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OPTIMIZATION OF DISSOLVED AIR FLOTATION FOR
DRINKING WATER TREATMENT
THROUGH CFD MODELING
by
Babak Lakghomi
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Civil Engineering
University of Toronto
© Copyright by Babak Lakghomi (2015)

ii
OPTIMIZATION OF DISSOLVED AIR FLOTATION FOR DRINKING
WATER TREATMENT THROUGH CFD MODELING
Babak Lakghomi
Doctor of Philosophy, 2015
Graduate Department of Civil Engineering
University of Toronto
0B0BABSTRACT
The dissolved air flotation (DAF) process is known for its efficiency in the removal of low
density particles from water. The performance of the system depends, in part, on the
hydrodynamics of the flow. Whereas experimental flow measurement methods for DAF can be
very challenging due to the presence of bubbles and particles, computational fluid dynamics
(CFD) can be applied as an alternative approach for improving the understanding of the
hydrodynamics, but would still require validation.
In this study, twophase and threephase analytical and CFD models of DAF were developed to
evaluate the formation of stratified flow (back and forth horizontal flow layers in the separation
zone) and its impact on bubble and particle removal. By including the effects of bubble
aggregation and bubbleparticle aggregation, the models were able to predict the formation of
stratified flow under different air fractions, bubble sizes, and loading rates.
The CFD model showed that stratified flow improved bubble removal as well as particle
removal, demonstrating that up to 130% higher loading rates can be achieved in the presence of
stratified flow. An increase in air fraction and bubble size was shown to improve bubble

iii
removal, but particle removal began to decrease when air fractions and bubble sizes increased
beyond optimum levels.
The CFD model was then validated with a pilotscale DAF system by comparing measurements
of residence time distribution (RTD), bubble layer position and bubbleparticle contact
efficiency. In general, the CFD model was able to represent the pilotscale DAF flow at different
loading rates with very good accuracy (R2 values higher than 0.75).
Finally, the validated model was applied to evaluate the effect of the addition of different
configurations of baffles in the separation zone. The results suggested that baffles in the
separation zone can enhance stratification of the flow and allow up to 86% higher loading rates.

iv
1B1BACKNOWLEDGMENTS
This research was financially supported by Walkerton Clean Water Centre, the Natural Sciences
and Engineering Research Council of Canada, and Corix Water Systems.
I would like to express my deepest gratitude to my supervisors, Professor Ron Hofmann, and
Professor Yuri Lawryshyn, for their guidance and encouragement in my research and my
professional life. I would also like to thank Professors Bob Andrews and Markus Bussmann for
being on my supervisory committee and offering their constructive and insightful suggestions.
I would like to appreciate Stephen Tang for his great help in setup of the pilot system.
Finally, I would like to thank my dear parents and my dearest wife, Sara, for their endless
support and encouragement along the way.

v
2B2BTABLE OF CONTENTS
0B0BABSTRACT .................................................................................................................................... ii
1B1BACKNOWLEDGMENTS ............................................................................................................. iv
2B2BTABLE OF CONTENTS ................................................................................................................ v
3B3BLIST OF TABLES ......................................................................................................................... ix
4B4BLIST OF FIGURES ........................................................................................................................ x
1. 5B5BIntroduction ............................................................................................................................. 1
1.1. 12B12BBackground ...................................................................................................................... 1
1.2. 13B13BObjectives ......................................................................................................................... 2
1.3. 14B14BThesis Chapters ................................................................................................................ 3
1.4. 15B15BAssociated Journal Publications ....................................................................................... 4
1.5. 16B16BReferences ........................................................................................................................ 4
2. 6B6BLiterature review...................................................................................................................... 6
2.1. 17B17BImportance of stratified flow ............................................................................................ 6
2.2. 18B18BBubbleparticle attachment models .................................................................................. 7
2.3. 19B19BPrevious attempts at CFD modelling ............................................................................. 10
2.4. Research gaps ................................................................................................................. 14
2.5. 21B21BReferences ...................................................................................................................... 14
3. 7B7BImportance of flow stratification and bubble aggregation in the separation zone of a
dissolved air flotation tank 0F0F ........................................................................................................ 18

vi
3.1. 22B22BIntroduction .................................................................................................................... 18
3.2. 23BMethodology .................................................................................................................. 20
3.3. 24B24BA conceptual model for bubble removal in the separation zone .................................... 21
3.4. 25B25BResults and Discussions ................................................................................................. 26
3.5. 26B26BConclusions .................................................................................................................... 32
3.6. 27B27BReferences ...................................................................................................................... 33
4. 8B8BA model for optimization of particle removal in a dissolved air flotation tank: importance
of stratified flow and bubble size1F1F .............................................................................................. 35
4.1. 28B28BIntroduction .................................................................................................................... 35
4.2. 29BMethodology29B .................................................................................................................. 37
4.4. 30B30BResults and Discussions ................................................................................................. 47
4.5. 31B31BSummary and Conclusions ............................................................................................. 57
4.6. 32B32BReferences ...................................................................................................................... 58
5. 9B9BEvaluation of flow hydrodynamics in a pilotscale dissolved air flotation tank: a
comparison between CFD and experimental measurements 2F2F .................................................... 60
5.1. 33B33BIntroduction .................................................................................................................... 60
5.2. 34B34BMethodology .................................................................................................................. 62
5.3. 35B35BResults ............................................................................................................................ 68
5.4. 36B36BConclusions .................................................................................................................... 76
5.5. 37B37BReferences ...................................................................................................................... 76
6. 10B10BCFD Applications: Effect of geometric modifications and 3D modelling ............................ 78

vii
6.1. 38B38BIntroduction .................................................................................................................... 78
6.2. 39B39BMethodology .................................................................................................................. 78
6.3. 40B40BResults ............................................................................................................................ 81
6.4. 41B41BConclusion ...................................................................................................................... 85
7. 11B11BConclusions and Recommendations for Future Research ..................................................... 86
7.1. 42B42BConclusions .................................................................................................................... 86
7.2. 43B43BResearch Contributions .................................................................................................. 86
7.3. 44B44BRecommendations for Future Research ......................................................................... 87
Appendix A: .................................................................................................................................. 89
A.1 62B62BModel set up and convergence ....................................................................................... 89
A.2 63B63BTwophase flow model ................................................................................................... 90
A.3 64B64BPopulation balance model for bubble coalescence and breakup ................................... 90
A.4 Threephase flow model ................................................................................................. 92
A.5 65B65BReferences ...................................................................................................................... 94
Appendix B: .................................................................................................................................. 95
B.1 66B66BUser defined function (UDF) for degassing ................................................................... 95
B.2 67B67BUser defined function (UDF) for aggregation ................................................................ 95
B.3 68B68BMATLAB code for analytical particle removal model .................................................. 98
Appendix C: ................................................................................................................................ 101
C.1 Analytical bubble and aggregate distribution ............................................................... 101

viii
C.2 CFD bubble distribution and collision frequency ........................................................ 102

ix
3B3BLIST OF TABLES
Table 2.1 Governing equations for bubbleparticle aggregation rates ............................................ 8
Table 2.2 A comparison of two phase CFD models for DAF ...................................................... 11
Table 3.1 Bubble size groups for each inlet bubble size ............................................................... 21
Table 4.1 Particle removal efficiency for varying air fractions and bubble sizes.. ....................... 53
Table 4.2 Particle removal efficiency for varying air fractions and bubble sizes.. ....................... 54
Table 4.3 Percentage of particle aggregation occurring in the separation zone at different air
fractions and bubble sizes.. ......................................................................................... 55
Table 5.1 Particle size ranges (bins) measured by the particle counter ........................................ 64
Table 5.2 Inlet bubble size distribution in the contact zone. ....................................................... 67
Table 5.3 Comparison between CFD predictions and experimental measurements. .................. 70
Table 5.4 Effect of attachment efficiency on CFD predictions. ................................................... 74

