EFFECT OF BUBBLE SIZE AND SPARGING FREQUENCY ON THE POWER TRANSFERRED ONTO MEMBRANES FOR FOULING CONTROL

by

Sepideh Jankhah

B.Sc. Shiraz University, 2003

M.Sc. Université de Sherbrooke, 2007

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

in

THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES

(Civil Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

(Vancouver)

December, 2013

© Sepideh Jankhah, 2013

Abstract

Fouling control through air sparging in membrane systems is governed by the

hydrodynamic conditions in the system and the resulting shear stress induced onto

membranes. However, the relationship between hydrodynamic conditions and the extent of

fouling control is not well understood. As a result, sparging approaches are designed using a

capital and time intensive empirical trial-and-error approach that does not guarantee that

optimal conditions are identified. To address this knowledge gap, the present research

focused on characterizing the hydrodynamic conditions in a membrane system under

different sparging conditions (bubble size and frequency) and on finding a correlation

between the induced hydrodynamic conditions and fouling control efficiency. New concepts

of zone of influence of bubbles and power transferred were defined to characterise the

hydrodynamic conditions in the system. A non-homogenous fouling distribution was

observed in the zone of influence of bubbles due to a non-homogenous distribution of

velocity and shear stress in this zone. Fouling rates generally decreased with an increase in

the area of the zone of influence, the root mean square of shear stress induced onto

membranes and the rise velocity of bubbles. However, none of these parameters on their own

could accurately describe the effect of the hydrodynamic conditions on fouling rate. On the

other hand, power transferred onto fibers, which incorporates the effect of all the three

parameters, could more effectively describe the effect of the hydrodynamic conditions on the

rate of fouling. Power transfer efficiency into the system, defined as the ratio of power

transferred onto membranes to the power input in the system, was used to identify optimal

sparging approaches. For all cases investigated, the power transfer efficiency to the system

was consistently much higher for pulse bubble than for coarse bubble sparging. The results

also indicated that as sparging frequency and the size of the bubbles increased, the width of

zone of influence increased, suggesting that the spacing between the spargers could be

increased when sparging with larger bubbles or at higher frequencies. Increasing the spacing

would not only decrease the number of spargers, but also the volume of the gas required for

sparging.

ii

Preface

I am the principal investigator of this research project, in charge of developing the

research proposal, i.e. identifying the research questions, planning the research program,

performing research experimental work, and analysing the research data. The following

manuscripts were submitted to peer reviewed journals summarizing some of the outcomes of

this research. I am the principal author of the first three manuscripts under supervision of

Professor Pierre Bérubé. The fourth manuscript was written in collaboration with Mr. Lutz

Boehm, PhD student at Technical University of Berlin, Germany for which I was responsible

for 50% of the work. In addition, I am the principal author of 10 conference publications and

a supporting author on one.

Journal papers:

• Sepideh Jankhah, Pierre R. Bérubé (2013) “Power induced by bubbles of different

sizes and frequencies onto hollow fibers in submerged membrane system”, Water

Research, DOI: 10.1016/j.watres.2013.08.020.

• Sepideh Jankhah, Pierre R. Bérubé (2013) “Fouling control in submerged hollow

fiber membrane systems with pulse and coarse bubble sparging”, Submitted.

• Sepideh Jankhah, Pierre R. Bérubé (2013) “Efficiency of coarse and pulse bubble

sparging in terms of fouling control in submerged hollow fiber membrane systems”,

Submitted.

• Lutz Böhm, Sepideh Jankhah, Jaroslav Tihon, Pierre R. Bérubé, Matthias Kraume

(2013) “Application of the electrodiffusion method to measure wall shear stress:

integrating theory and practice”, Submitted.

Podium presentations / Conference proceedings:

• Jankhah S, Bérubé P.R. (August, 2013) Efficiency of coarse and pulse bubble

sparging in terms of fouling control in submerged hollow fiber membrane systems,

podium presentation at the American Water Works Association (AWWA) Water

Quality Technology Conference, Toronto, Canada.

• Jankhah S, Bérubé P.R. (Nov., 2012) Designing High Performance Air Spargers For

Minimizing The Fouling Rate In Submerged HF Membranes, podium presentation at

the American Water Works Association (AWWA) Water Quality Technology

iii

Conference, Toronto, Canada.

• Jankhah S, Bérubé P.R. (April, 2011) Investigation of the relationship between

variable hydrodynamic conditions at the surface of air sparged submerged membrane

systems and membrane fouling rate. podium presentation at the BCWWA Annual

Conference & Trade Show/Canadian Association on Water Quality (CAWQ),

Kelowna, Canada

• Jankhah S, Bérubé P.R. (March, 2011) Behaviour of Foulants under Different

Hydrodynamic Conditions at the surface of submerged Membranes, podium

presentation at the AWWA Membrane Technology Conference, Long Beach,

California

• Jankhah S, Bérubé P.R. (Oct. 2010) Characterizing Hydrodynamics at Membrane

Surfaces in Air Sparged Submerged Systems through Direct Observation and Particle

Image Velocimetry, podium presentation at the IWA World Water Conference,

Montreal, Canada.

• Jankhah S, Bérubé P.R. (May 2010) Characterizing Hydrodynamic Conditions at

Membrane Surface in Air Sparged Membrane Systems through Direct Observation –

Development of the Technique, podium presentation at the BCWWA Annual

Conference & Trade Show, Whistler, Canada.

• Jankhah S., Bérubé P.R., Y.Ye, P. Le-Clech, V. Chen (Sept. 2009) Investigation of

Fouling Mechanisms in Submerge Membrane Systems, Proceedings of the 5th

International Water Association Membrane Technology Conference and Exhibition,

Beijing, China.

• N. Ratkovich, C.C.V. Chan, S. Jankhah, P.R. Bérubé and I. Nopens (Sept. 2009)

Analysis of shear stress and energy consumption in a tubular airlift membrane system,

podium presentation at 5th International Water Association Membrane Technology

Conference and Exhibition, Beijing, China.

• Jankhah S., and Bérubé P.R. (April 2009) Investigation of Fouling Mechanism in

Submerged Membrane Systems, podium presentation at the BCWWA Annual

Conference & Trade Show, Penticton, Canada

• Jankhah S., Bérubé P.R. and Chan C.C.V. (July 2008) Shear Forces and Fouling

Control in Membrane Systems, 2nd Workshop on CFD Modeling for MBR

iv

applications, European MBR-Network, Gent, Belgium.

• Jankhah, S., Bérubé, P., Mavinic. D. S., Andrews, S. A., Gagnon, G. A.,Walsh, M.

(April 2008) Addressing Water Quality Concerns Associated with Disinfection By-

Products in Drinking Water Systems for Small and Rural Communities, podium

presentation at the BCWWA Annual Conference & Trade Show, Whistler, Canada

v

Table of Contents

Abstract ...................................................................................................................................... i

Preface ...................................................................................................................................... ii

Table of Contents ...................................................................................................................... v

List of Tables ........................................................................................................................... ix

List of Figures ........................................................................................................................... x

Nomenclature .......................................................................................................................... xii

Acknowledgements................................................................................................................ xvi

Dedication ............................................................................................................................. xvii

1 Introduction....................................................................................................................... 1

1.1 Relationship between sparging approaches and hydrodynamic conditions induced on submerged hollow fiber membrane systems .............................................................. 6

1.2 Effect of hydrodynamic conditions on fouling rate in submerged hollow fiber membranes ................................................................................................................................................... 10

1.3 Approaches to investigate the effect of sparging scenarios on the hydrodynamic conditions, induced shear stress, and fouling control .................................................................. 12

1.4 Research tasks ............................................................................................................................... 14

2 Experimental setup and measurement approaches ......................................................... 15

2.1 Experimental setup and experimental conditions investigated ................................ 15

2.2 Filtration setup .............................................................................................................................. 20

2.3 Measurement approaches ......................................................................................................... 20 Imaging of sparged bubbles ................................................................................................ 20 2.3.1 Measurement of shear stress induced onto membranes ......................................... 21 2.3.2 Particle Image Velocimetry (PIV) ...................................................................................... 24 2.3.3

3 Bubble characteristics obtained using imaging .............................................................. 26

vi

3.1 General physical characteristics of sparged bubbles investigated ........................... 26

3.2 General behavior of sparged bubbles investigated ......................................................... 32 Coarse bubble sparging ......................................................................................................... 32 3.2.1 Small pulse bubble sparging ............................................................................................... 33 3.2.2 Medium pulse bubble sparging .......................................................................................... 35 3.2.3 Large pulse bubble sparging ............................................................................................... 36 3.2.4

3.3 Conclusion ....................................................................................................................................... 38

4 Characterisation of the hydrodynamic conditions induced by sparged bubbles............. 39

4.1 Distribution of vorticity and velocity for discrete sparging ........................................ 39 Vertical distribution of velocity for discrete bubble sparging ............................... 41 4.1.1 Horizontal distribution of velocity for discrete bubble sparging ......................... 42 4.1.2 Zone of influence ...................................................................................................................... 44 4.1.3 Vertical distribution of shear stress for discrete bubble sparging ....................... 53 4.1.4 Horizontal distribution of shear stress for discrete bubble sparging ................. 55 4.1.5

4.2 Effect of sparging frequency on the distribution of velocity, vorticity and shear stress 57

Effect of sparging frequency on the vertical distribution of vorticity, velocity 4.2.1and shear stress .......................................................................................................................................... 57

Effect of sparging frequency on the horizontal distribution of velocity and the 4.2.2shear stress ................................................................................................................................................... 74

4.3 Summary of the hydrodynamic conditions induced by bubbles of different sizes and sparging frequencies ........................................................................................................................ 86

4.4 Conclusion ....................................................................................................................................... 93

5 Relationship between the induced hydrodynamic conditions and power transfer efficiency in the system .......................................................................................................... 95

5.1 Power transfer and power transfer efficiency per bubble for discrete bubble sparging .......................................................................................................................................................... 96

5.2 Power transfer and power transfer efficiency per bubble for sparging at higher frequencies .................................................................................................................................................. 101

5.3 System-wide power transfer and power transfer efficiency at different sparging flow rates ..................................................................................................................................................... 102

5.4 Conclusion ..................................................................................................................................... 106

6 Effect of induced hydrodynamic conditions on the fouling rate .................................. 107

vii

6.1 Effect of bubble size and sparging frequency on fouling rate ................................... 107

6.2 Effect of bubble size and sparging frequency on the spatial distribution of fouling rate in the system ..................................................................................................................................... 120

6.3 Conclusion ..................................................................................................................................... 123

7 Conclusions and recommendation ................................................................................ 125

7.1 Overall conclusions .................................................................................................................... 125

7.2 Engineering significance.......................................................................................................... 127

7.3 Recommendations for future work ..................................................................................... 128

References............................................................................................................................. 130

APPENDIX A Calibration of the electrochemical shear probes .......................................... 142

Appendix B Application of the electrodiffusion method (EDM) to measure wall shear stress: integrating theory and practice ............................................................................................. 145

B-1 Introduction........................................................................................................................................ 145

B.2 Electrodiffusion Method (EDM): theory .................................................................................. 147 B.2.1 The basic electrical circuit ................................................................................................. 147 B.2.2 The electrodes ........................................................................................................................ 147 B.2.3 The electrolytic solution ..................................................................................................... 148 B.2.4 Limiting diffusion current .................................................................................................. 148 B.2.5 Steady state flow conditions ............................................................................................. 150 B.2.6 Dynamic flow conditions .................................................................................................... 153

B.3 Electrodiffusion Method (EDM): application ......................................................................... 156 B.3.1 Experimental setup ............................................................................................................... 156 B.3.2 Practical aspects influencing the measurement ........................................................ 156 B.3.3 Data conditioning .................................................................................................................. 158 B.3.4 Wall shear rate calculation and correction ................................................................. 162

B.4 Conclusions ......................................................................................................................................... 165

Appendix C : Matlab codes developed to process voltage signals ....................................... 166

V-step in-situ calibration of the shear probes ............................................................................... 166

Correction of data under transient flow condtions ..................................................................... 171

viii

Appendix D Matlab codes developed to process images and the data obtained from PIV .. 190

Appendix E Filtration data.................................................................................................... 206

Appendix F Horizontal distribution of the shear stress for medium and large pulse bubble sparging................................................................................................................................. 211

Appendix G: Correlation between cut off velocity and rate of fouling ................................ 218

ix

List of Tables

Table 2-1 Sparging conditions investigated ........................................................................... 19 Table 3-1 General characteristics of studied bubbles ............................................................. 30 Table 4-1 General characteristics of studied bubbles and the induced zone of influence ...... 50

x

List of Figures

Figure 1-1 Typical shear stress profile in a confined (tubular) membrane system .................. 8 Figure 1-2 Typical shear stress profile in unconfined (hollow fiber) membrane systems ....... 8 Figure 2-1 Picture of the system tank with membrane module .............................................. 16 Figure 2-2 Experimental system ............................................................................................. 17 Figure 2-3 Electrical circuit used for measurement of shear stress with EDM ...................... 22 Figure 2-4 A shear probe fixed on a test fiber shown on top of a ZW-500 hollow fiber membrane ............................................................................................................................... 23 Figure 2-5 Typical shear stress profile for coarse bubble sparging ........................................ 24 Figure 2-6 Typical 2 dimensional velocity map generated from the PIV data ....................... 25 Figure 3-1 Typical images of bubbles generated by coarse and pulse sparging .................... 27 Figure 3-2 Bubble rise velocity for bubble size and frequencies investigated ....................... 31 Figure 3-3 Typical images of bubbles generated by coarse bubble sparging ......................... 33 Figure 3-4 Typical images of bubbles generated by small (150 mL) pulse sparging ............. 34 Figure 3-5 Typical images of bubbles generated by medium (300 mL) pulse ....................... 36 Figure 3-6 Typical images of bubbles generated by large (500 mL) pulse sparging ............. 37 Figure 4-1 Typical vorticity and velocity distributions induced by discrete rising bubbles .. 40 Figure 4-2 Typical horizontal distributions of velocity across the width of system tank....... 43 Figure 4-3 Typical distribution of a) velocity and b) vorticity for discrete bubble sparging with the coarse bubble sparger ............................................................................................... 45 Figure 4-4 Typical distribution of a) velocity and b) vorticity for discrete bubble sparging with the small pulse bubble sparger........................................................................................ 46 Figure 4-5 Typical distribution of a) velocity and b) vorticity for discrete bubble sparging with the medium pulse bubble sparger ................................................................................... 47 Figure 4-6 Typical distribution of velocity a), and vorticity d) for discrete bubble sparging with the large pulse bubble sparger ........................................................................................ 48 Figure 4-7 Dimensionless area of zone of influence for discrete bubbles .............................. 52 Figure 4-8 Typical shear stress distribution induced by discrete rising bubbles at vertical centreline of the tank .............................................................................................................. 54 Figure 4-9 Horizontal distributions of shear stress across the width of system tank for discrete sparging frequency .................................................................................................... 56 Figure 4-10 Typical distribution of hydrodynamic conditions induced by coarse bubble sparging at discrete sparging frequency ................................................................................. 58 Figure 4-11 Typical distribution of hydrodynamic conditions induced by coarse bubble sparging at 0.25 Hz sparging frequency ................................................................................. 59 Figure 4-12 Typical distribution of hydrodynamic conditions induced by coarse bubble sparging at 0.5 Hz sparging frequency ................................................................................... 60 Figure 4-13 Typical distribution of hydrodynamic conditions induced by small (150 mL) pulse bubble sparging at discrete sparging frequency ............................................................ 63 Figure 4-14 Typical distribution of hydrodynamic conditions induced by small (150 mL) pulse bubble sparging at 0.25 Hz sparging frequency ............................................................ 64 Figure 4-15 Typical distribution of hydrodynamic conditions induced by small (150 mL) pulse bubble sparging at 0.5 Hz sparging frequency .............................................................. 65 Figure 4-16 Typical distribution of hydrodynamic conditions induced by medium (300 mL) pulse bubble sparging at discrete sparging frequency ............................................................ 68

xi

Figure 4-17 Typical distribution of hydrodynamic conditions induced by medium (300 mL) pulse bubble sparging at 0.25 Hz sparging frequency ............................................................ 69 Figure 4-18 Typical distribution of hydrodynamic conditions induced by medium (300 mL) pulse bubble sparging at 0. 5 Hz sparging frequency ............................................................. 70 Figure 4-19 Typical distribution of hydrodynamic conditions induced by large (500 mL) pulse bubble sparging at discrete sparging frequency ............................................................ 71 Figure 4-20Typical distribution of hydrodynamic conditions induced by large (500 mL) pulse bubble sparging at 0.25 Hz sparging frequency ............................................................ 72 Figure 4-21 Typical distribution of hydrodynamic conditions induced by large (500 mL) pulse bubble sparging at 0.5 Hz sparging frequency .............................................................. 73 Figure 4-22 Typical horizontal distributions of velocity across the width of system tank..... 75 Figure 4-23 Typical vertical distribution of shear stress induced by coarse bubble sparging at different locations for discrete sparging frequency ................................................................ 77 Figure 4-24 Typical vertical distribution of shear stress induced by coarse bubble sparging at different locations for 0.25Hz sparging frequency ................................................................. 78 Figure 4-25 Typical vertical distribution of shear stress induced by coarse bubble sparging at different locations for 0. 5Hz sparging frequency .................................................................. 79 Figure 4-26 Typical vertical distribution of shear stress induced by small (150 mL) at different locations for pulse bubble sparging at discrete sparging frequency ........................ 81 Figure 4-27 Typical vertical distribution of shear stress induced by small (150 mL) at different locations for pulse bubble sparging at 0.25Hz sparging frequency ......................... 82 Figure 4-28 Typical vertical distribution of shear stress induced by small (150 ml) at different locations for pulse bubble sparging at 0. 5 Hz sparging frequency ......................... 83 Figure 4-29 Horizontal distributions of shear stress across the width of system tank ........... 85 Figure 4-30 Area of zone of influence .................................................................................... 87 Figure 4-31 Average width of zone of influence .................................................................... 89 Figure 4-32 System wide RMS of bulk velocity .................................................................... 90 Figure 4-33 RMS of shear stress ............................................................................................ 92 Figure 5-1 Power transferred onto membranes per bubble .................................................... 97 Figure 5-2 Force per bubble ................................................................................................... 98 Figure 5-3 Power transfer efficiency per bubble .................................................................. 100 Figure 5-4 Relationship between power transfer and air sparging conditions ..................... 103 Figure 5-5 Power transfer efficiency for the sparging conditions investigated .................... 105 Figure 6-1 Typical results from filtration experiments......................................................... 108 Figure 6-2 System average fouling rate constant for different sparging conditions ............. 109 Figure 6-3 Relationship between fouling rate and power transferred onto membranes ....... 111 Figure 6-4 Relationship between fouling rate and root mean square of shear stress in the system ................................................................................................................................... 114 Figure 6-5 Relationship between fouling rate and root mean square of shear stress for individual fibers .................................................................................................................... 116 Figure 6-6 Power transfer efficiency with respect to power transferred onto membrane surface ................................................................................................................................... 117 Figure 6-7 Power cost distribution for MBR systems .......................................................... 119 Figure 6-8 Distribution of fouling rate in the system ........................................................... 121

xii

Nomenclature

A Electrode area (m2)

Ab The area of the bubbles (m2)

Az Area of zone of influence of a rising bubble (m2)

Az,bubble Area of zone of influence per bubble (m2)

ap Particle diameter (m)

C0 Concentration of the oxidizing ion at the wall (mol/ m3)

Cb Concentration of the oxidizing ion in the bulk solution (mole/ m3)

ic∇ Concentration gradient of the ferricyanide (mol/m4)

ci Concentration of the ferricyanide (mol/m3)

D Diffusion coefficient (m2/s)

d Diameter of the probe (m)

ds Diameter of the spherical cap (m)

de Bubble equivalent diameter; de = (6V/π)1/3

E0 Eötvös number; E0= gΔρde2/σ [unitless]

f Frequency (1/s)

f* Dimensionless frequency of the flow change ρτ

δ

W

ff =* [unitless]

F Faraday constant (A s/V)

Fb Buoyancy force

Fdrag, CF Drag force induced by the liquid cross flow (N)

Fdrag, permeations Drag force due to the permeation (N)

Flift,shear Lift force induced by the shear stress (N)

Fg Gravity force (N)

G Gravitational acceleration (9.82 m/s2)

h Height of the spherical cap (m)

H modified Peclet number [unitless]

I Current (A)

I0 Current correction for edge effects (A)

j Specific current (A/m2)

xiii

J permeate flux (L/m2/h)

kCot Cottrell coefficient ( A 21

s )

kLev Leveque coefficient (A 31

s )

km Mass transfer coefficient (m/s)

Lchar Characteristic length of the cathode (m)

Lz Length of zone of influence (m)

n Amount of exchanged electrons during the reaction [unitless]

n i,conv Molar flux due to convection (mol/(s m2))

n i,migr Molar flux due to migration (mol/(s m2))

n i,diff Molar flux due to diffusion ( mol/(s m2))

in Molar flux (mol/(s m2))

N Number of exchanged electrons during the reaction [unitless]

iN Molar flow rate (mol/s)

P Perimeter of the circular electrode (m)

Pe Peclet number Pe=γ d2/D [unitless]

Ptrans Power transferred onto membranes (watts)

P0 Initial pressure (Pa)

Pn Normalized pressure (Pa)

Q Electrical charge (A s)

r Homogeneous reaction term (mol/(m3 s))

r Radius of curvature (m)

Reb Bubble Reynolds number [unitless]

Rec Bubble corrected Reynolds number [unitless]

Refibers Reynolds for smooth cylinders, i.e. fibers, immersed in-line with the

flow[unitless]

Sc Schmidt number [unitless]

Sh Sherwood number [unitless]

t time (s)

t0 characteristic time of the probe (s)

τRMS Root mean square of shear stress (Pa)

xiv

ui Electrical mobility (m2/(V s))

v

Velocity vector (m/s)

vx Velocity vector in x direction (m/s)

vy Velocity vector in y direction (m/s)

Vm Voltage (V)

V Volume of the bubble (m3)

Vb Rise velocities of the bubbles (m/s)

Vbc Velocity predicted based on literature (m/s)

Wz Width of zone of influence

x x-coordinate (m)

y y-coordinate (m) *y Dimensionless distance from the wall [unitless]

z z-coordinate, m

β Relative shear rate fluctuation amplitude [unitless]

γ Velocity gradient or shear rate respectively (1/s)

cγ Transient corrected velocity gradient or shear rate respectively (1/s)

sγ Velocity gradient or shear rate respectively at steady state (1/s)

γ~ The amplitude of wall shear rate fluctuations (1/s)

γ The mean value of wall shear rate (1/s)

δ channel half width in a rectangular channel (m)

δc concentration boundary layer thickness (m)

ζ variable for the edge effect correction function [unitless]

κ Specific conductivity (1/( Ω m))

µ Dynamic viscosity (Pa s)

ν Kinematic viscosity (m2/s)

ρ Density (kg/m3)

ρp Particle density (kg/m3)

Δρ Difference between water and air density at 17°C (kg/m3)

σ Water-air surface tension (N/m)

τ Shear stress (Pa)

xv

ϕ∇ Electrical potential gradient (V/m)

Ψ correction function for edge effects [unitless]

xvi

Acknowledgements

I would like to acknowledge the people without whom this achievement would not be

possible. Firstly, I would like to thank my supervisor, Dr. Pierre Bérubé, for his guidance and

support during this project, and especially for being such a great mentor throughout my PhD

program. I would also like to thank my supervisory committee, Dr. Eric Hall, Dr. Greg

Lawrence, and Dr. Pierre Le-Clech, for their feedback and guidance throughout this project.

I have also been very lucky to have the support of great colleagues and friends through

these years, including Colleen Chan, Kelley Hishon, Lisa Walls, Isabelle Londonio, Mona,

Negar and Arezoo. I also want to thank Kaveh, for patiently encouraging me when I was

writing my thesis and for his endless support.

Last but not least, I would like to express my gratitude to my parents, Firouzeh and

Hesam, for supporting me and my decisions throughout these years, and my sisters, Sanaz

and Golnaz, for their love and moral support. And a final note to my dad who passed away

last week and was looking forward to seeing my graduation: you will always be in my mind

and heart.

This project was partially supported by the Canadian Natural Sciences and Engineering

Research Council (NSERC).

xvii

Dedication

To my parents, Firouzeh and Hesam

1

1 Introduction

Submerged membrane systems provide effective treatment meeting stringent

guidelines for the quality of drinking water or/and the discharge to surface waters. Compared

to the conventional treatment systems, membrane systems offer advantages such as higher

treated water quality, smaller footprint, higher volumetric loadings and lower sludge

production rates. However their relatively higher operating costs compared to the

conventional treatment systems can limit their use. Currently, the cost associated with

membrane fouling control accounts for more than 30% of the operation costs in membrane

bioreactor systems [1] .

Fouling of membranes, defined as accumulation of particles and organic matter at the

surface or in the pores of membranes, significantly affects membrane performance by

increasing the resistance to the permeate flow. Membrane fouling can be divided into three

types: hydraulically reversible, chemically reversible and irreversible fouling. Hydraulically

reversible fouling can be removed physically (e.g. by introducing turbulence at the proximity

of a membrane surface) or through backwashing of membranes. On the other hand,

chemically reversible fouling can only be removed by chemical cleaning methods, while

irreversible fouling is permanent. Unless otherwise indicated, in the present dissertation,

fouling refers to hydraulically reversible fouling.

Four mechanisms are typically used to describe the progression of membrane fouling:

complete blocking, standard fouling, intermediate blocking, and cake filtration. Depending

on the membrane pore size distribution and morphology, and foulant size distribution, one or

more of the above mechanisms may be dominating the fouling [2]. The hydrodynamic

conditions at the proximity of membrane also affect the rate of fouling of membranes.

However, the hydrodynamic conditions do not affect all of the components of a fouling

matrix similarly [3]. The transport of different foulants at a membrane surface is the result of

the balance of forces exerted on foulants such as buoyancy forces (Fb = 1.33π ρgap3) ,

gravifty forces (Fg = 1.33πρpgap3), drag forces incurred by the cross flow velocity Fdrag,CF =

(6.325𝜋𝜇𝑎𝑝𝑣𝑦 ), drag forces exerted due to the permeation flow through the membrane

2

(Fdrag,permeation = 3𝜋𝜇𝑎𝑝𝐽) and the lift forces exerted by the gradient of the velocity at the

membrane surface, i.e. shear stress (Flift, shear = 0.761 τ1.5ap3𝜌𝑝0.5

µ ), where ap is the particle

diameter, and τ is shear stress at the wall, i.e. membrane surface, ρp is particle density , g is

the acceleration due to gravity, μ is the dynamic viscosity, vy is the cross flow velocity, and J

is the permeate flux [4].

If the membrane surface is installed vertically in a module and a cross flow is applied

along the membrane surface, the buoyancy force, the gravity force, and the drag force are

exerted on the foulants parallel to the membrane surface. The balance of these forces results

in transport of foulants at the membrane surface. If the difference between the density of the

foulants and the density of the solution is very small (such as in MBR systems), the force

resulting from the balance between the buoyancy force and the gravity force is negligible.

The drag force exerted by the liquid cross flow results in the transport of foulants parallel to

the cross flow along the membrane surface. Perpendicular to the membrane surface, the drag

forces exerted by the permeation flow through the membrane result in accumulation of the

foulants at the membrane surface, and the lift force exerted by the velocity gradient, i.e. shear

stress, at the membrane surface results in the back transport of the foulants into the bulk

solution. The resulting balance between the permeation drag and the back transport of the

foulants into the bulk solution perpendicular to the membrane surface is presented in

Equation 1.1, when the first term corresponds to the permeation drag and the second term

corresponds to the lift forces [4].

F = 3𝜋𝜇𝑎𝑝𝐽 - 0.761 τ1.5ap3𝜌𝑝0.5

µ (1.1)

Based on the equation 1.1, a “critical permeation flux” in membrane filtration systems is

defined as the permeation flux for which the rate of accumulation of foulants at the

membrane surface is equal to the rate of back transport of the foulants into the bulk solution

[4]. If the operating permeation flux is higher than the critical flux, the rate of accumulation

of foulants at the membrane surface due to the permeation flow is larger than the rate of back

transport of the particles due to the shear lift forces and therefore membrane fouling occurs.

3

Equation 1.1 suggests that depending on the hydrodynamic conditions in the system, e.g.

permeate flux and the shear stress at the membrane surface, particles of different sizes will

tend to accumulate at membrane surfaces [5, 6]. For instance, smaller foulants may

preferentially accumulate at the membrane surfaces at low permeate flux and high cross-flow

velocities, i.e. high surface shear stress. Although the critical flux concept suggested by

Equation 1.1 has been observed experimentally [7, 8], a simple force balance approach

cannot be used to comprehensively describe the rate and direction of transport of particulate

foulants. Knutsen and Davis [8] observed that particles at a membrane surface do not travel

easily along the membrane surface at a higher permeate flux and therefore are not readily

removed as suggested by Equation 1.1. This discrepancy was attributed to the interactions

that can exist between particles and rough membrane surfaces at a higher flux. Knutsen and

Davis [8] also reported that although the permeate drag remains constant, particles decelerate

as they travel through the shear layer at a membrane surface.

The back transport of small particles has also been reported to be enhanced by the

presence of larger particles [7]. This was attributed to additional surface shear and boundary

layer disturbances caused by larger particles. It should be noted that the hydrodynamic

conditions also affect the structure of the cake layer formed by the accumulation of

particulate material. Tarabara et al. [3] reported that cakes formed at lower Peclet numbers

(Pe) or at higher collision efficiency are expected to have lower hydrodynamic resistance and

a more open morphology. Also, over time, restructuring of the fouling layer can modify both

its resistance and morphology. Restructuring can occur when a porous cake, formed at the

beginning of a filtration cycle, reaches a critical thickness, at which time the cake may

collapse. If this process repeats several times the result will be a more compact cake at the

base and more porous structure at the surface of the foulant layer [3].

Unlike colloidal fouling, biofouling is typically not homogeneously distributed on a

membrane surface, but tends to occur at discrete locations which can change over time [9]. A

number of studies suggest that the solution chemistry and surface interactions, along with

hydrodynamic conditions at the membrane surface, also control the rate of biofouling, i.e.

accumulation of biological foulants [10-13]. These surface interactions can promote

biofouling even in the absence of permeation flux through the membrane [13]. Soluble

4

organic foulants such as biopolymers can also accumulate at a membrane surface, increasing

the hydraulic resistance to permeate flow and the membrane fouling rate. Le-Clech et al. [9]

observed a concentration polarization layer of soluble alginate at the surface of the bentonite

cake layer formed on a membrane surface when filtering a solution of bentonite and alginate;

alginate was used as a model organic foulant to investigate the effect of biopolymers on

fouling rate. The layer could be observed as bentonite traveled through the accumulated

alginate towards the membrane surface. The bentonite velocity in this layer was inversely

related to the concentration of the accumulated alginate. Le-Clech et al. [9] also observed

that the alginate increased the specific resistance and decreased the compressibility of the

bentonite cake layer that formed on the membrane surface

The rate of fouling can be minimized by promoting the back transport of foulants away

from a membrane surface. A number of mechanisms have been suggested as contributing to

the back transport of foulants. Belfort et al. [6] suggested that, depending on the

hydrodynamic conditions and the size of the material in the solution being filtered, different

back transport mechanisms were likely to dominate fouling control. Molecular diffusion

dominates at low shear rates and when filtering molecular size material. Inertial lift (due to

the velocity gradient imposed on a foulant) dominates at high shear rates when filtering large

particles and shear-induced diffusion dominates at intermediate shear rates and when

filtering intermediate size material. The surface transport of particles, i.e. rolling or sliding of

the foulants along the membrane surface due to bulk tangential flow, can also contribute to

the transport of particles away from a membrane surface, affecting the rate of fouling. It

should be noted that for smaller particles other factors such as membrane surface charge,

Van der Waals forces, and physical-chemical properties of the membrane can also affect the

back transport of particles [13].

Although the lateral flow, i.e. permeation flow perpendicular to the membrane surface,

is generally small compared to the tangential flow parallel to the membrane surface in

membrane systems operated with cross flow, permeation through a membrane does affect the

near-surface mean velocities and the instantaneous velocity and shear force profiles at the

proximity of the membrane surface. The effect of surface suction, i.e. permeate flux, on the

hydrodynamics of the flow was studied numerically by Sofialidis and Prinos [14]. They

5

observed that the turbulence at the wall decreased with increasing permeate flux. Beavers

and Joseph [15] theoretically demonstrated the existence of a non-zero tangential velocity on

the surface of a permeable boundary. Therefore, although the permeation may not affect the

mean flow velocities and bulk Reynolds number, it has been suggested by Gaucher et al. [16]

that it may affect the velocity profile at the membrane surface, changing the surface

tangential velocity and consequently the shear force profiles at the membrane surface.

Gaucher et al. also suggested that high permeate flux increases the rate of fouling by

decreasing the turbulence and the variability of the shear forces at a membrane surface [16,

17]. However, in these studies, electrochemical shear probes were installed on the surface of

ceramic membranes to measure the shear stress [16, 17]. As a consequence of the geometry

and the installation technique of these probes (as described in Section 2.3.2 and Appendix

B), no permeation actually occurred at the surface of the electrochemical shear probes.

Therefore, the effect of different permeation fluxes on the shear stress induced on to the

shear probes cannot be properly investigated using this technique.

