EXPERIMENTAL INVESTIGATION OF MIXING ENHANCEMENT IN A SMALL MIXING
LAYER FACILITY AT LOW REYNOLDS NUMBER
By
Rohit Somnath Nehe

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering – Doctor of Philosophy
2013

ABSTRACT
EXPERIMENTAL INVESTIGATION OF MIXING ENHANCEMENT IN A SMALL MIXING
LAYER FACILITY AT LOW REYNOLDS NUMBER
By
Rohit Somnath Nehe

Many chemical and biological analyses are carried out in small devices which require rapid
mixing of reactants. These miniaturized devices involve low speed flow wherein mixing occurs
in the absence of turbulence. Microfluidic mixing devices are known to be poor mixers since
molecular diffusion at the interface of flow streams forms the only mechanism of mixing. The
key to enhance the mixing in such a low speed regime is to manipulate the contact area of two
initially segregated flow streams.
In regards to the above mentioned problem, an experimental investigation is performed to
understand the mixing field in a low Reynolds number forced wake flow. The flow velocity is so
low that, in the absence of the imposed perturbation, mixing is primarily governed by interfacial
diffusion mechanism which is similar to the situations commonly seen in microfluidic
applications. To enhance the mixing interfacial area, flow perturbation is provided over a range
of frequencies and amplitudes. The chemically reacting laser induced fluorescence technique
(LIF) is used to quantify the level of mixedness, while single component molecular tagging
velocimetry (MTV) technique is used to measure the amplitude of perturbation velocity. A nonreacting LIF technique is utilized for few selected forcing cases to study the distribution of
mixed fluid composition.
Each forcing frequency creates a unique interfacial mixed fluid structure with different levels
of chemical product. For low forcing frequencies, mixed and unmixed fluid regions were noticed

wherein mixed fluid was found on the interfacial structures. A large amount of chemical product
was observed for certain high forcing frequencies which also corresponded to the highest
perturbation velocity amplitudes, highlighting the large velocity dynamics involved in these
cases. These highly mixed cases are also found to show asymmetric mixing characteristics. A
chemically reacting LIF was also performed at lower forcing amplitude over all the forcing
frequencies, and the amount of mixedness is seen to be directly connected to the forcing
amplitude.
In addition to quantifying the mixedness, a stationary and reverse flow behavior of the mixed
fluid structure was observed in certain forced cases. This phenomenon is discussed in detail by
utilizing phase resolved streamwise chemically reacting LIF concentration fields.

Copyright by
ROHIT SOMNATH NEHE
2013

DEDICATION
I dedicate this dissertation to my mother, grandmother and (late) grandfather for their
love, support and guidance throughout my life.

v

ACKNOWLEDGEMENTS
I would like to acknowledge my advisor, Dr. Manoochehr M. Koochesfahani (Dr. K)
for his continuous guidance during my PhD studies. His mentorship and encouragement
throughout my research has always motivated me to work hard and strive for excellence.
Also, I would sincerely thank Dr. K for providing me an opportunity to work on a “gas
phase photochemistry” problem, in addition to the fluid dynamics research described in
this dissertation. Photochemistry project allowed me to enhance my knowledge and
broaden the research experience at Michigan State University.
I am very grateful to my doctoral committee members, Dr. Farhad Jaberi, Dr. Charles
Petty and Dr. Ahmed Naguib for the comments and suggestions recommended by them
during the course of Ph.D. program. I would also like to extend special thanks to Dr.
Ahmed Naguib for all the valuable discussion during the first year of PhD program as my
co-advisor.
Gratitude is also due to Michael Mclean, Roy Baliff and Alan Lawrenz for all the
technical assistance related to various aspect of the experimental setup.
I would like to extend my thanks to all of the current as well as the previous members
of ERC fluids group which includes laboratories TMUAL, FPaCL and TSFL for creating
a very lively and friendly research environment. I would like to specially acknowledge Dr.
Shahram Pouya for mentoring me throughout my PhD on operating different instruments
in the laboratory and providing me his inputs whenever it was needed. I would also like
to thank David Olson for helping me with the MTV and LIF data processing programs
and also for many other stimulating technical and non-technical discussions. Special

vi

thanks to Kyle and Lisa Bade, Dr. Bruno Monnier and Rachel for being good friends in
and out of the lab and also for the valuable words of encouragement throughout my PhD.
Last, but not the least, I would like to take this opportunity to thank my family, which
includes, my mother, grandparents, uncles and aunts for their support, patience and tacit
understanding yet warm enough to motivate me to achieve my dream of attending a
graduate school and performing scientific research.

vii

TABLE OF CONTENTS

LIST OF TABLES .........................................................................................................x
LIST OF FIGURES .......................................................................................................xi
KEY TO SYMBOLS......................................................................................................xix
1. INTRODUCTION....................................................................................................1
1.1. PREVIOUS WORK............................................................................................4
1.1.1. Forced mixing layer................................................................................4
1.1.2. Mixing in microfluidic devices ..............................................................6
1.2. OBJECTIVE OF THE CURRENT WORK .......................................................11
2. EXPERIMENTAL FACILITY AND INSTRUMENTATION ...........................12
2.1. EXPERIMENTAL FACILITY ..........................................................................12
2.2. FORCING MECHANISM AND CONDITIONS ..............................................14
2.3. IMAGING SYSTEM ..........................................................................................15
3. DIAGNOSTICS: NOTES ON CHEMICALLY REACTING LASER INDUCED
FLUORESCENCE ...................................................................................................20
3.1. WORKING PRINCIPLE ....................................................................................20
3.2. DATA REDUCTION PROCEDURE ................................................................24
4. RESULTS AND DISCUSSION ..............................................................................27
4.1. QUALITATIVE FEATURES OF UNFORCED AND FORCED WAKE FLOW
FROM STREAMWISE IMAGING (A3 = 60 µm, F = 0 - 25 Hz) .....................28
4.1.1. Chemically reacting spanwise LIF measurements
(A3 = 60 µm, F = 0 - 25 Hz) ...................................................................33
4.1.2. Non-reacting spanwise LIF measurement
(A3 = 60 µm, F = 12 and 19 Hz) ............................................................50
4.1.3. Streamwise velocity measurement of the unforced and forced flow
(A3 = 60 µm, F = 0 - 25 Hz) ...................................................................57
4.2. CHEMICALLY REACTING STREAMWISE AND SPANWISE LIF
MEASUREMENTS (A2 = 40 µm, F = 2 - 25 Hz) .............................................68
4.2.1. Streamwise velocity measurement of the forced flow
(A2 = 40 µm, F = 2 - 25 Hz) ...................................................................85
4.3. CHEMICALLY REACTING STREAMWISE LIF MEASUREMENTS AT
LOW FORCING AMPLITUDE (A1 = 25 µm, F = 2 - 25 Hz) ..........................92
4.4. STATIONARY FLOW BEHAVIOR OF MIXED FLUID ................................95
4.5. REVERSE FLOW CHARACTERISTICS .........................................................101