x
4B4BLIST OF FIGURES
Figure 1.1 Schematic diagram of the dissolved air flotation tank .................................................. 1
Figure 3.1 Configuration of the modeled DAF system................................................................. 20
Figure 3.2 The conceptualized flow models for separation zone, reverse flow on top and plug
flow at bottom ............................................................................................................. 22
Figure 3.3 Velocity vectors (00.03 m/s), a) Single phase, b) Air fraction 0.005, c) Air fraction
0.02 .............................................................................................................................. 27
Figure 3.4 Velocity vectors (00.03 m/s), a) Air fraction 0.005, b) Air fraction 0.01, c) Air
fraction 0.02. ............................................................................................................... 27
Figure 3.5 Effect of air inlet fraction on bubble removal at different loading rates. .................... 28
Figure 3.6 Effect of air inlet fraction on bubble removal in presence of bubble aggregation at
different loading rates, a) Inlet bubble size 80 µm, b) Inlet bubble size 20 µm. ........ 29
Figure 3.7 Velocity vectors (00.03 m/s) in the presence of bubble aggregation, a) Air fraction
0.005, b) Air fraction 0.008, c) Air fraction 0.01.. ...................................................... 30
Figure 3.8 Velocity vectors (00.05 m/s) in the presence of bubble aggregation, a) Air fraction
0.01, b) Air fraction 0.035, c) Air fraction 0.05. ......................................................... 30
Figure 3.9 Comparison of air content in the separation zone from Lundh et al. (2001) and the
present model. ............................................................................................................. 31
Figure 3.10 Velocity vectors (00.03 m/s) in presence of bubble aggregation, a) 11.8 m/hr, b)
23.6 m/hr, c) 47.2 m/hr. .............................................................................................. 32
Figure 4.1 The conceptual model for stratified flow in the separation zone ................................ 39
Figure 4.2 Configuration of the modeled DAF system................................................................. 45
Figure 4.3 The effect of air fraction and bubble size on particle removal calculated from the
analytical model, a) in the absence of stratified flow, b) in the presence of stratified
flow. ............................................................................................................................ 48
Figure 4.4 Loading rates at 60% particle removal in the absence and presence of stratified
flow. ............................................................................................................................ 48
Figure 4.5 The effect of air fraction and bubble size on particle removal from the theoretical
model, a) loading rate 11.8 m/hr, b) loading rate 23.6 m/hr ....................................... 49

xi
Figure 4.6 The effect of particle and bubble size on particle removal, a) loading rate 11.8
m/hr, air fraction 0.005, b) loading rate 11.8 m/hr, air fraction 0.01, c) loading rate
23.6 m/hr, air fraction 0.005, d) loading rate 23.6 m/hr, air fraction 0.01 (in
presence of stratified flow layer). ............................................................................... 50
Figure 4.7 Velocity vectors (00.1 m/s) at different air fractions, a) 0.008, b) 0.01, c) 0.02. ....... 52
Figure 4.8 The velocity vectors (00.1m/s) at different bubble sizes, a) 40 µm, b) 80 µm, c)
120 µm. ....................................................................................................................... 52
Figure 4.9 The effect of air fraction and loading rate on particle removal from the CFD model,
a) bubble size 40 µm, b) bubble size 80 µm. .............................................................. 53
Figure 4.10 The effect of air fraction and bubble size on particle and bubble removal from the
CFD model, a) bubble removal, loading rate 11.8 m/hr, b) bubble removal 23.6
m/hr, c) particle removal 11.8 m/hr, d) particle removal 23.6 m/hr. .......................... 55
Figure 4.11 The effect of particle and bubble size on particle removal from the CFD model ..... 57
Figure 5.1 A schematic diagram of the DAF pilot system ........................................................... 63
Figure 5.2 Geometry of the modeled DAF system ....................................................................... 67
Figure 5.3 RTD comparison between experimental and CFD results. ......................................... 70
Figure 5.4 The normalized position of bubble layer (hb/H) in the separation zone at different
loading rates. ............................................................................................................... 71
Figure 5.5 The effect of loading rate on the residence time distribution. ..................................... 73
Figure 5.6 Velocity vectors (00.1 m/s) at different loading rates.. .............................................. 73
Figure 5.7 The effect of attachment efficiency on the residence time distribution ...................... 75
Figure 5.8 Contact efficiency at different particle sizes from particle counts, CFD and
analytical model .......................................................................................................... 76
Figure 6.1 The geometry of pilot system with different baffle configurations, a) baffle 1, b)
baffle 2, c) baffle 3, d) baffle 4. .................................................................................. 79
Figure 6.2 Schematic diagram of Peekskill DAF tank ................................................................. 80
Figure 6.3 Air volume fraction in the tank for different baffle configurations, a) no baffle, b)
baffle 1, c) baffle 2, d) baffle 3. .................................................................................. 81
Figure 6.4 Velocity vectors for primary phase (water) in the tank for different baffle
configurations, a) baffle 1, b) baffle 2, c) baffle 3. ..................................................... 82

xii
Figure 6.5 Air volume fraction in the tank for a) porous (baffle 3), and b) nonporous
horizontal baffles (baffle 4). ....................................................................................... 82
Figure 6.6 The effect of loading rate on bubble removal for different baffle configurations ...... 83
Figure 6.7 Velocity vectors (00.2 m/s) on the symmetry plane showing the position of the
bubble layer (air volume fraction 0.0001), a) 2D model, b) 3D model. Flow rate
2.8 mgd, air concentration of 9 g/m3, inlet bubble size of 40 µm. .............................. 84
Figure 6.8 Velocity vectors (00.2 m/s) on the xz plane (top view) at the baffle overflow
height ........................................................................................................................... 85
Figure C.1 The effect of bubble size on bubble volume fraction distribution α1,0. a) inlet
bubble size 20 µm, b) inlet bubble size 80 µm. ........................................................ 101
Figure C.2 The effect of bubble size on aggregate N3,3/N0,1 distribution. a) inlet bubble size 20
µm, b) inlet bubble size 80 µm. ................................................................................ 101
Figure C.3 The effect of bubble size on bubble number concentration. a) inlet bubble size 80
µm, b) inlet bubble size 120 µm. .............................................................................. 102
Figure C.4 The effect of bubble size on collision frequency (m3/s). a) inlet bubble size 80 µm,
b) inlet bubble size 120 µm. ...................................................................................... 102

1
1. 5B5BIntroduction
1.1. 12B12BBackground
Dissolved air flotation (DAF) is a process for the separation of solid particles from water by the
injection of air bubbles. DAF has been used in water treatment for over 40 years (Edzwald,
1995) and is especially known as a good process for removing particles with low specific gravity
(Kwon et al., 2006). A schematic diagram of a DAF tank can be observed in Figure 1.1. The
DAF basin consists of two zones: a contact zone, and a separation zone. A baffle separates the
contact zone from the separation zone. A waterbubble mixture is injected through a nozzle at the
bottom of the contact zone, and the influent water is introduced into the basin close to the floor
of the contact zone. Air bubbles adhere to the particles and form particlebubble aggregates.
Aggregates have lower specific gravity than the surrounding liquid and as a result rise to the
surface. The particles on the surface form a discrete layer of solids that is usually removed from
the surface by means of a scraper.
Figure 1.1 Schematic diagram of the dissolved air flotation tank
Historical hydraulic loading rates (flow rate per unit surface area of the separation zone) for DAF
systems have been in the order of 510 m/hr. However, recently DAF systems have been
operated at loading rates as high as 2040 m/hr (Edzwald, 2007). Experimental measurements by
Lundh et al. (2000 and 2001) suggested the presence of back and forth horizontal flow layers at
the top of the separation zone (stratified flow) under certain conditions. Edzwald (2007) used the

2
concept of stratified flow to qualitatively explain the higher surface loading rates that have been
achieved.
The demonstration of the horizontal flow patterns known as stratified flow has been so far
limited to two phase flow (i.e. airliquid flow, with no particles present), and only in pilotscale
DAF systems (Lundh et al., 2001, Hague et al., 2001). As such, there is uncertainty about the
importance of stratified flow in real DAF systems. There is also a lack of a quantitative measure
of the impact of stratified flow on DAF performance. Computational fluid dynamics (CFD) can
be a useful tool to better understand the flow behavior, which can be easily applied to a variety
of conditions. However, previous CFD models (Ta et al., 2001; Hague et al., 2001; Bondelind et
al., 2010) of DAF systems have not accurately simulated conditions under which stratified flow
occurs, and have not evaluated the effect of stratification of the flow on bubble and particle
removal. In addition, very few of these models have incorporated bubbleparticle attachment
(Kostoglou et al., 2007; Bondelind et al., 2012), nor have they accounted for bubble aggregation
and the effects of the particles and aggregates on the flow pattern in a complete DAF unit.
Moreover, there has been a lack of experimental validation in the presence of the solid particles
(Edzwald, 2010).
There is a need for developing a CFD model that can predict the formation of stratified flow and
removal efficiency in the presence of bubbles, particles and aggregates. After validation, the
model can be applied as a tool in the optimization of the design and operation of DAF.
1.2. 13B13BObjectives
The main objective of this study is to develop a CFD model of a DAF system to better
understand and optimize operating and design conditions. The more detailed objectives are as
follows:
1. Investigate the effect of back and forth horizontal flow layers (stratified flow), air fraction
and bubble size on bubble removal (Chapter 3)
2. Investigate the effect of stratified flow, air fraction and bubble size on particle removal
(Chapter 4)
3. Validate the predictions of the CFD model for twophase and threephase conditions
(Chapter 5)

3
4. Apply the developed CFD model to optimize the geometric features of DAF by enhancing
stratified flow (Chapter 6)
1.3. 14B14BThesis Chapters
Chapter 2 provides a literature review of previous experimental and modeling studies of
flow hydrodynamics and bubbleparticle attachment in DAF.
Chapter 3 presents a twophase (bubbleliquid) model of DAF that is able to predict
formation of stratified flow under different operating conditions by including the effect of
bubble aggregation. A conceptual model of stratified flow is utilized to show the effect of
stratified flow on bubble removal under simplified conditions. The developed CFD model
is then applied to study the quantitative effect of air fraction, loading rate and bubble size
on the formation of stratified flow and bubble removal.
Chapter 4 presents an analytical model as well as a threephase CFD model of overall
particle removal in DAF. The models extend the previous models by including bubble
particle aggregation, the effect of particles and formed aggregates on the flow, clustering
(attachment of aggregates with multiple bubbles and particles), and the presence of
stratified flow. First, the analytical model is applied to provide a better understanding of
the effect of stratified flow, bubble size and air fraction on particle removal for simplified
scenarios. Then, the developed CFD model is used to study the effect of these parameters
under more realistic conditions.
Chapter 5 evaluates the predictions of the developed twophase and threephase CFD
models in the previous chapters by comparison with data obtained from a pilotscale
DAF tank. The residence time distributions (RTD) from tracer testing, position of the
bubble layer in the tank, and particle count data are used to validate the predictions of the
CFD model.
Chapter 6 applies the validated model in Chapter 5 to evaluate the effect of modifications
in DAF geometry and addition of different internal baffles on the formation of stratified
flow and bubble removal.
Chapter 7 summarizes the main conclusions and contributions of the research, and
provides recommendations for future research.