Different methods have been developed to minimize fouling in submerged membrane

systems. Gas sparging is one of the most common methods applied to control fouling in

submerged hollow fiber membrane systems [18, 19] and can reduce the rate of fouling by 30

to 100%, depending on the applications, operating conditions, membrane configuration and

characteristics of the foulants [20-26]. Sparging induces hydrodynamic conditions near the

membrane surface which promote the back transport of foulants. Gas sparging may also

physically remove the fouling layer if the bubbles contact and scour the fouling layer [27,

28]. However, the relationship between sparging conditions, bubble size and frequency, and

efficiency of fouling control is not well understood [27, 28]. As a result, sparging approaches

are designed using a capital and time intensive trial-and-error approach that does not

guarantee that optimal conditions are identified. To address this knowledge gap, a

comprehensive understanding of the relationship between bubble size and frequency and

induced hydrodynamic conditions at a membrane surface and the effect of these conditions

on the efficiency of fouling control is essential. The following sections reviews the work that

has been done prior to this research to investigate the relationship between bubble size and

6

frequency and the hydrodynamic conditions induced in the system, and their effects on the

efficiency of fouling control.

1.1 Relationship between sparging approaches and hydrodynamic conditions induced on submerged hollow fiber membrane systems

Although the mechanisms of fouling control through air sparging are not fully

understood, a number of models have been suggested to describe the effect of air sparging on

fouling control. In general, the models are based on the force balance between the back

transport of foulants away from the membranes (e.g. through shear-induced diffusion, inertial

lift, scouring and etc.) and the transport of foulants towards the membrane by the drag

introduced by permeate flux [5], similar to the models described in Equation 1.1.

The bulk liquid velocity induced by air sparged bubbles has been reported to contribute

to fouling control in air sparged submerged membrane systems [19]. However, Bérubé and

Lei [23] observed that the fouling rate for a given bulk cross flow velocity in a submerged

hollow fiber module was substantially lower for two-phase flow, i.e. with air sparging, than

for single-phase flow, i.e. without air sparging, for conditions where the bulk liquid

velocities were similar. In addition, for a given bulk cross flow velocity, the magnitudes of

both the average and maximum shear stress induced onto membranes were observed to be

substantially greater for two-phase flow than for single-phase flow [29]. Similar observations

were made by others when using flat sheet [30] and tubular membranes [31]. These

observations suggest that bulk liquid movement on its own does not significantly contribute

to fouling control.

Pressure instabilities caused by sparged bubbles at the proximity of membranes have

also been suggested as another mechanism of fouling control through air sparging [24, 32].

However, the potential beneficial impact of pressure instabilities in either confined or

unconfined membrane systems has not yet been experimentally quantified.

Secondary oscillating flows induced in the wake of sparged bubbles have been

suggested as contributing to fouling control. These secondary flows result in a highly

variable shear stress of relatively high magnitude at the membrane surface, which prevents

7

the accumulation of retained material on membrane surfaces [6, 20, 21, 33, 34], and/or

reduces the thickness of the mass transfer-limiting layer [30, 35]. In submerged membrane

systems, a lower fouling rate was observed at a higher variable liquid velocity at the

proximity of a membrane surface compared to a constant liquid velocity [36]. A lower

fouling rate was also observed at higher variable shear stress than in constant shear stress

[37, 38]. These observations suggest that oscillating flows induced by rising air sparged

bubbles significantly contribute to fouling control in membrane systems [39]. However, to

date, the secondary oscillating flows induced in the wake of sparged bubbles in hollow fiber

membrane systems have not been fully characterized. In addition, no information is available

regarding the relationship between the sparging conditions, i.e. bubble size and frequency,

and the characteristics of these secondary oscillating flows. Furthermore, the relationship

between the characteristics of these oscillations and fouling control efficacy is not known.

The shear stress induced at a membrane surface by gas sparging and the resulting

secondary flows has been recognized as one of the most significant parameters governing

fouling control [6, 19, 39-43]. Historically, it was assumed that because the packing density

of fibers in a submerged hollow fiber membrane system is relatively high, the magnitude,

variability and distribution of shear stress induced onto membrane surfaces in these types of

systems were similar to those induced by an air slug in a confined system [19, 44, 45].

However, recent studies demonstrated that shear stress induced by sparged bubbles in

unconfined systems, such as submerged hollow fiber membranes, is different from that

observed in confined systems [29, 46, 47]. In confined systems most of the shear stress

induced by slug flow is due to the flow reversal within the falling film between the slug and

the membrane surface [48]. Although shear stress induced by flow reversal has been

observed in unconfined systems, it is not common [38, 49]. Typical shear stress profiles in

confined and unconfined systems are presented in Figure 1-1 and Figure 1-2, respectively. In

unconfined systems, oscillatory flows in the wake of rising bubbles generated by gas

sparging are largely responsible for highly variable shear stress induced onto the membranes

(Figure 1-2) and therefore shear stress events (peaks) occur more frequently compared to the

shear events occurring in the confined systems (Figure 1-1) [50]. Also, in submerged hollow

fiber systems, the sway of fibers can also contribute to the variable shear stress [19, 51]. In

8

addition to the lateral movement of the fibers, physical contact of loosely held fibers could

also potentially scour the membrane surface and remove accumulated foulant [52]. Higher

frequencies of shear events [29], and higher magnitudes of shear stress induced on to a

membrane surface due to fiber contact were reported for loosely held fibers in comparison to

those of tightly held fibers [53]. As such, fouling control is likely to be greatly enhanced in

loosely-held systems where physical contact between fibers is promoted.

Figure 1-1 Typical shear stress profile in a confined (tubular) membrane system

(Adopted from [54])

Figure 1-2 Typical shear stress profile in unconfined (hollow fiber) membrane systems (Coarse bubble sparging in full scale membrane systems, adopted from [46])

9

The magnitude, variability and distribution of shear stress induced onto membranes in

submerged hollow fiber membrane systems is affected by the sparging conditions and the

membrane module configuration [46]. Increasing sparging flow rates generally increases the

bubble frequency and as a result, affects the number of shear events, i.e. peaks in time

variable shear stress, and the variability of shear stress induced on to membrane surface [20,

33, 46, 55]. The size and geometry of sparged bubbles also affect the magnitude, variability

and distribution of the shear stress induced onto membrane surface [35, 38].The magnitude

of shear stress induced by larger bubbles tends to be greater than those induced by smaller

bubbles. However, at a given sparging flow rate, sparging with larger bubbles decreases the

number of shear events compared to sparging with smaller bubbles [30, 35]. The optimal

conditions are likely a balance of the shear stress events of greater magnitude, achievable

using large bubbles, and more frequent shear stress of lower magnitude, achieved using small

bubbles.

The magnitude, variability and distribution of shear stress induced onto membrane

surfaces have also been suggested to be affected by the configuration of the membrane

module. The shear stress experienced by membrane fibers is dependent on the location of the

fibers in relation to the location of the sparged bubbles, and the fiber packing density in the

module. Fibers that are located closer to the sparged bubbles, such as those in the outer

sections of a module are exposed to higher bulk velocities [56] and highly variable shear

stress magnitude [46, 49]. Chan [49] reported that the amplitude of the shear stress was not

homogeneously distributed around a hollow fiber, where the amplitude of shear stress on the

fibers facing the bubbles was approximately three times greater than that on the other sides

of the fibers. The fiber packing density also affects the size and the rise velocity of bubbles in

a module and the resulting shear stress induced onto membranes. Chang and Fane [57]

observed smaller bubbles and lower bubble velocities in a high packing density module

compared to those of a low packing density module. Yeo et al. [36] reported that the axial

velocities inside a hollow fiber module were up to ten times lower than those outside of the

module where sparged air bubbles were introduced.

10

Although the characteristics of the secondary flows trailing sparged bubbles, and the

resulting shear stresses induced onto membrane surfaces have been recognized as two of the

most, if not the most, significant parameters governing fouling control in air sparged

membrane systems, the effect of the sparging conditions, i.e. bubble size and frequency, on

the characteristics of the secondary flows, as well as on the magnitude, variation and

distribution of shear stress induced onto membranes, have not yet been comprehensively

investigated. The first research question (presented below) considered as part of the present

dissertation was selected to address this knowledge gap.

Question 1: How do the sparging approaches affect the hydrodynamic conditions and

the resulting shear stress in a membrane system?

To answer to this research question, the secondary flows induced under different

sparging conditions, i.e. bubble size and frequency, were characterized based on the

distribution of liquid velocity and the vorticity in the system The shear stresses induced onto

the membrane surface by the sparging were also characterized for different sparging

conditions.

1.2 Effect of hydrodynamic conditions on fouling rate in submerged hollow fiber membranes

The rate of fouling control in air-sparged submerged membrane systems is dependent

on the hydrodynamic conditions and the resulting shear stress induced onto membranes

under different sparging conditions, i.e. bubble size and frequency, and the module

configurations (as discussed in Section 1.1). However, the effects of hydrodynamic

conditions and resulting shear stress on fouling rate remain poorly understood.

A number of studies have suggested that the variations in the shear stress over time

have a significant effect on fouling rate [11, 18, 36, 49]. In general, a lower fouling rate can

be achieved by inducing highly variable shear stress on membranes rather than inducing

constant shear conditions [39, 52, 57-61]. However, Chan [49] reported that above a given

frequency of shear events, fouling control could be inhibited.

11

A number of summative parameters have been considered to relate time-variable shear

stresses to fouling control, such as average shear stress, root mean square (RMS) of shear

stress, and the standard deviation of shear stress [36, 49, 58]. Of these, the RMS of the shear

stress has been reported to be most strongly correlated to the rate of fouling in submerged

hollow fiber membrane systems [49, 62]. However none of the summative parameters

considered to date can, on their own, be used to consistently relate the effect of time-variable

shear stresses to fouling control [49, 62].

The rate of fouling also generally decreases with increasing the air sparging flow rate

in unconfined systems [20, 33, 55]. However, a critical air sparging flow rate is observed

above which a further increased in the flow does not further decrease the rate of fouling [23,

26, 55, 63]. At this critical condition, the shear stress controlling particle back-transport is

likely high enough to prevent any particle deposition on membrane surfaces [23, 27, 28].

Therefore, further increases in the sparging flow rate (and therefore increase in shear stress

induced onto membranes) have no additional effect on the prevention of particle deposition

and hydraulically reversible fouling [30].

Although the hydrodynamic conditions generated by air sparging and the resulting

shear stresses induced onto membrane surfaces have been recognized as one of the most

significant parameters governing fouling control, the relationship between the hydrodynamic

conditions and fouling rate is poorly understood. In addition, the optimum sparging

conditions, in terms of power requirements, to reach a certain level of fouling control has not

been identified. The second research question (presented below) considered as part of the

present dissertation was selected to address this knowledge gap.

Question 2: How do the induced hydrodynamic conditions affect the rate of fouling?

To answer this question, the relationship between both the characteristics of the

secondary flows and the shear stress induced onto membranes and the rate of fouling was

studied.

12

1.3 Approaches to investigate the effect of sparging scenarios on the hydrodynamic conditions, induced shear stress, and fouling control

A number of different approaches have been applied by others to study the effect of

sparging on the hydrodynamic conditions, induced shear stress, and fouling control in

membrane systems. A summary of these approaches, along with their limitations, are

discussed below.

a. Direct observation methods

Different optical tools such as Direct Observation Through Membrane (DOTM) and

Direct Visual Observation (DVO) have been used for investigating the effect of

hydrodynamic conditions in the system on the structure of the fouling layer [9]. Direct

Observation through Membrane (DOTM) was recently developed as a non-destructive online

method providing information about the behaviour of foulants at the membrane surface [9].

However, it is only possible to observe the first fouling layer formed on a membrane surface

with DOTM. The subsequent fouling layers, and consequently the cake structure, cannot be

observed. On the other hand, the Direct Observation Technique (DOT) enables online

observation of the behaviour of foulants at the proximity of membrane surface [45, 64].

However, due to the limitations of the setup used by others to date [45, 64], such as line of

sight limitations, as well as limitations on scale, fouling could not be investigated for the

hydrodynamic conditions that are relevant to full scale/commercial membrane applications.

b. Electrodiffusion method (EDM)

Electrochemical probes, hereafter referred to as shear probes, can be used to measure the

shear stress on a submerged hollow fiber membrane [23]. It is also possible to detect flow

reversal using a double shear probe [38]. Shear probes have been widely used to measure

surface shear forces in steady state and transient flows. However, the response time of the

shear probe must be known in a transient flow before being used for shear measurements.

The response time of the probe is important because the limiting current of the shear probe is

calculated assuming a quasi-steadystate condition in the mass transfer boundary layer where

Pe is high enough to neglect the longitudinal and transverse diffusion. Therefore, the shear

probe could be used for shear force measurements in transient flow if the assumption of the

13

electrochemical reaction being faster than the fluctuation in shear force is valid. The response

time of shear probes can be determined by different models [65-68]. Consequently, it is

essential to develop an approach for correction and interpretation of data collected under

transient flow conditions. This limitation is addressed in the present research (Section 2.3.2

and Appendix B).

c. Image Velocimetry Tools

Particle Image Velocimetry (PIV) is a non-intrusive tool for quantifying shear stress.

In addition, PIV can be applied to quantify the distribution of velocity and vorticity induced

in the system by sparged bubbles. PIV could also be used to investigate particle trajectories

close to a membrane surface. A number of studies have investigated the mechanism of

fouling using PIV. The effects of bubble frequency and size on the fouling rate of hollow

fiber membrane systems under different hydrodynamic conditions were recently studied

using PIV for a biological model solution with two-phase flow [69]. Yang et al. [70] used

PIV to study fouling of hollow fiber membrane systems using Rhodamine B (fluorescent)

particle tracers. In their study, transparent fibers were used since real hollow fiber

membranes would have blocked the light sheet used for PIV. Gimmelshtein et al. [71]

studied the flow in membranes using PIV when filtering a solution containing fresh seeding

of yeast particles of approximately 5 μm diameter. However, the study did not consider the

effect of permeate flux on shear forces and flow distribution at the proximity of the

membrane. Yeo et al. [58] used PIV to investigate the effect of different air sparging

conditions, i.e. different bubble sizes, between 5 mm and 20 mm, and frequencies) on the

hydrodynamics of flow, i.e. bulk turbulence, in proximity to a hollow fiber. They reported

that PIV can overestimate the velocity at the surface of hollow fiber membranes by as much

as 30%. In addition, air sparging causes the fibers to sway. Swaying fibers change the

geometry of the system, making PIV analyses difficult [58]. However, one of the limitations

of this method is that it can only be applied where a sheet of light can be created at the

membrane surface and no obstacles are in the line of sight of the high speed camera.

Therefore, this method cannot be used to quantify the velocity and the shear stress at the

surface of hollow fiber membranes installed inside a packed hollow fiber module.

14

1.4 Research tasks

As discussed in the previous sections, the hydrodynamic conditions and the resulting

surface shear stress induced onto submerged hollow fiber membranes are significantly

affected by the sparging approach. However, the link between these conditions and fouling

rate remain unclear. To address this knowledge gap, the proposed research focused on

addressing two major questions outlined in sections 1.1 and 1.2 by performing the following

overall tasks.

Task 1. Characterize the hydrodynamic conditions in a membrane system under

different sparging conditions, i.e. bubble size and frequency.

The following intermediate tasks were performed to enable research question 1 to be

addressed:

Task 1.1. Design a system that mimics the secondary flows that are representative of

the conditions in real size submerged membrane systems (Chapter 2).

Task 1.2. Develop a method to characterize the secondary flows, i.e. velocity and

vorticity, and the induced shear stress onto membranes in the system (Chapter 2 and

Chapter 3).

Task 2. Find the correlation between induced hydrodynamic conditions and fouling

control efficiency in the system.

The following intermediate tasks were performed to enable research question 2 to be

addressed:

Task 2.1. Investigate the relationship between hydrodynamic conditions, i.e. velocity

and vorticity, and shear stress induced onto membranes in the system and the rate of

fouling (Chapter 4).

Task 2.2. Develop parameters that can accurately correlate the effects of bubble size

and frequency on the induced secondary flows in the system to the rate of fouling

(Chapters 4 and 5).

Task 2.3. Develop an approach to identify optimal sparging conditions, i.e. bubble

size and frequency, that induce optimal fouling control conditions (Chapter 6).

15

2 Experimental setup and measurement approaches

Chapter 2 presents the design of the experimental setup and the measurement

approaches developed for investigating the hydrodynamic conditions induced under different

sparging conditions and their effect on fouling rate.

2.1 Experimental setup and experimental conditions investigated

The system tank and the spargers designed in this research enabled the hydrodynamic

conditions that are representative of full size submerged membrane systems to be mimicked

(See section 2.3.2). All experiments were performed in a 2 m high, 1 m wide and 15 cm thick

rectangular Plexiglas tank (Figure 2-1 and Figure 2-2). A module containing seven fibers,

each 174 cm long, was placed vertically at the center of the tank. The fibers used when

filtering and when measuring shear stress are described in section 2.2 and 2.3.2, respectively.

The space between the fibers in the module was 7 cm. The spacing between the top and the

bottom module bulkheads was 172 cm, allowing the fibers to sway in the system. The

dimensions of the system tank and the module allowed commercially available, i.e. ZW500,

GE Water and Process Technologies) full length hollow fiber membranes to be used.

16

a

Figure 2-1 Picture of the system tank with membrane module

17

a b

Figure 2-2 Experimental system

(a: schematic of front view of system, probe locations identified with numbers [1 to 4];

b: schematic of side view of system)

Air spargers were fixed at the bottom of the center of the tank (Figure 2-1 and Figure

2-2). Two types of spargers were used: a coarse bubble sparger that generated small bubbles

of 0.73 mL to 2.5 mL in volume and a pulse bubble sparger that generated 150, 300 and 500

mL bubbles. The coarse sparger was a perforated pipe with three holes of 0.5 cm diameter,

one at the centerline of the tank, and the other two on either side, each spaced 5 cm apart.

The coarse bubble sparger generated small bubbles characteristic of those generally used in

MBR systems [1]. The pulse bubble sparger is a proprietary design provided by GE Water

and Process Technologies and therefore the details about the pulse bubble sparger design

cannot be disclosed in the present thesis.

The pulse bubble sparger was selected because sparging with relatively large pulse

bubbles, i.e. 150 mL, has been reported to result in less fouling compared to sparging with

coarse bubbles [62]. Pulse bubble spargers are commercially used by some membrane

manufacturers (e.g. Siemens, Samsung, and GE Water and Process Technologies) with

claims of better performance, in terms of fouling control, than coarse sparging. However, no

18

investigations have been done to characterize the hydrodynamic conditions induced by pulse

bubble spargers. Since both bubble size and frequency have been reported to affect fouling,

three sparging flow rates were selected to generate three different sparging frequencies: 1)

discrete pulse bubbles, 2) pulse bubbles at a frequency of 0.25 Hz, and 3) pulse bubbles at a

frequency of 0.5 Hz. The discrete sparging frequency was selected to generate single pulse

bubbles. The sparging frequency of 0.25 Hz was selected to generate a series of pulse

bubbles, with a distance between successive bubbles that was sufficiently large so that two

successive bubbles did not interact (See section 4.2 for more details). The sparging frequency

of 0.5 Hz was selected to generate a series of pulse bubbles where the distance between two

successive bubbles was short enough so that the two successive bubbles could interact, i.e.

the distance between the bubbles was shorter than the length of the wake of descrete bubbles.

For the coarse bubble sparger a sparging frequency could not be defined. Therefore, three

sparging flow rates of low, medium, and high were selected. The low sparging flow rate for

coarse bubble sparging was selected to be equivalent to that for discrete sparging of pulse

bubbles (996 mL/min). The medium flow rate for coarse sparging was selected to be

equivalent to that for the small pulse bubbles, i.e. 150 mL, at a 0.25Hz sparging frequency.

The high sparging flow rate for coarse bubble sparging was selected to be equivalent to the

sparging flow rate for the medium pulse bubble, i.e. 300 mL, at a 0.5Hz sparging frequency.

The sparging conditions investigated in the present research are summarized in Table 2.1.

19

Table 2-1 Sparging conditions investigated

Sparger type Coarse Small pulse Medium pulse Large pulse

Nominal Sparging frequency Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz

Bubble volume [mL] 0.73 0.75 2.5 150 150 150 300 300 300 500 500 500

Sparging flow rate [mL/min] 996 2600 9200 996 2600 4300 996 4700 9200 996 8100 13500

The sparging flow rate for discrete pulse bubble sparging resulted in bubble frequency of less than 0.06 Hz such that successive

bubbles do not interact; for course bubble sparging, nominal frequency of Discrete, 0.25 Hz and 0.5 Hz corresponded to 996, 2600,

and 9200 mL/min flow rates respectively.

20

2.2 Filtration setup

When filtering, the module contained hollow fiber membranes (ZW500, GE Water and

Process Technologies). The fibers had a 1.8 mm outer diameter with a normal pore size of

0.04 mm. Each hollow fiber in the module was connected to a separate permeate line, each

with an individual peristaltic pump, and a pressure transducer to measure the trans-

membrane pressure. The permeate flux collected from each fiber was monitored over time

enabling the fouling rate in each hollow fiber to be assessed independently. The fouling rate

was quantified based on the rate of change of normalized trans-membrane pressure, Pn,

(defined as the ratio of the trans-membrane pressure at a given time to the initial trans-

membrane pressure) with respect to the volume filtered. The total fouling rate in the system

was estimated as an average of the fouling rate of four fibers combined. Filtration was

performed at a constant permeate flux of 100 L/m2.h when filtering a solution containing 750

mg/L of bentonite with the average particle size of 3 µm in water (size distributions of the

particles in the bentonite solution were analyzed using a laser particle size analyzer,

Mastersizer Hydro 2000S, Malvern, with an average of 3 µm and the smallest particle of 0.3

µm) which corresponds to an overall solid mass flux of 75 g/m2.hr, which is typical for MBR

systems. All filtration experiments were performed in duplicate. Each filtration experiment

was terminated when the trans-membrane pressure (TMP) reached 60 KPa. Data obtained

from filtration experiments are presented in Appendix E.

2.3 Measurement approaches

Imaging of sparged bubbles 2.3.1

Imaging of bubbles was performed using a high-speed high-resolution camera

(Phantom Miro 4, with 800 x 640 pixel resolution) and VidPIV software (Oxford Lasers).

Two high intensity light sources were used to create a vertical thin (approximately 1 cm)

sheet of light (Figure 2-2a). The light sheet was created orthogonal to the focus axis of the

high-speed camera (Figure 2-2b). A video of 2 minutes duration was captured at each set of

sparging conditions. Recordings were repeated in duplicate for each sparging condition.

21

Measurement of shear stress induced onto membranes 2.3.2

When measuring shear stress, the module contained test fibers made of flexible Teflon

tubes with a diameter similar to that of hollow fiber membranes used in the present study

[29]. The shear probes were fixed half way along the length of the test fibers in the module.

The shear stresses induced by sparged bubbles at the surface of the test fibers were measured

using an electrodiffusion method (EDM) [29, 72]. The reagent used for the electrochemical

measurements contained 0.003 M ferricyanide, 0.006 M ferrocyanide, and 0.3 M potassium

chloride in deoxygenated, de-chlorinated tap water [46, 48]. A limiting diffusion current of

500 mV was selected as described by [72]. Measurements were collected at a frequency of

200 Hz and a water temperature of 170C. Experimental temperaute affects the physical

characteristics of the water, e.g. diffusion coefficient, see Appendix B for correction of data

for different temperatures. A stainless steel anode was used in all experiments.

The magnitude of the shear stress was obtained from the current measured at the

probes using the quasi-steady state Leveque relationship presented in Equation 2.1 [73]:

31

31

32

862.0 γ−= dDcFAnI b (2.1)

where D = diffusion coefficient (m2/s), d = diameter of the probe (m), γ = shear stress

(Pa), F = Faraday constant (A s/V), A = electrode area (m2), n = number of exchanged

electrons during the reaction [-], Cb = concentration of the oxidizing ion in the bulk (mole/

m3), and I = current (A).

Figure 2-3 illustrates the electrical circuit used for shear measurements. Figure 2-4

illustrates the shear probes used in this study [29].

22

Figure 2-3 Electrical circuit used for measurement of shear stress with EDM

(Adapted from [46])

23

Figure 2-4 A shear probe fixed on a test fiber shown on top of a ZW-500 hollow fiber

membrane (Adopted from [46])

Calibration of the probes was done exsitu prior to all experiments as presented in [45]

(See Appendix A for detailed calculations). Due to the turbulent nature of the hydrodynamic

conditions in air-sparged membrane systems, the flow conditions at the proximity of the

probes are highly transient. Measurement of shear stress using EDM under highly transient

conditions, such as the hydrodynamic conditions induced in the present system, requires V-

step insitu calibration and correction of the signal [72, 73]. Therefore, the magnitude of the

shear stress calculated by the steady state solution (Equation 2.1) was corrected to account

for the non-steady state, i.e. transient, conditions [72, 73]. Extensive literature exists on the EDM technique. Some reviews focusing on different

aspects of the technique have been published by [78-81], but none of these present the

derivations of the underlying theory and the correction necessary for transient flows. To

address this gap, a reference document was developed. The theoretical assumptions and

hypotheses used in developing the equations that are used in the post-processing to calculate

the shear stress under transient conditions were reviewed in detail. The calibration and

correction methods for the data collected under transient conditions were optimized, and

challenges regarding the calibration of this technique and the care that must be taken before

24

using the technique were also investigated as presented in Appendix B. Matlab codes

developed for correction of the data using the V-Step insitu calibration method are presented

in Appendix C.

Figure 2-5 presents a typical shear profile obtained in the present study for coarse

bubble sparging. The order of magnitude and the variation of the shear stress measured for

coarse bubbles observed in the present study (Figure 2-5) were similar to those measured in

full scale membrane modules (as presented in Figure 1-2), confirming that the designed

experimental system generated shear stress conditions similar to those in a full-scale system

(e.g. ZW500 systems). Measurements of shear stress were made in triplicate, with

measurements recorded for 2 minutes.

Figure 2-5 Typical shear stress profile for coarse bubble sparging (Coarse bubble sparging at 9200 mL/min [results from the present research)

Particle Image Velocimetry (PIV) 2.3.3

Particle Image Velocimetry (PIV) was performed to track seeding particles in the flow

and develop maps of the distribution of velocity and the distribution of vorticity. Seeding

particles with mean size of 0.490-0.690 mm, and relatively neutral density, i.e. 1.02 mg/L,

stained with Rodamine B were used. A cross-correlation algorithm with 50% overlap for a

32 x 32 pixel interrogation area, followed by a second cross-correlation with an interrogation

area of 16 x 16 pixels was used for PIV analyses. Local filters were applied to detect and

25

eliminate invalid velocity vectors using a local median filter. The filtered velocity vectors

were replaced using a median interpolation algorithm in a 3 x 3 matrix. The images were

captured at a frequency of 200 frames per seconds (fps), consistent with the rate at which

shear stress measurements were collected. At this frequency, each particle traveled less than

25% of the interrogation area during the time between subsequent images. The concentration

of particles was chosen to ensure that sufficient number of particles were present in each

interrogation zone, i.e. minimum of 4 per interrogation area [74]. A trigger was used to

synchronize the signals obtained by the electrochemical shear probes and the videos captured

by the high-speed camera. Matlab codes were developed to process the data generated by the

PIV software to enable further statistical analyses and to produce time resolved velocity and

vorticity maps (Appendix D). Figure 2-6 shows a typical image analysed by the PIV, the

vectors show the velocity in the system. The resolution of the captured images was not high

enough to calculate shear stress using the PIV.

Figure 2-6 Typical 2 dimensional velocity map generated from the PIV data

26

3 Bubble characteristics obtained using imaging

3.1 General physical characteristics of sparged bubbles investigated

Typical images of the bubbles generated for the sparging conditions investigated are

presented in Figure 3-1. The characteristics of bubbles, i.e. geometric shape and behavior,

were determined using the images captured by the high speed camera. Based on the 2-D

images obtained, the coarse bubbles were observed to be predominantly spherical although

some ellipsoidal bubbles were also observed (Figure 3-1) while the pulse bubbles were

observed to be spherical cap (Figure 3-1b).

27

a

b

Figure 3-1 Typical images of bubbles generated by coarse and pulse sparging

(a: coarse sparging [insert is the magnification of coarse bubbles], b: 500 mL pulse

sparging; each square in images is 2cmx2cm)

28

The radius of curvature of pulse bubbles was r = (h2 + (ds/2)2)/2h, where ds and h are

the diameter and height of the spherical cap. The rise velocities (Vb) of the bubbles were

estimated based on the vertical distance traveled over a given time. The bubble Reynolds

number (Reb) was calculated as Reb = deVb/υ where (Vb) is the bubble rise velocity, de is

bubble equivalent diameter (de = (6V/π)1/3), V is the volume of the bubble, and υ is water

dynamic viscosity at 17°C. The bubble corrected Reynolds number (Rec= (deVbc/υ)) was

calculated using the bubble equivalent diameter and the velocity of discrete bubbles

predicted based on literature (Vbc) [75] for a bubble with the corresponding equivalent

diameter. The projected area of the bubbles (Ab) was calculated with respect to the plane

orthogonal to the camera. The Eötvös number (E0) was calculated according to (E0=

gΔρde2/σ), where g is the gravitational acceleration (9.82 m/s2), Δρ is the difference between

water density at 17 °C and air density at the same temperature, and σ is the water-air surface

tension. The Froude number was calculated as 𝑉𝑏

�𝑔𝑑𝑒2 . Eötvös number and Reynolds number

can be used to predict the bubble characteristics, i.e. geometric shape, and behavior, under

different experimental conditions, such as for different solutions, bubble sizes and different

temperatures [75]. Non dimensional numbers such as Eötvös number and Reynolds number

can also be used to compare the data obtained under conditions investigated in the present

study to the data in the literature or with the future research.

The general physical characteristics of the sparged bubbles considered are summarized

in Table 3.1. The rise velocities of the bubbles were generally higher than expected [75-77].

This was likely due to the upward liquid flow induced by the sparging at the center of the

system tank, and the corresponding downward liquid flow at the sides of the system tank

(See Figure 4-2 for details). As a result, the Reynolds numbers of the entrained bubbles were

also higher than expected for their size. As previously indicated, the bubbles generated by

coarse sparging were observed to generally behave as wobbling spherical bubbles although

ellipsoidal bubbles were also observed, while those generated by pulse sparging behaved as

spherical cap bubbles. These observations were expected based on the Re and Eo numbers of

the bubbles (Table 3.1) [75]. For the large pulse bubbles, i.e. 300 and 500 mL, small satellite

bubbles were generally observed at the edges of the rising pulse bubbles, which is consistent

with observations by others [76]. The Froude number for single pulse bubbles, i.e. at discrete

29

sparging frequency, was between 0.9 and 1.1, which agrees well with data reported by others

for single bubbles rising in stationary liquids [77, 78].

30

Table 3-1 General characteristics of studied bubbles

Coarse Small pulse Medium pulse Large pulse

Nominal sparging frequency Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz

Bubble volume 0.73ml 0.75 mL 2.5 mL 150 mL 150 mL 150 mL 300 mL 300 mL 300 mL 500 mL 500 mL 500 mL Sparging flow rate [mL/min] 996 2600 9200 996 2600 4300 996 4660 9200 996 8100 13500

Bubble per minute 1330 3600 10830 5.48 15.38 27.15 2.94 14.08 27.33 2.03 15.83 26.9

Interaction No No yes No No yes No No yes No No yes

ra[m] 0.008

±0.001

0.008

±0.003

0.0125

±0.001

0.050

±0.004

0.041

±0.006

0.042

±0.004

0.058

±0.003

0.051

±0.006

0.053

±0.006

0.092

±0.008

0.074

±0.001

0.071

±0.057

de [m] 0.011 0.015 0.023 0.066 0.066 0.066 0.083 0.083 0.083 0.098 0.098 0.098

Vb [m/s] 0.52

±0.02

0.61

±0.02 0.77

±0.05 0.61

±0.01

0.68

±0.01 0.78

±0.02 0.59

±0.01

0.77

±0.01 0.87

±0.02 0.69

±0.01

0.82

±0.02 1.02

±0.03

Fr [-] 1.8 2.6 2.6 1.07 1.19 1.37 0.92 1.20 1.36 0.99 1.18 1.47

Reb [-] 7700 9090 12100 37200 41700 47700 45300 59500 67200 62900 74800 93000

Rec [-] 3200 N/A N/A 33583 N/A N/A 47447 N/A N/A 60764 N/A N/A Eo [-] 28 34 38 583 583 583 926 926 926 1300 1300 1300

Notes: ± corresponds to the standard error of repeated measurements; ra: radius of curvature; de: equivalent diameter; Vb: bubble

rise velocity; Reb: bubble Reynolds number; Rec: corrected Reynolds number; E0: Eötvös number; for course bubble sparging,

nominal frequency of Discrete, 0.25 Hz and 0.5 Hz correspond to 996, 2600, and 9200 mL/min sparging flow rates, respectively

31

The bubble rise velocities for the bubble sizes and frequencies investigated in the

present study are summarized in Figure 3-2. As expected, the bubble rise velocity increased

with size and frequency of sparged bubbles [75]. In a bubble swarm, i.e. at gas sparging

frequencies of 0.25 and 0.5 Hz, the trailing bubbles may accelerate due to the interaction

with the wake of the preceding bubble [78]. This interaction may also result in the rupture of

the successive bubbles [78].