viii

4.6. MIXING PERFORMANCE CORRESPONDING TO VARIOUS FORCING
FREQUENCIES AT FIXED VELOCITY AMPLITUDE .................................104
5. CONCLUSIONS ......................................................................................................110
6. FUTURE DEVELOPMENTS.................................................................................114
APPENDICES ................................................................................................................116
APPENDIX A. DELAY TIME BETWEEN UNDELAYED AND DELAYED
IMAGES USED FOR MTV EXPERIMENTS ..............................117
APPENDIX B. ESTIMATE OF PHOTOBLEACHING EFFECT ..........................121
APPENDIX C. CHEMICAL PRODUCT HISTOGRAM
(U = 20 mm/s, A3 = 60 µm, F = 2 - 25 Hz, SPANWISE
IMAGING) .....................................................................................122
APPENDIX D. CHEMICAL PRODUCT HISTOGRAM
(U = 20 mm/s, A2 = 40 µm, F = 2 - 25 Hz, SPANWISE
IMAGING) .....................................................................................132
BIBLIOGRAPHY ..........................................................................................................142

ix

LIST OF TABLES

Table 1-1. Typical diffusivities for various tracers at room temperature (Squires et al.
2005) ..............................................................................................................2
Table 2-1. Forcing conditions for the mixing experiments. The letters ST and SP
indicates the streamwise and spanwise LIF imaging .....................................15
Table A-1. Delay and Exposure time used for MTV experiments (U = 20 mm/s) .........119

x

LIST OF FIGURES

Figure 1-1. Schematic of flow through a microfluidic channel
(green color indicates mixing due to diffusion) ...........................................1
Figure 1-2. Mixing of two water streams downstream of a splitter plate tip
(a) A natural flow showing a passive (unperturbed) diffusion layer
(b)Actively perturbed flow showing a large increase in the mixing interface.
(Unpublished data by Jason Smith (1999) at TMUAL) ...............................3
Figure 1-3. Sketch of a wake flow ..................................................................................4
Figure 1-4. Schematic of various passive micromixers
(a) Three dimensional serpentine channel (Liu et al. 2000) (b) Herringbone
channel (Strook et al. 2002) (c) Zigzag channel (Mengeaud et al. 2002) ....7
Figure 1-5. Schematic of various active micromixers
(a) A magnetic mixing device using a blade in its mixing chamber. (b)
Magnetic micromixers using doped magnetic particles ...............................9
Figure 1-6. Numerical simulation result of two inlet flows pulsed at a 90 phase
difference (Contour plot of mass fraction from Glasgow et al. 2003) .........10
Figure 2-1. (a) Schematic of the mixing layer facility (Not drawn to scale) ..................13
Figure 2-1. (b) Forcing mechanism (Bellows) ................................................................13
Figure 2-2. Setup for (a) streamwise (x-y plane) and (b) spanwise imaging (y-z plane)
17
Figure 2-3. Optical experimental configuration for molecular tagging velocimetry
(MTV) experiments ......................................................................................18
Figure 3-1. Measured pH dependence of fluorescein dye...............................................21
Figure 3-2. Measured fluorescence intensity versus base volume fraction in chemically
reacting LIF ..................................................................................................22
Figure 3-3. Product concentration Cp versus base volume fraction ξB in chemically
reacting LIF ..................................................................................................26
Figure 4-1. Instantaneous normalized product concentration field C * ( x, y, t ) of unforced
P
flow at midspan (z = 0).................................................................................28
xi

Figure 4-2. Instantaneous normalized product concentration field C * ( x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A3 = 60 µm).........................................31
Figure 4-3. Instantaneous normalized product concentration field C * ( x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A3 = 60 µm).........................................32
Figure 4-4. Normalized chemical product area for range of forcing frequencies measured
at four different streamwise locations (U = 20 mm/s and A3 = 60 µm).......34
Figure 4-5. Instantaneous normalized chemical product concentration field at x = 4.2 mm
of unforced flow ...........................................................................................35
Figure 4-6. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 2 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................37
Figure 4-7. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 4 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................38
Figure 4-8. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 8 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................39
Figure 4-9. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 10 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................43
Figure 4-10. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 12 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................44
Figure 4-11. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 15 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................45
Figure 4-12. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 18 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................46
Figure 4-13. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 19 Hz, U = 20 mm/s and A3 = 60
xii

µm) ...............................................................................................................47
Figure 4-14. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 20 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................48
Figure 4-15. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 25 Hz, U = 20 mm/s and A3 = 60
µm) ...............................................................................................................49
Figure 4-16. Instantaneous normalized concentration field ξ ( y , z ) from non-reacting LIF
experiment corresponding to 12 and 19 Hz forcing frequency at x = 25 mm
(U = 20 mm/s, A3 = 60 µm, spanwise imaging) ..........................................51
Figure 4-17. (a) Total pdf of mixed fluid concentration from non-reacting LIF
Experiment (F = 12 Hz, A3 = 60 µm, x = 25 mm, Spanwise imaging).
(b) Total pdf of mixed fluid concentration from non-reacting LIF experiment
(F = 19 Hz, A3 = 60 µm, x = 25 mm, Spanwise imaging) ...........................53
Figure 4-18. Pdf of mixed fluid concentration from standard LIF experiment at various
span locations and fixed streamwise location x = 25 mm
(F = 12 Hz, A3 = 60 µm, x = 25 mm, Spanwise imaging) ...........................54
Figure 4-19. Pdf of mixed fluid concentration from standard LIF experiment at various
span locations and fixed streamwise location x = 25 mm
(F = 19 Hz, A3 = 60 µm, x = 25, Spanwise imaging) ..................................56
Figure 4-20. Undelayed and delayed MTV image of an unforced flow .........................57
Figure 4-21. Mean streamwise velocity profile of unforced wake flow at midspan ......59
Figure 4-22. Evolution of the wake velocity deficit of unforced wake flow in the
streamwise direction at midspan ..................................................................59
Figure 4-23. Normalized average RMS streamwise velocity for various forcing
frequencies and for a fixed perturbation amplitude A3 = 60 µm measured at x
= 3 mm..........................................................................................................61
Figure 4-24. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 2 and 4 Hz forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm)...62
Figure 4-25. Mean, phase resolved and RMS streamwise velocity profile of 8 Hz forcing
frequency at midspan (U = 20 mm/s, A3 = 60 µm) ......................................63
xiii