4
1.4. 15B15BAssociated Journal Publications
Chapter 3 waspreviouslypublishedas“B. Laghomi, Y. Lawryshyn, R. Hofmann, 2012. Effect
of stratified flow and bubble aggregation in the separation zone of a dissolved air flotation tank.
Water Research, 46 (14), 446876”.
Chapter 4 was published inWaterResearchas“B. Lakghomi, Y. Lawryshyn, R. Hofmann, 2014.
A model for particle removal in a dissolved air flotation tank: importance of stratified flow and
bubble size, In Press”.
Chapter 5 has been submitted to Water Science and Technology as “B. Lakghomi, Y.
Lawryshyn, R. Hofmann, 2014. Evaluation of flow hydrodynamics in a pilotscale dissolved air
flotation tank: a comparison between CFD and experimental measurements”.
The first two manuscripts have been reproduced in this thesis with permission of the publisher.
The third manuscript is still under review, and copyright permission will be obtained once the
publication is finalized.
1.5. 16B16BReferences
Bondelind, M., Sasic, S., Kostoglou, M., Bergdahl, L., Thomas, J.R.P., 2010. Single and two
phase numerical models of dissolved air flotation: comparison of 2D and 3D simulations.
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 365(13), 137144.
Bondelind, M., Ström, H., Sasic, S. and Bergdahl, L., 2012. Eulerian modelling of the formation
and flow of aggregates in dissolved air flotation. The 15th International Conference on Fluid
Flow Technologies, Budapest, Hungary, September 47, 2012.
Edzwald, J.K., 1995. Principles and applications of dissolved air flotation, Water Science and
Technology,31(3),1−23.
Edzwald, J.K., 2007. Developments of high rate dissolved air flotation for drinking water
treatment. Journal of Water Supply: Research and TechnologyAqua, 56(67), 399409.
Hague, J., Ta, C.T., Biggs, M.J, Sattary, J.A., 2001. Small scale model for CFD validation in
DAF application. Water Science and Technology, 43(8), 167173.

5
Kostoglou, M., Karapantsios, T.D., Matis, K.A., 2007. CFD model for the design of large scale
flotation tanks for water and wastewater treatment. Industrial Engineering and Chemistry
Research, 46(20), 65906599.
Kwon, S.B., Lee, S.J, Ahn, H.W, Wang, C.K., 2006. Examining the effect of length/width ratio
on the hydrodynamic behavior in a DAF system using CFD and ADV techniques. Water Science
and Technology, 53(7), 141149.
Lundh, M., Jonsson, L., Dahlquist, J., 2000. Experimental studies of the fluid dynamics in the
separation zone in dissolved air flotation. Water Research, 34(1), 2130.
Lundh, M., Jonsson, L., Dahlquist, J., 2001. The flow structure in the separation zone of a DAF
pilot plant and the relation to the bubble concentration. Water Science and Technology, 43(8),
185194.
Ta, C.T., Beckley, J., Eades, A., 2001. A multiphase CFD model of DAF process. Water Science
and Technology, 43(8), 153157.

6
2. 6B6BLiterature review
2.1. 17B17BImportance of stratified flow
Previous researchers have investigated the hydraulics in DAF systems in an effort to understand
how to optimize its efficiency. Early design of traditional DAF systems (Haarhoff and Vuuren,
1995) assumed vertical plug flow in the separation zone. Based on these models, free bubbles
and particlebubble aggregates are removed if their rise velocity exceeds the velocity of the
downward plug flow (loading rate), which was traditionally in the range of 510 m/h.
Development of DAF systems at high loading rates in early 2000s and pilot plant tests by
Edzwald (1999) showed that such simple models are not able to represent the hydrodynamics of
high rate DAF systems (Edzwald, 2007).
An experimental study of the hydrodynamics of the airwater flow using a pilotscale DAF
system was performed by Lundh et al. (2000) using acoustic Doppler velocimetry (ADV)
measurements. This study showed that when bubbles were added at a surface loading of 10 m/hr
and a 10% recyclerate, the flow features changed significantly compared to bubblefree flow.
The water reaching the far wall in a horizontal flow layer at the top of the tank turned around and
started to flow horizontally back towards the inlet baffle in a layer underneath the top flow layer.
Only beneath the horizontal flow layers the water moved downward in a pluglike flow towards
the collection pipes. The back and forth flow layers at top of the tank was referred to as stratified
flow by the authors. When increasing the hydraulic loading rate beyond a certain point, the
stratified flow pattern started to become unstable, leading to shortcircuiting of the flow towards
the outlet. The authors suggested that the stratified flow at the top of the tank is probably due to
lower water density due to the high bubble concentration, which does not allow the flow enough
momentum to penetrate the higher density water layer below. High loading rate and low recycle
rate would decrease the stability of the stratified layer and shift the flow toward shortcircuiting.
In another study, Lundh et al. (2001) measured the air concentration profile in the tank and found
a higher concentration of air in the upper part of the tank. Based on this observation, they
approved that the stratification of the flow can be explained by the density gradients caused by
differences in the air concentration in the tank.

7
Hague et al. (2001) used laser Doppler velocimetry (LDV) to study flow in a laboratoryscale
DAF tank. LDV is a noninvasive high resolution laser technique, and was used to measure
velocity for both single phase (water) and two phase (air/water) conditions. The authors observed
that vertical recirculation currents that were present in singlephase flow changed when air was
added to the system. Although LDV would be more precise than ADV for flow measurements in
the presence of bubbles, it cannot be applied to measure flow at fullscale due to the restricted
penetrating power of the laser.
The studies reported by both Lundh et al. (2001) and Hague et al. (2001) suggested that the
presence of bubbles changed the vertical recirculation currents relative to flow without air
injection. As a result, the simple assumption of completely vertical plug flow in the separation
zone would not be able to fully represent the hydrodynamics of airwater flow.
Edzwald (2007) analyzed a simplified form of stratified flow with two back and forth horizontal
layer, and suggested that such flow triples the clarification separation area, and as a result, the
theoretical acceptable surface loading in the tank. This analysis was purely theoretical, however.
It was also assumed that each additional horizontal layer below the first is of equal importance.
Edzwald (2010) suggested that research is needed on the hydraulic flow characteristics of the
separation zone and their incorporation into a performance model for DAF. The experimental
work by Lundh et al. (2001), although providing very useful information on the relationship
between the recycle rate (air fraction), hydraulic loading, and the flow pattern in the separation
zone, was limited to a specific DAF tank depth and length to width ratio and could not be
extended to all conditions. A detailed hydrodynamic model of the separation zone and a better
characterization of the possible flow patterns based on the various parameters such as air fraction
(recycle rate), surface loading rate, and bubble size, needs to be established for optimization of
the system.
2.2. 18B18BBubbleparticle attachment models
While hydraulics of the DAF system have been shown to be of great significance, another
important phenomenon in a DAF tank would be bubbleparticle attachment, which can have an
effect on the hydraulics as well. Although a variety of analytical models have been developed to
address the bubbleparticle collision and attachment in the DAF, they have mostly assumed a