Figure 3-2 Bubble rise velocity for bubble size and frequencies investigated

(Error bars correspond to the standard error of repeated measurements, for course bubble

sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200

mL/min sparging flow rates, respectively)

32

3.2 General behavior of sparged bubbles investigated

Coarse bubble sparging 3.2.1 Bubbles generated with the coarse sparger at the lowest sparging frequency (corresponding

to discrete) ascended as individual bubbles on a vertical path in the center of the system tank

where the spargers were installed (Figure 3-3a). Bubbles sparged with the coarse sparger at

an intermediate flow (corresponding to a frequency of 0.25 Hz) ascended on a vertical path

in the center of the system tank (Figure 3-3b); however, the successive bubbles interacted

with each other. The same trend was observed for bubbles sparged with the coarse sparger at

high flow (corresponding to a frequency of 0.5 Hz) (Figure 3-3c). At the highest sparging

flow, the number of sparged bubbles was high, and as a result, successive bubbles were

generally observed to coalesce and form larger bubbles (Table 3.1).

33

a

b

c

Figure 3-3 Typical images of bubbles generated by coarse bubble sparging (a: Discrete; b: 0.25 Hz; and c: 0.5 Hz ,

For course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates, respectively)

Small pulse bubble sparging 3.2.2

Small pulse bubbles, i.e. 150 mL, generated with the pulse bubble sparger at the lowest

sparging frequency, i.e. discrete, were wobbling spherical cap bubbles which ascended on a

vertical path with slight wobbling in the center of the system tank (Figure 3-4a).

Satellite bubbles were generally observed at the edges of the rising pulse bubbles,

which was consistent with observations by others [76]. Bubbles sparged at the higher

frequency of 0.25 Hz were also wobbling spherical cap bubbles, but unlike those observed at

the lower frequencies, they ascended following a zigzag path in the system tank (Figure

34

3-4b). The same trend was observed for bubbles sparged at the highest sparging frequency,

i.e. 0.5 Hz, however, breakage of large bubbles into small bubbles was periodically observed

at the sparging frequency of 0.5 Hz. In a bubble swarm, i.e. at a gas sparging frequency of

0.5 Hz, the trailing bubble may accelerate due to the interaction with the wake of the

preceding bubble [78]. This interaction may also result in the rupture of the successive

bubbles [78].

a b

c

Figure 3-4 Typical images of bubbles generated by small (150 mL) pulse sparging (a: Discrete; b: 0.25 Hz; and c: 0.5 Hz )

35

Medium pulse bubble sparging 3.2.3

Medium pulse bubbles, i.e. 300 mL, generated with the pulse bubble sparger at the

lowest sparging frequency, i.e. discrete, ascended following a zigzag path in the system tank

(Figure 3-5a). A zigzag path for the bubbles with this size and Reynolds number was

expected due to the vortex shedding of their wakes [75]. Similar to the small pulse bubbles,

medium pulse bubbles were wobbling spherical cap bubbles and satellite bubbles were

generally observed at the edges of the rising pulse bubbles. However, a larger number of

satellite bubbles followed the medium pulse bubbles, i.e. 300 mL, in comparison to the

number of satellite bubbles observed following small pulse bubbles (150 mL). Similar

behaviours were observed for medium pulse bubbles sparged at higher sparging frequencies

of 0.25 Hz (Figure 3-5b) and 0.5 Hz (Figure 3-5c). However, the breakage of large bubbles

into small bubbles was observed more frequently at the sparging frequency of 0.5 Hz. In a

bubble swarm, i.e. at gas sparging frequency of 0.5 Hz, the trailing bubble may accelerate

due to the interaction with the wake of the preceding bubble [78]. This interaction may also

result in the rupture of the successive bubbles [78].

36

a b

c

Figure 3-5 Typical images of bubbles generated by medium (300 mL) pulse (a: Discrete; b: 0.25 Hz; and c: 0.5 Hz)

Large pulse bubble sparging 3.2.4

Similar trends to those observed for medium pulse bubbles were observed for large

pulse bubbles, i.e. 500 mL. Bubbles generated with the pulse bubble sparger at the lowest

sparging frequency, i.e. discrete, were wobbling spherical cap bubbles which ascended on a

zigzag path in the system tank (Figure 3-6a). Satellite bubbles were generally observed at the

edges of the rising pulse bubbles. As the sparging frequency was increased, the width of the

zigzag path of the bubbles increased and a larger number of satellite bubbles followed the

pulse bubbles (Figure 3-6b and Figure 3-6c). A zigzag path for the bubbles with this size and

Reynolds number was also expected due to the vortex shedding of their wakes [75]. A larger

number of satellite bubbles followed the large pulse bubbles, i.e 500 mL, in comparison to

the number of satellite bubbles following the small and medium pulse bubbles. The breakage

37

of large bubbles into small bubbles was observed more frequently than for sparging at 150

and 300 mL. This could be explained because the largest stable bubble diameter in water is

predicted to be about 0.049 cm. At larger diameter bubbles breakage will be observed [75].

In addition, in a bubble swarm, i.e. at gas sparging frequency of 0.5 Hz, the trailing bubble

may accelerate due to the interaction with the wake of the preceding bubble [78]. This

interaction may also result in the rupture of the successive bubbles [78].

a b

c

Figure 3-6 Typical images of bubbles generated by large (500 mL) pulse sparging (a: Discrete; b: 0.25 Hz; and c: 0.5 Hz)

38

3.3 Conclusion

Characteristics of the sparged bubbles, geometrics shapes and behaviour, were

identified both qualitatively and quantitatively. The small bubbles generated by coarse

bubble sparging were observed to behave predominantly as wobbling spherical bubbles.

Their geometric shapes and behaviour were consistent with the work done in the literature.

Large bubbles generated by pulse sparging behaved as spherical cap bubbles. Limited data

exist about the geometric shapes and behavior of large bubbels with the volumes studied in

the present study. The results indicated that bubbles generated at the discrete sparging

frequency ascended on a vertical path in the center of the system tank. However, as the

sparging frequency was increased, the interactions between successive bubbles caused them

to wobble and move on a zigzag path. A zigzag path for the bubbles in this range of size and

Reynolds number was expected due to the vortex shedding of their wakes. The width of the

zigzag path increased with sparging frequency. This could be explained by the effect of

interaction of the succeeding bubbles with the wake of the preceding bubbles at higher

sparging frequencies.

Bubble break up was observed when sparging with the pulse sparger at the sparging

frequencies of 0.25 Hz and 0.5 Hz. The breakage of large bubbles into small bubbles was

observed more frequently at the sparging frequency of 0.5 Hz. In a bubble swarm, i.e. at gas

sparging frequency of 0.5 Hz, the successive bubble may accelerate due to the interaction

with the wake of the preceding bubble. This interaction may also result in the rupture of

successive bubbles. The breakage of large bubbles into small bubbles was also observed

more frequently as the size of bubbles increased from 150 mL to 500 mL. Breakage of the

bubbles could also be the result of the interaction of bubbles with the fibers installed in the

system. The effect of these characterisitcs is investigated as discussed in Chapters 4 to 7.

39

4 Characterisation of the hydrodynamic conditions induced by sparged

bubbles

As discussed in Chapter 1, secondary oscillating flows induced in the wake of the

sparged bubbles have been suggested to contribute to the fouling control [6, 20, 21, 33, 34].

These secondary flows result in high velocities and vorticities as well as highly variable

shear stress of high magnitude, which prevents the accumulation of retained material on

membrane surfaces. The rate of fouling in air-sparged submerged membranes, i.e.

unconfined systems, has been reported to be related to the local liquid velocity and vorticity

induced by the sparged bubbles near the membrane surface [16, 25, 58, 62, 79, 80]. In

addition, the RMS of the shear stress induced onto membranes by the secondary flows has

been reported to be the parameter that is most correlated to the rate of fouling in submerged

hollow fiber membrane systems [49, 62]. However, the effects of bubble size and sparging

frequency on the characteristics of the secondary flows and the resulting shear stress induced

at the membrane surface have not been yet been comprehensively investigated.

The effects of bubble size and frequency on the distribution of liquid velocity and

vorticity as well as on the distribution of the shear stress induced onto membranes for the

sparged bubbles conditions described in Chapter 3 are presented in the sections which

follow.

4.1 Distribution of vorticity and velocity for discrete sparging

The secondary flows induced by sparged bubbles in the system can be characterized

based on the distribution of the local liquid velocity and vorticity in the system. PIV was

used to quantify the liquid velocity and the vorticity over time in the system tank. Figures

Figure 4-1a and b present typical 2-dimensional vorticity distributions in the system for the

discrete sparging for coarse and pulse sparging, respectively.

Qualitatively, it can be observed that the fraction of the system tank with high vorticity,

for a pulse bubble was much larger than that for the coarse bubbles even though the volume

of gas delivered to the system for both sparging conditions was similar.

40

a

b

c

d

Figure 4-1 Typical vorticity and velocity distributions induced by discrete rising bubbles (a: distribution of vorticity for multiple coarse bubble (in 1/s); b: distribution of vorticity for a single pulse bubble (150 mL

bubble) (in 1/s); distributions based on vorticity measured at a fixed horizontal axis at probe location over time; c: distribution of

velocity at vertical centerline of tank for multiple coarse bubble [insert illustrates vertical distribution for a single coarse bubble]; d:

distribution of velocity at vertical centerline for single pulse bubble)

41

Vertical distribution of velocity for discrete bubble sparging 4.1.1

The vertical distributions of the velocity induced by coarse bubbles were characterized

by a rapid rise in the velocity followed by a rapid decrease in the wake trailing the bubbles

(Figure 4-1c). The vertical distributions of the velocity induced by pulse bubbles were also

characterized by a rapid rise in the velocities; however, this was followed by a gradual

decrease in the wake trailing the bubble (Figure 4-1d). A similar trend was observed by

Bhaga and Weber [81] when investigating the velocity distribution in wakes of small

bubbles. When comparing the velocity (and vorticity) measurements collected, for different

conditions investigated, to the images collected for the same conditions (Chapter 3), the

following observations could be made.

The magnitude of the liquid velocity (and vorticity) increased rapidly to a maximum

velocity (and vorticity) observed at the tail end of the bubble (between 3 and 4 seconds on

Figure 4-1 d). The magnitude of the liquid velocity (and vorticity) gradually decreases from

the tail end of the bubble to the bottom edge of the wake, i.e secondary flows, behind the

bubble where it reached the magnitude of the velocity (and vorticity) of the background bulk

liquid flow. These observations can be explained by the fact that the wake behind a rising

bubble is known to be in the form of power functions, with the maximum magnitude of the

velocity at the tail end of the bubble and a gradual decrease to the bottom edge of the wake

where the magnitude of the velocity in the wake is equal to that of the bulk liquid fluid [82,

83].

As illustrated in Figure 4-1d, the magnitude and the duration of the peaks observed in

the area of the zone of influence were a function of the pulse bubble size; the larger the pulse

bubble, the higher the magnitude of the velocity and the longer the duration of the peak.

This was expected because the magnitude of the maximum velocity, i.e peaks, and the

dimension of the wake generally increase with the bubbles size [82]. As the pulse bubble size

increased, the bubble rise velocity increased and as a result, the maximum velocity in the

wake and the dimension of the wake increased [82].

42

Horizontal distribution of velocity for discrete bubble sparging 4.1.2

The horizontal distributions of the velocity induced by sparging within the system were

bell shaped, with a maximum at the vertical centerline along the bubble rise path and a rapid

decrease to the side edges of the zone of influence (Figure 4-2). These results are similar to

those reported by others when investigating velocity distributions in wakes of small bubbles

[85] and are consistent with empirical models developed to describe the velocity profile in

the wake behind a rising bubble [82, 84]. For the horizontal distribution of velocity, the

magnitude of maximum velocity increased as the size of the bubbles increased (Figure 4-2b).

These results suggest that within the zone of influence, fouling control is likely to be

heterogeneous, with the lowest fouling occurring at the centerline of the system along the

bubble rise path, and the extent of fouling increasing towards the edges of the system. The

relationship between the hydrodynamic conditions, induced by sparging and fouling control

is discussed in Chapter 6.

Negative (downward) velocities were observed at the edges of the system tank. This

likely resulted from the upward liquid flow entrained by the bubbles rising at the centre of

the system and the resulting downward liquid flow at the edges of the system (the video

captures images in the centre and for only 60% of the width of the tank. It is likely that

negative velocities close to the walls of the tank occurred and were not captured by the

images presented for the bubbles of 150mL and 300 mL).

43

a b

Figure 4-2 Typical horizontal distributions of velocity across the width of system tank (a: coarse bubbles and b: pulse bubbles).

44

Zone of influence 4.1.3

Figure 4-3 to Figure 4-6 illustrate typical changes in liquid velocity and the vorticity

over time at the vertical center line of the system tank at the height of the probes (see Figure

2-2a) for different sparging conditions.

Figure 4-3 illustrates the distributions of the liquid velocity and vorticity for coarse

bubble sparging for the discrete sparging frequency. As presented, the trends in the liquid

velocity and the vorticity over time are similar to each other. A similar trend between

vorticity and the velocity profile in the wake behind a single rising bubble is expected

because vorticity is defined as 𝑑𝑣𝑦𝑑𝑥

− 𝑑𝑣𝑥𝑑𝑦

where vy and vx correspond to the velocity in the y

and x directions, respectively. The peaks observed in both liquid velocity and vorticity

profiles correspond to the passage of bubbles at the centerline of the system tank at the height

of the probes.

The distributions of the liquid velocity and vorticity over time for small pulse bubbles

(150 mL) sparged at the discrete sparging frequency is presented in Figure 4-4 . Again,

similar trends are observed for the liquid velocity and vorticity over time. The duration of the

periods over which elevated liquid velocities and the vorticities, i.e. velocities and vorticities

higher than the those for the bulk, were observed for small pulse bubbles (Figure 4-4) were

by an order of magnitude longer than those observed for coarse bubbles (Figure 4-3) and as a

result, the fraction of the system with a higher magnitude of velocity and vorticity induced by

pulse bubble was much larger than that induced by the coarse bubbles.

Similar trends to those observed for the small pulse bubbles were observed for the

larger pulse bubbles with respect to the liquid velocity and vorticity over time (Figure 4-5

and Figure 4-6). The magnitude and the duration of the peaks observed in the liquid velocity

and the vorticity profiles increased with pulse bubble size, as expected. Since the liquid

velocity and the vorticity profiles exhibit the same trend in terms of magnitude and variation,

the liquid velocity was selected in the present study to furher investigate the effect of bubble

characteristics, i.e. bubble size and frequency, on the induced hydrodynamic conditions.

45

a

b

Figure 4-3 Typical distribution of a) velocity and b) vorticity for discrete bubble sparging with the coarse bubble sparger (Measurements were made at the vertical centerline of the system at the height of the probes)

46

a

b

Figure 4-4 Typical distribution of a) velocity and b) vorticity for discrete bubble sparging with the small pulse bubble sparger (Measurements were made at the vertical centerline of the system at the height of the probes)

47

a

b

Figure 4-5 Typical distribution of a) velocity and b) vorticity for discrete bubble sparging with the medium pulse bubble sparger (Measurements were made at the vertical centerline of the system at the height of the probes)

48

a

b

Figure 4-6 Typical distribution of velocity a), and vorticity d) for discrete bubble sparging with the large pulse bubble sparger (Measurements were made at the vertical centerline of the system at the height of the probes)

49

The distributions of velocity and vorticity in the system delineate a zone of secondary

flows over which liquid velocities and vorticities are high. The size of the zone of influence

for different sparging conditions was defined as the area orthogonal to the imaging plane

(Az) where sparged bubbles induce secondary flows with a velocity greater than 0.2 m/s. The

cut-off velocity of 0.2 m/s was selected because it corresponded to that of the background

liquid movement induced by the rising bubble and did not consistently generate vorticities

that were greater than those associated with background bulk liquid movement. Selection of

0.2 m/s as the cut off velocity was also confirmed by statistical analyses of the effect of cut

off velocity on the area of zone of influence and its correlation to rate of fouling (See

Appendix G).

The width, length and area of the zone of influence for different sparging conditions

investigated are summarized in Table 4.1. When bubbles interacted, the length of the zone of

influence, (Lz), was defined as the distance between two successive bubbles (Table 4.1).

50

Table 4-1 General characteristics of studied bubbles and the induced zone of influence Sparger type Coarse Small pulse Medium pulse Large pulse

Nominal

sparging

frequency

Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz Discrete 0.25 Hz 0.5 Hz

Bubble volume 0.75ml 0.73 mL 2.5 mL 150 mL 150 mL 150 mL 300 mL 300 mL 300 mL 500 mL 500 mL 500 mL

Sparging flow

rate [mL/min] 996 2600 9200 996 2600 4300 996 4700 9200 996 8100 13515

Interaction No Yes Yes No No/minimal Minimal No No/minimal Yes No No/minimal Yes

Az [m2] 0.0024

±0.003

5.23

±0.077

17.3

±0.105

0.178

±0.004

12.42

±0.066

15.89

±0.083

0.463

±0.104

14.47

±0.0799

24.94

±0.169

0.825

±0.003

18.95

±0.081

30.61

±0.097

Az,bubble/Ab [-] 22.3 14 8 71 338 179 123 165 246 131 72 145

Az/Sparging

volume[1/m] 2.41 2011 1880 178 4776 3695 464 3078 2710 828 2339 2264

Wz [m] 0.01 0.14 0.37 0.17 0.303 0.34 0.24 0.311 0.47 0.3 0.385 0.5

Lz [m] 0.24 0.015 0.012 1.04 2.66 1.72 1.95 3.3 1.92 2.77 3.1 2.27

Notes: ± corresponds to the standard error of repeated measurements; Az: system average area of zone of influence; Az,bubble: area

of zone of influence per bubble; Ab: bubble area; Wz: width of zone of influence, Lz: length of zone f influence; for course bubble

sparging, nominal frequency of Discrete, 0.25 Hz and 0.5 Hz correspond to 996, 2600, and 9200 mL/min sparging flow rates

respectively.

51

A non-dimensional scaling was used to compare the results from the present study to

those reported by the others. The ratio of Az,bubble/Ab was defined as the “dimensionless area”

of the zone of influence, where Az,bubble is the area of the zone of influence per bubble, and

Ab is the area of the bubble itself, orthogonal to the imaging plane. The dimensionless area of

the zone of influence was substantially affected by the size and frequency of bubbles (Figure

4-7). For coarse bubbles, the dimensionless area of the zone of influence was approximately

20 (Figure 4-7 and Table 4.1), which is consistent with results reported by Komasawa et al.

[78]. However, Komasawa et al. suggested that beyond a given Re, the dimensionless area of

the zone of influence remains constant, which is not consistent with the observations from

the present study (Figure 4-7). For pulse bubbles the dimensionless area of the zone of

influence ranged from 71 to 131 for bubble sizes investigated (Table 4.1). Unfortunately,

limited quantitative published data exist on the dimensionless area of the zone of influence

for large bubbles at high Reynolds numbers. Dimensions of the zone of influence for small

single rising bubbles can be estimated using empirical models that describe the velocity

profile in the wake of the bubbles and which can be evaluated computationally using CFD

[75]. However, the spherical cap bubbles investigated in the present study had large

diameters, high Reynolds numbers, and a wobbling behavior. Extensive CFD analysis would

be required to estimate the dimension of their zone of influence [84, 86, 87], which is beyond

the scope of the present research.

The results from the present study indicate that the size of zone of influence of

secondary flows induced by a pulse bubble can be as much as an order of magnitude larger

than that induced by a coarse bubble, suggesting that for a given volume of sparged gas

added to a system, pulse bubbles could be more effective in control of fouling rate in

submerged membrane systems. The effect of the induced hydrodynamic conditions on the

fouling rate is presented in Chapter 6.

52

Figure 4-7 Dimensionless area of zone of influence for discrete bubbles

(Open shapes: experimental results from present study, lines and solid

squares adapted from Komasawa et al. [78] )

53

Vertical distribution of shear stress for discrete bubble sparging 4.1.4

Figure 4-8 illustrates the vertical distribution of the shear stress measured at probe 1,

located in the middle of the system tank (See Figure 2-2). The vertical distribution of the

shear stress was characterized by a rapid rise from the nose of the bubble to the wake area

immediately downstream of the tail of the bubble, followed by a gradual decrease to the

bottom edge of the zone of influence. These observations were expected because the liquid

velocity and kinetic energy are at their highest magnitudes in the wake immediately behind

the bubble and decrease gradually to the bottom edge of the zone of influence [82, 84].

The magnitude and duration of the peaks increased with the size of pulse bubbles

(Figure 4-8b). This was expected because as described in Section 4.1.1, the rise velocity of

the bubbles, and as a result, the liquid velocity (See figures 4.5 to 4.6) and the kinetic energy

in the wake immediately behind the bubble, increase with the size of sparged bubbles [83].

The higher kinetic energy in the wake of the larger pulse bubbles dissipates over a longer

time (or distance), resulting in longer duration of the peaks observed in the shear stress

profiles measured for larger pulse bubbles.

54

a b

Figure 4-8 Typical shear stress distribution induced by discrete rising bubbles at vertical centreline of the tank

(a: for multiple coarse bubbles [ insert illustrates distribution for a single bubble ]; b: for a single pulse bubble)

55

Horizontal distribution of shear stress for discrete bubble sparging 4.1.5

In order to characterize the horizontal distribution of shear stress in the system tank,

shear stresses induced onto membranes by sparged bubbles were measured at 4 locations as

illustrated in Figure 2-2. Probe 1 was installed on the fiber positioned in the center of the

system tank, and probes 2, 3 and 4 were installed 7, 14 and 21cm from the centerline,

respectively (Figure 2-2). As described in Section 2, four shear probes were installed on one

side of the system tank (Figure 2-2). It was assumed that the shear stress in the tank is

symmetrical, and therefore, the magnitudes of the shear stress presented for the other side of

the system tank are a mirrored image from the magnitude of shear stress measured.

Of the different summative parameters that have been used to express time variable

shear stress induced by gas sparging, the root mean square (RMS) of shear stress has been

reported to be most correlated to the rate of fouling in submerged hollow fiber membrane

systems [49, 62]. For this reason, RMS of the shear stress measured at each probe was used

in the analysis which follows.

The horizontal distribution of RMS of the shear stress is compared in Figure 4-9 for

discrete sparging and for coarse and pulse bubble spargers. The horizontal distributions of

shear stress in the system were bell shaped, with a maximum at the vertical centerline of the

system along the bubble rise path and a rapid decrease to the side edges of the system (Figure

4-9). This was expected because, as described in Section 4.1.2, the velocity profile in the

zone of influence of a rising bubble exhibited a bell shape with the highest magnitude of

velocity (and kinetic energy) in the center of the zone of influence. The higher liquid

velocities (and kinetic energy) induced in the zone of influence of larger bubbles resulted in

an increase in the magnitude of the shear stress with the size of pulse bubbles.

The above results suggests that fouling control over the width of the tank is likely to be

non-homogeneous, with the lowest fouling occurring at the centerline of the zone of

influence, the extent of fouling increasing towards the edges of the zone of influence, and

fouling being highest outside the zone of influence. This is investigated further in Chapter 6.

56

a b

Figure 4-9 Horizontal distributions of shear stress across the width of system tank for discrete sparging frequency

(a: coarse bubbles and b: pulse bubbles; For course bubble sparging, discrete corresponds to 996 mL/min sparging flow rate)

57

4.2 Effect of sparging frequency on the distribution of velocity, vorticity and shear stress

The information presented in Section 4.2 is qualitative. The figures presented in this

section are important because they provide two dimensional maps for vorticity, and illustrate

how the magnitude of velocity and shear stress changes with time when a bubble 1)

approaches the probe, 2) is on contact with the probe or 3) passes by the probes. Using these

figures, qualitative comparison of the maps of vorticity with velocity and shear stress profiles

and for different sparging conditions is also possible.

A quantitative analysis of the data extracted from section 4.2 is presented in Section

4.3.

Effect of sparging frequency on the vertical distribution of vorticity, velocity and 4.2.1shear stress

Figure 4-10 to Figure 4-12 illustrate the vertical distribution of maximum velocity and

maximum shear stress in the system for coarse bubble sparging at discrete, 0.25 Hz and 0.5

Hz sparging frequencies. For comparison purposes, the 2-D distribution of vorticity is also

presented. Qualitatively, it can be observed that the area of zone of influence, i.e. the area

over which high velocities and high vorticies were induced by sparged bubbles, increased

with the sparging frequency (Figure 4-10a, Figure 4-11a, and Figure 4-12a). The length of

the zone of influence for pulse bubbles at the discrete sparging frequency was delineated

based on the threshold of 0.2 m/s for the local velocity, as defined in Section 4.1.3.

A peak in the velocity and shear stress could be observed every time a bubble rises

through the system. As a result, the frequency of the peaks increased with the sparging

frequency. The magnitude of the peaks increased with the increase in the sparing frequency

(Figure 4-10 to Figure 4-12). Also, the magnitude of the baseline in the profiles increased

with an increase in the sparging frequency. This was likely due to the higher bulk liquid

velocity in the system at higher sparging frequencies. The quantitative analysis of the data is

presented in Section 4.3.

58

A

B

c

Figure 4-10 Typical distribution of hydrodynamic conditions induced by coarse bubble sparging at discrete sparging frequency

(a: distribution of vorticity for multiple coarse bubbles (in 1/s); distributions based on

vorticities measured at a fixed horizontal axis at probe location over time; b: velocity

distribution at vertical centerline of tank; c: shear stress distribution at vertical centerline of

tank; for course bubble sparging, discrete corresponds to 996 mL/min sparging flow rate)

59

a

b

c

Figure 4-11 Typical distribution of hydrodynamic conditions induced by coarse bubble sparging at 0.25 Hz sparging frequency

(a: distribution of vorticity fro multiple coarse bubbles (in 1/s); distributions based on

vorticities measured at a fixed horizontal axis at probe location over time; b: velocity

distribution at vertical centerline of tank; c: shear stress distribution at vertical centerline of

tank; for course bubble sparging, nominal frequency of 0.25 Hz corresponds to 2600 mL/min

sparging flow rate)

60

a

b

c

Figure 4-12 Typical distribution of hydrodynamic conditions induced by coarse bubble sparging at 0.5 Hz sparging frequency

(a: distribution of vorticity for multiple coarse bubbles (in 1/s); distributions based on

vorticities measured at a fixed horizontal axis at probe location over time; b: velocity

distribution at vertical centerline of tank; c: shear stress distribution at vertical centerline of

tank; for course bubble sparging, nominal frequency of 0.5 Hz corresponds 9200 mL/min

sparging flow rate)

61

Figure 4-13 to Figure 4-15 illustrate the distribution of vorticity, as well as the vertical

distribution of maximum velocity and maximum shear stress in the system for small pulse

bubble sparging at discrete, 0.25 Hz and 0.5Hz sparging frequencies. Qualitatively, it can be

observed that the area of the zone of influence, i.e. where high vorticies were induced by

sparged bubbles, increased with the sparging frequency (Figure 4-13a, Figure 4-14a, and

Figure 4-15a). The distance between successive bubbles at discrete sparging was much larger

than their length of zone of influence. Therefore, it was confirmed that the zones of influence

of successive pulse bubbles at discrete sparging did not interact.

The vertical distribution of maximum velocity at the sparging frequency of 0.25 Hz is

illustrated in Figure 4-14b. The same threshold of 0.2 m/s as for the pulse bubbles at discrete

sparging (defined in Section 4.1.3) was applied to identify the zone of influence. At this

sparging frequency, the distance between successive bubbles was smaller than the distance

between the successive bubbles at discrete sparging. However, the distance between

successive bubbles was larger than their length of zone of influence (Table 4.1). Therefore, it

was confirmed that no/minimal interaction occured between successive pulse bubbles at

sparging frequency of 0.25 Hz.

The vertical distribution of velocity at the sparging frequency of 0.5 Hz is illustrated in

Figure 4-15b. Again, the threshold of 0.2 m/s was applied to obtain the length of the zone of

influence. At the highest sparging frequency of 0.5Hz, the distance between successive pulse

bubbles was larger than the length of their zones of influence, but the difference was very

small (Table 4.1). Therefore, it was confirmed that the zone of influence of successive

bubbles could interact at the sparging frequency of 0.5Hz (Figure 4-15b).

At the discrete sparging, bubbles ascended on a relatively vertical path in the center of

the system tank, i.e. where the sparger was installed (Figure 4-13). As a result, maximum

velocity and shear stress was measured at the centreline of the system tank. However, at

higher sparging frequencies (Figure 4-14 and Figure 4-15) bubbles moved on a zigzag path

and therefore, the maximum velocity and shear stress were measured on the path of the

bubbles. This was consistent with observations of bubble behaviour under these conditions as

discussed in section 3.2.2.

62

A peak in the velocity and shear stress could be observed every time a bubble rrose

through the system. As a result, the frequency of the peaks increased with the sparging

frequency. The magnitude of the peaks increased with the increase in the sparing frequency

(Figure 4-13 to Figure 4-15). Also, the magnitude of the baseline in the profiles increased

with an increase in the sparging frequency. This was likely due to the higher bulk liquid

velocity in the system at higher sparging frequencies (See Section 4.3).

As discussed in Sections 4.1 and 4.2, the vertical distributions of the velocity and shear

stress within the zone of influence were characterized by a rapid rise from the nose of the

bubble to the wake area immediately downstream of the tail of the bubble, followed by a

gradual decrease to the bottom edge of the zone of influence (Figure 4-13b and c).

At 0.25 Hz, the vertical velocity and the shear stress also were characterized by a rapid

rise from the nose of the bubble to the wake area immediately downstream of the tail of the

bubbles, the velocity and shear stress gradually decreased from the tail end of the bubble to

the bottom edge of the zone of influence (Figure 4-14b and c). However, at 0.5 Hz, no

gradual decrease was observed in the distribution of vertical velocity and shear stress over

time. Because bubbles are rising closely at 0.5 Hz, the gradual decrease is interrupted by the

velocity and shear stress induced by the trailing bubble.

At higher sparging frequencies of 0.25 Hz and 0.5 Hz (Figure 4-14 and Figure 4-15),

the trend observed in the vertical distribution of the shear stress periodically differed from

the trend observed in the vertical distribution of velocity due to the fiber sway. If the fibers

sway, this may induce additional shear stress onto the fibers, which will result in the

measurements of higher magnitudes of shear stress than expected. It may also cause the

fibers to move in the tank in three dimensions and this could move them out of the zone of

influence trailing the bubbles. This would result in the measurements of lower magnitudes of

shear stress than expected.

63

a

b

c

Figure 4-13 Typical distribution of hydrodynamic conditions induced by small (150 mL) pulse bubble sparging at discrete sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

64

a

b

c

Figure 4-14 Typical distribution of hydrodynamic conditions induced by small (150 mL) pulse bubble sparging at 0.25 Hz sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at centerline of tank; b: velocity distribution at vertical centerline of tank; c: shear

stress distribution at vertical centerline of tank)

65

a

b

c

Figure 4-15 Typical distribution of hydrodynamic conditions induced by small (150 mL) pulse bubble sparging at 0.5 Hz sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticites

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

66

The same trend was observed for medium and large pulse bubbles as for small pulse

bubbles; qualitatively, it can be observed that the area of the zone of influence, i.e. where

high vorticies were induced by sparged bubbles, increased with the sparging frequency

(Figure 4-16a to Figure 4-21a).

The distance between successive bubbles at discrete sparging was much larger than the

length of their zone of influence. Therefore, it was confirmed that the zone of influence of

successive pulse bubbles at discrete sparging did not interact.

At a sparging frequency of 0.25 Hz, the distance between successive bubbles was

smaller than the distance between the successive bubbles with discrete sparging. However,

the distance between successive bubbles was larger than the length of their zone of influence

(Table 4.1). Therefore, it was confirmed that no/minimal interaction existed between

successive pulse bubbles at sparging frequency of 0.25 Hz.

At the highest sparging frequency of 0.5 Hz (Figure 4-18b and Figure 4-21b), the

distance between successive pulse bubbles was smaller than the length of the zone of

influence but the difference was very small (Table 4.1). Therefore, it was confirmed that the

zone of influence of successive bubbles could interact at the sparging frequency of 0.5Hz .At

the discrete sparging, bubbles ascended on a vertical path in the center of the system tank

where the sparger was installed (Figure 4-16 and Figure 4-19). However, at higher sparging

frequencies (Figure 4-17, Figure 4-18, Figure 4-20 and Figure 4-21) bubbles moved on a

zigzag path. This was consistent with observations of bubble behaviour under these

conditions as discussed in section 3.2.3 and 3.2.4.

A peak in the velocity and shear stress could be observed every time a bubble rose

through the system. As a result, the frequency of the peaks increased with the sparging

frequency. The magnitude of the peaks increased with the increase in the sparing frequency

(Figure 4-16 to Figure 4-21). Also, the magnitude of the baseline in the profiles increased

with an increase in the sparging frequency. This was likely due to the higher bulk liquid

velocity in the system at higher sparging frequencies.

As discussed in Section 4.1, the vertical distributions of the velocity and shear stress

within the zone of influence were characterized by a rapid rise from the nose of the bubble to

the wake area immediately downstream of the tail of the bubble, followed by a gradual

decrease to the bottom edge of the zone of influence (Figure 4-16 and Figure 4-19). At 0.25

67

Hz, the vertical velocity and the shear stress also gradually decreased from the tail end of the

bubble to the bottom edge of the zone of influence (Figure 4-17 and Figure 4-20). However,

at 0.5 Hz, no gradual decrease was observed in the distribution of vertical velocity and shear

stress over time. Because bubbles were rising in close proximity at 0.5 Hz, the gradual

decrease is interrupted by the velocity and shear stress induced by the trailing bubble.

At the higher sparging frequencies of 0.25 Hz and 0.5 Hz (Figure 4-17 and Figure

4-18), the trend observed in the vertical distribution of the shear stress periodically differed

from the trend observed in the vertical distribution of velocity due to the fiber sway. If the

fibers sway, this may induce additional shear stress onto the fibers, which will result in the

measurements of higher magnitudes of shear stress than expected. It may also cause the

fibers to move in the tank in three dimensions such that they could move out of the zone of

influence trailing the bubbles. This would result in the measurements of lower magnitudes of

shear stress than expected.