Figure 4-26. Mean, phase resolved and RMS streamwise velocity profile of 10 and 12 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm) .........................64
Figure 4-27. Mean, phase resolved and RMS streamwise velocity profile of 15 and 18 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm) .........................65
Figure 4-28. Mean, phase resolved and RMS streamwise velocity profile of 19 and 20 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm) .........................66
Figure 4-29. Mean, phase resolved and RMS streamwise velocity profile of 25 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm) .........................67
Figure 4-30. Instantaneous normalized product concentration field C * ( x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A2= 40 µm)..........................................69
Figure 4-31. Instantaneous normalized product concentration field C * ( x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A2= 40 µm)..........................................70
Figure 4-32. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 2 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................72
Figure 4-33. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 4 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................73
Figure 4-34. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 8 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................74
Figure 4-35. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 10 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................75
Figure 4-36. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 12 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................76
Figure 4-37. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 15 Hz, U = 20 mm/s and A2 = 40
xiv

µm) ...............................................................................................................77
Figure 4-38. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 18 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................78
Figure 4-39. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 19 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................79
Figure 4-40. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 20 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................80
Figure 4-41. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 25 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................81
Figure 4-42. Normalized chemical product area for range of forcing frequencies
measured at four different streamwise locations (U = 20 mm/s and A2 = 40
µm) ...............................................................................................................83
Figure 4-43. Normalized chemical product area for range of forcing frequencies
measured at x = 4.2 mm for two different forcing amplitudes .....................84
Figure 4-44. Normalized spatially averaged RMS streamwise velocity for various forcing
frequencies and for a fixed perturbation amplitude A2 = 40 µm measured at x
= 3 mm and z = 0 ..........................................................................................85
Figure 4-45. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 2 and 4 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm)...86
Figure 4-46. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 8 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm) ............87
Figure 4-47. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 10 and 12 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm)
88
Figure 4-48. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 15 and 18 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm)
89

xv

Figure 4-49. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 19 and 20 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm)
90
Figure 4-50. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 25 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm) ..........91
Figure 4-51. Instantaneous normalized product concentration field C * ( x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A1 = 25 µm) .........................................93
*
Figure 4-52. Instantaneous normalized product concentration field C P ( x, y, t ) of forced
flow at midspan (U = 20 mm/s and A1 = 25 µm) .........................................94

Figure 4-53. Instantaneous and average normalized product concentration field of forced
flow at midspan (U = 20 mm/s and A3 = 60 µm) .........................................95
Figure 4-54. Position of the mixed fluid structure whose displacement is measured
throughout a complete forcing cycle is marked by a solid circle .................97
Figure 4-55. (a) Phase resolved displacement of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A3 = 60 µm and forcing
frequency 4 and 8 Hz.
(b) Phase resolved velocity of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A3 = 60 µm and forcing
frequency 4 and 8 Hz....................................................................................98
Figure 4-56. (a) Phase resolved displacement of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A2 = 40 µm and forcing
frequency 4 and 8 Hz.
(b) Phase resolved velocity of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A2 = 40 µm and forcing
frequency 4 and 8 Hz....................................................................................100
Figure 4-57. Streamwise chemically reacting LIF image sequence at midspan showing
the transition of forced flow (F = 12 Hz and A3 = 60 µm) to unforced flow
condition .......................................................................................................102
Figure 4-58. Normalized spatially averaged RMS streamwise velocity for various forcing
frequencies and for a three different forcing amplitudes measured at x = 3
mm and z = 0 ................................................................................................104
Figure 4-59. Normalized chemical product area for range of forcing frequencies
xvi

measured at a fixed velocity perturbation amplitude URMS/UM = 1.45
(U = 20 mm/s) ...............................................................................................105
Figure 4-60. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 12 Hz, U = 20 mm/s and A1 = 25
µm) ...............................................................................................................107
Figure 4-61. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 18 Hz, U = 20 mm/s and A1 = 25
µm) ...............................................................................................................108
Figure 4-62. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 22 Hz, U = 20 mm/s and A2 = 40
µm) ...............................................................................................................109
Figure 6-1. A sample microfluidic Y-channel ................................................................115
Figure A-1. Filtering effect on high frequency periodic signal ......................................118
Figure A-2. Close-up view of filtering effect on high frequency periodic signal ...........118
Figure C-1. Pdf of chemical product at four different streamwise locations (F = 2 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................122
Figure C-2. Pdf of chemical product at four different streamwise locations (F = 4 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................123
Figure C-3. Pdf of chemical product at four different streamwise locations (F = 8 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................124
Figure C-4. Pdf of chemical product at four different streamwise locations (F = 10 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................125
Figure C-5. Pdf of chemical product at four different streamwise locations (F = 12 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................126
Figure C-6. Pdf of chemical product at four different streamwise locations (F = 15 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................127
Figure C-7. Pdf of chemical product at four different streamwise locations (F = 18 Hz, U
= 20 mm/s and A3 = 60 µm).........................................................................128
Figure C-8. Pdf of chemical product at four different streamwise locations (F = 19 Hz, U
xvii

= 20 mm/s and A3 = 60 µm).........................................................................129
Figure C-9. Pdf of chemical product at four different streamwise locations (F = 20 Hz, U
= 20 mm/s and A3 = 60 µm) ........................................................................130
Figure C-10. Pdf of chemical product at four different streamwise locations (F = 25 Hz,
U = 20 mm/s and A3 = 60 µm) .....................................................................131
Figure D-1. Pdf of chemical product at four different streamwise locations (F = 2 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................132
Figure D-2. Pdf of chemical product at four different streamwise locations (F = 4 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................133
Figure D-3. Pdf of chemical product at four different streamwise locations (F = 8 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................134
Figure D-4. Pdf of chemical product at four different streamwise locations (F = 10 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................135
Figure D-5. Pdf of chemical product at four different streamwise locations (F = 12 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................136
Figure D-6. Pdf of chemical product at four different streamwise locations (F = 15 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................137
Figure D-7. Pdf of chemical product at four different streamwise locations (F = 18 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................138
Figure D-8. Pdf of chemical product at four different streamwise locations (F = 19 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................139
Figure D-9. Pdf of chemical product at four different streamwise locations (F = 20 Hz, U
= 20 mm/s and A2 = 40 µm).........................................................................140
Figure D-10. Pdf of chemical product at four different streamwise locations (F = 25 Hz,
U = 20 mm/s and A2 = 40 µm) .....................................................................141

xviii

KEY TO SYMBOLS

Symbol

Description

A

Cross sectional area

A1, A2, A3

Bellows forcing amplitudes

Ap

Chemical product area

Cd

Local instantaneous dye concentration

Co, Cdo

Free stream dye concentration

Cp

Chemical product

Cp(max)

