
N (-) = (100) = 10

Hence N' = 4.7% N.








(3) Power consumption

P' D'3 3
P' = DD = (100) 3


Hence P' =


106 P = 106l


(c) 1,000 times larger

(1) Scale ratio = 1,000

Hence D' = 1,000D,...,' = 1,000 k.

(2) Impeller speed


N' D' -2/3
N D


= (1000)2/3 = 0.01
100


Hence N' = 1% N.

(3) Power consumption

P' D'3 3 9o
= (D) 3 = (1000) = 10

Hence P' = 109 P = 109 WV.

(d) 10,000 times larger

(1) Scale ratio = 10,000

Hence D' = 10,000 D,...,Z' = 10,000 k.

(2) Impeller speed


N' D' -2/3
N ~ D


= (10000) 2/


1
- 0.00215
465


Hence N' = 0.215% N.

(3) Power consumption


P' 104 3
p- = (10 )


1012


Hence P' = 1012 P = 1012 W.


10








In this example, the power consumption may also be calculated

assuming G' = G. For instance, in (a)

liquid volume in jar = TrT Z = V

liquid volume in tank V' = (T')2Z' = (10T)2(1OZ)r = 103T2Z = 103V

IV 1/2 =W' 1/2
Since G' =G ( /2 W 1/2

since W = P/V and W' = P'/V'

P/V 1/2 P'/V' 1/2
hence (-- = ---

In homologous systems, p = p'

P 1/2 P' 1/2 P P'
M( = ( V-F I' V I

P' P' P
V' 103 V

P' = 103


From this example, one may conclude that the establishment of

equal G values is a necessary but not a sufficient condition for

similarity. For two properly scaled-up geometrically similar systems,

G values in corresponding points have to be equal. On the other hand,

the same G values in two corresponding systems do not necessarily

mean they are geometrically, dynamically and kinematically similar.

The procedure of the example can be reversed for scale-down problems.

In this case, the most astonishing thing is the relationship of impeller

speed between prototype and model systems. When the prototype is

10 times larger than the jar, the impeller speed of the prototype

has to be 21.5% of that of the jar in order to maintain the kinematic

and dynamic similarities between two systems. When the prototype








is 100 times larger than the jar, the impeller speed of the prototype

has to be 4.7% of that of the jar in order to fulfill the similarity

conditions. When it is 1,000 times'larger, only 1% impeller speed

is required. When it is 10,000 times larger, only 0.2% of impeller

speed is required. If the flocculation basin were one of 2000-liter

(70.7 cubic feet) capacity and the proportional impeller [1,000 times

larger) was operating at 1 rpm the corresponding impeller speed in a

2-liter har has to be 100 rpm in order to establish similarities between

the two systems. Currently, the impellers used in flocculation basins

are multiple-bladed paddles with rather small projected areas. So it

is impossible to compare those results to actual plant data now.

Camp [47] has called attention to the following facts: (a) the

fluid condition in full-scale mixing and flocculation basins is always

turbulent, even when "G" values are relatively low; and (b) at speeds

commonly used in jar test procedures, laminar flow conditions may obtain.

Short-circuiting in mixing and flocculation basins is always

present in full-scale plants. However, this does not occur in jars.

Short-circuiting, hence, is responsible for the better flocculation

results from more turbulent flow conditions in the mixing basins.


Comparison of N and C
p t

From the definition of N and Ct, N = Pg C _
P p ps3D5' 124pas3

PN aV
it can be shown that 124 Thus the ratio of N /C
124pas'V t D3

is constant for specific systems. From Figures 17, 18 and 19








(Ct versus S) the data plotted in Figures 20, 21 and 22 (N versus

NRe) can be calculated so that one could compare those values

with literature values.


Applications

Since G values have been calibrated for 5 series of common jar

configurations, it would be to the advantage of water and waste-

water personnel performing jar tests to use these calibration curves

so that they know the exact G value in their studies. The use of

numbers such as "100 rpm", "40 rpm" do not provide any useful infor-

mation.

One of the most important functions of the jar test is to simulate

the existing full-scale plant in the laboratory. When simulation

is concerned, three similarity conditions, i.e., geometric, dynamic,

and kinematic, should be maintained. The two scaling equations

derived along with the velocity gradient calibration curves should

prove helpful as far as the upgrading of existing full-scale coagulation-

flocculation and sedimentation basins via the jar test technique is

concerned.

On the other hand, these two equations used in conjunction with

the G calibration curves are useful for engineers designing new full-

scale treatment plants since the general procedure should require

that the designer simulate the coagulation-flocculation and sedimentation

performance of the jar test for the specific raw water to be utilized

by the proposed new plant.









Floc Settling Characteristics Due to Different Flow
Patterns in Flocculation

This portion of the study is divided into four parts according

to the silica concentration and alum dose.

The jar test results were recorded on the jar test report is

a modification of the jar test report designed by a research corporation.*

They are shown as Tables. Each table has been used to record the

data from 6 jars simultaneously. The data for each jar included

the rapid-mix RPM, G, and time; flocculation RPM, G, and time; coagulant

used and concentration applied; alkali or acid added if any; raw,

final supernatant and settled turbidities; final pH, etc. The settled

turbidities were also expressed as % of raw water turbidity. In some

cases the turbidity of the sample taken one minute before the floc-

culation stopped (recorded as Sample A, 0 min. time of settling) was

higher than the raw water turbidity. When this happened (usually in

the lower silica concentration solutions), it was used as a basis for

calculating the % instead. However, the difference between those two

was usually quite insignificant.

The settling velocity distribution curves were drawn on prob-

ability -arithmetic papers as Vs (settling velocity) vs. % turbidity

remaining. The V varied from 0 to 4 cm/min. Comparisons drawn

from these curves are more useful than singular data points derived

from supernatant turbidity measurements taken at the end of the settling

period.


Water and Air Research, Inc., Gainesville, Florida.









In the test reports, jars 1, 3, and 5 usually utilized the P-B

paddle while jars 2, 4, and 6 usually utilized the marine-type propeller.

The comparison of the performance of the paddle with the propeller

was both by visual observation and from settling velocity distribution

curves. The visual comparison included the classification of the floc

just before the end of flocculation using the index developed by

Walker (54), as shown in Figure 23. The classification method served

as a qualitative measure only. The visual comparison also included

movies and still pictures. Although many good pictures were taken,

only a few are shown here. The pictures were taken using a Nikon

35 mm camera loaded with high-intensity black and white film. Initially,

the final supernatant alkalinity and hardness were measured. After

several series of tests it was found that the final alkalinity and

hardness were approximately constant in each individual series. For

instance, for jar tests of a 20 ppm silica suspension with 70 ppm

alum at the optimum pH, the final alkalinity was between 40 and 46 ppm

(as CaCO3), and final hardness was close to 0 ppm (as CaC03). For

a 200 ppm silica suspension, the final alkalinity was between 30 to

36 ppm (as CaCO3) and the final hardness was close to 2 ppm (as CaCO ).

Therefore the final alkalinity and hardness were not recorded on each

jar test report. The approximate final alkalinity and hardness were

recorded for each series only.

The quantitative comparison came from the curves showing % raw

turbidity remaining versus flocculation time at constant G. The data

points for those figures were drawn from the settling velocity

distribution curves as V (settling velocity) = 3 cm/min., which is
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