68

a

b

c

Figure 4-16 Typical distribution of hydrodynamic conditions induced by medium (300 mL) pulse bubble sparging at discrete sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

69

a

b

c

Figure 4-17 Typical distribution of hydrodynamic conditions induced by medium (300 mL) pulse bubble sparging at 0.25 Hz sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

70

a

b

c

Figure 4-18 Typical distribution of hydrodynamic conditions induced by medium (300 mL) pulse bubble sparging at 0. 5 Hz sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

71

a

b

c

Figure 4-19 Typical distribution of hydrodynamic conditions induced by large (500 mL) pulse bubble sparging at discrete sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

72

a

b

c

Figure 4-20Typical distribution of hydrodynamic conditions induced by large (500 mL) pulse bubble sparging at 0.25 Hz sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

73

a

b

c

Figure 4-21 Typical distribution of hydrodynamic conditions induced by large (500 mL) pulse bubble sparging at 0.5 Hz sparging frequency

(a: distribution of vorticity for pulse bubbles (in 1/s); distributions based on vorticities

measured at a fixed horizontal axis at probe location over time; b: velocity distribution at

vertical centerline of tank; c: shear stress distribution at vertical centerline of tank)

74

Effect of sparging frequency on the horizontal distribution of velocity and the 4.2.2shear stress

Horizontal distributions of the velocity induced by sparging within the system at higher

sparging frequencies are illustrated in Figure 4-22. The magnitudes of velocity were

generally higher within the zone of influence induced by sparged bubbles and gradually

decreased to the sides. The magnitude of velocity increased with an increase in the sparging

frequency. In addition, as discussed in Section 4.1, the area of zone of influence increased

with the sparging frequencies. With an increase in the area of the zone of influence, the

fraction of the system covered with secondary flows increased and therefore, higher

velocities were measured over a wider width within the system tank at higher sparging

frequencies. These results suggest that within the system, fouling control is likely to be

heterogeneous, with the lowest fouling occurring within the zone of influence, the extent of

fouling increasing towards the edges of the zone of influence and the fouling being highest

outside the zone of influence. The relationship between the hydrodynamic conditions,

induced by sparging and fouling control is discussed in Chapter 6.

Negative (downward) velocities were observed at the edges of the system. This likely

resulted from the upward liquid flow entrained by the bubbles rising at the center of the

system and the resulting downward liquid flow at the edges of the system.

The velocity distribution presented in Figure 4-22 is measured at the tail end of the

bubbles. At higher sparging frequencies of 0.25 Hz and 0.5 Hz, pulse bubbles ascended on a

zigzag path, as described in Chapter 3. As a result, the maximum velocity (peaks) is not

observed at the centerline of the system consistently (Figure 4-22). Rather, the maximum

velocity was observed at the centerline of the zone of influence trailing the sparged bubbles.

75

a

b

Figure 4-22 Typical horizontal distributions of velocity across the width of system tank (a: 0.25 Hz and b: 0.5 Hz frequencies)

76

In order to investigate the effect of sparging frequency on the horizontal distribution of

the shear stress within the system, shear stress was measured at 4 probe locations, as

described in Section 4.1.5, at discrete, 0.25 Hz and 0.5 Hz sparging frequencies. Shear stress

induced onto the fibers for sparging with the coarse sparger at discrete, 0.25 and 0.5 Hz

frequencies is illustrated in Figure 4.23 to Figure 4.25.

A peak in the shear stress was observed every time a bubble rose through the system.

As a result, the frequency of the peaks increases with the sparging frequencies. The

magnitude of shear stress measured at probe location 1 (located in the centerline of the

system tank), was consistently higher in comparison to the magnitude of shear stress

measured at probe locations 2, 3 and 4 (located further to the side of the system tank). As a

result, the horizontal distribution of the shear stress was not homogenous. This was expected

considering that bubbles sparged under these conditions were rising along the centerline of

the system tank, as previously discussed in section 3.2.1. A bubble rising along the centerline

of the system tank induced higher velocity (and kinetic energy) at the centre line of the

system tank in comparison to the sides of the system tank.

The magnitude of the shear stress generally increased with the increase in the sparging

frequency (Figure 4-24 and Figure 4-25). This was expected because, as discussed above, at

higher sparging frequencies bubbles induced higher velocities (Figure 4-22) and higher

kinetic energy and therefore, they were generally expected to induce higher shear stress on to

the membranes.

77

a

b

c

d

Figure 4-23 Typical vertical distribution of shear stress induced by coarse bubble sparging at different locations for discrete sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3; d: shear stress at position 4; for course bubble sparging, discrete corresponds to 996 mL/min sparging

flow rate)

78

a

b

c

d

Figure 4-24 Typical vertical distribution of shear stress induced by coarse bubble sparging at different locations for 0.25Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4; for course bubble sparging, nominal frequency of 0.25Hz corresponds to

2600 mL/min sparging flow rate)

79

a

b

c

d

Figure 4-25 Typical vertical distribution of shear stress induced by coarse bubble sparging at different locations for 0. 5Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4; for course bubble sparging, nominal frequency of 0.5 Hz corresponds to

9200 mL/min sparging flow rate)

80

The shear stress measured for sparging with small pulse bubble (150 mL) at discrete

sparging frequency is presented in Figure 4-26. A peak in the shear stress was observed

every time a bubble rose through the system. As a result, the frequency of the peaks increases

with the sparging frequencies. Shear stress measured at the probe location 1 (located in the

center of the system tank) had the highest magnitude in comparison to the shear stress

measured at probe locations 2, 3 and 4 (located further to the side of the system tank). As a

result, the horizontal distribution of the shear stress was not homogenous. This was expected

considering that bubbles sparged under these conditions were rising along the centerline of

the system tank, as previously discussed in section 3.2.2. A bubble rising along the centerline

of the system tank induced higher velocity (and kinetic energy) at the centre of the system

tank in comparison to the sides of the tank (Figure 4-22).

However, at higher sparging frequencies, the shear stress measured at probe location 1

(located in the center of the system tank) was not consistently higher than the magnitude of

shear stress measured at probe locations 2, 3 and 4 (located further to the side of the system

tank) as illustrated in Figure 4-27 and Figure 4-28. This was expected because at higher

sparging frequencies, sparged bubbles rose along zigzag paths (Section 3.2.2) and therefore,

higher magnitudes of the shear stress, i.e. the peaks, were measured at the probes located on

the path of the bubbles. For example, as presented in Figure 4-28, the shear stress was greater

at probe locations 2 and 3 compared to probe location 1 for the period examined.

The magnitude of the shear stress generally increased with the increase in the sparging

frequency (Figure 4-27 and Figure 4-28). This was expected because, as discussed above, at

higher sparging frequencies, bubbles induced higher velocities and higher kinetic energy and

therefore, they were generally expected to induce higher shear stress on to the membranes

(Figure 4-22).

Similar trends to those observed for small pulse bubbles were observed for medium

and large pulse bubbles. The typical vertical distributions of shear stress induced by medium

and large pulse bubbles at different locations are presented in Appendix F.

81

a

b

c

d

Figure 4-26 Typical vertical distribution of shear stress induced by small (150 mL) at different locations for pulse bubble sparging at discrete sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

82

a

b

c

d

Figure 4-27 Typical vertical distribution of shear stress induced by small (150 mL) at different locations for pulse bubble sparging at 0.25Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

83

a

b

c

d

Figure 4-28 Typical vertical distribution of shear stress induced by small (150 ml) at different locations for pulse bubble sparging at 0. 5 Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

84

To obtain the horizontal distribution of the RMS of the shear stress in the system, the

RMS of the shear stress measured at each probe location was plotted versus the width of the

system tank for the sparging frequencies of 0.25 Hz and 0.5 Hz (Figure 4-29). The results

were mirrored for the left side of the system tank (See Figure 2-2).

The magnitude of maximum RMS of the shear stress was generally higher in the

centerline of the system tank and gradually decreased to the edges of the system tank (Figure

4-9). The magnitude of maximum RMS of the shear stress induced onto the fibers increased

with an increase in the sparging frequency. This behavior is explained by higher liquid

velocities induced at higher sparging frequencies as described above (Figure 4-22). Higher

velocities result in higher kinetic energy in the zone of influence following the bubbles and

therefore, induce higher shear stress on to the fibers immersed in their zone of influence [84].

In addition, with an increase in the sparging frequency, the horizontal distribution of

shear stress was flattened (Figure 4-29) in comparison to the profile observed at the discrete

sparging frequency (Figure 4-9). This observation was expected because, as discussed in

Section 4.1 and also illustrated in Figure 4-22, the area of zone of influence increased at

higher sparging frequencies. With an increase in the area of the zone of influence, the

fraction of the system covered with secondary flows, i.e. higher local velocity and therefore

higher kinetic energy, increased. As a result, it was expected that higher shear stress would

be observed over a wider width within the system tank. The effect of the horizontal

distribution of the shear stress on the fouling control is discussed in Chapter 6.

85

a

b

Figure 4-29 Horizontal distributions of shear stress across the width of system tank

(a: 0.25 Hz and b: 0.5 Hz frequencies; fibers inside zone of influence are open

symbols, while those outside the zone of influence are solid symbols; Error bars corresponds

to minimum and maximum measurements as measurements were done in triplicates)

86

4.3 Summary of the hydrodynamic conditions induced by bubbles of different sizes and sparging frequencies

Previous sections presented a semi-qualitative comparison of the hydrodynamic

conditions induced by bubbles for the different sizes and frequencies investigated. In the

discussions which follows, the hydrodynamic conditions induced by bubbles of different

sizes and frequencies are quantitatively compared.

The total system area of zone of influence, i.e. summation of the zones of influence for

all bubbles in the system at a given time, increased with bubble size and frequency (Figure

4-30a). However, the total system area of zone of influence induced at 0.5 Hz was not two

times larger than the total system area of zone of influence at 0.25 Hz, even though the

number of bubbles in the system at any given time was greater. At a bubble frequency of 0.5

Hz, the distance between successive bubbles was less than the length of the zones of

influence of the bubbles rising discretely (Table 4.1), indicating that the zone of influence of

successive bubbles overlapped. As a result, the area of the zone of influence per bubble was

smaller (Figure 4-30b). The zone of influence per bubble was calculated based on the total

system zone of influence devided by the number of bubbles in the system.

87

a

b

Figure 4-30 Area of zone of influence (a: total system area of zone of influence; b: area of zone of influence per bubble; area of zone of influence of coarse bubbles was very small in comparison to the area of zone of influence of pulse bubbles and therefore is not visible on the graph; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200

mL/min sparging flow rates respectively; Error bars correspond to the standard errors in the measurements)

88

The increase in the dimensionless area of zone of influence per bubble with bubble size

resulted in an increase in the average width of the zone of influence (Wz) (Table 4.1 and

Figure 4-31). The average width of the zone of influence for pulse bubbles was much larger

than that of coarse bubbles. The average width of the zone of influence also increased with

the increase in the sparging frequency. These observations were expected because of the

zigzag movement of the pulse bubbles at the higher sparging frequency which resulted in a

wider area of zone of influence, as well as the higher rise velocities of the bubbles (Table

4.1).

These results are of significant importance because they suggest that the spacing

between spargers can be greater when sparging with larger pulse bubbles. For instance

increasing the sparging frequency from 0.25 Hz to 0.5 Hz increases the width of influence by

a factor of approximately 1.3 for large pulse bubbles (500 mL), and therefore, the spacing

between the spargers could be increased by the same factor, reducing the number of air

spargers. Reducing the overall number of air spargers could result in reducing the overall

power requirement for air sparging in the system by 30%.

89

Figure 4-31 Average width of zone of influence

(For course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996,

2600, and 9200 mL/min sparging flow rates respectively)

90

System wide RMS of the bulk liquid velocity (Figure 4.32) was calculated as the

average of RMS of the liquid velocity measured at the probe locations 1 to 4 (See probe

locations on Figure 2-2). The RMS of the velocity generally increased with the size of

sparged bubbles, although the increase was not statistically significant. The RMS of the

velocity also generally increased with sparging frequency for a given bubble size (again, not

consistently statistically significant). This increase was likely due to the larger number of

bubbles presented in the system at a higher frequency (and therefore more secondary flows in

the system).

Figure 4-32 System wide RMS of bulk velocity

(Error bars correspond to the standard errors in the measurements)

91

System wide RMS of the shear stress (Figure 4.33) was calculated as the average of the

RMS of the shear stress for all probes. The RMS of the shear stress increased with sparging

frequency for a given bubble size (Figure 4-33a). This increase was likely due to the greater

number of bubbles in the system at a higher frequency and therefore, more secondary flows

in the system, as well as the higher RMS of bulk velocity. The increase in the system wide

RMS of shear stress is consistent with the increase in the RMS of bulk velocity (Figure

4-33). However, as presented in Figure 4-33a, the RMS of the system wide shear stress at 0.5

Hz was not twice the RMS of the system wide shear stress at 0.25 Hz. As a result of the

bubble interactions, the area of the zone of influence per bubble decreased (Figure 4-30b). As

a result, the RMS of the shear stress per bubble (Figure 4-33b), which was calculated by

dividing the RMS of the system wide shear stress by the number of bubbles in the system,

decreased at higher frequencies.

92

a

b Figure 4-33 RMS of shear stress

(a: system wide average RMS of shear stress; b: system wide average RMS of the shear stress per bubble; RMS of the shear stress per

bubble of coarse bubbles was very small in comparison to the RMS of the shear stress per bubble of pulse bubble sparging and therefore is not visible on the graph; for course bubble

sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively; Error bars correspond to the standard errors in the

measurements)

93

4.4 Conclusion The rate of fouling in air-sparged submerged membranes has been reported to be

related to the liquid velocity and the vorticities as well as to the shear stress induced by the

secondary flows induced by the sparged bubbles. Therefore, the fraction of the system where

high vorticities and velocities are induced by the secondary flows trailing a sparged bubble

was defined as the area of “zone of influence” of a bubble.

The two dimensional maps for vorticity compared the size, the shape, and the location

of the zone of influence of a bubble in the system for different sparged bubble sizes and

frequencies. The information provided by the graphs of velocity and shear stress illustrated

how the magnitude of velocity and shear stress changed with the time when a bubble 1)

approached the probe, 2) was in contact with the probe or 3) passed by the probes. They also

qualitatively illustrated how the change of the magnitude of velocity and shear stress with the

time was affected by the sparged bubble size and frequency. Using the figures presented in

Section 4.2, qualitative comparison of the maps of vorticity with velocity and shear stress

profiles and for different sparging conditions was also possible.

The results indicated that the system-wide area of the zone of influence was

substantially affected by the size and frequency of bubbles induced. The system-wide area of

the zone of influence increased with bubble size and frequency. The results also indicate that

the zone of influence induced by pulse bubbles is an order of magnitude larger than that

induced by coarse bubbles.

The average width of the zone of influence became larger as the bubble size and

sparging frequency increased. These results are of significant importance because they

suggest that the spacing between spargers can be greater when sparging with larger bubbles.

This can reduce the overall number of air spargers and therefore, reducing the overall power

requirement for the system.

The velocities and the shear stresses within the zones of influence of bubbles were not

homogenously distributed. The vertical distributions of the velocity and shear stress within

the zone of influence for discrete bubbles were characterized by a rapid rise from the nose of

the bubble to the wake area immediately downstream of the tail of the bubble, followed by a

gradual decrease to the bottom edge of the zone of influence.

94

Velocity and system-wide RMS of the shear stress increased with bubble size and

frequency. For interacting bubbles, the velocity and shear stress were characterized by a

rapid rise from the nose of the bubble to the zone of influence immediately downstream of

the tail end of the bubble, followed by a gradual decrease. However, at higher sparging

frequencies, the decrease in the velocity and shear stress was interrupted by the trailing

bubbles.

The horizontal distributions of the velocity and the shear stress within the zone of

influence were bell shaped, with a maximum at the vertical centerline of the zone of

influence and a rapid decrease to the side edges of the zone of influence. The magnitude of

maximum velocity and shear stress increased with the size of the pulse bubbles. The

horizontal distribution of the shear stress in the system was flattened at higher sparging

frequencies. The magnitude of the shear stress also increased with sparging frequency.

Because the horizontal distribution of the velocity and shear stress in the system is non-

homogenous, fouling control over the width of the flow cell is likely not to be even, as

discussed in Chapter 6.

These results also indicated that the system-wide area of zone of influence did not only

increase with the size of pulse bubbles but also the maximum velocity and the shear stress in

the zone of influence increased with the size of pulse bubbles. The larger area of system-

wide zone of influence and greater magnitude of velocity observed for larger pulse bubbles

are expected to result in better fouling control in the system. The reported improvement in

fouling control that has been achieved using pulse bubble sparging compared to that which

can be achieved with coarse bubble sparging, as claimed by commercial membrane

manufacturers such as GE Water and Process Technologies, is likely due to the difference in

the characteristics of the induced zones of influence (i.e. their size), induced RMS of shear

stress, and rise velocity, between pulse bubble and coarse bubble sparging. This hypothesis is

considered in Chapter 6.

95

5 Relationship between the induced hydrodynamic conditions and power

transfer efficiency in the system

As discussed in Chapter 1, depending on the characteristics of the solution being

filtered and the permeation flux, a certain amount of force is required for the transport of the

foulants away from the membrane surface to minimize the rate of fouling. The transport of

the foulants away from the membrane surface is induced by the forces generated by

secondary flows (characterized by liquid velocities and vorticities) and the shear stress

induced at the surface of the membranes (as described in Equation 1.1). However, as

discussed in Chapter 1, none of these parameters, i.e. liquid velocity and shear stress, on their

own can fully characterize the hydrodynamic conditions induced by sparged bubbles in

membrane systems, and the resulting effect of fouling control.

To assess the efficiency of different sparging scenarios in terms of fouling control, for

the first time a new parameter was in the present thesis to quantify the power transferred

onto the fibers by sparged bubbles. Power transfer was defined as the product of the force

induced onto the fibers, estimated as the RMS of the shear stress induced on the fibers

multiplied by the area over which the shear stress is applied, i.e. zone of influence, and the

rise velocity of the bubbles, assuming that the zone of influence rises at the same velocity as

the bubbles, as presented in Equation 5.1. The root mean square (RMS) was used to quantify

the time variable shear force, as this parameter has been demonstrated to be correlated to

fouling control [49, 62].

Ptrans = (τRMS Az)Vb (5.1)

where τ RMS is the root mean square shear stress for all fibers in the system [Pa], Az is the

system wide area of zone of influence induced by the bubbles [m2], and Vb is the average rise

velocity of the bubbles in the system [m/s]. Values of the system wide area of the zone of

influence (Az) and the RMS of the shear stress (τRMS) for the different sparging conditions

investigated are summarized in Figure 4-30 and Figure 4-33, respectively.

96

5.1 Power transfer and power transfer efficiency per bubble for discrete bubble sparging

As illustrated in Figure 5-1, the power transferred onto the membranes per sparged

bubble, when sparging with discrete pulse bubbles, was significantly higher than when

sparging with coarse bubbles. In addition, the power transferred onto the membranes per

sparged bubble generally increased with the size of sparged bubbles. This was expected

because the area of zone of influence and the magnitude of shear stress induced onto the

membranes increased with the size of pulse bubbles as discussed in Chapter 4. As a result,

the force induced per bubble, estimated as the RMS of the shear stress induced on the fibers

multiplied by the area over which the shear stress is applied, increased with the size of pulse

bubbles (Figure 5-2). In addition, the rise velocity of the bubbles increased with the size of

pulse bubbles as discussed in Chapter 4.

97

Figure 5-1 Power transferred onto membranes per bubble

(Power transfer per bubble of coarse bubbles was very small in comparison to the power transfer per bubble of pulse bubble sparging and therefore is not visible on the graph; for

course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates, respectively; Error bars correspond to the standard

errors in the measurements)

98

Figure 5-2 Force per bubble

(Force per bubble of coarse bubbles was very small in comparison to the force per bubble of pulse bubble sparging and therefore is not visible on the graph; for course bubble sparging,

discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively; Error bars correspond to the standard errors in the

measurements)

99

To compare the different sparging conditions, a power transfer efficiency term for fouling

control was defined as the ratio of the power transferred to the fibers to the actual total power

added to the system. The total power added to the system was directly proportional to the

sparging flow rate [88] and therefore, was similar for all the sparged bubble sizes at a given

sparging flow rate.

The power transfer efficiency per bubble for pulse bubble sparging was significantly

higher than the power transfer efficiency per bubble of coarse bubble sparging when

sparging at discrete sparging frequency (Figure 5-3). The power transfer efficiency per

bubble also increased with the size of pulse bubbles at discrete sparging frequency.

These results indicated that when sparging at a very low sparging frequency (discrete),

large pulse bubbles transfer a larger portion of the total power input to the system onto the

fibers in comparison to sparging with coarse bubble sparging or smaller pulse bubbles. These

results suggest that large pulse bubbles are more efficient in terms of delivering power for

fouling control at discrete sparging. However, as discussed in the next section, interaction

between bubbles can significantly affect the power transfer efficiency.

100

Figure 5-3 Power transfer efficiency per bubble

(Power transfer efficiency per bubble of coarse bubbles was very small in comparison to the power transfer efficiency per bubble of pulse bubble sparging and therefore is not visible on

the graph; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates, respectively; Error bars correspond to the

standard errors in the measurements)

101

5.2 Power transfer and power transfer efficiency per bubble for sparging at higher frequencies

When the sparging flow rate increases, the frequency at which the bubbles are released

into the system also increases. At a given frequency, when bubbles interact (Table 4.1) the

bubbles can no longer be considered to be rising discreetly.

The higher gas sparging flow rates required to achieve the higher frequencies increased

the upward liquid flow at the center of the system tank, and as a result, the rise velocity of

the bubbles (Figure 3-2). However, due to the decrease in the RMS of shear stress per bubble

at higher sparging frequencies compared to the discrete sparging (Figure 4.31), the force

induced onto the fibers per bubble (defined as τ RMS*Az per bubble) also decreased at higher

sparging frequencies (Figure 5-2). The combined effect of the decrease in the force induced

by the pulse bubbles and the increase in the rise velocity of bubbles on the power transferred

to the fibers resulted in a decrease in the power transfer per bubble at higher sparging

frequencies compared to discrete bubble sparging (Figure 5-1).

As was observed for discrete bubbles, the power transferred per bubble increased with

bubble size when bubbles interacted at 0.5 Hz sparging frequency, i.e. when trailing bubbles

rise within the wake of leading bubbles (see Table 4.1). However, the difference between

small pulse bubbles and large pulse bubbles was not as pronounced for interacting bubbles as

for discrete bubbles. At the sparging frequency of 0.25 Hz, when no, or minimal interaction

of bubbles was observed, no consistent trend existed between bubble size and the power

transferred.

The higher gas sparging flow rate required to achieve the higher frequencies combined

with a decrease in the power transferred onto the fibers per bubble at higher sparging

frequencies compared to those for discrete sparging resulted in an overall decrease in the

power transfer efficiency per bubble at higher sparging frequencies (Figure 5-3).

102

5.3 System-wide power transfer and power transfer efficiency at different sparging flow rates

The power transfer and the power transfer efficiency per bubble only provide insights

into the ability of individual bubbles to contribute to fouling control for each sparging

frequency. In terms of practical applications, the total power and power transfer efficiency to

the system when sparging with bubbles of different sizes and sparging frequencies at given

sparging flows are of interest.

As presented in Figure 5-4, for the conditions studied, the total power transferred to the

system by coarse bubbles increased linearly with the sparging flow rate while that for pulse

bubble sparging increased exponentially. This indicates that for the same incremental

increase in the sparging flow rates, the power transfer increases more rapidly for pulse

bubble sparging than for coarse bubble sparging. For small and medium pulse bubbles, the

power was generally greater than for coarse bubble sparging. At low sparging flows, larger

pulse bubbles transferred less power compared to the small and medium pulse bubbles or

coarse bubbles at a given sparging flow rate. This was because of the low bubble release

frequency for larger pulse bubbles which resulted in longer periods when no air was added to

the system. However, at higher sparging flow rates, small and medium pulse bubbles may

not be able to induce large magnitudes of power required for fouling control. This is

discussed in Chapter 6.

103

Figure 5-4 Relationship between power transfer and air sparging conditions (Dashed lines correspond to the linear and exponential relationships fitted to the data; for

course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600,

and 9200 mL/min sparging flow rates respectively)

104

As observed for power transfer, for consistency, trend lines for coarse and pulse

bubbles were also assumed to be linear and exponential respectively, for the relationship

between the system wide power transfer efficiency and the sparging flow rate (Figure 5-5).

These trend lines imply that the power transfer efficney for pulse bubbles increases

exponentially with an increase in the sparging flow rate (over the range investigated),

however, the power transfer efficiney for coarse bubbels increased linearly with the increase

in the sparging flow rate. System-wide power transfer efficiency (Figure 5-5) is different

from the power transfer efficiency per bubble because of the time gaps between the bubbles

(See Figure 5-3 for power transfer efficieny per bubble).

In terms of power transfer efficiency into the system, over the range of conditions

investigated, pulse bubble sparging with small bubbles, i.e. 150 mL, was consistently the

most efficient condition at inducing power onto the membranes for fouling control at low and

intermediate sparging flow rates (Figure 5-5). Medium pulse bubbles, i.e. 300 mL, were most

efficient in terms of power transfer efficiency onto the system over the intermediate sparging

flow rates. If a large amount of power is required for fouling control, it may not be possible

to generate the required amount of power for fouling control with small and medium pulse

bubbles (e.g. if require greater than 15 watts). In such a case, pulse bubble sparging with

larger bubbles may be required. Pulse bubble sparging with large pulse bubbles, i.e. 500 mL,

was most efficient at inducing a given amount of power to the system for fouling control.

This will be discussed in more details in the next Chapter.

105

Figure 5-5 Power transfer efficiency for the sparging conditions investigated

(Solid lines represents trends; dashed lines represents linear and exponential relationships fitted to the data; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies

correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively)

106

5.4 Conclusion

To assess the efficiency of different sparging scenarios in terms of fouling control, a

new parameter was defined in the present study to quantify the power transferred onto the

fibers by bubbles. The hydrodynamic conditions and the resulting power induced on to the

membranes for fouling control were substantially affected by the sparged bubble size and

frequency, i.e. sparging flow rate. The power transfer per bubble increased with bubble size

when sparging with discrete bubbles. However, the extent of the increase in power with

bubble size was not as pronounced when sparging at higher frequencies.

For small and medium pulse bubbles, the power transfer was generally greater than for

coarse bubble sparging. At low sparging flows, larger pulse bubbles transferred less power

than the small pulse bubbles or coarse bubbles at a given sparging flow rate.

Power transfer and power transfer efficiency were defined to quantify the

hydrodynamic conditions induced by sparged bubbles of different sizes and frequencies by

incorporating the area of the zone of influence, the liquid velocity, and the RMS of the shear

stress induced in the system. However, of interest is the relationship between the fouling rate

and the power transferred onto the membranes. This is discussed in Chapter 6.

107

6 Effect of induced hydrodynamic conditions on the fouling rate

As discussed in Chapter 5, power transfer was defined to quantify the hydrodynamic

conditions induced by sparged bubbles of different size and frequency by incorporating the

area of zone of influence, the liquid velocity, and the RMS of the shear stress induced in the

system (Equation 5.1). For the sparging conditions investigated, at high sparging flows, the

power transfer efficiency to the system was higher for pulse bubble sparging than for coarse

bubble sparging. The present chapter summarizes the results of the filtration experiments

conducted with different sparging approaches. The different sparging conditions were

compared in terms of 1) power transfer and 2) power transfer efficiency and 3) rate of

fouling control.

6.1 Effect of bubble size and sparging frequency on fouling rate

The filtration experiments were conducted for the sparging conditions, i.e. bubble size

and frequency, presented in Table 4.1. Typical trans-membrane pressure measurements

collected during filtration are presented in Figure 6-1 (filtration data for all investigated

sparging conditions are presented in Appendix E). For all cases, the normalized trans-

membrane pressure could be modeled with the exponential relationship presented in equation

6.1.

P=PoeKV (6.1)

where P is the trans-membrane pressure (kPa), K is the fouling rate constant (1/mL) , V is the

volume filtered (mL), and the subscript “o” corresponds to initial conditions.

The exponential increase in TMP observed in the present study was consistent with the

exponential increases in TMP observed by others for filtration of solutions containing

bentonite through commercially available hollow fiber membranes [52, 62]. For this reason,

in the discussion which follows, the rate of fouling is expressed in terms of the exponential

fouling rate constant.

108

a b

Figure 6-1 Typical results from filtration experiments (a: coarse bubble sparging (results presented for 0.75 mL bubbles and discrete sparging); b: pulse bubble sparging ( results presented

for 500 mL pulse bubbles and discrete sparging); HF1: Hollow Fiber at location 1; HF2: Hollow Fiber at location 2; HF3: Hollow

Fiber at location 3; HF4: Hollow Fiber at location 4)

109

The fouling rate constants calculated for all experimental conditions investigated are

summarized in Figure 6-2. The system average fouling rate constant was calculated by

averaging the fouling rate constants measured for each fiber. The average fouling rate is

representative of the overall fouling rate in the system because all fibers were individually

connected to an individual pump which enabled the flux in all fibers to be similar.

Figure 6-2 System average fouling rate constant for different sparging conditions (Error bars correspond to minimum and maximum measurements as filtration tests were done

in triplicates; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively)

110

When sparging with discrete bubbles, the rate of fouling remained relatively constant

as the size of the sparged bubbles increased. This was somewhat expected because the

volume of sparged gas per unit time added to the system was similar for all sparged bubble

sizes. When sparging at an intermediate frequency of 0.25 Hz, the rate of fouling was lower

than that observed when sparged with discrete bubbles. Additionally, the rate of fouling

generally decreased as the size of the sparged bubbles increased. Again, this was expected

because the volume of sparged gas per unit time added to the system at a given frequency

increases with bubble size. When sparging at the highest frequency of 0.5 Hz, the rate of

fouling was again lower than those observed at the lower frequencies. However, as observed

for discrete bubbles, no clear trend was observed between bubble size and fouling rate.

As previously discussed in Chapter 5, the sparging conditions significantly affected the

shear stress induced onto the hollow fibers, the zone of influence of secondary flows and the

bubble rise velocities and, as the result, the power transferred onto the membrane surface.

Power transferred onto the membrane surface was defined as presented in Equation 5.1 to

characterise the hydrodynamic conditions induced by sparged bubbles of different sizes and

frequencies. Power transfer efficiency was defined to quantify the percentage of the total

power input the system through air sparging that was transferred onto the membrane surface

for fouling control.

The relationship between the fouling rate and the power transferred is presented in

Figure 6-3. The fouling rate was observed to be significantly affected by the power

transferred.

1) At low power transfer values (<2 w), the fouling rates were high and

decreased linearly with an increase in the power transferred.

2) At intermediate power transfer values (2-35 w), the incremental change in the

fouling rate decreased as the power increased.

3) At high power transfer values (>35 w), the fouling rate was essentially zero.

No other studies have investigated the relationship between the fouling rate and the

power transferred onto the membranes prior to the present study. However, when

investigating the relationship between the fouling rate in hollow fiber membranes and coarse

111

bubble sparging, similar trends, i.e. an initial fast decrease in the rate of fouling with

sparging flow, a transition range at intermediate sparging flows, and a range over which

fouling is essentially zero, have been reported by others [52, 90].

Figure 6-3 Relationship between fouling rate and power transferred onto membranes (Error bars correspond to minimum and maximum measurements as filtration tests were done

in triplicates; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively)

112

As previously discussed in Chapter 1, the accumulation of foulants on a membrane

surface is the result of the force balance between the drag forces towards the membrane

surface due to the permeation flow, and shear stress-induced back transport of foulants away

from the membrane surface. As presented in Equation 1.1, this force balance is a function of

both the size of the foulants and the applied shear stress. Therefore, for a given shear stress,

there is a critical particle size for which all the particles with a larger size than the critical

size will be transported back into the solution through the lift forces exerted by the shear

stress [4]. Therefore, depending on the power transferred, three fouling behaviors are

possible.

1) When the power applied is high, the shear stress induced onto the membrane is

high enough for the back transport of foulants of all sizes. Under these conditions

Fdrag,permeation < Flift, shear for foulants of all sizes and therefore, minimal, or no fouling

is observed. This likely corresponds to the fouling rates observed when the power

transfer was larger than 35 w.

2) When the power applied is lower, the back transport forces exerted by the shear

stress may not be high enough to overcome the permeation drag forces for small

foulants. In this transition range a foulant layer forms that is likely to be populated

mainly by smaller foulants, for which the back transport forces are lower [4]. When

the power applied further decreased, the accumulation of foulants increased. Also,

when the power applied is decreased, the fouling layer is expected to be composed

of increasingly larger particle sizes [5, 52]. This likely corresponds to the fouling

rates observed when the power transfer was in the range of 2-35 w.

3) When the power applied is low, the back transport forces are not large enough to

overcome the permeation drag forces for most of the foulants with different sizes.

Under these conditions, the foulant layer is likely to be populated by foulants of all

sizes. Under these conditions Fdrag,permeation > Flift, shear for foulants of all sizes and

therefore, high fouling rates are observed. This likely corresponds to the fouling

rates observed when the power transfer was less than 2w.

113

When considering power transfer, above a given value, the rate of fouling was

negligible (Figure 6-3). These results indicate that for a given water matrix, negligible

fouling occurs when sufficient power is transferred to the membranes to prevent the

accumulation of hydraulically reversible fouling. For the solution filtered, fouling could be

effectively controlled by transferring approximately 5 watts of power to the system by

sparging (Figure 6-3). This threshold of power, i.e. 5 watts, is the point of diminishing

returns for the data presented in Figure 6-3. Other studies have also reported limited benefits

of increased sparging above a given sparging intensity (the threshold sparging intensity

differed in different experimental setups) [23, 39, 55].