Maximum chemical product

*
CP

Normalized chemical product

*
CP

Average normalized chemical product

D

Molecular diffusivity

d

Span length

F

Forcing frequency

IB

Background signal

Icorr

Corrected intensity

If, I

Fluorescence intensity

Io

Reference intensity

xix

Iref, If (max)

Maximum fluorescence intensity

l

Length of channel

Ld

Characteristic length scale for diffusive mixing

n

Number of active dye molecules

no

Initial total number of dye molecules

N

Number of images

Pe

Peclet Number

Qb

Bleaching quantum efficiency

Re

Reynolds number based on channel width

Reθ

Reynolds number based on momentum thickness

S

Length of one zig-zag pattern

t

Time

T

Time period

Td

Characteristic time scale for diffusive mixing

U

Streamwise velocity

UM

Spatially averaged streamwise velocity

Umin

Minimum streamwise velocity in wake

Umax

Maximum streamwise velocity in wake

URMS

Streamwise RMS velocity

W, w

Width of channel

x

Co-ordinate, streamwise direction
xx

y

Co-ordinate, direction normal to wall

z

Co-ordinate, spanwise direction

α

Absorption coefficient

δp

Product thickness

∆t, td

Time between undelayed and delayed image (MTV
measurements)

ε0

Dye molar absorption coefficient

λ

Wavelength of laser

ξB

Base volume fraction

ξ

Normalized concentration

ξs

Stoichiometric base volume fraction

σ

Dye absorption cross section

τb

Photobleaching time constant

Φ

Phase

φp

Laser photon flux

xxi

1. INTRODUCTION
This study involves the experimental investigation of mixing field developed from a
forced wake of a very low Reynolds number flow. Motivation of this mixing
enhancement study arises from the requirement of rapid mixing in miniaturized devices
commonly used in biological and chemical analyses. Many biological processes at small
scale involve reactions which require mixing of reactants for initiation. The challenge in a
low speed flow regime is the absence of mixing due to turbulence. Microfluidic devices
are poor mixers since the interfacial contact area is usually small. So in this case,
molecular diffusion at the interface of flow streams forms the primary mechanism of
mixing. Consider a flow in a channel of width W (see Figure 1-1), wherein the
streamwise velocity U is so low such that mixing is limited to molecular diffusion
mechanism.

Note: For interpretation of the
references to color in this and all
other figures, the reader is
referred to the electronic version
of dissertation.

U

W
Figure 1-1. Schematic of flow through a microfluidic channel
(green color indicates mixing due to diffusion)
The Peclet number for this flow is Pe =

UW
, where D is the molecular diffusivity. The
D

characteristic time scale for diffusive mixing is Td =

scale is Ld =

L
W 2U
= Pe × W or d = Pe
D
W
1

W2
, and the characteristic length
D

. Thus, the distance along the channel

required to mix the flow streams solely by the diffusion process grows linearly with
Peclet number, which is unacceptably high for the flows of practical interest to the
microfluidic community. For example, consider the diffusivities shown in Table 1-1, for
a small protein flowing in a 100 µm width channel at 100 µm/s requires Pe ~ 250 channel
widths for complete mixing by molecular diffusion alone (Squires et al. 2005). The key to
enhance the mixing in such a low speed regime is to increase the contact area of two
initially segregated flow streams or to decrease the length scale over which diffusion acts.
(This is the reason we usually stir the fluid to mix the two different species e.g. stirring of
cream by spoon in a coffee mug reduces the diffusion length scale and thus it quickly
reduces the mixing time).
Table 1-1. Typical diffusivities for various tracers at room temperature (Squires et al.
2005)
Particle
Typical size Diffusion constant
-1

3

2

Solute Ion

10 nm

2 ×10 µm /s

Small Protein

5 nm

40 µm /s

Virus

100 nm

2 µm /s

Bacterium

1 µm

0.2 µm /s

Mammalian/Human Cell

10 µm

0.02 µm /s

2

2

2

2

The present investigation utilizes an active method to enhance the mixing in a very
low speed flow. A high amplitude sinusoidal perturbation is applied on one of the flow
stream of the mixing layer facility. Prior to this work, a preliminary flow visualization
performed in TMUAL (Turbulent Mixing and Unsteady Aerodynamics Laboratory, East
2

Lansing, MSU) showed that the perturbed mixing layer exhibits local flow dynamics near
the splitter plate tip enhancing the interfacial area to increase the mixedness (see Figure
1-2). This forms the main motivation of utilizing a small mixing layer facility as a mixing
device. Another main reason for choosing a mixing layer facility for the mixing study is
the geometric resemblance with some of the small scale mixing devices e.g. Y- mixer
which are commonly used in microfluidic assay devices.
Flow stream 1

Splitter plate tip

Flow stream 2

(a)

(b)

Figure 1-2. Mixing of two water streams downstream of a splitter plate tip
(a) A natural flow showing a passive (unperturbed) diffusion layer (b) Actively perturbed
flow showing a large increase in the mixing interface.
(Unpublished data by Jason Smith (1999) at TMUAL)
A mixing layer facility can be operated as a wake or a two stream shear layer facility.
A mixing layer is said to be a shear layer when the two streams of different velocity
interact downstream of splitter plate. A wake flow is seen in a mixing layer when the two
streams have the same velocity (Figure 1-3). For the experiments described in this study,
the mixing layer facility is operated as a wake flow.

3

Figure 1-3. Sketch of a wake flow

1.1.

PREVIOUS WORK

Several research groups have been studying mixing control and enhancement
strategies in shear layers and wakes. Most of the previous studies are focused on higher
Reynolds number compared to the Reynolds number flow studied in this report ( Re = 75,
based on channel width and streamwise velocity). Although much of the previous studies
performed by researchers in the mixing layer do not relate to the current flow regime ( Re
= 75), it does provide background information on the mechanism used for mixing
enhancement. The following two subsections will cover the literature review on forced
mixing layers and mixing in microfluidic devices.
1.1.1.