8
simple flow pattern in the tank independent of the operating conditions. In addition, the models
have considered that the bubbleparticle aggregation only happens in the contact zone and have
neglected aggregations in the separation zone (Edzwald, 2010). Bubbleparticle attachment
models for DAF can be divided into two main groups (Edzwald, 2006 and 2010): turbulent
flocculation models and single collector collision models. A summary of main collision models
and their governing equations is given in Table 2.1.
Table 2.1 Governing equations for bubbleparticle aggregation rates
Model Equations
Fukushi et al. (1995)
Rate equation for particles without previously attached particles:
𝑑𝑛𝑃0𝑑𝑡
= −3
2𝜋𝛼𝑝𝑏 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑛𝑏𝑛𝑃0 (2.1)
Rate equation for particles with previously attached particles from 𝑖 to 𝑁𝑏,𝑚𝑎𝑥:
𝑑𝑛𝑝,𝑖𝑑𝑡
= −3
2𝜋 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑛𝑏(𝛼𝑝𝑏,𝑖𝑛𝑝,𝑖
− 𝛼𝑝𝑏,𝑖−1𝑛𝑓,𝑖−1)
(2.2)
𝑁𝑏,𝑚𝑎𝑥 = 𝜋 (𝑑𝑝𝑑𝑏
)
2
(2.3)
Edzwald et al. (1990)
𝑛𝑝,𝑒𝑛𝑝,𝑖
= (𝑒𝑥𝑝 (−3
2𝛼𝑝𝑏𝜂𝑇𝜙𝑏𝑣𝑏𝑡𝑐𝑧 𝑑𝑏⁄ )) (2.4)
𝜂𝑇 = 𝜂𝐷 + 𝜂𝐼 + 𝜂𝑆 (2.5)
Yoon and Luttrell
(1989)
Koh and Schwartz
(2003)
𝑑𝑛𝑃𝑑𝑡
= −3
2𝜋𝛼𝑝𝑏 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑛𝑏𝑛𝑝𝑃𝑐 (2.6)
𝑃𝑐 = (1.5 +4
15𝑅𝑒𝑏
0.72)𝑑𝑝
2
𝑑𝑏2 (2.7)
Kostoglou et al. (2007)
𝑑𝑛𝑃𝑑𝑡
= −𝐾𝑛𝑏𝑛𝑝 (2.8)
𝐾 = 𝐾𝐵 + 𝐾𝐺 + 𝐾𝑇 (2.9)
𝐾𝐵 = 𝑃𝑐𝐵𝑈𝑏(𝑅𝑝 + 𝑅𝑑)2 (2.10)
𝑃𝑐𝐵 = (1.5 +4
15𝑅𝑒𝑏
0.72 + 37.5𝜑)𝑑𝑝
2
𝑑𝑏2 (2.11)
𝐾𝐺 = 𝜋𝑢𝑝(𝑅𝑝 + 𝑅𝑑)2 (2.12)
𝐾𝑇 = 3
2𝜋 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑃𝑐𝑇 (2.13)
𝑃𝑐𝑇 = (1.5 +4
15𝑅𝑒0.72 + 37.5𝜑)
𝑑𝑝2
𝑑𝑏2 (2.14)

9
The turbulent flocculation model is developed based on a population balance in turbulent flow
(Fukushi et al., 1995) and assumes that turbulent diffusion is the only significant mechanism in
the attachment of the particles to bubbles. The turbulent flocculation model equations are
summarized in Table 2.1. Equation (2.1) is the rate equation that applies to the collision of
bubbles with particles without any previously attached bubbles. Equation (2.2) represents
collision rates between bubbles and particles containing attached bubbles, and Equation (2.3)
considers the maximum possible number of bubbles that can attach to a particle, where 𝑑𝑝 and
𝑑𝑏 represent particle and particle diameters, 𝑛𝑝,𝑖 and 𝑛𝑏 are particle and bubble number
concentrations, and 𝜇 and 𝜖0 are viscosity and turbulence dissipation rate. The authors tried to
verify their model by coupling the model with separation zone rise velocities and comparisons to
the overall flotation with experimental data. However, their experimental work addressed
particles of about 1001000 µm, larger than the typical particle size of 10100 µm usually found
in dissolved air flotation.
The single collector collision model was first developed by Edzwald et al. (1991) and assumed
that air bubbles collect the particles through different transport mechanisms including Brownian
motion, interception and settling. The single collector efficiency model can be presented by
Equations (2.4) and (2.5) where 𝜂𝑇 is single collector efficiency and can be calculated by
summing up collision efficiencies from diffusion (𝜂𝐷), interception ( 𝜂𝐼), and settling (𝜂𝑆)
mechanisms. 𝛼𝑝𝑏 is the attachment efficiency, and 𝜙𝑏, 𝑣𝑏 and 𝑑𝑏 are the bubble volume
concentration, bubble rise velocity and diameter, and 𝑡𝑐𝑧 represents the contact zone detention
time. The model is based on the plug flow assumption in the contact zone and neglects the effect
of turbulent mixing.
Both modeling approaches show restrictions in terms of including the effects of different
transport mechanisms on bubbleparticle collision. They also assume a simple flow pattern in the
tank independent of the operating conditions, and assume that bubbleparticle aggregation only
happens in the contact zone. In addition, these models do not take the effects of the attachment
between aggregates including multiple bubbles and particles (clustering) as shown by Leppinen
and Dalziel (2004).

10
2.3. 19B19BPrevious attempts at CFD modelling
Previously, a variety of CFD models have been developed to study the flow hydrodynamics of
DAF tanks. Most of these models have focused on the waterair flow and neglected the solid
phase interaction with the bubbles. To model the twophase flow, EulerianLagrangian and
EulerianEulerian approaches have been used. An overview of the CFD DAF models can be
observed in Table 2.2.
Hague et al. (2001) simulated the flow in a smallscale DAF system using a threedimensional
(3D) singlephase CFD model. The singlephase CFD model was not able to predict the vertical
recirculation zones (stratified flow pattern) as shown by LDV measurements. The presence of the
bubbles changed the flow importantly indicating that a singlephase model cannot capture the
hydrodynamics of flow in a DAF tank completely.
Ta et al. (2001) built a CFD model of a fullscale tank and evaluated the capability of their model
by ADV measurements. They used a 3D grid and applied an EulerianEulerian multiphase
approach for the air/water flow. The particles were then introduced and tracked in the air/water
flow in a Lagrangian frame of reference. The kepsilon turbulence model was used for both
air/water phases as it showed better convergence behavior in comparison with laminar or other
turbulence methods. It was assumed that particles have minor effects on the main flow and that
their effect can be neglected. In addition, bubbleparticle collisions and the changes in the
particle size and properties were not included in the model. The stratified flow just below the
water surface measured by ADV was not predicted by CFD. The authors suggested that
formation of stratified flow observed from ADV could be because of lower density of the bubbly
layer at the top.
Kwon et al. (2006) used a two phase (waterair) EulerianEulerian approach and a 3D grid to
investigate the effect of L/W (length/width ratio) on the hydrodynamic behavior of a fullscale
DAF tank, and compared their modeling results to experimental measurements using ADV. The
experimental validation of CFD results was limited to the bottom region of the tank, and no flow
measurements were performed at the top bubbly layer. Considering the inability of previous CFD
models in the prediction of the stratified flow at the top bubbly layer (Ta et al., 2001), and
importance of this phenomenon in operation of DAF (Lundh et al., 2000), verification of the

11
CFD results at this region might be of importance. The CFD model showed that at L/W ratios of
1:1 and 2:1 no dead zone between the outlet pipe and slope baffle was observed, but when L/W
ratio increased from 3:1 to 4:1 and 5:1, a significant dead zone could be seen in the upper side of
the outlet part. As a result, it was suggested to design the flotation tanks with L/W ratios smaller
than 2:1, but no elaboration or quantitative data on the effect of presence of dead zones on
bubble or particle removal was provided.
Table 2.2 A comparison of two phase CFD models for DAF
Model Multiphase model Number of phases 2D/3D Scale Validation
Fawcett (1997) EulerianEulerian 2 2D Fullscale 
Hague et al. (2001)  1 2D Small
scale LDV
Hague et al. (2002) EulerianEulerian 2 3D Small
scale
LDV &
PIV
Kwon et al. (2006) EulerianEulerian 2 3D Fullscale ADV
Emmanouil et al.
(2007) EulerianLagrangian 2 2D Fullscale
_
Kostoglou et al. (2007) EulerianEulerian 3 2D Fullscale 
Amato and Wicks
(2009) EulerianEulerian 2
2D,
3D Fullscale 
Bondelind et al. (2010) EulerianLagrangian 2 2D,
3D Pilotscale 
Bondelind et al. (2012) EulerianEulerian
Lagrangian 2
2D,
3D Pilotscale 
Strom et al. (2013) EulerianEuleian
Lagrangian 3 2D  
Bondelind et al. (2010) used an EulerianLagrangian approach and compared the ability of both
2D and 3D models to predict the experimental measurements presented by Lundh et al. (2000).
They suggested that the distribution of the bubble layer in the separation zone could be observed
from both their 2D and 3D simulations, although the 3D model showed better agreement.
However, the predictions were not able to capture the horizontal flow layers at the top of the