A threshold, was also observed for the RMS of shear stress, below which fouling rate

generally decreased with an increase in RMS of the shear stress. Fouling was essentially zero

above this critical RMS of the shear stress (Figure 6-4). However, in contrast to the

relationship observed between the fouling rate and the power transfer, substantial

discontinuities were observed when considering the relationship between fouling rate and the

RMS of shear stress, such that substantially different fouling rates were observed at a given

RMS of shear stress (e.g. at a RMS of 0.9 Pa, the fouling rate ranged from essentially 0 to

over 0.0002/mL). These results are consistent with those from previous studies that have

concluded that single summative parameters, such as RMS of the shear stress, cannot

consistently describe the effect of hydrodynamic conditions on the rate of fouling [49].

114

Figure 6-4 Relationship between fouling rate and root mean square of shear stress in the system

(Error bars correspond to minimum and maximum measurements as filtration tests were done in triplicates; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies

correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively

115

The minimum average constant shear stress required for all particles in a minimal to no

fouling condition for the solution of bentonite particles with an average diameter of 2 um and

a constant permeation flux of 100 L/m2.hr was calculated using Equations 1.1 to be 4 Pa.

However, as presented in Figure 6-4 (Relationship between fouling rate and root mean

square of shear stress for individual fibers), the threshold of shear stress for which no or

minimum fouling was observed in the present research was 1 Pa. This discrepancy is likely

due to the fact that Equation 1.1 assumes constant shear stress conditions, while those in the

present study were variable. As previously discussed, variable shear stress is more efficient

in terms of fouling control than constant shear stress. Also, the values presented in Figure

6-5, are RMS values of time-variable shear stress, while the peak shear stress values were

much higher.

116

Figure 6-5 Relationship between fouling rate and root mean square of shear stress for individual fibers

(For course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively

117

The power transfer efficiency, defined as the ratio of power transferred onto

membranes to the actual power added to the system, was used to identify the optimal

sparging approach to effectively control fouling. The relationship between power transfer

efficiency and power transfer is presented in Figure 6-6. Also presented in Figure 6-6 is the

amount of power selected in the present study for effective fouling control (i.e. 5 watts).

For the present study, sparging with small pulse bubbles was the most efficient

approach to transfer the required amount of power, i.e. 5 watts, for fouling control (Figure

6-6). For the sparging conditions investigated, it was not possible to generate more than

about 15 watts with small pulse bubble sparging. Therefore, if more than 15 watts of power

is needed for fouling control, pulse bubble sparging with small pulse bubbles at a frequency

greater than 0.5 Hz or sparging with larger bubbles may be required.

Figure 6-6 Power transfer efficiency with respect to power transferred onto membrane

surface (Dashed lines correspond to power required in the present study for effective fouling control

and corresponding power transfer efficiency for coarse and small pulse bubble sparging; solid lines present overall trends,for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively

118

These results indicate that pulse bubble sparging is substantially more efficient at

transferring power to a membrane than coarse bubble sparging. For the solution filtered,

pulse sparging with small bubbles is expected to be approximately two times more efficient

than coarse bubble sparging for fouling control at low-to-intermediate sparging flow rates.

Considering that coarse bubble sparging in MBR systems accounts for over % 30 of the total

operating cost of these systems (Figure 6-7a), the use of pulse sparging instead of coarse

sparging can therefore reduce the overall power requirements from approximately 0.62

kWh/m3 of permeate to less than 0.53 kWh/m3 of permeate (Figure 6-7b).

119

a

b

Figure 6-7 Power cost distribution for MBR systems

(a: for continuous coarse bubble sparging; b: with small pulse bubble sparging. Assuming a

50% reduction in power cost for small pulse bubble sparging compared to coarse bubble

sparging; Figure 6-7a was adapted from [1])

120

6.2 Effect of bubble size and sparging frequency on the spatial distribution of fouling rate in the system

The spatial distribution of the fouling rate in the system was not homogeneous, where

the fouling rate generally was lower at the centerline of the system tank directly above the

spargers (Figure 6-8). Fibers located in the zone of influence are marked with clear symbols

and fibers out of zone of influence are marked with solid symbols. It was observed that

fouling rate was generally lower in the zone of influence induced by sparged bubbles. This

observation could be explained by the non-homogeneous distribution of velocity and shear

stress in the system, as described in Chapter 4. Higher velocity and higher kinetic energy in

the zone of influence of sparged bubbles result in higher shear stress induced onto the

membranes located in the zone of influence of sparged bubbles compared to the membranes

located at the edges (as discussed in Chapter 4). Higher shear stress induced onto the

membranes could result in a higher rate of back transport of foulants from the membrane

surface and therefore, a lower fouling rate (Equation 1.1). As a result the lower fouling rates

were observed in the zone of influence of sparged bubbles than at the edges of the zone of

influence of sparged bubbles.

121

a

b

c

Figure 6-8 Distribution of fouling rate in the system (a: discrete bubble sparging; b: sparging at 0.25 Hz; c: sparging at 0.5 Hz; fibers inside zone

of influence marked clear, fibers outside zone of influence marked solid; error bars corresponds to minimum and maximum measurements as filtration tests were done in

triplicates; for course bubble sparging, discrete, 0.25 Hz and 0.5 Hz frequencies correspond to 996, 2600, and 9200 mL/min sparging flow rates respectively

122

As the size and frequency of bubbles increased, the zone of influence became wider,

flattening the distribution of the fouling rate (as discussed in Chapter 4). These results

suggest that as the size and frequency of the bubbles increase, the spacing between the

spargers could be increased reducing the overall number of spargers and therefore reducing

the volume of gas required for sparging the system. For instance increasing the sparging

frequency from 0.25 Hz to 0.5 Hz increases the average width of influence by approximately

a factor of 1.3, and therefore the spacing between the spargers could be increased by the

same factor, reducing the number of air spargers. Reducing the overall number of air

spargers results in reducing the overall power requirement for air sparging in the system by

% 30.

When considering individual fibers, it is not possible to estimate the power transferred

because the membrane area over which the shear stress is induced by gas sparging cannot be

accurately estimated. For this reason, the RMS of the shear stress was used as a surrogate to

characterize the spatial distribution of the power transferred. The spatial distribution of shear

stress in the system tank is illustrated in Figure 4-9 and Figure 4-29 for the different sparging

conditions investigated. As observed, the distribution of shear stress in the system tank was

characterized with the highest magnitude of shear stress generally in the middle of the system

tank and gradual decrease to the sides of the system tank. As previously discussed, athough

the correlation between the RMS of the shear stress and fouling rate for individual fibers is

scattered, a lower fouling rate was consistently observed for fibers which were exposed to

higher RMS of the shear stress (Figure 6-4 and Figure 6-5). Also, as observed for the system-

wide RMS of shear stress, when considering individual fibers, for the solution filtered, when

applying more than approximately more than 1Pa, the rate of fouling was negligible.

123

6.3 Conclusion

Power transferred, which considers the combined effects of the bubble rise velocity,

the area of the zone of influence and the RMS of the shear stress could be used to accurately

characterise the relationship between the hydrodynamic conditions induced by gas sparging

and the rate of fouling observed. When sparging with discrete bubbles, the rate of fouling

remained relatively constant as the size of the sparged bubbles increased. When sparging at

an intermediate frequency of 0.25 Hz, the rate of fouling was lower than that observed when

sparging with discrete bubbles. Additionally, the rate of fouling generally decreased as the

size of the sparged bubbles increased. When sparging at the highest frequency of 0.5 Hz, the

rate of fouling was again lower than those observed at the lower frequencies. However, as

was observed for discrete bubbles, no clear trend was observed between bubble size and

fouling rate. The higher power transfer onto the membranes using pulse bubble spargers in

comparison to that using coarse bubble spargers resulted in better fouling control. This is

consistent with the claims made by commercial membrane manufacturers such as Siemens,

Samsung, and GE Water and Process Technologies and two recent studiedies [62,147]

The fouling rate was observed to be significantly affected by the power transferred.

1) At a low power transfer (< 2 watts), the fouling rates were high and decreased

linearly with an increase in the power transferred.

2) At an intermediate power transfer (2-35 watts), the incremental change in the

fouling rate decreased as the power increased.

3) At a high power transfer (> 35 watts), the fouling rate was essentially zero.

For the solution filtered in the present research, pulse sparging with small bubbles is

expected to be approximately two times more efficient than coarse bubble sparging for

fouling control. Considering that coarse bubble sparging in MBR systems accounts for over

30% of the total operating cost of these systems, the use of pulse sparging instead of coarse

sparging can reduce the overall power requirements from approximately 0.62 kWh/m3 of

permeate to less than 0.53 kWh/m3 of permeate .

For the first time it is demonstrated that the spatial distribution of the fouling rate in the

system was not homogeneous. The fouling rate generally was lower in the zone of influence

of bubbles. This observation could be explained by the non-homogeneous distribution of

124

velocity, vorticity, and shear stress in the zone of influence. Higher velocity and higher

kinetic energy in the zone of influence of sparged bubbles resulted in higher shear stress

induced onto the membranes located in the zone of influence of sparged bubbles compared to

the membranes located at the edges. Higher shear stress induced onto the membranes

resulted in a lower fouling rate (due to the increase in the rate of backtransport of the

foulants).

As the size of the bubbles was increased, the horizontal distribution of fouling was

flattened and the fouling rate decreased. The width of the relatively flat portion of the

distribution corresponded to the width of zone of influence of the sparged bubbles. The width

of the zone of influence increased with bubble size and frequency (Chapter 4), suggesting

that as the size and frequency of the bubbles increase, the spacing between the spargers could

be increased, reducing the overall number of spargers, and therefore reducing the volume of

gas required for sparging the system.

125

7 Conclusions and recommendation

7.1 Overall conclusions

The present research identified the optimum sparging conditions in terms of power

requirement for fouling control in submerged membrane systems. The investigations focused

on addressing two main questions: 1) how do the sparging approaches affect the

hydrodynamic conditions and the resulting shear stress in a membrane system, and 2) how do

the induced hydrodynamic conditions affect the rate of fouling?

The designed experimental system mimicked the hydrodynamic conditions that are

representative of full size submerged membrane systems. Direct measurement of the shear

stress induced onto membranes was made using an Electrodiffusion Method (EDM). A

procedure was developed for correction and interpretation of the data collected under

transient flow conditions (which occur in submerged membrane systems). The results of this

investigation were compiled comprehensively in a form that can be used as a reference for

future work that applies EDM in practical applications under steady state or transient

conditions. An approach was developed to measure velocity and vorticity of the liquid in the

system as well as bubble characteristics using a high speed camera, high intensity light

sources, and particle image velocimetry.

For the first time, the zone of influence and the power transferred by bubbles onto

fibers were defined as parameters that could be used to characterize the complex

hydrodynamic conditions induced under different sparging conditions. The zone of influence

was defined as the fraction of the system in which high velocities and high vorticities are

induced by the bubbles.

The velocity and the shear stress within the zones of influence of bubbles were not

homogeneously distributed. The results also indicated that the area of the zone of influence

was not only larger for larger pulse bubbles (dimonsionless zone of influence was 10 times

larger for the pulse bubbles), but also the maximum velocity and the shear stress in the zone

126

of influence were greater for larger pulse bubbles. The larger area of the zone of influence

and the larger magnitude of velocity observed for larger pulse bubbles are expected to result

in better fouling control in the system.

For the first time, the horizontal distribution of the velocity and the shear stress induced

within the zone of influence of sparged bubbles in a submerged membrane system was

characterized. The horizontal distributions of the velocity and the shear stress within the zone

of influence indicated that the maximum velocity and shear stress occurred at the vertical

centerline of the zone of influence with a rapid decrease to the side edges of the zone of

influence. The knowledge regarding the horizontal distribution of the velocity and shear

stress in the system is of importance because as it was demonstrated in the present research

that non-homogeneous distribution of the velocity and shear stress in the system induced

non-homogeneous fouling control over the width of the system tank.

Results from this investigation indicated that as the size and frequency of the bubbles

increased, the average width of the zone of influence increased. These results suggest that as

the size and frequency of the bubbles increase, the spacing between the spargers could be

increased. The latter could reduce the overall number of spargers and therefore, reducing the

volume of gas required for sparging the system.

For all cases investigated, a clear relationship was observed between the fouling rate

and the power transferred onto membranes. Fouling rate decreased consistently with an

increase in the magnitude of the power transferred onto membranes, until the fouling rate

reached a minimum above which no further improvement in fouling control was achieved.

For the solution filtered in the present research, pulse sparging with small bubbles is

expected to be approximately two times more efficient than coarse bubble sparging for

fouling control. Considering that coarse bubble sparging in MBR systems accounts for over

30% of the total operating cost of these systems, the use of pulse sparging instead of coarse

sparging can reduce the overall power requirements from approximately 0.62 kWh/m3 of

permeate to less than 0.53 kWh/m3 of permeate .

127

With the insight into the hydrodynamic conditions induced under different sparging

conditions, i.e. bubble size and frequency, (which can be obtained by using the concepts of

the zone of influence, power transfer onto membranes, and power transfer efficiency

developed in the present research) the optimal sparging conditions in submerged membrane

systems can be identified without solely relying on an empirical pilot-testing approach which

will result in significant savings in time and cost.

7.2 Engineering significance

This research addressed the knowledge gap that existed in determining the optimum

sparging conditions, i.e. bubble size and frequency, in air sparged submerged membrane

systems. For the first time, the methods developed in this research enabled the multiple

effects of sparged bubbles on the hydrodynamic conditions in submerged membrane systems

to be quantitatively characterized. The zone of influence and power transfer concepts

developed made it possible to optimize the sparging approach for fouling. Optimizing

sparging conditions can reduce power requirements for fouling control by more than 50%,

significantly reducing the operation costs of membrane systems, and making their

widespread adoption more likely. Moreover, the zone of influence could be used to design

the spacing between the spargers. Optimal spacing of spargers could reduce the volumetric

flowrate of gas required for sparging the system.

With the insight into the hydrodynamic conditions induced under different sparging

conditions (which can be obtained by using the concepts of the zone of influence, power

transfer onto membranes, and power transfer efficiency developed in the present research),

the optimal sparging conditions in submerged membrane systems can be identified without

solely relying on an empirical pilot-testing approach which will result in significant savings

in time and cost. The knowledge gained from the present research is being used by industrial

collaborators (GE Water and Process Technologies) to design their next generation of

sparging systems

128

The EDM reference manual is the first document to cover the theoretical aspects of

EDM, the practical aspects of EDM, and the limitations of EDM for practical applications.

This document can be used as a reference for application of EDM in practice under steady

state and transient conditions.

7.3 Recommendations for future work The result from this research opens the opportunity for further investigation on the items

listed below.

• The effect of packing density on the behavior of sparged bubbles and the induced

hydrodynamic conditions in a full module. Physical characteristics of bubble (size,

path, rise velocity, and etc.) may change when sparged in a packed module. This may

affect the hydrodynamic conditions induced in the system and as a result the

efficiency of sparging conditions. This is currently being investigated as part of an

independent study.

• Characterizing the hydrodynamic conditions induced in the system and the power

transfer efficiency at sparging frequencies higher than those investigated in the

present research for the small and medium pulse bubbles.

• The contribution of fiber contact or fiber sway to the magnitude and time variation of

shear stress induced on the fibers in comparison to the contribution of the turbulence

induced by sparged bubbles.

• The effect of multiple spargers or the spacing of spargers on the induced

hydrodynamic conditions. This can lead to an optimum design with minimum power

requirements.

• The relationship between solution physical and chemical characteristics and the

behavior of bubbles and the induced hydrodynamic conditions in the system. This is

of significance considering that solutions filtered in real systems generally contain

organic materials in addition to particulate matter.

• Different combinations of sparging flow rates and bubble sizes that haven’t been

studied in the present study. One of the main challenges in this research was time

constrains. PIV technique is a time consuming process that generates a great amount

129

of data to analyze. This limits the number of experiments that can be done in a

limited amount of time, for examples, the number of replicates or the number of

combinations of bubble sizes and frequencies.

130

References

[1] S. Judd and C. Judd, "MBR Book - Principles and Applications of Membrane Bioreactors for Water and Wastewater Treatment", Butterworth-Heinemann, 2nd Edition, 2011 .

[2] P. H. Hermans and H. L. Bredee, "Principles of mathematical treatment of constant-pressure filtration," Society of Chemical Industry -- Journal -- Transactions and Communications, vol. 55, pp. 1-4, 1936.

[3] V. V. Tarabara, I. Koyuncu and M. R. Wiesner, "Effect of hydrodynamics and solution ionic strength on permeate flux in cross-flow filtration: Direct experimental observation of filter cake cross-sections," J. Membr. Sci., vol. 241, pp. 65-78, 2004.

[4] A. Drews, H. Prieske, E. Meyer, G. Senger and M. Kraume, "Advantageous and detrimental effects of air sparging in membrane filtration: Bubble movement, exerted shear and particle classification," Desalination, vol. 250, pp. 1083-1086, 2010.

[5] S. Chellam and M. R. Wiesner, "Evaluation of crossflow filtration models based on shear-induced diffusion and particle adhesion: Complications induced by feed suspension polydispersivity," J. Membr. Sci., vol. 138, pp. 83-97, 1998.

[6] G. Belfort, R. H. Davis and A. L. Zydney, "The behavior of suspensions and macromolecular solutions in crossflow microfiltration," J. Membr. Sci., vol. 96, pp. 1-58, 1994.

[7] Y. P. Zhang, A. G. Fane and A. W. K. Law, "Critical flux and particle deposition of bidisperse suspensions during crossflow microfiltration," J. Membr. Sci., vol. 282, pp. 189-197, 2006.

[8] J. S. Knutsen and R. H. Davis, "Deposition of foulant particles during tangential flow filtration," J. Membr. Sci., vol. 271, pp. 101-113, 2006.

[9] P. Le-Clech, Y. Marselina, Y. Ye, R. M. Stuetz and V. Chen, "Visualisation of polysaccharide fouling on microporous membrane using different characterisation techniques," J. Membr. Sci., vol. 290, pp. 36-45, 2007.

[10] Q. Y. Li, R. Ghosh, S. R. Bellara, Z. F. Cui and D. S. Pepper, "Enhancement of ultrafiltration by gas sparging with flat sheet membrane modules," Separation and Purification Technology, vol. 14, pp. 79-83, 1998.

[11] Q. Y. Li, Z. F. Cui and D. S. Pepper, "Effect of bubble size and frequency on the permeate flux of gas sparged ultrafiltration with tubular membranes," Chem. Eng. J., vol. 67, pp. 71-75, 1997.

131

[12] A. Subramani and E. M. V. Hoek, "Direct observation of initial microbial deposition onto reverse osmosis and nanofiltration membranes," J. Membr. Sci., vol. 319, pp. 111-125, 2008.

[13] S. Kang, A. Subramani, E. M. V. Hoek, M. A. Deshusses and M. R. Matsumoto, "Direct observation of biofouling in cross-flow microfiltration: Mechanisms of deposition and release," J. Membr. Sci., vol. 244, pp. 151-165, 2004.

[14] D. Sofialidis and P. Prinos, "Wall suction effects on the structure of fully developed turbulent pipe flow," J Fluids Eng Trans ASME, vol. 118, pp. 33-39, 1996.

[15] G. S. Beavers and D. D. Joseph, "Boundary conditions at naturally permeable wall," J. Fluid Mech., vol. 30, pp. 197-207, 1967.

[16] C. Gaucher, P. Legentilhomme, P. Jaouen, J. Comiti and J. Pruvost, "Hydrodynamics study in a plane ultrafiltration module using an electrochemical method and particle image velocimetry visualization," Exp. Fluids, vol. 32, pp. 283-293, 2002.

[17] P. Velikovska, P. Legentilhomme, J. Comiti and P. Jaouen, "Suction effects on the hydrodynamics in the vicinity of an ultrafiltration plane ceramic membrane," J. Membr. Sci., vol. 240, pp. 129-139, 2004.

[18] W. D. Mores and R. H. Davis, "Direct observation of membrane cleaning via rapid backpulsing," Desalination, vol. 146, pp. 135-140, 2002.

[19] Z. F. Cui, S. Chang and A. G. Fane, "The use of gas bubbling to enhance membrane processes," J. Membr. Sci., vol. 221, pp. 1-35, 2003.

[20] S. R. Bellara, Z. F. Cui and D. S. Pepper, "Gas sparging to enhance permeate flux in ultrafiltration using hollow fibre membranes," J. Membr. Sci., vol. 121, pp. 175-184, 1996.

[21] C. Cabassud, S. Laborie and J. M. Laine, "How slug flow can improve ultrafiltration flux in organic hollow fibres," J. Membr. Sci., vol. 128, pp. 93-101, 1997.

[22] T. W. Cheng, H. M. Yeh and C. T. Gau, "Enhancement of permeate flux by gas slugs for crossflow ultrafiltration in tubular membrane module," Sep. Sci. Technol., vol. 33, pp. 2295-2309, 1998.

[23] P. R. Berube and X. Lei, "Erratum: The effect of hydrodynamic conditions and system configurations on the permeate flux in a submerged hollow fiber membrane system," J. Membr. Sci., vol. 276, pp. 308-308, 2006.

[24] Z. F. Cui and K. I. T. Wright, "Gas-liquid two-phase cross-flow ultrafiltration of BSA and dextran solutions," J. Membr. Sci., vol. 90, pp. 183-189, 1994.

132

[25] Q. Y. Li, R. Ghosh, S. R. Bellara, Z. F. Cui and D. S. Pepper, "Enhancement of ultrafiltration by gas sparging with flat sheet membrane modules," Separation and Purification Technology, vol. 14, pp. 79-83, 1998.

[26] T. Ueda, K. Hata, Y. Kikuoka and O. Seino, "Effects of aeration on suction pressure in a submerged membrane bioreactor," Water Res., vol. 31, pp. 489-494, 1997.

[27] A. Drews, "Membrane fouling in membrane bioreactors-Characterisation, contradictions, cause and cures," J. Membr. Sci., vol. 363, pp. 1-28, 2010.

[28] A. Drews, C. Lee and M. Kraume, "Membrane fouling - a review on the role of EPS," Desalination, vol. 200, pp. 186-188, 2006.

[29] P. R. Berube, G. Afonso, F. Taghipour and C. C. V. Chan, "Quantifying the shear at the surface of submerged hollow fiber membranes," J. Membr. Sci., vol. 279, pp. 495-505, 2006.

[30] N. V. Ndinisa, A. G. Fane and D. E. Wiley, "Fouling control in a submerged flat sheet membrane system: Part I - Bubbling and hydrodynamic effects," Sep. Sci. Technol., vol. 41, pp. 1383-1409, 2006.

[31] F. C. Mercier M. and C. Lafforgue-Delorme, "Influence of the flow regime on the efficiency of a gas-liquid two-phase medium filtration. Biotechnology Techniques," vol. 9, pp. 853, 1995.

[32] F. C. Mercier M. and C. Lafforgue-Delorme, "How slug flow can enhance the ltrafiltration flux in mineral tubular membranes." Journal of Membrane Science, vol. 128, pp. 103, 1997.

[33] C. Cabassud, S. Laborie, L. Durand-Bourlier and J. M. Laine, "Air sparging in ultrafiltration hollow fibers: Relationship between flux enhancement, cake characteristics and hydrodynamic parameters," in 2001, pp. 57-69.

[34] L. Vera, S. Delgado and S. Elmaleh, "Gas sparged cross-flow microfiltration of biologically treated wastewater," in 2nd International Conference on 'Membrane Technology in Environmental Management', November 1, 1999 - November 4, 2000, pp. 173-180.

[35] S. R. Smith, Z. F. Cui and R. W. Field, "Upper- and lower-bound estimates of flux for gas-sparged ultrafiltration with hollow fiber membranes," Industrial and Engineering Chemistry Research, vol. 44, pp. 7684-7695, 2005.

[36] A. P. S. Yeo, A. W. K. Law and A. G. Fane, "Factors affecting the performance of a submerged hollow fiber bundle," J. Membr. Sci., vol. 280, pp. 969-982, 2006.

133

[37] H. Nagaoka, A. Tanaka and Y. Toriizuka, "Measurement of effective shear stress working on flat-sheet membrane by air-scrabbling," in 2003, pp. 423-428.

[38] C. C. V. Chan, P. R. Berube and E. R. Hall, "Shear profiles inside gas sparged submerged hollow fiber membrane modules," J. Membr. Sci., vol. 297, pp. 104-120, 2007.

[39] O. Le Berre and G. Daufin, "Skimmilk crossflow microfiltration performance versus permeation flux to wall shear stress ratio," J. Membr. Sci., vol. 117, pp. 261-270, 1996.

[40] O. Al Akoum, "An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module. Journal of Membrane Science," vol. 197, pp. 37, 2002.

[41] G. Ducom, F. P. Puech and C. Cabassud, "Air sparging with flat sheet nanofiltration: A link between wall shear stresses and flux enhancement," Desalination, vol. 145, pp. 97-102, 2002.

[42] S. K. Sayed Razavi and J. L. Harris, "Shear controlled model of the ultrafiltration of soy suspensions," J. Membr. Sci., vol. 118, pp. 279-288, 1996.

[43] C. M. Silva, "Model for flux prediction in high-shear microfiltration systems. Journal of Membrane Science," vol. 173, pp. 87, 2000.

[44] J. Busch, A. Cruse and W. Marquardt, "Modeling submerged hollow-fiber membrane filtration for wastewater treatment," J. Membr. Sci., vol. 288, pp. 94-111, 2007.

[45] S. Chang and A. G. Fane, "Characteristics of microfiltration of suspensions with inter-fiber two-phase flow," Journal of Chemical Technology and Biotechnology, vol. 75, pp. 533-540, 2000.

[46] B. G. Fulton, J. Redwood, M. Tourais and P. R. Berube, "Distribution of surface shear forces and bubble characteristics in full-scale gas sparged submerged hollow fiber membrane modules," Desalination, vol. 281, pp. 128-141, 2011.

[47] C. C. V. Chan, P. R. Berube and E. R. Hall, "Shear profiles inside gas sparged submerged hollow fiber membrane modules," J. Membr. Sci., vol. 297, pp. 104-120, 2007.

[48] C. C. V. Chan, P. R. Berube and E. R. Hall, " An investigation of the hydrodynamic conditions inside a submerged membrane module under aeration." British Columbia Water and Wastewater Association Annual General Meeting,Whistler, British Columbia., 2006.

[49] C. C. V. Chan, "An investigation of hydrodynamic conditions inside gas-sparged hollow fiber membrane modules," Dissertation, Doctor of Philosophy, University of British Columbia, 2010.

134

[50] C. C. V. Chan, P. R. Bérubé and E. R. Hall, "Shear profiles inside gas sparged submerged hollow fiber membrane modules," J. Membr. Sci., vol. 297, pp. 104, 2007.

[51] S. Chang and A. G. Fane, "Filtration of biomass with laboratory-scale submerged hollow fibre modules - Effect of operating conditions and module configuration," Journal of Chemical Technology and Biotechnology, vol. 77, pp. 1030-1038, 2002.

[52] P. R. Berube and E. Lei, "The effect of hydrodynamic conditions and system configurations on the permeate flux in a submerged hollow fiber membrane system," J. Membr. Sci., vol. 271, pp. 29-37, 2006.

[53] C. C. V. Chan, P. R. Berube and E. R. Hall, "Shear stress at radial positions of submerged hollow fiber under gas sparging, and the effects of physical contact between fibers on shear profiles," in 2007 Membrane Technology Conference and Exposition, March 18, 2007 - March 21, 2007, .

[54] N. Ratkovich, C. C. V. Chan, P. R. Berube and I. Nopens, "Analysis of shear stress and energy consumption in a tubular airlift membrane system," Water Science and Technology, vol. 64, pp. 189-198, 2011.

[55] R. Ghosh and Z. F. Cui, "Mass transfer in gas-sparged ultrafiltration: Upward slug flow in tubular membranes," J. Membr. Sci., vol. 162, pp. 91-102, 1999.

[56] N. Liu, Q. Zhang, G. Chin, E. Ong, J. Lou, C. Kang, W. Liu and E. Jordan, "Experimental investigation of hydrodynamic behavior in a real membrane bio-reactor unit," J. Membr. Sci., vol. 353, pp. 122-134, 2010.

[57] S. Chang and A. G. Fane, "Filtration of biomass with axial inter-fibre upward slug flow: Performance and mechanisms," J. Membr. Sci., vol. 180, pp. 57-68, 2000.

[58] A. P. S. Yeo, A. W. K. Law and A. G. (. Fane, "The relationship between performance of submerged hollow fibers and bubble-induced phenomena examined by particle image velocimetry," J. Membr. Sci., vol. 304, pp. 125-137, 2007.

[59] A. Sofia, W. J. Ng and S. L. Ong, "Engineering design approaches for minimum fouling in submerged MBR," Desalination, vol. 160, pp. 67-74, 2004.

[60] F. Wicaksana, A. G. Fan and V. Chen, "The relationship between critical flux and fibre movement induced by bubbling in a submerged hollow fibre system," Water Science and Technology, vol. 51, pp. 115-122, 2005.

[61] F. Wicaksana, A. G. Fane and V. Chen, "Fibre movement induced by bubbling using submerged hollow fibre membranes," J. Membr. Sci., vol. 271, pp. 186-195, 2006.

135

[62] D. Ye, "Shear stress and fouling control in hollow fiber membrane systems under different gas sparging conditions," Thesis, Master of Applied Science, University of British Columbia, 2012.

[63] E. H. Bouhabila, R. B. Aim and H. Buisson, "Microfiltration of activated sludge using submerged membrane with air bubbling (application to wastewater treatment)," Desalination, vol. 118, pp. 315-322, 1998.

[64] Y. Marselina, P. Le-Clech, R. Stuetz and V. Chen, "Detailed characterisation of fouling deposition and removal on a hollow fibre membrane by direct observation technique," Desalination, vol. 231, pp. 3-11, 2008.

[65] N. Brauner, "On the frequency response of wall transfer probes," Int. J. Heat Mass Transfer, vol. 34, pp. 2641-2652, 1991.

[66] G. FORTUNA and T. J. HANRATTY, "Frequency response of the boundary layer on wall transfer probes," Int. J. Heat Mass Transfer, vol. 14, pp. 1499-1507, 1971.

[67] J. Pallares and F. X. Grau, "Frequency response of an electrochemical probe to the wall shear stress fluctuations of a turbulent channel flow," Int. J. Heat Mass Transfer, vol. 51, pp. 4753-4758, 2008.

[68] L. Talbot and J. J. Steinert, "Frequency Response of Electrochemical Wall Shear Probes in Pulsative Flow," J. Biomech. Eng., vol. 109, pp. 60-64, 1987.

[69] L. Martinelli, C. Guigui and A. Line, "Experimental analysis of mechanisms induced by a spherical cap bubble injection in submerged hollow-fibre bioreactor," Desalination, vol. 200, pp. 720-721, 2006.

[70] X. Yang, C. Shang and P. Westerhoff, "Factors affecting formation of haloacetonitriles, haloketones, chloropicrin and cyanogen halides during chloramination," Water Res., vol. 41, pp. 1193-1200, 2007.

[71] M. Gimmelshtein and R. Semiat, "Investigation of flow next to membrane walls," J. Membr. Sci., vol. 264, pp. 137-150, 2005.

[72] J. E. Mitchell and T. J. Hanratty, "A study of turbulence at a wall using an electrochemical wall shear-stress meter," J. Fluid Mech., vol. 26, pp. 199-221, 1966.

[73] V. Sobolik, J. Tihon, O. Wein and K. Wichterle, "Calibration of electrodiffusion friction probes using a voltage-step transient," J. Appl. Electrochem., vol. 28, pp. 329-335, 1998.

[74] M. Raffel, C. Willert, S. Wereley and J. Kompenhans, Particle Image Velocimetry: A Practical Guide. 2007.

136

[75] Clift, R., Grace, J.R., and Weber, M.E., Bubbles, Drops and Particles. Mineola, New York: Dover Publication Inc., 2005.

[76] J. R. Landel, C. Cossu, and C. P. Caulfield, "Spherical cap bubbles with a toroidal bubbly wake," Phys. Fluids, vol. 20, pp. 122101, 2008.

[77] Wegener, P.P., and Parlange, J., "Spherical Cap bubbles," Annu. Rev. Fluid Mech., vol. 5, pp. 100, 1973.

[78] I. Komasawa, T. Otake and M. Kamojima, " Wake behavior and its effect on interaction between spherical cap bubbles," Journal of Chemical Engineering of Japan, vol. 13, pp. 103-109, 1980.

[79] C. Gaucher, P. Legentilhomme, P. Jaouen and J. Comiti, "Influence of Fluid Distribution on the Wall Shear Stress in a Plane Ultrafiltration Module Using an Electrochemical Method," Chem.Eng.Res.Des., vol. 80, pp. 111, 2002.

[80] C. Gaucher, P. Jaouen, P. Legentilhomme and J. Comiti, "Suction effect on the shear stress at a plane ultrafiltration ceramic membrane surface," Sep. Sci. Technol., vol. 37, pp. 2251-2270, 2002.

[81] D. Bhaga and M. E. Weber, "In line interaction of a pair of bubbles in a viscous liquid, Chemical Engineering Science," vol. 35, pp. 2467-2474, 1980.

[82] R. W. Fox, Fox and McDonald's Introduction to Fluid Mechanics. Hoboken, NJ: John Wiley & Sons, 2011.

[83] D. C. Wilcox, Turbulence Modeling for CFD. La Cãnada, Calif.: DCW Industries, 2006.