Forced mixing layer

Oster & Wygnanski (1982) is one of the earliest research work performed on a forced
mixing layer. The main impetus of this work was to understand the sensitivity of the
mixing layer (growth rate) to the finite amplitude oscillations introduced at the origin of
the flow. Oster & Wygnanski (1982) showed the different growth characteristics of the
turbulent shear layer depending upon the forcing frequency and amplitude used for the
4

given velocity ratio. Koochesfahani and Dimotakis (1989) studied the flow structure of a
turbulent plane mixing layer by introducing two dimensional disturbances at some
distance downstream of the splitter plate. The response of the mixing layer in the
upstream and downstream region of the disturbance was investigated. The result showed
that the upstream and downstream region can be selectively forced by the proper choice
of the frequency. Although this study didn’t quantify the molecular level mixedness, the
results provided sufficient reasoning and motivation for researchers to manipulate and to
control the spreading rate of the mixing layer by introducing artificial excitation of
different frequency and amplitude.
Roberts and Roshko (1985) and Roberts (1985) used external forcing to study the
mixing in a wake flow (Reθ = 160, based on momentum thickness) perturbed at different
frequencies. The forced wake studied by Roberts (1985) showed a great variety of
interesting flow features. In the case of unforced wake, flow structure appeared to be a
Karman vortex street with mixing product appearing at the interface. When the flow was
forced at a frequency equal to its natural frequency (5 Hz) a well-organized flow structure
was observed. Forcing at the frequency less than the natural frequency produced a double
Karman vortex street. When the wake was forced at frequencies greater than the natural
frequencies, the breakdown of the initial street was observed followed by a dramatic
increase in mixing. The finite width of the test section and the thick side wall boundary
layer were considered to be responsible for the three dimensional nature of the flow,
causing enhanced level of mixing.
Koochesfahani and MacKinnon (1991) studied the influence of forcing on the mixed
fluid composition of two stream shear layer using the non-reacting LIF technique. For the
5

cases they studied, the distribution of mixed fluid composition was found uniform across
the width of the shear layer and an increase in the amount of mixed fluid was noted.
Another mixing study was performed by MacKinnon and Koochesfahani (1993) to
examine the effect of forcing amplitude on the mixing field of a low Reynolds number
wake flow, the same flow studied by Roberts (1985). The forcing frequency was fixed at
the natural frequency (F = 6 Hz), and Reynolds number was measured as Reθ = 100
(based on momentum thickness). A significant increase in mixing was noted for a forced
flow compared to unforced flow. Nelson (1996) performed chemically reacting LIF
experiments at the same experimental conditions as mentioned in MacKinnon and
Koochesfahani (1993). In his study, a high amplitude 2-D perturbation of the wake was
used to generate strong spanwise vortices. Similar to Roberts, they also observed
spanwise vortices - side wall interaction resulting in a dramatic increase in the three dimensionality and chemical product. The quantitative measurements made in this study
indicated an increase in mixing product by a factor of 40 over the unforced case. Also,
the maximum level of mixing for a forced wake flow was recorded as three times higher
than that observed for higher Reynolds number shear flow. A major conclusion of this
study was that a forced low Reynolds number flow can mix much better than an unforced
high Reynolds number flow.
1.1.2.

Mixing in microfluidic devices

Microfluidic research groups have been working actively on improving the
performance of mixing in microfluidic devices. In general, microfluidic devices used for
mixing (micromixers) are classified as passive or active micromixers. Mixing in passive
micromixers is obtained without using any moving part or external energy input. Passive

6

micromixers use the modifications in the geometry to introduce chaotic particle paths,
ultimately increasing the mixing. An active micromixer uses an external source of energy
for mixing process. The external source of energy or disturbance could be pressure,
temperature, electrokinetics, magneto hydrodynamics or acoustics. The detail review of
both passive and active micromixers used in microfluidics community could be found in
Stone et al. (2004) and Nguyen et al. (2005).
Outlet

300 µm
600 µm
300 µm

z
x

(a)

(b)

Stream
1 and 2

(c)

Figure 1-4. Schematic of various passive micromixers
(a) Three dimensional serpentine channel (Liu et al. 2000) (b) Herringbone channel
(Strook et al. 2002) (c) Zigzag channel (Mengeaud et al. 2002).
Liu et al. (2000) designed a three dimensional serpentine microchannel (twisted
channel) leading to chaotic advection mechanism to passively enhance fluid mixing (For
details about chaotic advection phenomenon see Aref 1984, 1990, 2002; Ottino 1989).
7

The basic building blocks of this channel were the “C-shaped” mixing segments
connected in series (Figure 1-4a). Mixing measurements were performed, and a
comparison of mixing performance of serpentine channel was made with respect to
“square-wave” and straight channel. Serpentine channel produced 16 times more mixed
product than a straight channel and 1.6 times more than a “square-wave” channel.
The distortion of the interface, twisting and turning of the flow through the serpentine
channel (chaotic advection) was explained as a reason for mixing enhancement. In
general an increase in the mixing was observed with the increase in Re for the serpentine
channel, and it was always higher than that observed for straight and square wave
channels.
Strook et al. (2002) used a herringbone channel to generate transverse flows in a
microchannel to induce chaotic stirring (Figure 1-4b). Channel geometry consisted of
ridges on the floor at an oblique angle with respect to the axis of the channel. As a result,
flow had less resistance in the direction parallel to ridges than in the orthogonal direction
leading to a transverse component of velocity. Repeated helical motion of fluid volumes
within channel produced a chaotic motion increasing the mixing. Another method to
generate chaotic advection is to use a zigzag geometry to produce flow with recirculation
regions along the channel (Figure 1-4c). Mengeaud et al. (2002) found the highest mixing
efficiency for a geometry ratio S/W = 4 using numerical simulation for Re 0.26 to 267.
For S/W = 4, below the critical Reynolds number of 80, mixing was found to be entirely
dependent on molecular diffusion mechanism. For higher Reynolds number, (80 < Re <
267) the recirculation regions observed in the channel induced a transversal component of
velocity, improving the mixing process. Lin et al. (2007) designed a planar serpentine

8

convergent-divergent channel and studied mixing using numerical simulation at Re = 160.
Alternating convergent-divergent pattern of channel caused a local rotating flow at the
turns and as a result, stretching and folding of interfaces was enhanced. This created
irregular and chaotic flow trajectories along the channel promoting the fluid mixing.
Figures 1-5 and 1-6 show few examples of active micromixers. Mensing et al. (2004)
showed an in-expensive and easy–to-fabricate magnetic mixer (see figure 1-5a). The
basic working principle of this mixer was to use a mixing blade in the mixing chamber
and to control the rotation of this blade using externally applied magnetic field. This
mixer was tested in a small channel and it was found to operate up to a flow rate of 10
ml/min.