12
separation zone. As the effect of bubbles on the main flow are important in DAF, with a
Lagrangian model, the number of bubbles must be close to reality and a twoway coupling
should be applied to include the effects of bubbles on the primary phase flow. This would
dramatically increase the numerical costs for the solution of the problem. However, Bondelind et
al. (2010) did not model the total number of bubbles and used an uncoupled solver.
The effect of bubble aggregation is not taken into account in any of the twophase CFD models
of DAF. The previous CFD studies in the field of bubble columns have tried to improve the
prediction of the local recirculation zones and the gas volume fraction in the columns by
including bubble aggregation by means of a population balance model (Chen et al., 2004). In the
case of DAF that bubble aggregation are reported be of significance (Hedberg et al., 1998;
Amato et al., 2001), taking bubble aggregation into account may have an effect in better
prediction of the stratified flow.
The effect of solid particles and bubbleparticle aggregation is also rarely included in the
previous CFD models of DAF. The first study to employ the flotation kinetic concepts in CFD
modeling was by Koh and Schwartz (2003) on a flotation cell with external mixing, typical in
mineral processing, using a threephase EulerianEulerian approach. The local bubbleparticle
collision rates were calculated based on the local turbulent velocities, and the size and number of
particles and bubbles obtained from CFD modeling. The flotation effect was modeled as three
substeps involving collision, attachment and detachment based on the model of Yoon and
Luttrell (1989). The only mechanism that they accounted for was turbulent diffusion. The
governing equations of their model are shown in Table 2.1.
A study to adapt this model for CFD modeling of DAF was performed by Kostoglou et al.
(2007) by linear addition of the collision frequencies from settling (𝐾𝐺) and buoyancy (𝐾𝐵) to
collision frequencies from turbulence (𝐾𝑇) (Equations 2.8 and 2.9). As Equation (2.7) was
developed for a single bubbleparticle collision, to account for the presence of other bubbles, the
37.5𝜑 term was added to the buoyancy and turbulence frequency terms, where 𝜑 was the gas
holdup in the system (Equations 2.11 and 2.14). It was assumed that the particle mass loading is
low, so the saturation limit of the bubbles is never reached and the amount of attached particles is
not enough to change the bubble properties (e.g effective density). In drinking water DAF

13
systems, unlike mineral processing flotation systems, the number of solid particles is not in a
range that saturates the bubbles because of the much smaller concentration of solids. However,
previous studies have shown that higher solid concentrations (Lundh et al, 2001) or addition of a
coagulant to the system (Haarhoff and Edzwald, 2004) can have an impact on the position of the
bubble layer (white milky layer). These phenomena show that the bubbleparticle aggregation
can affect the flow pattern as a result of the change in the rise velocity of the aggregates and their
effect on the primary phase flow. As a result, the CFD model needs to account for the effect of
the particles and the formation of the aggregates on the flow pattern.
In addition, in the model of Kostoglou et al. (2007), it is assumed that all the particles colliding
with the bubbles attach to them, while in reality, bubble–particle attachment efficiency is a
function of the properties of the particle and bubbles, such as surface charge. Han et al. (2001)
developed a collision–efficiency diagram based on the size of particles and bubbles and the zeta
potential using trajectory analysis. Their work could show the importance of pretreatment on
collision efficiency. Fukushi et al. (1995) reported that the attachment efficiency of 0.4 provided
agreement between their modeling and experimental results for aluminum dosage of 5 mg/L and
pH of 6.7. The importance of pretreatment (ionic strength, contact angle and particle size) was
also investigated by Hewitt et al. (1993).
Bondelind et al. (2012) attempted to include the effects of the aggregates on the flow pattern, but
limited their Eulerian model to water and aggregate phases to reduce the computational cost. In
addition, the developed model was only applied to model the contact zone.
Strom et al. (2013) developed a hybrid scheme for modeling general threephase flow conditions
with bubbles, particles and aggregate formation. An EulerianEulerian model was applied for
water (primary phase) and aggregates, whereas bubbles were tracked in a Lagrangian frame of
reference. The interaction of the bubbles with the primary phase was modeled through a
momentum source term. Particles were modeled as passive scalars and their effect on the flow
pattern was neglected. The developed model was only applied in a rectangular geometry, and
was not utilized to study a DAF unit, and no verification of the modeling results was provided.
The CFD models including particles and aggregates are based on multiple simplifying
assumptions and are not applied to evaluate the performance of a complete DAF unit; there is

14
also in general a lack of validation when the solid and aggregate phases are present in the system
(Edzwald, 2010).
2.4. Research gaps
A better characterization of the stratified flow under various conditions and its effect on bubble
particle aggregation and DAF performance is needed. Previous CFD models have not
represented conditions under which the stratified flow pattern in the DAF tanks occur (Hague et
al., 2001, Ta et al., 2001, Bondelind et al., 2010). The experimental work by Lundh et al. (2000),
although providing very useful information on the relationship between the recycle rate,
hydraulic loading and the flow pattern in the separation zone, was limited to specific DAF tank
geometry in the absence of the particles. The effect of bubble aggregation is critical but is not
modeled. In addition, the effects of flow pattern on bubbleparticle aggregation and particle
removal are not quantified in any of the previous models.
The previous models accounting for bubbleparticle aggregation do not take the effects of the
aggregates and particles on the flow pattern into account in a DAF unit, and do not evaluate the
effect of stratified flow in the separation zone on bubble and particle removal. There is also a
general lack of validation when the solid phase is present in the system (Edzwald, 2010).
The effects of bubble aggregation, solid particles, and bubbleparticle aggregation need to be
included in DAF models for more accurate representation of the flow and DAF performance.
The developed model should be applied to characterize the effects of stratified flow, air fraction
and bubble size on bubble and particle removal under different conditions. The model
predictions also need to be validated in presence of the solid particles. Once validated, the
developed model can be used as an optimization tool for DAF under different conditions.
2.5. 21B21BReferences
Amato, T., Edzwald, J.K., Tobiason, J.E., Dahlquist, J., Hedberg, T., 2001. An integrated
approach to dissolved air flotation. Water Science and Technology, 43(8), 1926.
Amato, T., Wicks, J., 2009. Dissolved air flotation and potential clarified water quality based on
computational fluid dynamics modeling. Journal of Water Supply: Research and Technology
AQUA, 58(1), 6573.

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Bondelind, M., Sasic, S., Kostoglou, M., Bergdahl, L., Thomas, J.R.P., 2010. Single and two
phase numerical models of dissolved air flotation: comparison of 2D and 3D simulations.
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 365(13), 137144.
Bondelind, M., Ström, H., Sasic, S. and Bergdahl, L., 2012. Eulerian modelling of the formation
and flow of aggregates in dissolved air flotation. The 15th International Conference on Fluid
Flow Technologies, Budapest, Hungary, September 47.
Chen, P., Sanyal, J., Dudukovic, M.P., 2004. CFD modeling of bubble columns flows:
implementation of population balance. Chemical Engineering Science, 59(22), 52015207.
Crittenden, J.C., Trussell, R.R., Hand, D.W., Howe, K.J., Tchobanoglous, G., 2005. Water
treatment: Principles and Design. John Wiley & Sons, Inc., Hoboken, New Jersey.
Edzwald, J.K., Malley, J.P, Yu, C., 1991. A conceptual model for dissolved air flotation in water
treatment, Water Supply, 9(1), 141150.
Edzwald, J.K., 1995. Principles and applications of dissolved air flotation. Water Science
Technology,31(3),1−23.
Edzwald, J.K., Tobiasen, J.E., Amato, T., Maggi, L.J., 1999. Integrating high rate dissolved air
flotation technology into plant design. Journal of American Water Work Associations, 91(12),
4153.
Edzwald, J.K., 2007. Developments of high rate dissolved air flotation for drinking water
treatment. Journal of Water Supply: Research and TechnologyAqua, 56 (67), 399409.
Edzwald, K., 2010. Dissolved air flotation and me. Water Research, 44(7), 20772106.
Emmanouil, V., Skaperdas, E.P., Karapantsios, T.D. and Matis, K.A., 2007. Twophase
simulations of an offnominally operating dissolvedair flotation tank, International Journal of
Environment and pollution, 30(2), 213–230.
Fawcett, N.S.J, 1997. The hydraulics of flotation tanks, computational modeling. Proceedings of
the International conference charted institute of Water and Environmental Management, London,
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Fukushi, K., Tambo, N., Matsui, Y., 1995. A kinetic model for dissolved air flotation in water
and wastewater treatment. Water Science and Technology, 31(3), 3747.
Haarhoff, J., 2008. Dissolved air flotation: progress and prospects for drinking water treatment.
Journal of Water Supply: Research and TechnologyAQUA, 57(8), 555567.
Haarhoff, J., Van Vuuren, L., 1995. Design parameters for dissolved air flotation in South
Africa. Water Science and Technology, 31(34), 203212.
Haarhoff, J., Edzwald, J.K., 2004. Dissolved air flotation modelling: insights and shortcomings.
Journal of Water Supply: Research and TechnologyAQUA, 53(3), 127150.
Hague, J., Ta, C.T., Biggs, M.J, Sattary, J.A., 2001. Small scale model for CFD validation in
DAF application. Water Science and Technology, 43(8), 167173.
Han, M., Kim, W., Dockko, S., 2001. Collision efficiency factor of bubble and particle in DAF:
theory and experimental verification. Water Science and Technology, 43(8), 139144.
Hedberg, T., Dahliquist, J., Karlsson, D., Sorman, L.O., 1998. Development of an air removal
system for dissolved air flotation. Water Science and Technology, 37(9), 8188.
Hewitt, D., Fornasiero, D., Rulston, J., 1994. Bubbleparticle attachment efficiency. Mineral
Engineering, 7(56), 657665.
Koh, P.T.L, Schwarz, M.P., 2003. CFD modeling of bubbleparticle collision rates and
efficiencies in a flotation cell. Mineral Engineering, 16 (11), 10551059.
Koh, P.T.L, Schwarz, M.P., 2008. Modeling attachment rates of multisized bubbles with
particles in a flotation cell. Mineral Engineering, 21 (1214), 989993.
Kostoglou, M., Karapantsios, T.D., Matis, K.A., 2007. CFD model for the design of large scale
flotation tanks for water and wastewater treatment. Industrial Engineering and Chemistry
Research, 46(20), 65906599.
Kwon, S.B., Lee, S.J, Ahn, H.W, Wang, C.K., 2006. Examining the effect of length/width ratio
on the hydrodynamic behavior in a DAF system using CFD and ADV techniques. Water Science
and Technology, 53(7), 141149.