[84] P. A. A. Davidson, Turbulence :An Introduction for Scientists and Engineers. Oxford, UK ;New York : Oxford University Press, 2004.

[85] W. Fan, Y. Ma, X. Li and H. Li, "Study on the Flow Field around Two Parallel Moving Bubbles and Interaction Between Bubbles Rising in CMC Solutions by PIV," FLUID FLOW AND TRANSPORT PHENOMENA, Chinese Journal of Chemical Engineering, vol. 17, pp. 904-913, 2009.

[86] A. B. Tayler, D. J. Holland, A. J. Sederman and L. F. Gladden, "Exploring the origins of turbulence in multiphase flow using compressed sensing MRI," Phys. Rev. Lett., vol. 108, 2012.

[87] W. L. Shew and J. Pinton, "Dynamical model of bubble path instability," Phys. Rev. Lett., vol. 97, 2006.

137

[88] G. Tchobanoglous, F. Burton and H. D. Stensel, Eds., Wastewater Engineering :Treatment and Reuse /Metcalf & Eddy, Inc. Boston: McGraw-Hill, .

[89] R. W. Field and P. Aimar, "Ideal limiting fluxes in ultrafiltration: Comparison of various theoretical relationships," in International Conference on Engineering of Membrane Processes, may 13, 1992 - may 15, 1993, pp. 107-115.

[90] L. Xia, A. W. Law, C. Ma and A. G. Fane, "Air sparging on hollow fiber membranes in a bubble column reactor," in AWWA/AMTA Membrane Technology Conference and Exposition 2012, February 27, 2012 - March 1, 2012, pp. 817-822.

[91] W. Nitsche and A. Brunn, Strömungsmesstechnik (in German). Springer, 2006.

[92] T. J. Hanratty and J. A. Campbell, "Fluid mechanics measurement," in , R. Goldstein, Ed. Springer Berlin, 1996, pp. 575-648.

[93] J. H. Haritonidis, "Advances in fluid mechanics measurements," in , M. Gad-el-Hak, Ed. Springer Berlin, 1989, pp. 229-261.

[94] T. Mizushina, "The electrochemical method in transport phenomena," in Advances in Heat TransferAnonymous Elsevier, 1971, pp. 87.

[95] J. R. Selman and C. W. Tobias, "Mass-transfer measurements by the limiting-current technique," in Advances in Chemical EngineeringAnonymous Academic Press, 1978, pp. 211.

[96] T. J. Hanratty, "Use of the polarographic method to measure wall shear stress," J. Appl. Electrochem., vol. 21, pp. 1038-1046, 1991.

[97] D. A. Szánto, S. Cleghorn, C. Ponce-de-León and F. C. Walsh, "The limiting current for reduction of ferricyanide ion at nickel: The importance of experimental conditions," AICHE J., vol. 54, pp. 802-810, 2008.

[98] A. Etebari, "Recent Innovations in Wall Shear Stress Sensor Technologies," Recent Patents on Mechanical Engineering, vol. 1, pp. 22-28, January, 2008.

[99] W. Nitsche, P. Mirow and J. Szodruch, "Piezo-electric foils as a means of sensing unsteady surface forces," Exp. Fluids, vol. 7, pp. 111-118, 1989.

[100] J. Domhardt, I. Peltzer and W. Nitsche, "Measurement of distributed unsteady surface pressures by means of piezoelectric copolymer coating," in Imaging Measurement Methods for Flow AnalysisAnonymous Springer Berlin / Heidelberg, 2009, pp. 217-226.

138

[101] C. Dobriloff and W. Nitsche, "Surface pressure and wall shear stress measurements on a wall mounted cylinder," in Imaging Measurement Methods for Flow Analysis, W. Nitsche and C. Dobriloff, Eds. Springer Berlin / Heidelberg, 2009, pp. 197-206.

[102] J. H. Preston, "The determination of turbulent skin friction by means of Pitot tubes," J.Royaero.Soc, vol. 58, pp. 109-121, 1954.

[103] V. C. Patel, "Calibration of the Preston tube and limitations on its use in pressure gradients," J. Fluid Mech., vol. 23, pp. 185-208, 1965.

[104] H. H. Bruun, Hot-Wire Anemometry: Principles and Signal Analysis. Oxford University Press, 1995.

[105] R. Mayer, R. A. W. M. Henkes and J. L. v. Ingen, "Quantitative infrared-thermography for wall-shear stress measurement in laminar flow," Int. J. Heat Mass Transfer, vol. 41, pp. 2347-2356, 1998.

[106] F. Kost and C. Kapteijn, "Application of laser-two-focus velocimetry to transonic turbine flows," in Proc. 7th International Conference on Laser Anemometry-Advances and Applications, University of Karlsruhe, Germany, 1997, .

[107] N. Nishizawa, I. Marusic, A. Perry and H. Hornung, "Measurement of wall shear stress in turbulent boundary layers using an optical interferometry method," in 13th Australian Fluid Mechanics Conference, 1998, .

[108] D. K. Heist and I. P. Castro, "Point measurement of turbulence quantities in separated flows - a comparison of techniques," Meas Sci Technol, vol. 7, pp. 1444-1450, 1996.

[109] F. J. H. Gijsen, A. Goijaerts, F. N. van de Vosse and J. D. Janssen, "A new method to determine wall shear stress distribution," J. Rheol., vol. 41, pp. 995-1006, Sep-Oct, 1997.

[110] C. Poelma, K. Van der Heiden, B. P. Hierck, R. E. Poelmann and J. Westerweel, "Measurements of the wall shear stress distribution in the outflow tract of an embryonic chicken heart," J.R.Soc.Interface, vol. 7, pp. 91-103, 2010.

[111] N. Fujisawa, Y. Oguma and T. Nakano, "Measurements of wall-shear-stress distribution on an NACA0018 airfoil by liquid-crystal coating and near-wall particle image velocimetry (PIV)," Meas Sci Technol, vol. 20, pp. 065403, 2009.

[112] L. P. Reiss and T. J. Hanratty, "Measurement of instantaneous rates of mass transfer to a small sink on a wall," AICHE J., vol. 8, pp. 245-247, 1962.

[113] G. Cognet, M. Lebouche and M. Souhar, "Wall shear measurements by electrochemical probe for gas-liquid two-phase flow in vertical duct," AICHE J., vol. 30, pp. 338-341, 1984.

139

[114] V. Sobolik, J. Tihon, J. Pauli and U. Onken, "Sensitivity of three-segment electrodiffusion probes to eddy shedding," Exp. Fluids, vol. 16, pp. 368-374, 1994.

[115] O. Wein, "Autocalibration of electrodiffusion friction probes in microdispersion liquids," Int. J. Heat Mass Transfer, vol. 53, pp. 1874-1881, 2010.

[116] A. J. Arvía, J. C. Bazán and J. S. W. Carrozza, "The diffusion of ferro- and ferricyanide ions in aqueous potassium chloride solutions and in solutions containing carboxy-methylcellulose sodium salt," Electrochim. Acta, vol. 13, pp. 81, 1968.

[117] E. Eroglu, S. Yapici and O. N. Sara, "Some Transport Properties of Potassium Ferri/Ferro-Cyanide Solutions in a Wide Range of Schmidt Numbers," J. Chem. Eng. Data, vol. 56, pp. 3312-3317, 2011.

[118] J. Legrand, E. Dumont, J. Comiti and F. Fayolle, "Diffusion coefficients of ferricyanide ions in polymeric solutions -- comparison of different experimental methods," Electrochim. Acta, vol. 45, pp. 1791, 2000.

[119] J. S. Newman and K. E. Thomas-Alyea, Electrochemical Systems. Wiley Hoboken, NJ, 2004.

[120] V. M. Schmidt, Elektrochemische Verfahrenstechnik (in German). Wiley-VCH, 2003.

[121] G. Ducom, F. -. Puech and C. Cabassud, "Gas/Liquid Two-phase Flow in a Flat Sheet Filtration Module: Measurement of Local Wall Shear Stresses," Can. J. Chem. Eng., vol. 81, pp. 771-775, 2003.

[122] C. C. V. Chan, P. R. Berube and E. R. Hall, "Shear profiles inside gas sparged submerged hollow fiber membrane modules," J. Membr. Sci., vol. 297, pp. 104-120, 2007.

[123] J. Tihon, V. Tovchigrechko, V. Sobolik and O. Wein, "Electrodiffusion detection of the near-wall flow reversal in liquid films at the regime of solitary waves," J. Appl. Electrochem., vol. 33, pp. 577-587, 2003.

[124] J. Tihon, "Electrodiffusion diagnostics of the near-wall flows," Chem.Pap.- Chem.Zvesti, vol. 56, pp. 45-51, 2002.

[125] C. Gaucher, P. Jaouen, J. Comiti and P. Legentilhomme, "Determination of cake thickness and porosity during cross-flow ultrafiltration on a plane ceramic membrane surface using an electrochemical method," J. Membr. Sci., vol. 210, pp. 245, 2002.

[126] L. P. Reiss and T. J. Hanratty, "An experimental study of the unsteady nature of the viscous sublayer," AICHE J., vol. 9, pp. 154-160, 1963.

140

[127] J. Tihon, J. Legrand, H. Aouabed and P. Legentilhomme, "Dynamics of electrodiffusion probes in developing annular flows," Exp. Fluids, vol. 20, pp. 131-134, 1995.

[128] Z. -. Mao and T. J. Hanratty, "The use of scalar transport probes to measure wall shear stress in a flow with imposed oscillations," Exp. Fluids, vol. 3, pp. 129-135, 1985.

[129] V. Sobolík, S. Martemyanov and G. Cognet, "Study of mass transfer in viscoelastic liquids by segmented electrodiffusion velocity probes," J. Appl. Electrochem., vol. 24, pp. 632-638, 1994.

[130] S. Pannek, J. Pauli and U. Onken, "Determination of local hydrodynamic parameters in bubble columns by the electrodiffusion method with oxygen as depolarizer," J. Appl. Electrochem., vol. 24, pp. 666-669, 1994.

[131] M. Lighthill, "Contributions to the theory of heat transfer through a laminar boundary layer," Proc.R.Soc.London, Sera, vol. 202, pp. 359-377, 1950.

[132] D. J. Pickett, Electrochemical Reactor Design. Elsevier Publishing Company, 1979.

[133] A. Acrivos, "Solution of the laminar boundary layer energy equation at high prandtl numbers," Phys. Fluids, vol. 3, pp. 657-658, 1960.

[134] H. G. Dimopoulos and T. J. Hanratty, "Velocity gradients at the wall for flow around a cylinder for Reynolds numbers between 60 and 360," J. Fluid Mech., vol. 33, pp. 303-319, 1968.

[135] W. K. Lewis and W. G. Whitman, "Principles of Gas Absorption." Ind.Eng.Chem., vol. 16, pp. 1215-1220, 1924.

[136] M. Kraume, Transportvorg\ange in Der Verfahrenstechnik (in German). Springer, 2012.

[137] L. Böhm, A. Drews and M. Kraume, "Bubble induced shear stress in flat sheet membrane systems - Serial examination of single bubble experiments with the electrodiffusion method," J. Membr. Sci., vol. 437, pp. 131-140, 2013.

[138] R. Higbie, The Rate of Absorption of a Pure Gas into Still Liquid during Short Periods of Exposure. The University of Michigan, 1935.

[139] J. Crank, The Mathematics of Diffusion. Clarendon Press, 1975.

[140] O. Wein, "Convective diffusion from convex microprobes into colloidal suspensions: The edge effects," Int. J. Heat Mass Transfer, vol. 53, pp. 1868, 2010.

141

[141] O. Wein, V. V. Tovcigrecko and V. Sobolik, "Transient convective diffusion to a circular sink at finite Peclet number," Int. J. Heat Mass Transfer, vol. 49, pp. 4596, 2006.

[142] P. Kaiping, "Unsteady forced convective heat transfer from a hot film in non-reversing and reversing shear flow," Int. J. Heat Mass Transfer, vol. 26, pp. 545, 1983.

[143] V. Sobolik, O. Wein and J. Cermak, "Simultaneous measurement of film thickness and wall shear-stress in wavy flow of non-newtonian liquids," Collect. Czech. Chem. Commun., vol. 52, pp. 913-928, 1987.

[144] D. M. Wang and J. M. Tarbell, "An approximate solution for the dynamic response of wall transfer probes," Int. J. Heat Mass Transfer, vol. 36, pp. 4341, 1993.

[145] F. Rehimi, F. Aloui, S. B. Nasrallah, L. Doubliez and J. Legrand, "Inverse method for electrodiffusional diagnostics of flows," Int. J. Heat Mass Transfer, vol. 49, pp. 1242, 2006.

[146] R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory. New York, NY, USA: Springer-Verlag New York, Inc, 1991.

[147] H. Wray, A. Robert, and P.R. Bérubé, “Surface shear stress and membrane fouling when considering natural water matrices”, Desalination, vol 330, pp 22-27, 2013

142

APPENDIX A Calibration of the electrochemical shear probes

Electrochemical shear probes were fixed vertically in the middle of a cylinder with internal

radius of r0=0.025m as illustrated in Figure A.1. The magnitude of shear stress induced onto the

test fiber under a laminar flow condition was calculated analytically using Equations A.1 to A.5.

Figure A.1 Experimental set up used for calibration of the probes

143

𝑢(𝑟) = 14𝜇

𝑑𝑝𝑑𝑥�𝑟2 − 𝑟02 + �𝑟02−𝑟12�

ln�𝑟𝑖𝑟0�

ln � 𝑟𝑟0�� (A.1)

𝑄 = ∫ 𝑢(𝑟)2𝜋𝑟𝑑𝑟𝑟2𝑟1

(A.2)

𝑄 = − 𝜋8𝜇�𝑑𝑃𝑑𝑧

+ 𝜌𝑔� �𝑟04 − 𝑟𝑖4 −�𝑟02−𝑟𝑖

2�2

ln�𝑟0𝑟1�� (A.3)

𝛾 = 𝜕𝑉𝑧𝜕𝑟

(A.4)

𝛾𝑡ℎ𝑒𝑜 = − 2𝑄𝜋

�2𝑟+

𝑟𝑖2−𝑟0

2

ln�𝑟0𝑟𝑖�𝑟�

�𝑟04−𝑟𝑖4−

�𝑟02−𝑟𝑖

2�2

ln�𝑟0𝑟𝑖��

(A.5)

where r corresponds to radius; ri= 0.0018m, radius of fibers; ro= 0.025m, radius of the

cylinder; u(r) :velocity at any given r [m/s]; p: pressure; Q: liquid flow rate [m3/s]; and γ : shear

rate [1/s]. Using the electrochemical shear probes installed onto the fibers and the EDM method,

the current induced in the system was measured using Equation A.6.

𝐼𝑒𝑥𝑝 = 𝑉𝑒𝑥𝑝𝑅×𝐴

(A.6)

where Iexp corresponds to current measured in the system[A] ; Vexp, to voltage [volts] ; R,

to resistance of the resister in the circuit, i.e100 ohms, and A,to amplification (1000). Using the

theoretical Leveque Equation for steady state conditions (Equation E.7), Klev_theo is calculated as

illustrated in Equation A.8.

𝐼 = 0.862 𝑛𝐴𝐹𝑐𝑏𝐷23� 𝑑−1 3� 𝛾1 3� (A.7)

𝐾𝑙𝑒𝑣_𝑡ℎ𝑒𝑜 = 0.862 𝑛𝐴𝐹𝑐𝑏𝐷23� 𝑑−1 3� (A.8)

Using Equation (A.6) and (A.8) Klev_exp can be calculated as in Equation A.9.

𝐾𝑙𝑒𝑣_𝑒𝑥𝑝 = 𝐼𝑒𝑥𝑝𝛾𝑡ℎ𝑒𝑜13�

(A.9)

Using Equation (A.9) and (A.8) correction factor for each probe is calculated as follows:

144

𝑐𝑜𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 = 𝐾𝑙𝑒𝑣_𝑒𝑥𝑝

𝐾𝑙𝑒𝑣_𝑡ℎ𝑒𝑜 (A.10)

Correction factors for the four probes used in this study are summarized in Table A.1.

Table A. 0-1 Calibration parameters

Probe 1 Probe 2 Probe 2 Probe 3

I analytical [A] 2.39E-06 2.39E-06 2.39E-06 2.39E-06

V analytical [V] 0.23904198 0.23904198 0.23904198 0.23904198

V measured [V] 0.303 0.347 0.314 0.345

alpha 0.79 0.69 0.76 0.69

C correction factor 4.44 2.94 4 3.11

t0 [s] 1.2 4.06E-01 5.52E-01 1.67E-01

145

Appendix B Application of the electrodiffusion method (EDM) to measure

wall shear stress: integrating theory and practice

B-1 Introduction

This chapter describes the research done on integrating the theory and application of the

electrodiffusion method for measurements of shear stress at the membranes under transient flow

conditions.

Various techniques have been developed for the measurement of wall shear stress by

mechanical, thermal, optical or chemical methods (see Table 3.1). In general, these techniques

are non-intrusive at a macro scale and relatively complex data processing is required to obtain

shear stress values from the measured parameter (for more information about the different

techniques see also [91-93].

Of the measurement techniques listed in Table B.1, the electrodiffusion method (EDM) is

of particular interest due to its high sensitivity to near-wall flow fluctuations and its ability to

detect local flow phenomena that appear only on small areas. Extensive literature exists on the

EDM technique. Major Reviews of the techniques focussing on different aspects of the technique

have been published by [94-97] but none of these present the derivations of the underlying

theory and the correction necessary for transient flows. To address this gap, the present reference

document is developed. The theoretical assumptions and hypotheses used in developing the

equations that are used in the post-processing to calculate the shear stress under transient

conditions are reviewed in detail. The calibration and correction methods for the data collected

under transient conditions are optimized. Challenges regarding the calibration of this technique

and the care that must be taken before using the technique are also discussed.

146

Table B-1 Shear stress measurement techniques sorted by their measurement principle

Type Principle Measured

Parameter

Exemplary

Publication

Micro

Electromechanical

Sensor

mechanical /

thermal / optical

shear stress /

temperature / particle

movement

[98]

Piezo foils mechanical pressure [99]

Pressure

sensitive copolymers mechanical pressure [100]

Pressure

transducer mechanical pressure [101]

Preston pipe mechanical pressure [102]

Shear force scale mechanical pressure [37]

Surface fence

cathode mechanical pressure [103]

Hot wire/film

anemometry thermal temperature [104]

Infrared

thermography thermal temperature [105]

Laser-2-focus

anemometry optical

particle

movement [106]

Laser-oil-film

interferometry optical oil film slope [107]

Laser Doppler

Anemometry optical

particle

movement [108]

Laser Speckle

Anemometry optical

particle

movement [109]

Particle Image

Velocimetry optical

particle

movement [110]]

Liquid crystal chemical molecular

changes [111]

Electrodiffusion

Method chemical mass transfer [112]

147

B.2 Electrodiffusion Method (EDM): theory

For measurement of shear stress with the EDM two electrodes and an electrolytic solution

are necessary when a voltage is applied between the cathode and the anode, a heterogeneous

reaction takes place at the electrodes. The transfer of the reducing ions to the cathode and the

electron exchange leads to charge equalization between anode and cathode which induces a

measurable current. The stronger the mass transfers of the ions, the higher the measured value of

the current. Because the rate of mass transfer of ions at the cathode is directly related to the

hydrodynamic conditions at the proximity of the cathode in the system which are governed by

local shear stress, the magnitude of current induced at the cathode can be used to measure the

magnitude of shear stress.

B.2.1 The basic electrical circuit

Reiss and Hanratty [112] show the basic electrical circuit of an EDM system. The signal is

amplified and an ohmic resistance is used in the circuit (about 100 Ω). This should be two orders

of magnitude higher than the ohmic resistance of the electrochemical system so that the latter

one does not affect the signal.

B.2.2 The electrodes

Both circular [73] and rectangular strip [96] cathodes have been used. Platinum or Nickel

is often used as anode and cathode material (see e.g. [112] and [29]). Application of stainless

steel as an anode has also been reported [49]. The cathode has to be very small in contrast to the

anode which needs to have a much larger surface area so that the oxidizing reaction is not

limiting the process.

By installing two or more cathodes each with its own circuit with a very small distance

from each other in the flow it is possible to determine the direction of the flow [72, 92, 113,

114]. Having multiple cathodes very close to each other in the flow, the concentration boundary

layer of the upstream cathode influences the concentration boundary layer formed on the

downstream flow and therefore the signal measured by the downstream cathode is smaller than

the signal measured by the upstream cathode. Using a two segmented cathodes, which is most

common in literature, the direction can only be obtained in a range of 0 to 180° relative to the

alignment axis of the cathode. Using a multi-segmented cathode with proper calibration (the

148

measurement of the all signals in a defined flow while turning the combination of cathodes to

defined angles) both the direction and the shear rate can be determined quantitatively [114].

B.2.3 The electrolytic solution

There are various combinations of electrolytes mentioned in literature (Table B.2). For

most of these solutions, ferri- and ferrocyanide are used as oxidizing and reducing ions. The

reaction that takes place at the cathode is:

( ) ( ) 46

36

−−− →+ CNFeeCNFe

Oxygen existing in the system can cause side reactions and influence the induced current.

Therefore, oxygen should be purged from the used deionized water.

An inert electrolyte needs to be added to the solution to avoid electrical migration.

Potassium compounds are the most commonly used electrolyte. As one example, potassium

sulphate has the additional beneficial effect, that it can also suppress the solubility of oxygen in

the solution [115] and therefore it is commonly used in cases of long usage of the solution to

ensure, no side reactions with oxygen occurs.

As the EDM is based on mass transfer, the diffusion coefficient which is a function of the

temperature is of interest. The Stokes-Einstein relationship, i.e. .constTD =µ , is valid for

solutions with a viscosity similar to that of water [95, 116]. Values of the diffusion coefficient

and viscosity of the electrolyte solution at 30°C have been reported to be 8.36*10-10 m2/s and

8.33*10-4 Pa s, respectively [16, 117]. The viscosity of the electrolyte solution at 20°C is

comparable to that of pure water, i.e sPa10 3−=µ . According to the Stokes-Einstein Equation

mentioned above, for a temperature of 25°C, the diffusion coefficient then has a value of 7.4*10-

10m²/s. Other Equations have to be used for high viscosity or non-Newtonian liquids [118].

B.2.4 Limiting diffusion current

For measurement of wall shear stress using the EDM, a threshold for the applied voltage

exists at which the rate of reaction of oxidizing ions at the cathode is a function of the mass

transfer of the ions and is not limited by the number of electrons available at the cathode. This

well-known effect is often described by polarization curves in electrochemistry [92, 94, 119,

120]. The plateau in these curves indicates the limiting current conditions and the current

149

measure is called the limiting diffusion current [73, 112]. This range of limiting current

conditions should be obtained for each investigated electrochemical system.

Table B-2 Materials used in literature for the electrolytic solution

Publica

tion Electrolyte [M] Comment

[113,

116]

Potassium ferricyanide 0,0028-0,01 equimolar

Potassium ferrocyanide 0,0028-0,01

Potassium chloride 1

[41, 121, 122]

Potassium ferricyanide 0,003

Potassium ferrocyanide 0,006

Potassium chloride 0,3-0,33

[73, 114, 118,

123, 124]

Potassium ferricyanide 0,003-0,025 equimolar

Potassium ferrocyanide 0,003-0,025

Potassium sulfate 0,057-0,25

[79, 80, 125]

Potassium ferricyanide 0,002-0,004

Potassium ferrocyanide 0,05

Potassium sulfate 0,1

[72, 126]

Potassium ferricyanide 0,01 equimolar

Potassium ferrocyanide 0,01

Sodium hydroxide 2

[127]

Potassium ferricyanide 0,02

Potassium ferrocyanide 0,05

Sodium hydroxide 0,5

[128, 129] Iode 0,0038

Potassium iodide 0,1

[130] Oxygen 9.5-97*10-4

Potassium sulfate 0,01

150

B.2.5 Steady state flow conditions

A theoretical relationship can be derived to calculate the magnitude of wall shear stress

from the magnitude of current measured by EDM when the following conditions apply [92]:

- The concentration boundary layer at the cathode is within the region where the

velocity gradient is linear.

- The flow is homogeneous over the cathode.

- The concentration boundary layer thickness at the cathode is thin compared to the

width of the electrode.

- Diffusion in the direction of the bulk convective flow in negligible at the cathode.

- Flow normal to the surface of the cathode is negligible.

- The reacting ion is completely consumed at the cathode.

- No reaction happens in the bulk of the electrolyte solution.

- Steady state conditions are apparent.

The Planck-Nernst-Equation can be used to describe the specific molar flux of ions at the

cathode based on diffusion, migration and convection (Equation (B.1) and (B.2)).

conv,imigr,idiff,ii nnnn ++= (B.1)

vccucDn iiiiii

+ϕ∇−∇−= . (B.2)

If the conditions listed above are negligible and the specific conductivity of the solution is

high, the electrical potential gradient is negligible. Assuming no-slip conditions at the surface of

the cathode, the Planck-Nernst-relationship can be simplified as presented in Equation (B.3):

0y

iii dy

dcDn

=

−= (B.3)

Because the mass flux of ions at the cathode results from reduction, Equation (B.3) can be

equated to Faraday’s law, yielding Equation (B.4). Assuming limiting current conditions are

applied, this is equal to the product of the mass transfer and the concentration in the bulk

solution.

bm0y

ii ck

dydc

DFAn

I=

−=

=

. (B.4)

151

In Equation (B.4), the concentration gradient as well as the mass transfer coefficient is

unknown. To find a describing Equation for the concentration gradient, the general mass balance

with the conditions described above can be used which yields in Equation (B.5) [72, 73, 131-

134].

2

2

yx yc

Dyc

vxc

v∂∂

=

∂∂

+∂∂

(B.5)

Keeping in mind that the actual goal is to determine the wall shear stress, the velocity

terms vx and vy in Equation (B.5) are the relation to Newton’s law for viscosity. For the relatively

high Schmidt numbers typically found in aqueous solutions (1500-2000), as mentioned above the

velocity profile can be assumed to have a linear slope in the concentration boundary layer, and

therefore can be defined using the relationship presented in Equation (B.6). Note that the

assumption of linearity is valid regardless of the flow regime for relatively high Schmidt

numbers.

y)x(yyv

v xx γ=

∂∂

= (B.6)

Assuming no dependency in the z-direction, i.e. no flow normal to the cathode, Equation

(B.6) can be substituted into the continuity Equation yielding the relationship for vy presented in

Equation (B.7)

2y y

x)x(

21

v∂γ∂

−= (B.7)

Substituting Equation (B.6) and (B.7) in Equation (B.5) and applying the boundary

conditions c=0 at all x and y=0, c=cb at all x and y∞ and c=cb at x=0 and all y based on the

boundary layer and film theory [135, 136] yields in Equation (B.8) [72, 131, 133, 134]

describing the concentration gradient at the surface of the cathode which still depends on x.

( )

( )3

1x

0

21

21

b3

1

0ydx)x(

)x(893.0c

D91

yc

γ

γ

=

∂∂

∫=

(B.8)

For a very small cathode, a very thin concentration boundary layer is established on the

cathode, making the solution presented in Equation (B.8) independent of the geometry of the

system being investigated. The mean mass transfer coefficient over the entire cathode can be

described using Equation (B.9).

152

∫=

∂∂

=charL

0 0ycharbm dx

yc

L1

Dck (B.9)

Introducing Equation (9) into the relationship for the Sherwood number yields Equation

(B.10)

dx

dx893.0c

D91

c1

DLk

ShcharL

0 31

x

0

21

21

b3

1

b

charm ∫∫

γ

γ

==

(B.10)

which when solved yields in Equation (B.11).

31

2charcharm

DL

807.0DLk

Sh

γ== (B.11)

Lchar for a rectangular cathode is the length of the cathode in the main flow direction. For

circular electrodes the characteristic length Lchar is equal to the diameter multiplied by a factor of

0.82 [92, 126] as presented in Equation (B.12):

31

22m

Dd82.0

807.0D

d82.0kSh

γ== (B.12)

Therefore, for a circular cathode, the mass transfer coefficient can be estimated using

Equation (B.13).

31

31

32

m dD862.0k γ=− . (B.13)

Combining Equations (B.4) and (B.13) and rearranging yields Equation (B.14) that

describes the relationship between the current and the shear rate for a circular cathode which can

be simplified to Equation (B.15) where the Leveque coefficient describes the relationship

between the shear rate at the surface of the cathode and current measured through the electrical

system.

31

31

32

b dDcFAn862.0I γ=−

(B.14)

31

LevkI γ= . (B.15)

Because many of the parameters in Equation (B.14) are not accurately known for a given

system (e.g. exact cathode surface and diameter) the Leveque coefficient can be estimated by

153

applying a known shear rate at the cathode and measuring the current through the

electrochemical system [e.g. [137]].

B.2.6 Dynamic flow conditions

- Voltage step response

The relationship developed for steady state conditions are valid if the concentration

boundary layer at the cathode establishes itself more rapidly than changes in the velocity

boundary layer [94]. If not, the mass transfer relationship presented in Equation (B.4) must be

modified to take into account that the mass transfer is time dependent as presented in Equation

(B.16):

( ) ( ) bmt,0y

ii ctk

dydc

DFAn

tI=

−=

=

(B.16)

The development of the concentration profile as a function of time and distance from the

cathode can be described by using Fick’s second law of diffusion [120] presented in Equation

(B.17) with c=cb at t=0 and all y, c=0 at y=0 and t>0 and c=cb at t>0 and y∞:

2

2

yc

Dt

)t,y(c∂∂

=

∂

∂ . (B.17)

Solving Equation (B.17) based on the penetration theory which is only valid for a short

time after the change [138, 139], for a circular cathode, the mass transfer coefficient can be

estimated using Equation (18)

tD

k m π= . (B.18)

Combining Equations (B.16) and (B.18) and rearranging yields Equation (B.19) that

describes the relationship between the current and the time for a circular cathode which can be

simplified to Equation (B.20) where the Cottrell coefficient describes the relationship between

the time and current measured through the electrical system

21

21

21

b tDcFAnI−−

π= (B.19)

21

Cot tkI−

= . (B.20)

154

The Cottrell coefficient can be estimated by applying a voltage step and measuring the

current through the electrical system over time [73, 115]. The characteristic time of the EDM

system, which is the time it takes for the current from an applied voltage step (Equation (B.20))

to reach steady state conditions (Equation (B.15)), can be estimated by equating Equations

(B.15) and (B.20) yielding Equation (B.21) which describes the characteristic response time of

the cathode

32

2Lev

2Cot

0 kk

t−

γ= . (B.21)

The edge effect, i.e. augmenting the diffusion with additional mass transport from the

sides, can also change the behaviour of the cathode under the transient condition [133, 134]. One

approach to include the edge effects is to describe this effect with the help of an additional term

in Equation (B.20).

02

1

Cot2

1

Cot Itk2

FnPDtkI +=+=

−− , (B.22)

where the intercept I0 stands for the correction for edge effects.

As another approach to consider the spatial diffusion related to the edge effect, a numerical

model for the solution to a 3 dimensional mass transfer model over the surface of the cathode

was developed [140]. Based on this model, a correction of Sh/ShDLA =1+ψ is suggested, where

Sh is the actual Sherwood number, ShDLA is the Sherwood number for diffusion layer

approximation where the effect of streamwise and lateral diffusion is neglected (1 dimensional

model). For a circular cathode, ψ was estimated for a range of modified Pe numbers between 1

and 100. The edge effect can be neglected at high Pe numbers where 1) the area of the spatial

diffusion is very small compared to the total area of the cathode or 2) the velocity and therefore

the convection is high so that the spatial diffusion is negligible [140, 141] (see also section

B.2.6).

- Approximate model of the cathode dynamic response

Knowing the characteristic time of the system, it is possible to correct the wall shear rate

measured at conditions when the concentration boundary layer is not able to follow rapid

changes in the velocity boundary layer. To take into account that the mass transfer is time

dependent, Equation (B.6) is modified as presented in (B.23).

155

y)t,x(vx γ= . (B.23)

As described above, the mass transfer relationship presented in Equation (B.4) must be

modified to take into account that the mass transfer is time dependent as presented in Equation

(B.16). In Equation (B.16), the concentration gradient as well as the mass transfer coefficient is

unknown. To find a describing Equation for the concentration gradient, the general mass balance

with the conditions described above can be used in combination with Equation (B.23) which

yields in Equation (B.24).

∂∂

+∂∂

=∂∂

γ+∂∂

2

2

2

2

yc

xc

Dxc

y)t,x(tc

. (B.24)

The concentration profile at the surface of the cathode can be approximated using Equation

(B.25)[142-145].

δ−=

31

b xl

)t(y

G1c)t,y,x(c (B.25)

where G=f(ζ) is a decreasing function assuring G(0)=1, G(∞ )=0, G’(0)=-1. By substituting

Equation (B.25) into Equation (B.24), assuming axial diffusion is negligible and integrating near

the cathode surface in the viscous boundary layer yields Equation (B.26) that can be used to

calculate a transient, i.e corrected, shear rate from the shear rate obtained assuming steady state

conditions (Equation(B.15)).

∂γ∂

+γ=γt

t32

)t()t( s0sc . (B.26)

Substituting Equation (B.15) and (B.21) into Equation (26) yields a relationship similar to

that presented in Equation (15) but that can be used for steady and unsteady flow conditions as

presented in Equation (B.27).