(b)

(a)

Figure 1-5. Schematic of various active micromixers
(a) A magnetic mixing device using a blade in its mixing chamber. (b) Magnetic
micromixers using doped magnetic particles.
Campbell et al. (2004) used magnetically doped particles to introduce the mixing.
Polymeric particles were doped with magnetite and were made to rotate in the liquid
using a magnetic field of a permanent rotating bar magnet (Figure 1-5b). As a result of
externally applied magnetic field and the hydrodynamic forces, a system of rotating
particles was formed to enhance the mixedness. Bau et al. (2001) presented the
9

theoretical and experimental investigation of a magneto-hydrodynamic stirrer. In his
experiments, arrays of electrodes were deposited on a conduit wall. The conduit was
filled with electrolyte solution and a potential difference was applied across the pair of
electrodes establishing a flow of current in the solution. In presence of magnetic and
electric field a body force (Lorentz) was generated to drive the fluid. This principle was
utilized to create a complex flow field to enhance the mixing. Glasgow et al. (2003)
introduced a time pulsing cross flow into a main channel to enhance the level of mixing.
In this work, a liquid is pulsed from one inlet to periodically distort the interface between
the two flow streams. A study was also performed wherein both of the flow streams
where pulsed at a different phase. Mixing in this work was studied only at one pulsing
frequency using Fluent 6 software and it was found that the pulsed flow with 90 degree
phase difference provided the better mixing performance.

1

y
0

z

x

Figure 1-6. Numerical simulation result of two inlet flows pulsed at a 90 phase
difference (Contour plot of mass fraction from Glasgow et al. 2003)

10

1.2.

OBJECTIVE OF THE CURRENT WORK

The objective of this project is to quantify the amount of chemical product formed in a
forced wake of a low Reynolds number flow. The flow studied in this dissertation is at
such a low velocity that the natural flow (i.e. unperturbed flow) has mixing only across a
planar diffusion layer, commonly seen in microfluidic geometries. To enhance the level
of mixedness we use an active method of mixing. All the mixing measurements are made
using chemically reacting laser induced fluorescence (LIF) technique. The amount of
chemical product or the degree of mixedness is calculated from the time series data
obtained through spanwise planar measurements.
Some of the questions which will be addressed through this dissertation are as follows:
1) What is the maximum amount of chemical product for a forced mixing layer at a
very low Reynolds number?
2) How does the chemical product vary along and across the flow channel?
3) What is the range of mixing control parameters (perturbation amplitude and
frequency) to enhance the mixing at the given Reynolds number?
4) What is the flow structure dynamics within a forcing cycle?

11

2. EXPERIMENTAL FACILITY AND INSTRUMENTATION
All the experiments were performed in a small mixing layer facility located in
Turbulent Mixing and Unsteady Aerodynamics Laboratory (TMUAL). This chapter will
provide details about the experimental facility, forcing mechanism and conditions and the
imaging system used for both chemically reacting LIF and MTV experiments.
2.1.

EXPERIMENTAL FACILITY

The experiments were performed in a gravity-driven liquid two-stream mixing layer
facility with a test section of size 5 mm (w-width) × 10 mm (d-span) × 50 mm (l-length).
A schematic of the facility is shown in Figure 2-1(a). Water was pumped from two
separate reservoirs to constant head tanks, located approximately 0.4 m above the inlet of
the test section. The constant head tanks were connected to the contraction chamber by
tygon tubes. The contraction chamber housed a splitter plate separating the two streams.
th

Here, the contraction chamber is designed such that it follows 5 order polynomial with
ratio of inlet width to outlet as approximately 4. Beyond the contraction chamber, flow
was allowed to mix in the test section. The test section was constructed from quartz glass
allowing optical access for LIF and MTV measurements. The flow from the test section
entered the end section and finally it was discharged into the dump tank. An important
aspect in terms of flow quality is the air bubble entrapment or the air pockets formed in
the facility. This problem was eliminated by filling the facility with water from end
section at the start of every experiment. The flow rate through the facility was controlled
using three valves: one each along the two fluid supply lines and one at the end section.

12

Constant head tank
Reservoir

Reservoir

Position sensor

Pump
Flow
valve
sTube
Bellows

Electromagnetic
Shaker

y
z

x

Test section
Area = 5 mm x 10 mm
Length = 50 mm

End section
Dump tank

Figure 2-1(a). Schematic of the mixing layer facility (Not drawn to scale)

Bellows
Connector
between bellows
and shaker

Connector
between bellows
and tube

Figure 2-1(b). Forcing mechanism (Bellows)

13

2.2.

FORCING MECHANISM AND CONDITIONS

Perturbations were introduced in one of the flow streams using bellows attached
approximately 0.18 m upstream of the test section inlet. The diameter of bellows is 35.6
mm (Figure 2-1b). This mechanism is driven by an electromagnetic shaker (Lab works
Inc., ET-132) powered by Haffler power amplifier (P1000) whose command signal
originates from a function generator (Stanford Research systems – DS345). A position
sensor (Schaevitz sensor, 200 DCD) is used to track the actual motion of the bellows. The
signal from the position sensor is digitized by a 16 bit Analog to Digital converter (NIPCI 6221). The forcing mechanism used in this study provides an active method of
control of mixing such that the flow rate of one of the flow stream is continuously
modulated at desired frequency and amplitude. For the results described in this
dissertation, the forcing amplitude (A) defined is the actual displacement of the bellows.
The forcing amplitude in terms of velocity and the relevant analysis for each of the forced
cases will be presented in Chapter 4. Sinusoidal perturbation signals were used at three
forcing amplitudes A1 = 25 µm, A2 = 40 µm and A3 = 60 µm over the range of
frequencies F = 2 Hz to F = 25 Hz. A list of all of the forcing conditions used in this
study is tabulated in Table 2-1.
The forced cases described in this dissertation corresponds to the wake velocity U =
20 mm/s. The detail mixedness was measured for two amplitudes (A2 = 40 µm and A3 =
60 µm) while the qualitative features of the flow will be presented for the amplitude A1 =
25 µm. Detail LIF measurements corresponding to A1 = 25 µm was limited to only few
cases since typically a lower amount of mixing was measured at A1 = 25 µm.
14

Table 2-1. Forcing conditions for the mixing experiments. The letters ST and SP
indicates the streamwise and spanwise LIF imaging.
Forcing
Forcing amplitude
frequency (F Hz)

A2 = 40 µm

A3 = 60 µm

2

ST

ST, SP

ST, SP

4

ST

ST, SP

ST, SP

8

ST

ST, SP

ST, SP

10

-

ST, SP

ST, SP

12

ST, SP

ST, SP

ST, SP

15

ST

ST, SP

ST, SP

18

ST, SP

ST, SP

ST, SP

19

-

ST, SP

ST, SP

20

ST

ST, SP

ST, SP

21

-

ST, SP

ST, SP

22

-

ST, SP

-

25

2.3.