17
Leppinen, D.M., Dalziel, S.B., 2004. Bubble size distribution in dissolved air flotation tanks.
Journal of Water Supply: Research and TechnologyAQUA, 53(8), 531543.
Lundh, M., Jonsson, L., Dahlquist, J., 2000. Experimental studies of the fluid dynamics in the
separation zone in dissolved air flotation. Water Research, 34 (1), 2130.
Lundh, M., Jonsson, L., Dahlquist, J., 2001. The flow structure in the separation zone of a DAF
pilot plant and the relation to the bubble concentration. Water Science and Technology, 43(8),
185194.
Strom, H., Bondelind, M., Sasic, S., 2013. A novel hybrid scheme for making feasible numerical
investigations of industrial threephase flows with aggregation. Industrial Engineering and
Chemistry Research, 52(29),10022−10027.
Ta, C.T., Beckley, J., Eades, A., 2001. A multiphase CFD model of DAF process. Water Science
and Technology, 43(8), 153157.
Yoon, R.H., Luttrell, G.H., 1989. The effect of bubble size on fine particle flotation. Mineral
processing and Extractive Metallurgy Review, 5(14), 101122.

18
3. 7B7BImportance of flow stratification and bubble aggregation in the separation
zone of a dissolved air flotation tank 0F0F1
ABSTRACT
The importance of horizontal flow patterns and bubble aggregation on the ability of dissolved air
flotation (DAF) systems to improve bubble removal during drinking water treatment were
explored using computational fluid dynamics (CFD) modeling. Both analytical and CFD
analyses demonstrated benefits to horizontal flow. Two dimensional CFD modeling of a DAF
system showed that increasing the amount of air in the system improved the bubble removal and
generated a beneficial stratified horizontal flow pattern. Loading rates beyond a critical level
disrupted the horizontal flow pattern, leading to significantly lower bubble removal. The results
also demonstrated that including the effects of bubble aggregation in CFD modeling of DAF
systems is an essential component towards achieving realistic modeling results.
Keywords dissolved air flotation, bubble, stratified flow, computational fluid dynamics, CFD,
DAF
3.1. 22B22BIntroduction
Dissolved air flotation (DAF) is growing in popularity as a method of drinking water treatment
(Haarhoff, 2008). Early models of flow in the separation zone of DAF systems assumed vertical
plug flow from the surface to the underdrain system. Based on this assumption, the maximum
surface loading rate to avoid bubble washout was calculated to be in the order of 510 m/hr
(Haarhoff and Vuuren, 1995). More recent pilot plant testing demonstrated that higher loading
rates were possible, with excellent particle removal efficiency at rates as high as 41 m/hr, but
with increased bubble carryover to downstream processes (Edzwald et al., 1999). Based on the
experimental results of Lundh et al. (2000 and 2001), Haarhoff and Edzwald (2004) and Edzwald
(2007) attributed the concept of stratified flow to explain the higher loading rates observed in
practice. Stratified flow was explained as water travelling in a horizontal flow layer along the top
1 ThisChapterispublishedas“B.Laghomi,Y.Lawryshyn, R. Hofmann, 2012. Effect of stratified flow and bubble
aggregation in the separation zone of a dissolved air flotation tank. Water Research, 46 (14), 446876”.

19
of the tank to the far end, and then traveling back towards the front in a second horizontal layer
below the first layer. However, based on the study by Lundh et al. (2000 and 2001), the stratified
flow was only present at certain flow conditions, and the second horizontal layer was disrupted
as the loading rate increased or as the air fraction decreased, leading to shortcircuiting of the
flow. Several studies using computational fluid dynamics (CFD) models of DAF systems have
also predicted stratified flow, however, they did not identify limiting conditions required to
create the desirable stratified flow conditions, and did not predict the quantitative impact of the
stratification on bubble removal (Ta et al., 2001; Hague et al. 2001; Bondelind et al., 2010).
While flow stratification is one important phenomenon that should be better understood to
improve bubble removal efficiency in DAF systems (and hence, implicitly, particle removal),
bubble aggregation is another factor that may be associated with better bubble removal.
Empirical studies by Hedberg et al. (1998) and Amato et al. (2001) suggested that increasing
bubble aggregation in the separation zone by means of adding internal plates (such as lamella
plates) can improve removal of free bubbles in the separation zone by producing larger bubbles
that have a larger rise velocity. Leppinen and Dalziel (2004) also reported that large bubble
aggregates (clusters) in the separation zone improved removal efficiency. Previous CFD models
of DAF, such as those reported by Kwon et al. (2006) and Amato and Wicks (2009 and 2010),
were based on the assumption of a uniform bubble size and neglected bubble aggregation. CFD
studies from other applications have included bubble coalescence and breakup models by using
a population balance algorithm (Chen et al., 2004), and it is hypothesized that implementation of
bubble aggregation in a CFD model of a dissolved air flotation system would make the model
more accurate.
In this work, a simple theoretical model was first developed to understand the effect of horizontal
flow layers on bubble removal; with and without bubble aggregation. Then, CFD was used to
predict conditions under which the flow stratification pattern happens and its effect on bubble
removal. The model was then enhanced with a population balance model to account for bubble
aggregation and breakup. The enhanced model was used to understand how changes in air
fraction and flow rate affect bubble removal by affecting bubble aggregation and creating a
stratified flow. It was expected that the optimal air fraction and maximum flow rate could be
determined for a prototype DAF system based on the developed model.

20
Note that the effects of solid particles and the presence of a coagulant on bubble aggregation
were not included in this chapter.
3.2. 23BMethodology
The geometric dimensions of the pilot DAF tank used by Lundh et al. (2001) were chosen for
modeling, so that obtained CFD results could be compared qualitatively to their observations.
The configuration of the flow domain modeled in CFD is shown in Figure 3.1. A two
dimensional model, capable of representing the flow characteristics in the separation zone
(Bondelind et al., 2010), was used to reduce the computational demand. The two dimensional
model did not allow for complete modeling of the recycle air/water injection system, so a pre
blended mixture of air/water was introduced into the contact zone through the water flow inlet.
All of the simulations were performed for a water temperature of 20°C. The governing equations
and details of the modeling setup can be found in Appendix A.
Figure 3.1 Configuration of the modeled DAF system.
For the case with no bubble aggregation, a uniform bubble size of 80 µm was used (average
bubble size in the contact zone is reported to be in the range of 4080 µm; Edzwald, 2010). For
models that included bubble aggregation and breakup, a discrete population balance (fixed
pivot) model was used. The governing equations and details of the applied population balance
model can be found in Appendix A.

21
Two different initial inlet bubble sizes (i.e. at the inlet to the contact zone) of 20 and 80 µm
were tested in the presence of bubble aggregation based on the lower and upper limits of bubble
sizes in the contact zone reported in Edzwald (2010). These initial bubble sizes were then
allowed to grow in the model as the bubbles aggregated. The bubble size distribution was
divided into four discrete groups (bins) for each inlet bubble size, as shown in Table 3.1.
Generally, a greater number of bins would provide a more precise representation of the bubble
size distribution, but the effect of different bin sizes and numbers of bins were not evaluated in
this study due to the high numerical cost.
Table 3.1 Bubble size groups for each inlet bubble size
Bubble size groups (bins) Group 1 (µm) Group 2 (µm) Group 3 (µm) Group 4 (µm)
Inlet bubble size 20 µm 20 40 80 160
Inlet bubble size 80 µm 80 160 320 640
3.3. 24B24BA conceptual model for bubble removal in the separation zone
A study by Edzwald (2007) commented on the importance of horizontal flow layers on bubble
removal. Edzwald (2007), however, assumed that each additional horizontal layer is of equal
importance in improving bubble removal (i.e. the presence of two horizontal layers triples the
maximum loading rate), and did not evaluate the importance of bubble aggregation. In this
section, a similar conceptual model of flow in the separation zone is followed, but bubble
removal from each horizontal layer is evaluated independently by also looking at the effects of
bubble aggregation. This simple model will show that in the absence of bubble aggregation,
bubble removal only occurs from the first layer. In the presence of bubble aggregation, the
addition of multiple layers will be demonstrated to be beneficial, but with diminishing returns for
each subsequent horizontal layer.
3.3.1. 45B45BBubble removal model in the absence of bubble aggregation
The importance of the horizontal flow layers is first assessed, starting with a simplistic scenario
with two perfect plug flow horizontal backandforth layers as shown in Figure 3.2.