∂∂

+=γ −

tI

k2Ik)t( 2Cot

33Levc

(B.27)

Note that Equation (B.27) is not valid at conditions with very large or rapid flow

fluctuations. Under these conditions, Equation (B.27) provides only rough estimates of extreme

values, with maxima determined more precisely (as probe response is better at high wall shear

rates). Similarly, when large wall shear rate fluctuations with dimensionless amplitudes

156

1~ ≥γγ=β lead to the near-wall flow reversal, negative values obtained using Equation (B.27)

can be used only as qualitative indicators of the flow reversal phenomenon [123].

B.3 Electrodiffusion Method (EDM): application

The theory presented in section B.2 was applied to measure the shear rate induced by a gas

bubble rising in a vertical flow cell. This application is motivated by the measurement of wall

shear stress in membrane systems where aeration is used to detach fouling layers from the

membranes. Several groups in this field worked with EDM [137].

The experimental setup, the procedure of data processing and the resulting wall shear rate

obtained in this study are discussed in the following sections.

B.3.1 Experimental setup

The experimental apparatus used consisted of a vertical flow cell, a liquid recirculation

system and a gas bubble release mechanism. Details of the system are presented in [137] and

summarize as follows. The flow cell consisted of a thin vertical acrylic glass tank (height:

1200mm; width: 160mm; thickness: 7mm). An electrochemical solution [38] was circulated

through the flow cell at an average upward velocity of 0.2m/s. Single 3 mm diameter bubbles

were introduced into the upflowing liquid at the base of the flow cell. An array of 8 x 0.5 mm

diameter platinum EDM cathodes were installed along the width of the flow cell on the inside

wall, perpendicular to the liquid and bubble rise path 800 mm from the base of the flow cell.

Data from the EDM cathodes was collected and conditioned using a custom electrical circuit and

data collection system. Nitrogen gas was used to generate the bubble and purge oxygen from the

electrochemical solution used. Other than the cathode and anode, all system components in

contact with the electrochemical solution were non-conductive.

B.3.2 Practical aspects influencing the measurement

Knowing the theoretical background of the EDM, it is an obvious fact that it is a very

delicate measurement technique to work with. This section summarises the main factors

influencing the results of measurements.

There are several factors influencing the calibration:

• Surface area of the cathode

o Not perfectly circular

157

o Scratches

o Breakages or air bubbles in the epoxy resin near the surface

o Oxidized layer on the cathode / poisoned cathode

• Concentrations of the electrolytes

o degeneration due to photo catalytic reaction

• Concentration of oxygen in the solution as it can cause side reactions

• Material properties

o Mainly influenced by the temperature of the solution

During the measurement the following hardware related factors can affect the measured

signal:

• Current

o Magnetic field / Electrostatic field

from equipment

• e.g. frequency converter of the pump

mobile phone

electrolytic solution flowing in (long) tubing

o Galvanic cell

o resistance in the system

Conductivity of the electrolyte

Distance between cathode and anode

o Size of the anode

o Anything that might influence the circuit (power supply) of the equipment

o Amplification (linear/non-linear)

o Ohmic resistance in the system

o Grounding

Chan [49] gives a sensitivity study of the signal to selected parameters from the list above.

This list doesn’t claim completeness as there are always factors specific to the used setup and its

surroundings.

158

B.3.3 Data conditioning

Data conditioning consisted of first establishing a relationship between the measured

current and the imposed wall shear rate, i.e. calibration, and then correcting the acquired wall

shear rate signal in respect to the unsteady near-wall flow conditions observed during the bubble

rise.

- Calibration

Both direct and indirect calibration is possible. For direct calibration, a known shear rate is

applied at the surface of the cathode and a resulting current through the EDM system measured.

Equation (B.15) is then applied to determine the relationship between the measured current and

the imposed wall shear rate. Ideally, direct calibration is done in-situ. However, for some more

complex flow systems where it is not possible to achieve well defined flow conditions in-situ, the

calibration should be performed ex-situ. In this case, a versatile removable probe is temporarily

moved from the system of interest into a separate ex-situ calibration system where the Leveque

coefficient is estimated. Care must be taken to ensure that the temperature and composition of

the electrolyte solution in the ex-situ calibration system are the same as those in the system of

interest.

For indirect calibration, a voltage step approach described in section 2.6.1 is used not only

to determine the Cottrell coefficient but also to estimate the Leveque coefficient (see [73]). A

typical result obtained from such voltage step experiments for our cathodes is presented in Figure

B.1. The Cottrell coefficient is estimated from the slope of the log-log plot of the current

measured over time during the transient period of the voltage step. As the current at the

beginning and ending of the transient process is influenced by additional effects (such as cathode

surface roughness or gradual approaching the magnitude of steady current), only a middle linear

part of the transient response is considered for data regression. Our experience indicates that

such a relevant time interval is ranging from 0.01 s to 0.5 t0. As the characteristic response time

t0 is not known beforehand, it has to be estimated by an iterative procedure schematically

illustrated in Figure B.2. Here t0 value is determined by the interception between the transient

and steady state asymptotes. For the data presented in Figure B.1, this procedure provides for the

Cottrell coefficient a value of kCot=1.13*10-6 As1/2. The theoretical relationship for the Cottrell

coefficient (compare Equations (B.19) and (B.20)) is presented in Equation (B.28).

159

21

21

bCot DcFAnk−

π= (B.28)

Equation B.28section can be used to obtain an estimate of the diffusion coefficient D. For

the known parameters of applied electrochemical system (n=1, F=96485 C/mol, cb=3 mol/m3,

d=0.0005 m, and A=πd2/4= 0.196 mm2), it provides a value of 1.24*10-9 m2/s. This value is in

good agreement with those measured in previous experiments (see chapter B.2.3) and therefore it

can be also applied to determine indirectly the Leveque coefficient. Combining the Equations

(B.14) and (B.15) klev can be calculated using Equation B.29.

31

32

bLev dDcFAn862.0k−

= (B.29)

The theoretical value calculated was kLev=6.9*10-7 As1/3. For comparison, the Leveque

coefficient obtained by direct calibration done in our experimental set-up under conditions of the

laminar single-phase channel flow has a similar value of 6.3*10-7 As1/3.

Figure B-1 Voltage step data and the different regression lines

10-4 10-3 10-2 10-1 100 10110-6

10-5

10-4

10-3

t [s]

I [A

]

measured current

steady state

transient (iterations)

t0log

log

160

Figure B-2 Structured flow chart for the iteration to determine kCot

Considering the influence of edge effects as discussed in section B.2.6, the Peclet number

calculated for typical wall shear rate in our experimental set/up (γ=100 s-1) has a value of Pe=γ

d2/D = 31000. The modified Peclet number H= 52 then provides a small edge-effect correction

factor of ψ = 0.02 (see [141] for details), which means that a correction factor of 2% would be

needed to find the actual Sherwood number considering the edge effects.

- Signal acquisition and pre-processing

The accuracy of the correction for dynamic flow conditions can be affected by the signal

sampling rate. If the sampling frequency is too small, peaks, i.e. maximums and minimums, in

the signal can be damped, whereas background noise in the measured signal can be amplified if

the sampling rate is too large. In general, the sampling frequency should be at least twice that of

t0,counter=10-1s

i,0

i,01i,00 t

ttt

−=∆ +

steady

2i,Cot

1i,0 Ik

t =+

Δt0<0.1%

i,CotCot kk =yes

no

1ii +=

kCot,i from linear regression of I=kCot,ix+n with x=t-½ for interval t=[10-2s 0.5t0,i]

161

the frequency of expected flow fluctuations in the system [146]. For the investigated flow

system, this frequency can be estimated from the time necessary for a bubble to pass the sensor

(bubble size/bubble velocity). Considering 3 mm bubbles rising in co-current liquid flow of

0.2 m/s, the minimal sampling frequency is estimated to be 200 Hz. To obtain wall shear rate

response to a rising bubble in more detail, the sampling frequency ranging from 500 to 750 Hz

have been used [137]. The advantage of using higher frequencies is that a moving average can be

used to remove background noise without substantially dampening the peaks in the signal. Figure

B.3a presents typical results for a signal sampling frequency of 500 Hz, with and without

averaging. As presented, averaging over up to 8 sampling events significantly reduces the

background noise of the signal (Figure B.3b) without significantly affecting the overall profile of

the signal (Figure B.3a). Taking into account the characteristic response time of the sensor

(estimated to be in the order of 0.1 s), the signal pre-processing is necessary also for the correct

calculation of time derivatives needed for the signal correction.

162

Figure B-3 Current generated by a bubble with moving averages of different averaging

ranges

(a) and standard deviations of the signal for different averaging ranges (b)

B.3.4 Wall shear rate calculation and correction

With the Leveque and Cottrell coefficient determined from direct or indirect calibration,

the properly measured current signal through the electrochemical system can be converted to

wanted wall shear rate course. When time variations of the current are slow, i.e. dI/dt values

become negligibly small, the quasi-steady Equation (B.15) can be applied to calculate the actual

wall shear rates. As a general rule of thumb based on experience, a criterion for such quasi-

steady measurement conditions can be expressed by an equality tI

k2 2Cot ∂

∂< 0.05 I³, holding for

the whole time of measurement. Under unsteady flow conditions, as in the case of near-wall flow

induced by rising bubbles, this condition is not fulfill, the frequency response of electrodiffusion

400 420 440 460 480 500

4

5

6

7x 10-6

curre

nt [A

]

0 10 20 30 40 500

0.5

1

1.5

2

stan

dard

dev

iatio

n [%

]

a)

b)

0 20 100sampling events

averaging range

40 60 803

original signal

averaging range

2 4 8 16

163

sensors should be taken into account, and Equation (B.27) has to be used for wall shear rate

calculations.

Typical results from wall shear rate measurements are presented in Figure B.4. The shear

rate calculated with Equation (B.15) is illustrated in Figure B.4a is demonstrated for two

conditions, first condition where the steady state flow conditions prevail and second where the

dynamic flow conditions prevail. Before and after the data shown here a steady state flow was

apparent as well. Figure B.4b shows the same data treated with a moving average with an

averaging range of 10 data points. Here the noise is reduced and the peak value is marginally

lowered as well. Figure B.4c and Figure B.4.d show the data from Figure B.4b treated with

Equation (B.27) for two different linearization ranges. In Figure B.4c a rather large linearization

range of 400 data points, i.e. ∂t=∆t=0.8 s, was chosen. As expected with such a large

linearization range, only minor changes to the data appear. The peak value is slightly increased

approximately back to the value before the noise reduction step without increasing the noise as

well. In Figure B.4.d on the other hand, a smaller linearization range of 30 data points, i.e.

∂t=∆t=0.06 s, was chosen. Here, a strong enhancement of the fluctuations is visible. The peak

value is increased by more than 100%, a negative peak directly following the positive peak value

is apparent and the fluctuations after the peak are enhanced as well. As mentioned earlier in

section 2.6.2, the actual value of the negative peak should not be used in the analysis but it

should rather be seen qualitatively as an indicator for flow reversals. This is reasonable here as,

when the bubble passes by the cathodes, only a thin liquid film between bubble and cathode

exists in which a flow reversal due to displacement of the liquid around the bubble can happen.

164

Figure B-4 Shear rate from the raw data (Equation (B.15))

(a), treated with a moving average with an averaging range of 10 (b), then corrected with

Equation (B.27) with a linearization range of 0.8 s (=400 sampling events) (c) and 0.06 s (=30

sampling events) (d)

0 200 400-1000

0

1000

2000

sampling events

shea

r rat

e [1

/s]

0 200 400-1000

0

1000

2000

sampling events

shea

r rat

e [1

/s]

0 200 400-1000

0

1000

2000

sampling events

shea

r rat

e [1

/s]

0 200 400-1000

0

1000

2000

sampling eventssh

ear r

ate

[1/s

]

a) b)

c) d)

165

B.4 Conclusions

The purpose of this chapter was to study the theoretical background necessary to interpret

the data provided by the EDM in practical applications. Complete derivations of the steady flow

equations that govern the mass transfer induced by the electrochemical reaction in the system are

gathered from the available EDM literature. Methods used for transient flow conditions are

introduced. A procedure for correction of the signal under transient conditions is developed. A

new algorithm is suggested to evaluate transient calibration data where the Cottrell calibration

factor is determined iteratively. Practical aspects and limitations of the in-situ calibrations are

discussed.

This optimized method is then applied to a system where a single bubble rises in a vertical,

narrow rectangular channel with a co-current flow of the electrolyte solution. These unsteady

wall shear stress data are used here as an example to demonstrate the practical aspects of the data

interpretation. As illustrated in the case of resulting wall shear rate response to a rising bubble,

the optimized EDM method and the correction procedure enables measuring shear stress under

transient flow conditions and revealing a short-time near-wall flow reversal even if the

measurement is carried out with a single-segment probe.

166

Appendix C : Matlab codes developed to process voltage signals

V-step in-situ calibration of the shear probes clear all; close all; % find the directory where the files are in % there should be no text header for the files, i.e. only containe numbers direc='D:\jan-30-2012-probe calibration\'; %Load bias for each channel fileIn=strcat('BiasAverage.txt'); O(:,:)=load(fileIn); %Load files for probe calibration Format "calibration_.txt" %_ is the name of the txt file=probe identification\ for a =1:4; number=num2str(a); file=[direc '150-50_trigger_1_',number,'.txt']; T(:,:)=load(file); [m,n]=size(T); S(m,2)=0; %correct data for channel bias %put corrected data in matrix S % c is the number of columns (n-1, channel, or probe)here is 2 because % only one channel (zero on the box) was used for calibration % %0.00025 because data was collected at 4000Hz for c=2; S(:,c)=T(:,c)-O(1,c-1); end %plot((1:m),squeeze(S(:,2))); %% %%IMPORTANT %Stop here plot S and find the time where the graph starts to rise: 1700 is %the difference between the max and min where the graph is linear %create a matrix (S) where the calibration resutls will be stored %Add time to the first column of matrix

167

%%%%%%%duration of the rise of V signal from infinity, it can be %%%%%%%less than nop!!! %0.01 because data was collected at 1000Hz % number of points=nop nop=6000; for d=1:nop M(d,1)=0.001*d; end %add t^(-0.5) to column 2 %data is fitted to this value V=(AR)at^(-05) %V from the probes, AR is amplification x resistance (1000x100) M(1:nop,2) = (M(1:nop,1)).^(-0.5); %Cycle through different columns (column 1 is time so start at 2) %c is the column number % for c=2; %set threshold above which data of interest starts %this corresponds to point when current is applied %t is the threshold value %sign needs to be reversed since data in file is negative t=-min(S(:,c)); %cycle through each row %%%% important : r is the row number % for r=1:m; %v is the value in row r and column c %sign needs to be reversed since data in file is negative v=-S(r,c); %is current value greater than the threshhold %if yes, collect data for 0.75 seconds if v==t %if abs(v-t)<=abs(t)*0.001 %collect all data for rows below v

168

%save to column C+1 since column 2 in M is for t^-.5 %sign needs to be reversed since data in file is negative M(1:nop,c+1)=-S(r:r+nop-1,c); %exit from the current for loop that cycles through rows break end end %end %fit line to data V=a(AR)t^(-0.5) %V is y value and t^(-0.5) is x value %two first parameters in polytif function are x and y %ignore the first data points i.e start at 10. %consider points until the 200 % IMPORTANT********************** %% for some reason the graph is inveresly ploted so the data should %% be taken from the end st=145; fn=1030; %% same comment we measure only one channel c=2; P=polyfit(M(st:fn,2),M(st:fn,c+1),1); %save resutls in a matrix R %firt row = fitted a[AR], slope %second row=residuals R(a,c-1)=P(1,1); R(a,c)=P(1,2); %% Signal correction %f is the slope of quasi-steady shear signal, taken from the last %points of the graph f=mean (M(2000:6000,c+1)); %find the Equation for cottrelle part PP=polyfit(M(st:fn,1),M(st:fn,c+1),1); %save resutls in a matrix R %firt row = fitted a[AR], slope %second row=residuals

169

RR(a,c-1)=PP(1,1); RR(a,c)=PP(1,2); %calculate the intersection of Cottrelle and Leveque asymptots t0(a,1)= (f-RR(a,c))/RR(a,c-1); % M is plotted versus (t^-0.5) % t0(a,2)= (t0(a,1))^(-2); Ave_t0=mean(t0(a,1)); %% %%plot fitted results %plot of data V vs. t^(-0.5) subplot(2,3,a) plot(M(st:fn,2),M(st:fn,c+1)) hold on; %Plot of fitted data V vs. t^(-0.5) X = linspace(min(M(st:fn,2)),max(M(st:fn,2)),500); Y = polyval(P,X); % values for fit curve plot(X,Y,'--k'); % draw fit curve xlabel('t^ (-0.5) (1/s ^ (-0.5))'); ylabel('V(volts)'); hold off; % a; %Generate correction factors ????? U(a,:)=R(a,:)/(1000*100); % 100 is the resistance of the first channel % IMPORTANT***************** resistancew should be checked for diff % channels end %% you can change the parameters for T and viscosity correction % b=0.67521; % is the constant 1/(Pi*k^-2) d=0.000000000676; %Diffusion coefficent m2/s ra=0.0005; %diameter or radius , m u=0.00097; % viscosity %eq 5-Sobolik: K/a=((b^(-1/2))*(d^(1/6))*(ra^(-1/3))); %Klev: K(:,:)=U(:,:).*((b^(-1/2))*(d^(1/6))*(ra^(-1/3))); clear C1; Klev=mean(K(:,1));

170

C1(:,1)=u*((K(:,1).*100000).^(-3)); %Calculate mean of all replicate calibration tests %only aerage between first and last file (in case first file in not 1) Ca=mean(C1(:,1)) %% signal correction % Cottrell Coeff. = slope of V versus t^(-0.5)/RA kc= mean(R(:,1))./(100*1000); % Leveque Coeff.= (Ca*(RA)^3)/viscosity k1(1,1)= ((100000^3)*Ca(1,1))/u; fileOut = strcat('Leveque_Coeff_probe0.txt'); save( fileOut ,'Klev','-ascii'); fileOut = strcat('(Leveque_Coeff)^-3_probe0.txt'); save( fileOut ,'k1','-ascii'); fileOut = strcat('t0_probe0.txt'); save( fileOut ,'Ave_t0','-ascii'); fileOut = strcat('cottrell coeff_probe0.txt'); save( fileOut ,'kc','-ascii'); %% fileOut = strcat('CalibrationFactorAverage_probe0.txt'); save( fileOut ,'Ca','-ascii'); %% figure (2) for d=1:10000 S(d,1)=0.001*d; end plot(S(:,1),-S(:,c),'. b'); %hold on %plot(M(:,1),M(:,c+1),'. k'); %hold on %plot(M(st:fn,1),M(st:fn,c+1),'. r'); %plot(M(:,2),M(:,c+1),'. k'); figure (3) plot(M(:,1),M(:,c+1),'. k');

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hold on plot(M(st:fn,1),M(st:fn,c+1),'. r'); figure(4); plot(M(:,2),M(:,c+1),'. k'); hold on plot(M(st:fn,2),M(st:fn,c+1),'. r'); %Save matrix Ca to File %% change the name of the file % fileOut = strcat('CalibrationFactorAverageDouble.txt'); % save( fileOut ,'Ca','-ascii');

Correction of data under transient flow condtions clear all; close all; % find the directory where the files are in % there should be no text header for the files, i.e. only containe numbers direc='D:\January-29-2012-shear data\'; %Load bias for each channel fileIn=strcat('BiasAverage.txt'); Q(:,:)=load(fileIn); %% %viscosity u=0.00097; %% there are four Leveque Coefficients, one for each channel fileIn = strcat('(Leveque_Coeff)^-3_probe0.txt'); k1(1,1)=load(fileIn); fileIn = strcat('(Leveque_Coeff)^-3_probe1.txt'); k1(1,2)=load(fileIn); fileIn = strcat('(Leveque_Coeff)^-3_probe2.txt'); k1(1,3)=load(fileIn); fileIn = strcat('(Leveque_Coeff)^-3_probe3.txt'); k1(1,4)=load(fileIn); %theretical 1/Klev ^3 %k1(1,1)=1.05e19; %% there are four t0, one for each channel fileIn = strcat('t0_probe0.txt'); Ave_t0(1,1)=load(fileIn); fileIn = strcat('t0_probe1.txt'); Ave_t0(1,2)=load(fileIn); fileIn = strcat('t0_probe2.txt'); Ave_t0(1,3)=load(fileIn); fileIn = strcat('t0_probe3.txt');

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Ave_t0(1,4)=load(fileIn); %% %% there are four Cottrell Coefficients , one for each channel fileIn = strcat('cottrell coeff_probe0.txt'); kc(1,1)=load(fileIn); fileIn = strcat('cottrell coeff_probe1.txt'); kc(1,2)=load(fileIn); fileIn = strcat('cottrell coeff_probe2.txt'); kc(1,3)=load(fileIn); fileIn = strcat('cottrell coeff_probe3.txt'); kc(1,4)=load(fileIn); k2=2*kc.^2; %Cottrelle theory %k2(1,1)=1.2e-12; j=0; for f=1:3; number=num2str(f); %O is the correction factor for channels O(:,:)=[0.49 0.33 0.44 0.33]; % P2-test-F=1CC=8.txt is the name of the shear measurements fileIn=strcat('150-10_',number,'.txt'); V(:,:)=load(fileIn); [m,n]=size(V); for c=2:5; G(:,c)=V(:,c)-Q(1,c-1); end %remove the first part of the graph before trigger %t= mean(V(:,6)); % for c=2:5; % for r=1:m; % if V(r,6)< (t-0.5) %if abs(v-t)<=abs(t)*0.001 %collect all data for 0.75 seconds in rows below v %data acquired at 4000 hz so 3000 rows) %save to column C+1 since column 2 in M is for t^-.5 %sign needs to be reversed since data in file is negative % T(1:(m-r+1),c)=G(r:m,c); %exit from the current for loop that cycles through rows % break % end

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%end %end %move time scale %nop=m-r+1; % for d=1:nop % T(d,1)=0.01*d; %end T(:,:)=G(:,:); %change m and n to new values [m,n]=size(T); U(:,2)=-(T(:,2).^3); U(:,3)=-(T(:,3).^3); U(:,4)=-(T(:,4).^3); U(:,5)=-(T(:,5).^3); %for s=1:m; S(:,2)=U(:,2).*O(1,1); S(:,3)=U(:,3).*O(1,2); S(:,4)=U(:,4).*O(1,3); S(:,5)=U(:,5).*O(1,4); %%converting voltage signal to current I=-V/RA T(:,:)=-T(:,:)./100000; for c=2:5; a=mean(S(:,c)); s=std(S(:,c)); % use z factor for 90 % will be 1.64 e=1.64*s; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R R(f,c-1)=a; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) P(f,c-1)=e; %% 0.00025 because data was collected at 4000Hz %% removing outliers, larger than 90% in a normal distribution % check for the number of changed values due to a too high change of the % value from one time step to the other for dm=4

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for i=1:m if i>0 andand i<dm+1 if ((abs(S(i,c)-mean(S((1:dm),c))))> 2.*std(S((1:dm),c))) S_clean(i,c)= mean (S(1:dm,c)); else S_clean (i,c)= S(i,c); end elseif i>dm andand i<m-dm dev=std(S((i-dm):(i+dm),c)); if abs(S(i,c)- (mean(S((i-dm):(i+dm),c))))> 2*dev S_clean(i,c)= mean(S((i-dm):i+dm,c)); else S_clean (i,c)= S(i,c); end elseif i>m-(dm+1) andand i<m+1 dev=std(S((m-dm):m,c)); if abs(S(i,c)-mean(S((m-dm):m,c)))> 2*dev S_clean(i,c)=mean(S((m-dm):m,c)); else S_clean (i,c)= S(i,c); end end end a_clean=mean(S_clean(:,c)); s_clean=std(S_clean(:,c)); % use z factor for 90 % will be 1.64 e_clean=1.64*s_clean; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R R_clean(f,c-1)=a_clean; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) P_clean(f,c-1)=e_clean; figure (6); subplot(2,3,f) plot( dm, s_clean, '*r'); xlabel('number of points'); ylabel('STD for cleaned shear stress'); %hold on

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%% Exponentially weighted moving average constant Q=0.3 QQ=0.3 i=1; for i=1:m if i>0 andand i<dm+1 S_moving_ave(i,c)=mean(S_clean(1:dm,c)) ; S_ave(i,c)=mean(S_clean(1:dm,c)); elseif i>dm andand i<m-dm S_ave(i,c)=mean(S_clean((i-dm):(i+dm),c)); S_moving_ave(i,c)= (1-QQ).*S_clean(i,c)+ (1-QQ)*(QQ)*S_clean (i-1,c)+(1-QQ)*(QQ^2)*S_clean (i-2,c)+(1-QQ)*(QQ^3)*S_clean (i-3,c)+(1-QQ)*(QQ^4)*S_clean (i-4,c); elseif i>m-(dm+1) andand i<m+1 S_ave(i,c)=mean(S_clean((m-dm):m,c)); S_moving_ave(i,c)= ((1-QQ).*S_clean(i,c))+ ((1-QQ)*(QQ)*S_clean (i-1,c))+((1-QQ)*(QQ^2)*S_clean (i-2,c))+((1-QQ)*(QQ^3)*S_clean (i-3,c)+(1-QQ))*((QQ^4)*S_clean (i-4,c)); end end a_ave=mean(S_ave(:,c)); s_ave=std(S_ave(:,c)); % use z factor for 90 % will be 1.64 e_ave=1.64*s_ave; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R R_ave(f,c-1)=a_ave; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) P_ave(f,c-1)=e_ave; a_moving_ave=mean(S_moving_ave(:,c)); s_moving_ave=std(S_moving_ave(:,c)); % use z factor for 90 % will be 1.64 e_moving_ave=1.64*s_moving_ave; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R R_moving_ave(f,c-1)=a_moving_ave; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) P_moving_ave(f,c-1)=e_moving_ave; figure (8); subplot(2,3,f) plot( dm, s_ave, '*b');

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%hold on xlabel('number of points averaged'); ylabel(' STD for averaged shear stress'); figure (18); subplot(2,3,f) plot( dm, s_moving_ave, '*b'); %hold on xlabel('number of points averaged'); ylabel(' STD for averaged shear stress'); figure (17); plot((1:m).*0.005,squeeze(S_clean(:,c)-S_ave(:,c)),' r'); xlabel('time'); ylabel(' S-S_ave'); end %% put the first column as time for r=1:m S(r,1)=0.005*r; end % S_clean: shear stress without outiers for r=1:m S_clean(r,1)=0.005*r; end % S_correct: corrected shear stress for r=1:m S_correct(r,1)=0.005*r; end % S_ave is the shear stress smooth for r=1:m S_ave(r,1)=0.005*r; end %T_clean: smooth curve for voltage signal for r=1:m T_clean(r,1)=0.005*r; end % T_correct: corrected voltage signal for r=1:m T_correct(r,1)=0.005*r; end %current for r=1:m T(r,1)=0.005*r; end % smooth current for r=1:m

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T_ave(r,1)=0.005*r; end %% % Correcting the signal based on personal communication with Dr. Tihon changes=1; i=1; for dt=10 % dt=50; for i=1:m if i>0 andand i<dt+1 S_correct(i,c)=S_ave(i,c); elseif i>dt andand i<m-dt slope(i,c)=regress(S_ave((i-dt):(i+dt),c),S_ave(((i-dt):(i+dt)),1)); % S_correct(i,c)= S_ave(i,c)+((2/3).*Ave_t0(1,c-1).*(S_ave(i-dt,c)-S_ave(i+dt,c))/(S_ave(i-dt,1)-S_ave(i+dt,1))); % S_correct(i,c)= S_ave(i,c)+((2/3).*Ave_t0(1,c-1).*slope(i,c)); % dI/dt from polyfit.m with y=mx+n param3=polyfit(S_ave(((i-dt):(i+dt)),1),S_ave((i-dt):(i+dt),c),1); slope3(i,c)=param3(1); S_correct(i,c)= S_ave(i,c)+((2/3).*Ave_t0(1,c-1).*slope3(i,c)); elseif i>m-dt-1 andand i<m+1 S_correct(i,c)=S_ave(i,c); end end a_correct=mean(S_correct(:,c)); s_correct=std(S_correct(:,c)); % use z factor for 90 % will be 1.64 e_correct=1.64*s_correct; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R R_correct(f,c-1)=a_correct; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) P_correct(f,c-1)=e_correct; figure (9); subplot(2,3,f) plot( dt, s_correct, '*b'); hold on xlabel('number of points');

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ylabel('STD for corrected shear stress'); %figure (f) %subplot(8,8,changes) %plot((1:m).*0.005,squeeze(S(:,c)),'- b'); %hold on %plot((1:m).*0.005,squeeze(S_clean(:,c)),' y'); %hold on; %plot((1:m).*0.005,squeeze(S_ave(:,c)),'k'); %hold on %plot((1:m).*0.005,squeeze(S_correct(:,c)),'- r'); %hold on %plot((1:m).*0.005,squeeze(S_moving_ave(:,c)),'- g'); %hold on %changes = changes+1; end %% i=1; changes =1; dm=4 for i=1:m if i>0 andand i<dm+1 if ((abs(T(i,c)-mean(T((1:dm),c))))> 2.*std(T((1:dm),c))) T_clean(i,c)= mean (T(1:dm,c)); else T_clean (i,c)= T(i,c); end elseif i>dm andand i<m-dm dev=std(T((i-dm):(i+dm),c)); if abs(T(i,c)- (mean(T((i-dm):(i+dm),c))))> 2*dev T_clean(i,c)= mean(T((i-dm):i+dm,c)); else T_clean (i,c)= T(i,c); end elseif i>m-(dm+1) andand i<m+1 dev=std(T((m-dm):m,c)); if abs(T(i,c)-mean(T((m-dm):m,c)))> 2*dev T_clean(i,c)=mean(T((m-dm):m,c)); else T_clean (i,c)= T(i,c); end end

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end a_clean=mean(T_clean(:,c)); s_clean=std(T_clean(:,c)); % use z factor for 90 % will be 1.64 e_clean=1.64*s_clean; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R RT_clean(f,c-1)=a_clean; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) PT_clean(f,c-1)=e_clean; figure (7); subplot(2,3,f) plot( dm, s_clean, '*r'); xlabel('number of points'); ylabel('STD for cleaned current'); hold on %% i=1; for i=1:m if i>0 andand i<dm+1 T_ave(i,c)=mean(T_clean(1:dm,c)); elseif i>dm andand i<m-dm T_ave(i,c)=mean(T_clean((i-dm):(i+dm),c)); elseif i>m-(dm+1) andand i<m+1 T_ave(i,c)=mean(T_clean((m-dm):m,c)); end end a_ave=mean(T_ave(:,c)); s_ave=std(T_ave(:,c)); % use z factor for 90 % will be 1.64 e_ave=2*s_ave; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R RT_ave(f,c-1)=a_ave; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) PT_ave(f,c-1)=e_ave; figure (10);

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subplot(2,3,f) plot( dm, s_ave, '*b'); xlabel('number of points'); ylabel('STD for averaged current'); hold on %changes=changes+1; % Correcting the signal changes=1; i=1; for dt=10; % dt=50 for i=1:m if i>0 andand i<dt+1 T_correct(i,c)=u*((k1(1,c-1)).^(1)).*((T_ave(i,c)).^3); elseif i>dt andand i<m-dt %T_correct(i,c)= u*((k1(1,c-1)).^(-3)).* (((T_ave(i,c)).^3) + (k2(1,c-1)).*((T_ave(i-dt,c)-T_ave(i+dt,c))/(T_ave(i-dt,1)-T_ave(i+dt,1)))); %slope_T(i,c)=regress(T_ave((i-dt):(i+dt),c),T_ave(((i-dt):(i+dt)),1)); %T_correct(i,c)= u*((k1(1,c-1)).^(-3)).* (((T_ave(i,c)).^3) + (k2(1,c-1)).*(slope_T(i,c))); param4=polyfit(T_ave(((i-dt):(i+dt)),1),T_ave((i-dt):(i+dt),c),1); slope4(i,c)=param4(1); T_correct(i,c)= u*((k1(1,c-1)).^(1)).* (((T_ave(i,c)).^3) + (k2(1,c-1)).*(slope4(i,c))); elseif i>m-dt-1 andand i<m+1 T_correct(i,c)=u*(k1(1,c-1).^(1)).*((T_ave(i,c)).^3); end end a_correct=mean(T_correct(:,c)); s_correct=std(T_correct(:,c)); % use z factor for 90 % will be 1.64 e_correct=1.64*s_correct; %Save resutls in a matrix format with first row having averages %and second row having errors (rows= txt files= replicates, %columns= probes=channels) %means stored in matrix R RT_correct(f,c-1)=a_correct; %errors stored in matrix P,(rows= txt files= replicates, %columns= probes=channels) PT_correct(f,c-1)=e_correct; figure (16); subplot(2,3,f)

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plot( dt, s_correct, '*b'); hold on xlabel('number of points'); ylabel('STD for corrected current'); % figure (f) %subplot(8,8,changes) %plot((1:m).*0.005,squeeze((T_correct(:,c))),'b'); %hold on %xlabel('time(s)'); % ylabel('current'); % changes = changes+1; % end %% put a line where the video is recorded at %plot ([7752.*0.005 7752.*0.000667], [0 0.4]); %hold on %plot ([7752.*0.005 7752.*0.000667], [0 0.4]); end %% put all S corrected data in one matrix % j number of columns j=j+1; TotalS_correct(:,j)= S_correct(:,c); TotalT_correct(:,j)=T_correct(:,c); end % as f changes j needs to change %j=j+1; figure(1); subplot(2,3,f) %plot((1:m).*0.005,squeeze(S(:,2)),'. y'); %hold on %plot((1:m).*0.005,squeeze(S_clean(:,c)),' y'); %hold on;