A1 = 25 µm

-

ST, SP

ST, SP

IMAGING SYSTEM

The chemically reacting laser induced fluorescence (LIF) technique is used to
measure the mixedness (details about LIF technique is discussed in chapter 3). For these
experiments, a Genesis CX488-2000 STM optically pumped semiconductor laser (light
mode, λ = 488 nm) was used as the light source. The laser power was typically in the
range 0.60 to 0.75 W. The laser beam was transformed into a thin sheet (~ 0.5 mm) using
a cylindrical lens (focal length fl = 6.35 mm) and a spherical lens (fl= 200 mm).
15

Streamwise and spanwise measurements were performed by aligning the laser sheet in
the x-y plane (i.e. along the flow direction at midspan) and in a y-z plane (i.e.
perpendicular to the flow direction) at different downstream locations. Figure 2-2
illustrates the streamwise imaging and spanwise imaging setup and the coordinate system
used in this study.

16

z x y
Laser sheet
Flow
Direction

Camera
(a)

Flow
Direction

Laser sheet

Camera
(b)
Figure 2-2. Setup for (a) streamwise (x-y plane) and (b) spanwise imaging (y-z plane).
The fluorescence signal was recorded by CCD camera (Pulnix TM-9700) operating at
30 frames per sec (2 ms exposure) and images were digitized to 8 bits. Nikkor 50 mm
f/1.2 (streamwise imaging) and Micro-Nikkor 105 mm f/2.8 (spanwise imaging) lenses
were used with an orange filter to eliminate the scattered laser light from the test section
side walls and from the unwanted impurities in the flow. For each run, 1900 continuous
17

LIF images were acquired. The in-plane spatial resolution for streamwise imaging (x-y
plane) was 65 × 65 µm, and that for spanwise (y-z plane) imaging was about 45 × 45 µm.
Multiple line molecular tagging velocimetry (MTV) was used to measure the
streamwise component of velocity in the mixing layer facility. In order to measure the
velocity, the laser beam from a Lambda-Physik LPX 220i excimer laser was used to tag
the tracer molecules. The laser beam was transformed into thin lines using the necessary
optical set up such that the distance between the lines was 0.8 mm (Figure 2-3).
Beam blocker

Cylindrical lens

Mirror

Mirror

Figure 2-3. Optical experimental configuration for molecular tagging velocimetry
(MTV) experiments.
The tagged lines were imaged using an intensified CCD camera (12 bit, DiCam Pro,
Cooke Corp.) in a double frame mode at 5 Hz (1950 images) equipped with Nikkor 105
mm f/2.8 lens. In general, the pixel resolution was maintained in the range 17.5 µm to
15.5 µm. The laser and the camera were synchronized using a digital delay generator
(Stanford Research Systems -model DDG535). The delay time td between undelayed and
delayed image was chosen such that maximum pixel displacement as well as high signal
18

to noise ratio was obtained. Another factor, which puts a constraint on choosing a delay
time, is its averaging effect on velocity measurement for high frequency forced cases.
Appendix A shows the analysis of the above mentioned problem and also lists the delay
and exposure time used for all of the different forcing cases.

19

3. DIAGNOSTICS: NOTES ON CHEMICALLY REACTING LASER INDUCED
FLUORESCENCE
This chapter will describe the working principle of the chemically reacting laser
induced fluorescence technique, data reduction procedure and also the definition of some
of parameters which are used to define mixedness.
3.1.

WORKING PRINCIPLE

A chemically reacting laser induced fluorescence (LIF) technique is used to measure
the extent of molecular mixing. This technique is an extension of non-reacting LIF
technique. A brief working principle is explained in this section while more details could
be found in Koochesfahani (1984) and Koochesfahani and Dimotakis (1986). The
chemically reacting LIF technique uses the pH sensitivity of a fluorescent dye, disodium
fluorescein, to selectively induce fluorescence only in the mixed region. At low pH the
fluorescence is essentially “off” (quenched) while at high pH (pH > 9) the fluorescence is
“on” (Figure 3-1). In the mixing layer experiment, one stream is mixed with fluorescein
dye (2.4 × 10

-7

M, disodium fluorescein) and its fluorescence is turned off by diluting it

with sulfuric acid (0.002 M, H2SO4). The second stream has no dye but it is buffered to a
high pH by adding sodium hydroxide (0.06 M, NaOH) solution. When mixing between
the two streams occurs, depending upon the local pH and the dye concentration, a
fluorescence signal is seen. The resultant fluorescence intensity is a measure of chemical
product which is formed due to a fast acid-base reaction of type A + B → P. Here, the
chemical product is defined as the dye bearing fluid whose local pH is above the
fluorescence threshold.

20

Fluorescence Intensity (If - arbitrary units)

3000
2500
2000
1500
1000
500
0

0

3

6

9

12

Solution pH
Figure 3-1. Measured pH dependence of fluorescein dye.
Figure 3-2 illustrates the relation between fluorescence intensity (chemical product
concentration Cp) and the base volume fraction ξB in the titration of a fixed volume of
acid/dye solution. Initially, fluorescence is off since the pH of the solution is below the
threshold. As the base volume fraction is increased beyond a threshold value
(stoichiometric base volume fraction ξs), the fluorescence intensity sharply rises to
maximum value. Here, the stoichiometric base volume fraction ξs defines the relative
amount of acid and base required for chemical product to form. Beyond ξs, any more
increase in base volume fraction merely dilutes the dye solution and, as a result, the
21

fluorescence intensity decreases linearly with base volume fraction. It should be noted
that “stoichiometric” base volume fraction can be adjusted by the choice of acid and base
concentrations. For the experiments described in this report, stoichiometric base volume
fraction was typically measured between 0.06 and 0.07. This base volume fraction
defines the maximum possible chemical product concentration Cp(max) or the
fluorescence intensity If(max). The instantaneous local chemical product concentration
Cp is defined by following relation
CP
C P (max)

=

If

(1)

I f (max)

If(arbitrary units)

3000

2000

1000

0

0

0.2

0.4

0.6

0.8

1.0

ξ
ξB B (Base volume fraction)

Figure 3-2. Measured fluorescence intensity versus base volume fraction in chemically
reacting LIF.
22

In chemically reacting LIF experiments, due to different concentrations of acid and
base a small density mismatch was recorded such that the density of acid and base was
3