22
Figure 3.2 The conceptualized flow models for separation zone, reverse flow on top and plug
flow at bottom
The bubble removal efficiency of the top layer (with length 𝐿 and thickness of 𝐻) for a bubble
rise velocity of 𝑉𝑏 can be calculated based on Hazen theory using a similar approach to
calculating particle removal in sedimentation basins (Crittenden et al., 2005):
𝐵𝑢𝑏𝑏𝑙𝑒 𝑟𝑒𝑚𝑜𝑣𝑎𝑙 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = (𝐿
𝑈) (
𝑉𝑏𝐻
) = (𝐿
𝑄 (𝑤𝐻)⁄) (
𝑉𝑏𝐻
) = (𝐿𝑤
𝑄) 𝑉𝑏 =
𝑉𝑏𝑉𝑠
(3.1)
where 𝑈 is the horizontal velocity, 𝑤 is the tank width, 𝑄 is the flow rate and 𝑉𝑠 is the surface
loading rate.
For any bubble, the vertical travel in the first layer is (𝐿
𝑈) (𝑉𝑏). If this vertical travel is not
enough to reach the surface, then the bubble will not be removed and will descend to the second
layer. If the same bubble reaches the top of the second layer and reenters the first layer, its
horizontal travel in the first layer will be smaller than 𝐿 this time: so its vertical travel will be
even smaller than (𝐿
𝑈) (𝑉𝑏). Thus, the bubble cannot reach the surface this time either. Based on
this theory, bubbles can only be removed from the top horizontal layer in the absence of bubble
bubble aggregation, and the formation of a second horizontal layer is not beneficial. This theory
is based on the assumption of a uniform bubble size, uniform horizontal velocity and uniform

23
mixing of bubbles in each layer. In addition, the effects of turbulence and bubblebubble
aggregation are neglected.
3.3.2. 46B46BBubble removal model in the presence of bubble aggregation
The effect of bubble aggregation on bubble removal is now assessed for cases of both perfect
plug flow (no horizontal flow layers), and the conceptual model of Figure 3.2. In the presence of
bubble aggregation, assuming second order rate kinetics for bubblebubble collision, the
population balance for original bubble size can be written as:
𝑑𝑛𝑏0𝑑𝑡
= −𝑘00𝑛𝑏0𝑛𝑏0 (3.2)
where 𝑛𝑏0 is the number concentration of the original bubble size per unit volume, and 𝑘𝑖𝑗 is the
attachment frequency between the bubble sizes of groups 𝑖 and 𝑗. The larger bubbles formed
(group 1) can coalesce with smaller bubbles from group 0, or the bubbles with the same size in
group 1. Therefore, the population balance for the bubbles in group 1, with the bubble
concentration of 𝑛𝑏1, can be written as:
𝑑𝑛𝑏1𝑑𝑡
=1
2𝑘00𝑛𝑏0𝑛𝑏0 − 𝑘01𝑛𝑏0𝑛𝑏1 − 𝑘01𝑛𝑏1𝑛𝑏1 (3.3)
Following the same pattern, the above equation can be extended for n groups of bubble sizes. An
analytical solution that incorporates 𝑛 > 2 population balance equations and realistic
(complicated) fluid mechanics is not feasible. Instead, a simplified conceptual model is presented
to highlight the important theoretical aspects.
If two bubbles, with the same diameter, ∅𝑏0, attach together, the diameter of the formed bubble
can be calculated as:
∅𝑏1 = 213∅𝑏0 (3.4)
and therefore the bubble rise velocity after attachment can be calculated as:
𝑉𝑏1 = 223𝑉𝑏0 = 1.587𝑉𝑏0 (3.5)

24
where 𝑉𝑏0 is the rise velocity of the original bubbles.
For a DAF system with complete vertical plug flow throughout the separation zone (i.e. no
horizontal layers), the total number of bubbles removed can be calculated as the number of
bubbles in each of the size groups that have a rise velocity greater than the loading rates. For the
plug flow case, if 𝑉𝑏0 < 𝑉𝑠 < 1.587 𝑉𝑏0, only bubbles that were attached to other bubbles would
be removed. The ratio of bubbles converted to larger bubbles (and removed in this case), α, can
be derived by integrating Equation (3.2):
α = 1 −𝑛𝑏0,𝑜𝑢𝑡
𝑛𝑏0= (1 −
1
1 + 𝑘00𝜏𝑛𝑏0) (3.6)
where 𝜏 = (2𝐻+𝑠
𝑉𝑠−𝑉𝑏0) is the bubble residence time in the separation zone. For plug flow, the
residence time can be calculated as 𝜏 = (2𝐻+𝑠
𝑉𝑠−𝑉𝑏0), where 𝐻 and 𝑠 are the thicknesses of the
horizontal and vertical plug flow layers as shown in Figure 3.2. This simple model shows that
even for a plug flow system, bubblebubble attachment can add to bubble removal and, as the
bubblebubble contact time and bubble concentration increase, more bubble removal is expected.
In the case where horizontal flow segments and bubble aggregation both exist, the ratio of
bubbles that are converted to larger bubbles, 𝛽, can be calculated using Equation (3.7), but the
residence time for this case will be estimated differently as 𝜏 = (𝐿
𝑈). If bubble aggregation occurs
at a distance 𝛾𝐿 from the inlet (0 < 𝛾 < 1), the total vertical travel distance, Y, of a bubble in the
first layer can be derived by adding its vertical travel before and after attachment. Applying the
same principle as used to derive Equation (3.1), the vertical travel distance becomes,
𝑌 =𝛾𝐿
𝑈𝑉𝑏0 +
(1 − 𝛾)𝐿
𝑈𝑉𝑏1 =
𝛾𝐿
𝑈𝑉𝑏0 +
(1 − 𝛾)𝐿
𝑈1.587𝑉𝑏0 = (1.587 − 0.587𝛾)
𝐿
𝑈𝑉𝑏0 (3.7)
and the average vertical travel for all of the bubbles can be calculated by averaging 𝑌 for all
values of between 0 and 1 to get 1.293𝐿
𝑈𝑉𝑏0. As a result, if the total number of bubbles is 𝑛𝑏0,
the number of converted bubbles will be 𝛽𝑛𝑏0, from which a fraction of 1.293(𝐿
𝑈)(
𝑉𝑏0
𝑡) or
1.293(𝑉𝑏0
𝑉𝑠) can be removed based on the calculated average vertical travel. Therefore, the

25
number of original bubbles removed after coalescence can be estimated as 1.293(𝑉𝑏0
𝑉𝑠)𝛽𝑛𝑏0.
From the number of bubbles remaining at their original size, equal to(1 − 𝛽)𝑛𝑏0, a fraction of
𝑉𝑏0
𝑉𝑠 can be removed based on Equation (3.1). As a result, the total bubble removal can be
calculated as follows:
𝐵𝑢𝑏𝑏𝑙𝑒 𝑟𝑒𝑚𝑜𝑣𝑎𝑙 =(1 − 𝛽)
𝑉𝑏0𝑉𝑠
𝑛𝑏0 + 1.293𝛽𝑉𝑏0𝑉𝑠
𝑛𝑏0
𝑛𝑏0= (1 − 𝛽)
𝑉𝑏0𝑉𝑠
+ 1.293𝛽𝑉𝑏0𝑉𝑠
= (1 + 0.293𝛽)𝑉𝑏0𝑉𝑠
(3.8)
The removal ratio from Equation (3.8) is larger than the removal ratio without bubble
aggregation shown in Equation (3.1).
In addition, there will be a chance for the removal of bubbles that aggregate and form larger
bubbles in the second horizontal layer. Assuming that bubblebubble attachment occurs at a
distance 𝛾𝐿 from the right wall, the total vertical travel, 𝑌𝑡, of a bubble can be calculated as the
sum of the vertical travel in the second layer before and after attachment, and the vertical travel
in the first layer:
𝑌𝑡 = (𝛾𝐿
𝑈) 𝑉𝑏 + (
(1 − 𝛾)𝐿
𝑈) (1.587𝑉𝑏) + (
𝐿
𝑈) 1.587 𝑉𝑏 = (
𝐿
𝑈) 𝑉𝑏(3.174 − 0.587𝛾) (3.9)
As a result, for all 𝛾 values where the total vertical travel as calculated in Equation (3.9) is larger
than the thickness of the back and forth horizontal layers (2𝐻 as shown in Figure 3.2), i.e. for
2𝐻 < (𝐿
𝑈) 𝑉𝑏(3.174 − 0. 587𝛾), the bubbles will be able to reach the surface and be removed.
The addition of a second horizontal flow layer can therefore be of benefit for additional bubble
removal in the presence of bubble aggregation, unlike the case where bubble aggregation was
absent. In general, it can be shown based on Equation (3.6) that increasing the residence time can
increase bubble aggregation (the denominator in Equation (3.6) becomes larger, and bubble
aggregation becomes larger as a result) leading to the formation of larger bubbles with greater
rise velocities that are removed more easily. Multiple horizontal flow layers can help to achieve
this objective by increasing the residence time and bubblebubble contact. However, it is

