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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
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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
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