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%plot((1:m).*0.005,squeeze(S_ave(:,c)),'r'); %hold on %plot((1:m).*0.005,squeeze(S_moving_ave(:,c)),'- g'); %hold on plot((1:m).*0.005,squeeze(T_correct(:,2)),'. k'); hold on plot((1:m).*0.005,squeeze(T_correct(:,3)),'. r'); hold on plot((1:m).*0.005,squeeze(T_correct(:,4)),'. b'); hold on plot((1:m).*0.005,squeeze(T_correct(:,5)),'. g'); hold on xlabel('Time(s)'); ylabel('T correct-shear stress (Pa)'); figure(45); subplot(2,3,f) plot((1:m).*0.005,squeeze(S(:,2)),'. y'); hold on %plot((1:m).*0.005,squeeze(S_clean(:,c)),' y'); %hold on; %plot((1:m).*0.005,squeeze(S_ave(:,c)),'r'); hold on %plot((1:m).*0.005,squeeze(S_moving_ave(:,c)),'- g'); %hold on plot((1:m).*0.005,squeeze(S_correct(:,2)),'. k'); hold on plot((1:m).*0.005,squeeze(S_correct(:,3)),'. r'); hold on plot((1:m).*0.005,squeeze(S_correct(:,4)),'. b'); hold on plot((1:m).*0.005,squeeze(S_correct(:,5)),'. g'); hold on xlabel('Time(s)'); ylabel('S correct-shear stress (Pa)'); %% end fileOut = strcat(' shear profiles.txt'); save( fileOut ,'T_correct','-ascii'); % plot the trigger %figure(1) %hold on %plot((1:m).*0.005,squeeze(V(:,6).*(10)),'-r'); %% % area under shear profiles

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area_S_correct (:,:)= (sum(TotalS_correct(:,j),1)).*0.005; area_T_correct (:,1:12)= (sum(TotalT_correct(:,1:12))).*0.005; %std_area_T_correct(:,1:12)=std((TotalS_correct(:,1:12))); fileOut = strcat('area under shear profiles.txt'); save( fileOut ,'area_T_correct','-ascii'); %fileOut = strcat('std_area under shear profiles.txt'); %save( fileOut ,'std_area_T_correct','-ascii'); %% %total data for each probe probe0(1:m,1)= TotalT_correct(:,1); probe0(m+1:2*m,1)= TotalT_correct(:,5); probe0(2*m+1:3*m,1)= TotalT_correct(:,9); probe1(1:m,1)= TotalT_correct(:,2); probe1(m+1:2*m,1)= TotalT_correct(:,6); probe1(2*m+1:3*m,1)= TotalT_correct(:,10); probe2(1:m,1)= TotalT_correct(:,3); probe2(m+1:2*m,1)= TotalT_correct(:,7); probe2(2*m+1:3*m,1)= TotalT_correct(:,11); probe3(1:m,1)= TotalT_correct(:,4); probe3(m+1:2*m,1)= TotalT_correct(:,8); probe3(2*m+1:3*m,1)= TotalT_correct(:,12); %% %RMS n=length(probe0(:,:)); rms= norm(probe0)./sqrt(n); fileOut = strcat('RMS of shear-150_10_replicates-probe0.txt'); save( fileOut ,'rms','-ascii'); n=length(probe0(:,:)); rms= norm(probe1)./sqrt(n); fileOut = strcat('RMS of shear-150_10_replicates-probe1.txt'); save( fileOut ,'rms','-ascii'); n=length(probe0(:,:)); rms= norm(probe2)./sqrt(n); fileOut = strcat('RMS of shear-150_10_replicates-probe2.txt'); save( fileOut ,'rms','-ascii'); n=length(probe0(:,:)); rms= norm(probe3)./sqrt(n);

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fileOut = strcat('RMS of shear-150_10_replicates-probe3.txt'); save( fileOut ,'rms','-ascii'); %% % threshold valuse for shear clear Thresh clear rms n=length(probe0(:,:)); T=1; t=1; r=1; for Th=0.3:0.1:1.5 for T=1:n if probe0(T,:)>=Th Thresh(t,1)=probe0(T,:); t=t+1; end end for T=1:n if probe1(T,:)>=Th Thresh(t,1)=probe1(T,:); t=t+1; end end for T=1:n if probe2(T,:)>=Th Thresh(t,1)=probe2(T,:); t=t+1; end end for T=1:n if probe3(T,:)>=Th Thresh(t,1)=probe3(T,:); t=t+1; end end nn=length(Thresh(:,:)); rms(r,:)= norm(Thresh(:,:))./sqrt(nn); r=r+1; end fileOut = strcat('RMS of shear-150-10_trigger_1_between_0.3_to_1.5_Pa.txt'); save( fileOut ,'rms','-ascii'); %% % STD and Avergae

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Probe0total_average=mean(probe0(:,:)); Probe0total_std=std(probe0(:,:)); fileOut = strcat('Total Average Shear-Probe0-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe0total_average','-ascii'); fileOut = strcat('Total STD of Shear-Probe0-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe0total_std','-ascii'); Probe1total_average=mean(probe1(:,:)); Probe1total_std=std(probe1(:,:)); fileOut = strcat('Total Average Shear-Probe1-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe1total_average','-ascii'); fileOut = strcat('Total STD of Shear-Probe1-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe1total_std','-ascii'); Probe2total_average=mean(probe2(:,:)); Probe2total_std=std(probe2(:,:)); fileOut = strcat('Total Average Shear-Probe2-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe2total_average','-ascii'); fileOut = strcat('Total STD of Shear-Probe2-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe2total_std','-ascii'); Probe3total_average=mean(probe3(:,:)); Probe3total_std=std(probe3(:,:)); fileOut = strcat('Total Average Shear-Probe3-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe3total_average','-ascii'); fileOut = strcat('Total STD of Shear-Probe3-150_10_replicates_trigger_1.txt'); save( fileOut ,'Probe3total_std','-ascii'); %% figure; hist(probe0(:,:),100); title('Total shear-T-correct- probe0'); kk=0:0.001:10; n_elements=histc(probe0(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('Total shear-T-correct- probe0'); xlabel('Shear stress (Pa)'); ylabel('cumulative frequency');

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figure; hist(probe1(:,:),100); title('Total shear-T-correct- probe1'); kk=0:0.001:10; n_elements=histc(probe1(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('Total shear-T-correct- probe1'); xlabel('Shear stress (Pa)'); ylabel('cumulative frequency'); figure; hist(probe2(:,:),100); title('Total shear-T-correct- probe2'); kk=0:0.001:10; n_elements=histc(probe2(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('Total shear-T-correct- probe2'); xlabel('Shear stress (Pa)'); ylabel('cumulative frequency'); figure; hist(probe3(:,:),100); title('Total shear-T-correct- probe3'); kk=0:0.001:10; n_elements=histc(probe3(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('Total shear-T-correct- probe3'); xlabel('Shear stress (Pa)'); ylabel('cumulative frequency'); %% cumulative histograms (if change 2 to c, then it will be for each %% channel) for c=2:5; figure; hist(S_ave(:,c),100); title('shear-S-Ave-probe');

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xlabel('shear stress (Pa)'); ylabel('frequency'); kk=0:0.001:50; n_elements=histc(S_ave(:,c),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('shear-S-Ave-probe'); xlabel('shear stress (Pa)'); ylabel('frequency'); figure; hist(S_correct(:,c),100); title('shear-S-correct');xlabel('shear stress (Pa)'); ylabel('frequency'); kk=0:0.001:50; n_elements=histc(S_correct(:,c),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('shear-S-correct-probe'); xlabel('shear stress (Pa)'); ylabel('frequency'); figure; hist(T_correct(:,c),100); title('shear-T-correct-probe');xlabel('shear stress (Pa)'); ylabel('frequency'); kk=0:0.001:50; n_elements=histc(T_correct(:,c),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('shear-T-correct');xlabel('shear stress (Pa)'); ylabel('frequency'); end %% %Average and STD of corrected shear values with Klev fileOut = strcat('T_correct_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'RT_correct','-ascii'); fileOut = strcat('T_std_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'PT_correct','-ascii'); %Average and STD of shear values with Calibration factor fileOut = strcat('S_ave_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'R_ave','-ascii');

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fileOut = strcat('S_std_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'P_ave','-ascii'); %Average and STD of shear values with Calibration factor fileOut = strcat('S_correct_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'R_correct','-ascii'); fileOut = strcat('S_correct_STD_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'P_correct','-ascii'); %Average and STD of ave current signal values with Klev fileOut = strcat('T_ave-current signal_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'RT_ave','-ascii'); fileOut = strcat('T_std-current signal_probe_flowcell-150-15psi_50_trigger.txt'); save( fileOut ,'P_ave','-ascii'); %hold on %plot((1:m).*.00025,squeeze(S(:,3))); %fileOut = strcat('Average-Shear_0.081m_s_F1C5.txt'); %save( fileOut ,'average','-ascii'); %fileOut = strcat('STD-Shear_0.081m_s_F1C5.txt'); %save( fileOut ,'Deviation','-ascii'); %% Histogram of corrected S for each probe but total of f files instead of %% c 2:5, choose c =2 ; total=f*m; Total=reshape(TotalS_correct,total,1); figure; hist(Total(:,:),100); title('shear-S-correct-'); kk=0:0.02:1; n_elements=histc(Total(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('shear-S-correct'); xlabel('Shear stress (Pa)'); ylabel('cumulative frequency'); %% %%

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% total histogram total=f*m; Total=reshape(TotalS_ave,total,1); figure; hist(Total(:,:),100); title('shear-S-ave-'); kk=0:0.02:1; n_elements=histc(Total(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); title('shear-S-ave'); xlabel('Shear stress (Pa)'); ylabel('cumulative frequency');

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Appendix D Matlab codes developed to process images and the data obtained

from PIV

clear all file='D:\Jan-29-2012\300-10-trigger2-full\300-10-trigger2avi'; nframes=aviinfo(file); nframes=nframes.NumFrames; nx=103;%number of int zones in x ny=78;%number of int zones in y n1=142252;%number of first file nend=144050;%number of last file n=nend-n1+1;% the total number of files bigim2(1:ny,1:nx,1:n)=0; bigim4(1:ny,1:nx,1:n)=0; for i=1:n; im=aviread(file,i); im=double(im.cdata); im2=imresize(im,[ny nx],'bilinear'); im3=colfilt(im2,[5 5],'sliding',@min); im4=colfilt(im3,[5 5],'sliding',@max); bigim2(:,:,i)=im2; bigim4(:,:,i)=im4; i; end save video_Jan_29_2012_300-10-trigger2.mat clear all direc='D:\Jan-29-2012\300-10-trigger2-8888\velocity2\'; nx=103;%number of int zones in x ny=78;%number of int zones in y n1=165639;%number of first file nend=167325;%number of last file n=nend-n1+1;% the total number of files bigdata(1:(nx*ny),1:4,1:n)=0; for i=1:n; file=[direc 'A' num2str(n1+i-1) '.DAT']; bigdata(:,:,i)=load(file); i; end save velocity_Jan_29_2012_300-10-trigger2-full.mat %% %vorticity clear all

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direc='D:\Jan-29-2012\300-10-trigger2-8888\vorticity3\'; nx=103;%number of int zones in x ny=78;%number of int zones in y n1=165639;%number of first file nend=167325;%number of last file n=nend-n1+1;% the total number of files vorticity(1:(nx*ny),1:3,1:n)=0; for i=1:n; file=[direc 'A' num2str(n1+i-1) '.DAT']; bigdata(:,:,i)=load(file); i; end save vorticity_Jan_29_2012_300-10-trigger-8800_996ml_min.mat %% %vorticiy analysis load vorticity_Jan_29_2012_300-10-trigger-8800_996ml_min.mat name='300-10-trigger-8800-996ml/min-trigger3'; uu=bigdata(:,3,:); x=squeeze(bigdata(:,1,1)); y=squeeze(bigdata(:,2,1)); X=reshape(x,nx,ny); Y=reshape(y,nx,ny); x1=X(:,1); y1=Y(1,:); clear bigdata UU=reshape(uu,nx,ny,n); clear uu UU2(1:size(UU,2),1:size(UU,1),1:size(UU,3))=0; for i=1:size(UU,3); UU2(:,:,i)=squeeze(UU(:,:,i))'; end UU=UU2; %% plot vorticity magnitude at image #i figure; i=1140; Vel=((((UU(:,:,:))).^2)).^0.5; imagesc(-x1,-y1,squeeze(Vel(:,:,i))); xlabel('width(mm) ');title(name); ylabel('height (mm)'); figure imagesc((1:n)./200,-x1,squeeze(nanmean(Vel(41:43,:,:),1)))

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ylabel('channel width(Vy) (mm)');title(name); xlabel('Time(s) '); % contours figure contour(UU(:,:,1140)); %% plot vorticity magnitude versus width of the channel Vel=(((nanmean(UU(41:43,:,:),1)).^2)).^0.5; z=squeeze(nanmean(Vel(:,10:12,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); figure plot((1:n)./200, zfilt1,'g')% hold on z=squeeze(nanmean(Vel(:,20:22,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'b')% hold on z=squeeze(nanmean(Vel(:,30:32,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'r')% hold on z=squeeze(nanmean(Vel(:,40:42,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'k')% hold on z=squeeze(nanmean(Vel(:,50:52,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'.k')% hold on z=squeeze(nanmean(Vel(:,60:62,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'.r')% hold on z=squeeze(nanmean(Vel(:,70:72,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean);

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plot((1:n)./200, zfilt1,'b')% hold on z=squeeze(nanmean(Vel(:,80:82,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'.g')% hold on z=squeeze(nanmean(Vel(:,90:92,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'-g')% hold on z=squeeze(nanmean(Vel(:,100:102,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'*g')% hold on xlabel('Time(s) ');title(name); ylabel('averaged vorticity profile'); %% %velocity analysis % changing the two long columns of U and V %into 3-d matrices that match the images loaded %from the video above load velocity_Jan_29_2012_300-10-trigger-8800_996ml_min.mat name='300-10-trigger2-full'; u=bigdata(:,3,:); v=bigdata(:,4,:); x=squeeze(bigdata(:,1,1)); y=squeeze(bigdata(:,2,1)); X=reshape(x,nx,ny); Y=reshape(y,nx,ny); x1=X(:,1); y1=Y(1,:); clear bigdata U=reshape(u,nx,ny,n); V=reshape(v,nx,ny,n); clear u v U2(1:size(U,2),1:size(U,1),1:size(U,3))=0; V2(1:size(V,2),1:size(U,1),1:size(V,3))=0;

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for i=1:size(U,3); U2(:,:,i)=squeeze(U(:,:,i))'; V2(:,:,i)=squeeze(V(:,:,i))'; end U=U2;V=V2; %% %% %check for exact place of the probes on the image z=(nanmean(V(41,:,:),3)); % 41 is the Y level where the probes are fixed at figure (1); plot(z); figure; %imagesc(squeeze(bigim2(:,:,i))); %f is the X position of the probe 0 (middle probe) f=41; l=42; % V profile (average over time at the Y level of the probe ) z=(nanmean(V(41,:,:),3)); figure (1) plot(-x1, z); title(name); xlabel('Width of Channel (mm)'); ylabel('average velocity profile in the middle - Vy (m/s)'); % U profile at one point %z=(squeeze(U(41,50,:))); %zfilt1=colfilt(z,[10 1],'sliding',@mean); %figure(2) %plot((1:n)./200,zfilt1); %title(name); %ylabel('Average velocity profile at the probe- Ux(m/s)'); % xlabel('Time(s) '); % U profile versus x z=(nanmean(U(41,:,:),3)); figure plot(-x1,z); xlabel('Width of Channel (mm)'); ylabel('avergae velocity profile in the middle - Ux (m/s)'); title(name);

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%% % plot velocity at one point (probe) versus time %figure %plot((1:n)./200,squeeze(V(41,50,:))); % xlabel('Time(s) ');title(name); % ylabel('Velocity at the probe 0 in Y direction'); %velocity profile averaged z=(nanmean(V(:,f:l,:),2)); z=squeeze(nanmean(z(41:43,1,:),1)); zfilt1=colfilt(z,[10 1],'sliding',@mean); figure plot((1:n)./200, zfilt1,'b')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 0'); % Plot Vy versus time versus X figure imagesc((1:n)./200,-x1,squeeze(nanmean(V(41:43,:,:),1))) ylabel('channel width(Vy) (mm)');title(name); xlabel('Time(s) '); % plot on log scale (absolute value of Vy) logVy(:,:)=nanmean(V(41:43,:,:),1); figure; imagesc((1:n)./200,-x1,squeeze(log(abs(logVy(:,:))))); ylabel('channel width(Vy) (mm)');title(name); xlabel('Time(s) '); %Plot Ux versus time versus X figure imagesc((1:n)./200,-x1,squeeze(nanmean(U(41:43,:,:),1))) ylabel('channel width(Ux) (mm)');title(name); xlabel('Time(s) '); logUx(:,:)=nanmean(U(41:43,:,:),1); figure; imagesc((1:n)./200,-x1,squeeze(log(abs(logUx(:,:))))); ylabel('channel width(Ux) (mm)');title(name); xlabel('Time(s) '); %% %find interval between bubbles

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%bulk velocity profile kkk=(10.8*200):(34*200); z=squeeze(V(41,:,kkk)); %z=squeeze(V(41,:,:)); [mmm,nnn]=size(z); Vtotal=reshape(z,1,(mmm*nnn)); z=squeeze(U(41,:,kkk)); %z=squeeze(U(41,:,:)); Utotal=reshape(z,1,(mmm*nnn)); %figure %z=(nanmean(V(:,f,:),2)); %z=squeeze(nanmean(z(41,1,:),1)); %zfilt1=colfilt(z,[10 1],'sliding',@mean); %hist(zfilt1, 100); %xlabel(' velocity at the probe 0 (m/s)');title(name); % ylabel('frequency'); figure; hist(Vtotal, 50); xlabel('velocity in the middle over time and width(Vy,m/s)');title(name); ylabel('frequency'); figure; hist(Utotal, 50); xlabel('velocity in the middle over time and width(Ux,m/s)');title(name); ylabel('frequency'); % cumulative histograms max_c_elements =n; %h=abs((1-0)./((max_c_elements)^0.5)); %kk=-2:0.001:2; %z=(nanmean(V(:,f,:),2)); %z=squeeze(nanmean(z(41,1,:),1)); %zfilt1=colfilt(z,[10 1],'sliding',@mean); %n_elements=histc(zfilt1(:,:),kk); %c_elements= cumsum(n_elements); %figure %plot(kk,c_elements./(max(c_elements))); %xlabel(' velocity at probe(m/s)');title(name); % ylabel('cumulative frequency'); %hh=abs((1-0)./((max(c_elements))^0.5)); max_Vtotal=max(Vtotal); min_Vtotal=min(Vtotal); %kk= min_Vtotal:((max_Vtotal-min_Vtotal)/50):max_Vtotal;

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kk= min_Vtotal:0.005:max_Vtotal; %kk=-1.1:0.001:1.1; n_elements=histc(Vtotal(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); xlabel('vertical velocity along the middle line (Vy,m/s)');title(name); ylabel('cumulative frequency'); max_Utotal=max(Utotal); min_Utotal=min(Utotal); %kk= min_Utotal:((max_Utotal-min_Utotal)/50):max_Utotal; kk= min_Utotal:0.005:max_Utotal; n_elements=histc(Utotal(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); xlabel('horizontal velocity along the middle line (Ux, m/s)');title(name); ylabel('cumulative frequency'); %% % plot magnitude of velocity= (Vy^2+Ux^2)^0.5 % plot magnitude of velocity= (Vy^2+Ux^2)^0.5 Vel(:,:,:)=(((nanmean(U(41:43,:,:),1)).^2)+((nanmean(V(41:43,:,:),1)).^2)).^0.5; % Vel(:,:)=(((nanmean(U(41:43,:,:),1)).^2)+((nanmean(V(41:43,:,:),1)).^2)).^0.5; z=squeeze(nanmean(Vel(:,10:12,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); figure plot((1:n)./200, zfilt1,'g')% hold on z=squeeze(nanmean(Vel(:,20:22,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'b')% hold on z=squeeze(nanmean(Vel(:,30:32,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean);

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plot((1:n)./200, zfilt1,'r')% hold on z=squeeze(nanmean(Vel(:,40:42,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'k')% hold on z=squeeze(nanmean(Vel(:,50:52,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'.k')% hold on z=squeeze(nanmean(Vel(:,60:62,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'.r')% hold on z=squeeze(nanmean(Vel(:,70:72,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'b')% hold on z=squeeze(nanmean(Vel(:,80:82,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'.g')% hold on z=squeeze(nanmean(Vel(:,90:92,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'-g')% hold on z=squeeze(nanmean(Vel(:,100:102,:),2)); zfilt1=colfilt(z,[10 1],'sliding',@mean); plot((1:n)./200, zfilt1,'*g')%

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hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile'); %% %plot vertical velocity z=squeeze(nanmean(V(41,40:42,:),2)); figure plot((1:n)./200, z,'k')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 0'); z=squeeze(nanmean(V(41,50:52,:),2)); plot((1:n)./200, z,'r')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 1'); z=squeeze(nanmean(V(41,60:62,:),2)); plot((1:n)./200, z,'b')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 2'); z=squeeze(nanmean(V(41,70:72,:),2)); plot((1:n)./200, z,'b')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 3'); z=squeeze(nanmean(V(41,80:82,:),2)); plot((1:n)./200, z,'.g')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 3'); z=squeeze(nanmean(V(41,90:92,:),2)); plot((1:n)./200, z,'*g')% hold on xlabel('Time(s) ');title(name); ylabel('averaged velocity profile at the probe 3'); %% %plot velocity map figure;

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imagesc((1:n)./200,-x1,squeeze(Vel(:,:))); ylabel('channel width(Vel) (mm)');title(name); xlabel('Time(s) '); % plot log scale of Velocity magnitude figure; imagesc((1:n)./200,-x1,squeeze(log((Vel(:,:))))); ylabel('channel width(Vel) (mm)');title(name); xlabel('Time(s) '); %% % Magnitude of Velocity in the middle between two bubbles z=squeeze(Vel(:,2208:6833)); [mmm,nnn]=size(z) Veltotal=reshape(z,1,(mmm*nnn)); figure; hist(Veltotal, 50); xlabel('velocity in the middle over time and width(Vel,m/s)');title(name); ylabel('frequency'); max_Veltotal=max(Veltotal); min_Veltotal=min(Veltotal); %kk= (0.00001+min_Veltotal):((max_Veltotal-min_Veltotal)/500):max_Veltotal; kk= (0.00001+min_Veltotal):0.005:max_Veltotal; n_elements=histc(Veltotal(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); xlabel('velocity along the middle line (Vel,m/s)');title(name); ylabel('cumulative frequency'); % Magnitude of Velocity in the middle between two bubbles z=squeeze(V(41,:,2208:6833)); [mmm,nnn]=size(z) Vtotal=reshape(z,1,(mmm*nnn)); figure; hist(Vtotal, 50); xlabel('velocity in the middle over time and width(V,m/s)');title(name); ylabel('frequency'); max_Vtotal=max(Vtotal); min_Vtotal=min(Vtotal); %kk= (0.00001+min_Veltotal):((max_Veltotal-min_Veltotal)/500):max_Veltotal; kk= (0.00001+min_Vtotal):0.005:max_Vtotal;

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n_elements=histc(Vtotal(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); xlabel('velocity along the middle line (V,m/s)');title(name); ylabel('cumulative frequency'); %% %% % velocity for one image includes bubble Vel2=((((U(:,:,6874))).^2)+(((V(:,:,6874))).^2)).^0.5; kk=0; for ii=10:10:60 kk=kk+1; z=squeeze(nanmean(Vel2(ii:ii+2,:),1)); zfilt1=colfilt(z,[1 10],'sliding',@mean); figure (100); %subplot(2,3,kk) plot(-x1, zfilt1,'b')% xlabel('velocity versus x at 6874 (Vel,m/s)');title(name); ylabel('velocity'); hold on z=squeeze(nanmean(V(ii:ii+2,:,6874),1)); zfilt1=colfilt(z,[1 10],'sliding',@mean); figure (101); %subplot(2,3,kk) plot(-x1, zfilt1,'b')% xlabel('vertical velocity versus x at 6874 (Vel,m/s)');title(name); ylabel('velocity'); hold on z=squeeze(nanmean(U(ii:ii+2,:,6874),1)); zfilt1=colfilt(z,[1 10],'sliding',@mean); figure (102); %subplot(2,3,kk) plot(-x1, zfilt1,'b')% xlabel('horizontal velocity versus x at 6874 (Vel,m/s)');title(name); ylabel('velocity'); hold on end

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%% %matrix with probe velocities [m,n]=size(Vel); i=1; for i=1:n new(i,1)=i./200; end new(:,2)=(nanmean(Vel(50:52,:),1)); new(:,3)=(nanmean(Vel(60:62,:),1)); new(:,4)=(nanmean(Vel(70:72,:),1)); new(:,5)=(nanmean(Vel(80:82,:),1)); new(:,6)=(nanmean(Vel(90:92,:),1)); fileOut = strcat('velocity at 5 position-500-10.txt'); save( fileOut ,'new','-ascii'); %%ArcTan(:,:)= atand(((nanmean(U(41:43,:,:),1))./ (nanmean(V(41:43,:,:),1)))); figure; hist(new(:,2), 10); xlabel('50 velocity(m/s)');title(name); ylabel('frequency'); figure; hist(new(:,3), 10); xlabel('60 velocity(m/s)');title(name); ylabel('frequency'); figure; hist(new(:,4), 10); xlabel('70 velocity(m/s)');title(name); ylabel('frequency'); figure; hist(new(:,5), 10); xlabel('80 velocity(m/s)');title(name); ylabel('frequency'); figure; hist(new(:,6), 10); xlabel('90 velocity(m/s)');title(name); ylabel('frequency');

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figure kk=0:0.001:1; n_elements=histc(new(:,2),kk); c_elements= cumsum(n_elements); plot(kk,c_elements./(max(c_elements)),'g'); hold on kk=0:00.001:1; n_elements=histc(new(:,3),kk); c_elements= cumsum(n_elements); plot(kk,c_elements./(max(c_elements)),'b'); hold on kk=0:0.001:1; n_elements=histc(new(:,4),kk); c_elements= cumsum(n_elements); plot(kk,c_elements./(max(c_elements)),'b'); hold on kk=0:0.001:1; n_elements=histc(new(:,5),kk); c_elements= cumsum(n_elements); plot(kk,c_elements./(max(c_elements)),'p'); hold on kk=0:0.001:1; n_elements=histc(new(:,6),kk); c_elements= cumsum(n_elements); plot(kk,c_elements./(max(c_elements)),'r'); title(name); xlabel(' (Vel,m/s)');title(name); ylabel('cumulative frequency'); %% %Avergae and STD Veltotal_average=nanmean(Veltotal(:,kkk)); Veltotal_std=nanstd(Veltotal(:,kkk)); fileOut = strcat('Average V in the middle-300-10-trigger2-full.txt'); save( fileOut ,'Veltotal_average','-ascii'); fileOut = strcat('STD of V in the middle_300-10-trigger2-full.txt'); save( fileOut ,'Veltotal_std','-ascii');

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%RMS n=length(Veltotal(:,kkk)); rms= norm(Veltotal)./sqrt(n); fileOut = strcat('RMS of V in the middle_300-10-trigger2-full.txt'); save( fileOut ,'rms','-ascii'); %% % Arctan angle Utry(:,kkk)=nanmean(U(41,:,kkk),1); Vtry(:,kkk)=nanmean(V(41,:,kkk),1); i=0; j=0; [mm,nn]=size(Vtry); for i=1:mm for j=1:nn if Utry(i,j)>0 andand Vtry(i,j)>0 andand Utry(i,j)~=0 ArcTan(i,j)= atand(Vtry(i,j)./Utry(i,j)); elseif Utry(i,j)<0 andand Vtry(i,j)>0 andand Utry(i,j)~=0 ArcTan(i,j)= (atand(Vtry(i,j)./Utry(i,j)))+180; elseif Utry(i,j)<0 andand Vtry(i,j)<0 andand Utry(i,j)~=0 ArcTan(i,j)= (atand(Vtry(i,j)./Utry(i,j)))+180; elseif Utry(i,j)>0 andand Vtry(i,j)<0 andand Utry(i,j)~=0 ArcTan(i,j)= (atand(Vtry(i,j)./Utry(i,j)))+360; elseif Utry(i,j)==0 andand Vtry(i,j)>0 ArcTan(i,j)=90; elseif Utry(i,j)==0 andand Vtry(i,j)<0 ArcTan(i,j)=270; elseif Vtry(i,j)==0 andand Utry(i,j)>0 andand Utry(i,j)~=0 ArcTan(i,j)=0; elseif Vtry(i,j)==0 andand Utry(i,j)<0 andand Utry(i,j)~=0 ArcTan(i,j)=180; end end end %%ArcTan(:,:)= atand(((nanmean(U(41:43,:,:),1))./ (nanmean(V(41:43,:,:),1)))); z=squeeze(ArcTan(:,:));

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[mmm,nnn]=size(ArcTan(:,:)); AngelTotal(:,:)=reshape(z,1,(mmm*nnn)); figure; hist(AngelTotal(:,:), 50); xlabel('Angle velocity in the middle over time and width(Vel,m/s)');title(name); ylabel('frequency'); kk=0.1:0.1:360; n_elements=histc(AngelTotal(:,:),kk); c_elements= cumsum(n_elements); figure plot(kk,c_elements./(max(c_elements))); xlabel('Angle velocity along the middle line (Vel,m/s)');title(name); ylabel('cumulative frequency'); %Avergae and STD AngelTotal_average=nanmean(AngelTotal(:,:)); AngelTotal_std=nanstd(AngelTotal(:,:)); fileOut = strcat('Average V Angle in the middle_300-10-trigger2-full.txt'); save( fileOut ,'AngelTotal_average','-ascii'); fileOut = strcat('STD of V Angle in the middle_300-10-trigger2-full.txt'); save( fileOut ,'AngelTotal_std','-ascii'); %RMS n=length(AngelTotal(:,:)); rms= norm(AngelTotal(:,:))./sqrt(n); fileOut = strcat('RMS of V Angle in the middle_300-10-trigger2-full.txt'); save( fileOut ,'rms','-ascii');

206

Appendix E Filtration data

In this chapter typical results from filtration experiments are presented for the sparging

conditions studied.

207

a

b

c

Figure D.1 Typical results from filtration experiments for coarse bubble sparging

(a: discrete; b: 0.25 Hz;c:0.5Hz)

208

a

b

c

Figure D.2 Typical results from filtration experiments for pulse bubble sparging at 150 mL

(a: discrete; b: 0.25 Hz;c:0.5Hz)

209

a

b

c

Figure D.3 Typical results from filtration experiments for pulse bubble sparging at 300 mL

(a: discrete; b: 0.25 Hz;c:0.5Hz)

210

a

b

c

Figure D.4 Typical results from filtration experiments for pulse bubble sparging at 500 mL

(a: discrete; b: 0.25 Hz;c:0.5Hz)

211

Appendix F Horizontal distribution of the shear stress for medium and large

pulse bubble sparging

The same trend was observed for medium and large pulse bubbles; with an increase in bubble

size and sparging frequency the magnitude of shear stress increased (Figures F.1 to F.6). At the

discrete sparging frequency, bubbles ascended on a vertical path in the center of the system tank

where the sparger was installed and therefore the highest magnitude of shear stress was measured

in the center of the system tank (Figure F.1 and Figure F.4). However, at higher sparging

frequencies (Figures F.2, F.3, F.5 and F.6) bubbles moved on a zigzag path and therefore the

highest magnitude of shear stress was measured on the probes that were on the moving path of

the ascending bubbles. The magnitude of velocity and shear stress was observed to increase with

the increase in the sparing frequency and bubble size (Figures F.2, F.3, F.5 and F.6).

212

a

b

c

d

Figure F-1 Typical distribution of shear stress induced by medium (300 mL) pulse bubble sparging at discrete sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

213

a

b

c

d

Figure F-2 Typical distribution of shear stress induced by medium (300 mL) pulse bubble sparging at 0.25Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

214

a

b

c

d

Figure F-3 Typical distribution of shear stress induced by medium (300 mL) pulse bubble sparging at 0. 5Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

215

a

b

c

d

Figure F-4 Typical distribution of shear stress induced by medium (500 mL) pulse bubble sparging at discrete sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

216

a

b

c

d

Figure F-5 Typical distribution of shear stress induced by medium (500 mL) pulse bubble sparging at 0.25 Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

217

a

b

c

d

Figure F-6 Typical distribution of shear stress induced by medium (500 mL) pulse bubble sparging at 0. 5 Hz sparging frequency

(a: shear stress at position 1; b: shear stress at position 2; c:shear stress at position 3;d: shear stress at position 4)

218

Appendix G: Correlation between cut off velocity and rate of fouling

As described in Section 4.1.3, a cut off velocity of 0.2 m/s was selected for the zone of

influence induced by bubbles, based on the velocity and vorticity measurements. This was

confirmed by comparing the effect of cut of velocity on the area of zone of influence and its

correlation with the fouling rate. The area of zone of influence was calculated for different cut

off velcoities of 0.1, 0.15, 0.2, 0.25, 0.3, and 0.4 m/s. The correlation between the area of zone of

influence at each cut off velocity and rate of fouling was found using curve fitting. The

coefficient of determination (R2) of each fitted curve was compared, as illustrated in Figure G-1.

Figure G-1 illustrates that cut off velocities of 0.2 m/s and lower resulted in the same correlation

between fouling rate and area of zone of influence (using a cut off velocity of 0.2 m/s and lower

will result in a zone of influence that covers all the system).

Figure G – 1 Statitical analyses of the effect of cut off velocity on the area of zone of

influence and the induced fouling rate