26
expected that as the concentration of the bubbles decreases deeper in the tank, the possibility of
bubblebubble contact becomes less (the denominator in Equation (3.6) becomes smaller) and
additional horizontal flow layers will have a less important effect on bubble removal.
The described theory was used to conceptually show the importance of bubble aggregation and
horizontal stratification of flow on bubble removal. The theory showed that under idealized flow
conditions, bubble aggregation, in general, can help to improve bubble removal, and is of
additional benefit when multiple horizontal flow layers are present. In practice, however, flows
are not perfectly stratified and there is an important coupling between the bubble aggregation and
flow pattern. A CFD model can be used to estimate under what conditions stratified horizontal
flow may be present in a typical DAF system, and characterize its effects on bubble removal in
the presence of bubble aggregation.
3.4. 25B25BResults and Discussions
3.4.1. 47B47BEvaluation of the CFD model in the absence of bubble aggregation
The effect of volume air fraction and loading rate on flow pattern and bubble removal was first
evaluated in the absence of bubble aggregation. The main objective of this step was to evaluate
whether a CFD model that neglects bubble aggregation would be able to describe realistic flow
patterns in a DAF separation zone, and would therefore be useful for characterizing DAF
performance. Figure 3.3 shows the CFD generated velocity vectors for increasing air fraction in
the absence of bubble aggregation at a loading rate of 11.8 m/hr (flow rate of 10 m3/hr). The
chosen loading (flow) rates were based on those of Lundh et al. (2001), and similar to their
study, only velocity vectors in the range of (00.03 m/s) are shown to allow comparison with
their results. As can be seen, a top horizontal flow layer was present even without air in the
system. As air was added, however, a back flow layer (travelling from right to left in the figure)
was formed underneath the top layer, returning the water toward the baffle. The horizontal back
flow continued to be present when the air fraction was increased to 0.02. At a loading rate of
23.6 m/hr (flow rate of 20 m3/hr), as shown in Figure 3.4, the flow pattern did not change
significantly as the air fraction increased. This observation, however, was not in agreement with
the results of Lundh et al. (2001). Experimentally, Lundh et al. (2001) observed that at this
loading rate the flow pattern shifted from shortcircuiting flow to stratified flow as the air
fraction increased from 0.005 to 0.01. The discrepancy between the results of Lundh et al. (2001)

27
and model predictions at this loading rate may be related to the formation of bubble aggregates
that was not accounted for in the CFD model.
Figure 3.5 plots bubble removal as a function of air fraction at different loading rates, based on
the CFD model (with no bubble aggregation) and the theoretical approach (i.e. Equation (3.1)).
The results demonstrate a good agreement between CFD and the theoretical approach for both
assumed bubble sizes. In addition, CFD results confirm that an increase in the loading rate
reduces the bubble removal efficiency as suggested by Equation (3.1).
Figure 3.3 Velocity vectors (00.03 m/s), a) Single phase, b) Air fraction 0.005, c) Air fraction
0.02. Loading rate 11.8 m/hr, bubble size = 80 µm.
Figure 3.4 Velocity vectors (00.03 m/s), a) Air fraction 0.005, b) Air fraction 0.01, c) Air
fraction 0.02. Loading rate 23.6 m/hr, bubble size = 80 µm.

28
In the absence of bubble aggregation, bubble removal showed only a weak dependence on air
fraction. In addition, no relationship between the presence of a second horizontal layer (reverse
flow) and bubble removal was observed in the absence of bubble aggregation. The theoretical
model in Equation (3.6) suggested that the reverse flow layer may become important when
bubbles collide and coalesce. Bubble aggregation therefore needs to be modeled for more
realistic results.
0
0.2
0.4
0.6
0.8
1
0.004 0.006 0.008 0.01
Bu
bb
le r
em
ova
l
Air fraction
11.8 m/hrCFD no aggregation
23.6m/hr CFD no aggregation
47.2m/hrCFD no aggregation
11.8m/hrTheoretical
23.6m/hrTheoretical
47.2m/hrTheoretical
Figure 3.5 Effect of air inlet fraction on bubble removal at different loading rates. Bubble size
80 µm.
3.4.2. 48B48BEffects of operating conditions on bubble removal in the presence of bubble aggregation
The theory demonstrated that, in principle, the formation of horizontal flow layers in the
separation zone would help to improve bubble removal in a real DAF system, and that bubble
aggregation would enhance the beneficial effects of the horizontal flow layers. The CFD model
was used to explore these phenomena under more realistic flow conditions by including a bubble
population balance model that allowed bubble aggregates to form. The bubble removal rates
calculated at different air fractions and loading rates from CFD modeling accounting for bubble
aggregation and breakup are shown in Figure 3.6.

29
0
0.2
0.4
0.6
0.8
1
0.004 0.006 0.008 0.01
Bu
bb
le r
em
ova
l
Air fraction
a) Inlet bubble size 80 µm
11.8 m/hr
23.6 m/hr
47.2 m/hr
0
0.2
0.4
0.6
0.8
1
0.01 0.02 0.03 0.04 0.05
Bu
bb
le r
em
ova
l
Air fraction
b) Inlet bubble size 20 µm
11.8 m/hr
23.6 m/hr
47.2 m/hr
Figure 3.6 Effect of air inlet fraction on bubble removal in presence of bubble aggregation at
different loading rates, a) Inlet bubble size 80 µm, b) Inlet bubble size 20 µm.
The CFD results in Figure 3.6 showed that bubble removal increased with increasing air fraction
in the system. This is because a larger air fraction increases bubble aggregation and, as a result,
forms larger bubbles that have larger rise velocities and can be more easily removed.
In addition, similar to the case with no bubble aggregation, increasing the loading rate reduced
bubble removal. For an inlet bubble size of 80 µm, perfect removal was observed for loading
rates up to 23.6 m/hr at an air fraction of 0.008, and for loading rates up to 47.2 m/hr at an air
fraction of 0.01. For a smaller inlet bubble size of 20 µm and an air fraction of 0.035, perfect
removal could be observed at loading rates up to 23.6 m/hr.
An important factor that may be associated with the bubble removal is the presence of reverse
(stratified) flow. The CFD results demonstrated that this reverse flow is strengthened with
increasing air fraction. This is demonstrated in Figure 3.7 and Figure 3.8, which show the
velocity vectors at different air fractions for a loading rate of 23.6 m/hr and inlet bubble sizes of
80 µm and 20 µm, respectively. For both initial bubble sizes, there was little observed stratified
flow at the lowest air fractions, but the stratified flow became more evident at an air fraction of
about 0.01 (for the 80 µm bubbles) and 0.035 (for the 20 µm bubbles). These results indicate that
a certain minimum air fraction is required before flow stratification can be observed and is in
agreement with the experimental results of Lundh et al. (2001). The CFD model also suggests
that as the initial bubble sizes increase, the minimum air fraction that must be applied to create
the horizontal stratified flow is lower. This suggests that the introduction of larger bubbles, for

30
the same total amount of air, might help to encourage horizontal stratified flow, thereby
improving the efficiency of the separation zone of a DAF tank.
Figure 3.7 Velocity vectors (00.03 m/s) in the presence of bubble aggregation, a) Air fraction
0.005, b) Air fraction 0.008, c) Air fraction 0.01. Loading rate 23.6 m/hr, inlet bubble size 80
µm.
Figure 3.8 Velocity vectors (00.05 m/s) in the presence of bubble aggregation, a) Air fraction
0.01, b) Air fraction 0.035, c) Air fraction 0.05. Loading rate 23.6 m/hr, inlet bubble size = 20
µm.
The observation that an increasing air fraction helps to encourage horizontal stratified flow was
explained by Lundh et al. (2001). Their measurements of the air concentration at different depths
led them to propose that the reverse flow was due to a lower density top layer with a higher air
fraction that does not have enough momentum to push through the higher density lower layer.

31
The air fractions calculated from the CFD model show a distribution of air that is in relatively
good agreement with the experimental results of Lundh et al. (2001) (Figure 3.9). However, the
CFD model slightly over predicts the air concentrations shown by Lundh et al. (2001) for the
loading rate of 11.8 m/hr. This may be due to a discrepancy between the applied inlet bubble size
based on Edzwald (2010) with the bubble size distribution in the pilot system used by Lundh et
al. (2001).
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8
He
igh
t (m
)
Air content (mL air/L water)
CFD11.8 m/hr
CFD24m/hr
Lundh et al.(2001)11.8m/hr
Lundh et al.(2001)24m/hr
Figure 3.9 Comparison of air content in the separation zone from Lundh et al. (2001) and the
present model. Inlet air fraction 0.005 (air content at 1.35 m from left wall).
While a larger a