3

measured as 995 kg/m and 1000 kg/m respectively. The densities of the two free
streams are matched by adding a sufficient amount of sodium sulfate (Na2SO4) to the
lighter stream.
Laser beam attenuation by dye molecules forms one of the possible sources of error in
LIF experiments. Koochesfahani (1984) measured the absorption coefficient α of the
fluorescein dye to be 0.16 cm

-1

corresponding to dye concentration Cd = 1 × 10

-5

M and

laser wavelength λ = 514.5 nm. The absorption coefficient scales with the dye
concentration and dye molar absorption coefficient ( ε 0 ) as α = ε 0 C d . Corresponding to
the dye concentration and the laser wavelength (λ = 488 nm) used in this experiment, an
absorption coefficient of 0.03104 cm

-1

is calculated. Attenuation of the fluorescent

intensity at any distance y is given by I = I 0 e −αy . In the worst case scenario, the
difference in the intensity between side walls of the test section would be 1.5 %. Thus,
laser beam attenuation due to dye molecules was considered negligible.
Continuous excitation of fluorescein dye causes a decrease in its absorption efficiency.
As a result, the fluorescence intensity of bleached molecule decreases continuously with
respect to time. For the current mixing problem under study, due to the long convective
time scale of the flow through the laser sheet, dye molecules are typically seen to be
photobleached in streamwise imaging. This effect is typically seen near the walls wherein
they are exposed to laser light throughout its travel time within the test section. In case of
spanwise images although the flow velocity is small, dye molecules are exposed to laser
23

light only for small period of time corresponding to passage through the thickness of laser
sheet (~ 0.5 mm) (see Appendix B for calibration of photobleaching time constant). Apart
from photobleaching time constant characterization, the fluorescence intensity at
stoichiometric mixture fraction ξs was monitored for two different velocity conditions in
the mixing layer facility. The fluorescence intensity was found to be independent of the
velocity which showed the absence of photobleaching effect in case of spanwise imaging.
Thus, the spanwise measurements will be used for quantifying the mixedness while
streamwise measurements will be referred to discuss the qualitative features of the mixed
flow.

3.2.

DATA REDUCTION PROCEDURE

The data reduction procedure used in this dissertation is discussed in this section. The
LIF technique relies on the fact that the ratio of the product concentration Cp at any
location to its value at fluorescence turn on, (Cp)max, is the same as the ratio of the
fluorescent intensity If at that location to its maximum value (If)max. Because of this, it is
necessary to remove the effect of non-uniform laser beam profile and camera pixel
response. This was accomplished by dividing all images (1900 images) by a uniform dye
concentration reference image. The reference image was generated by using uniform dye
solution in both of the streams i.e. flooding the test-section with uniform dye
concentration solution. The uniform dye concentration solution was prepared at
stoichiometric mixture fraction (ξs) which defines the maximum chemical product

24

(Cp)max. This was achieved without altering the positions of the camera, laser sheet and
test section.
Each frame in the image sequence was corrected pixel-by-pixel using the formula,
I corr =

I − IB
I ref − I B

(2)

Where I corr is the corrected pixel intensity, I is the original pixel intensity and I ref is
the fluorescent intensity of the same pixel from the reference image. Note, both I and Iref
were corrected for background signal IB . Background signal was obtained by acquiring
an image of the flow, wherein water was flooded in the test section in absence of dye
solution.
Here, the corrected intensity at each pixel of a spanwise LIF image is actually a
normalized chemical product, given as
C * ( x, y , z , t ) =
P

If
CP
=
C do I fo

(3)

Where Cdo is free stream dye concentration and I fo =

I f (max)
(1 − ξ s )

(see Figure 3-3).

The time average value of C * defines the normalized average product concentration at
P
each pixel of LIF image. The normalized average product concentration field at any
streamwise location is given as,

N

∑ (C * ) i
P

C * ( x, y, z ) = i =1
P

N

where, N defines the total number of images.

25

Cdo
Cp(max)

Cp(ξB)

0

ξs
ξS

1
ξB

Figure 3-3. Product concentration Cp versus base volume fraction ξB in chemically
reacting LIF.
It is customary to quantify the amount of mixing product across the wake width using the
product thickness δ p defined as (see Koochesfahani, 1984),

δ p ( x, z ) =

+w 2

∫

C * ( x, y , z ) dy
P

(4)

−w 2
Integrating δ p across the test section span results in the total amount of product at a
downstream distance x. This quantity is called the product area Ap and is defined as

A p (x ) =

+d 2

∫ δ p ( x, z )dz

(5)

−d 2

In this thesis, mixedness will be quantified using product area A p ( x ) obtained from
spanwise measurements.

26

4. RESULTS AND DISCUSSION
This chapter provides the results and discussion of the forced flow in the mixing layer
facility operated at velocity U = 20 mm/s. Experimental runs were performed at two
forcing amplitudes A2 = 40 µm and A3 = 60 µm and at a range of forcing frequencies (F
= 2, 4, 8, 10, 12, 15, 18, 19, 20, 25 Hz). Mixedness results are obtained from chemically
reacting LIF technique. Chemically reacting streamwise LIF imaging was performed at z
≈ 0 while spanwise imaging at x = 4.2, 9, 15 and 25 mm. The chemically reacting
streamwise LIF imaging was also performed at A1 = 25 µm to show the effect of very
low forcing amplitude on the mixedness, however the detail mixing measurements are
limited to forcing amplitudes A2 = 40 µm and A3 = 60 µm. All the mixing results and its
discussion will be made based on streamwise and spanwise imaging.
Molecular Tagging Velocimetry (MTV) is used to obtain the streamwise velocity
information. Here, U = 20 mm/s represents the maximum streamwise velocity of both of
the unforced flow streams measured at x = 3 mm which is the most upstream location
where the velocity profile measurements were possible. The streamwise velocity
measurements were performed for forced flow at midspan i.e. z ≈ 0 to quantify the
velocity perturbation amplitude. The mean streamwise velocity and RMS velocity profile
of the forced flow will be utilized to quantify the flow dynamics within one forcing cycle.

27

4.1.

QUALITATIVE FEATURES OF UNFORCED AND FORCED WAKE
FLOW FROM STREAMWISE IMAGING ( A3 = 60 µm, F = 0-25 Hz)

A typical instantaneous LIF image of unforced flow is shown in Figure 4-1,
illustrating the normalized chemical product field C * ( x, y , t ) due to mixing of two
P
streams (acid + dye, base) at a given time (t) over the x-y plane at the midspan of the test
section. The instantaneous normalized concentration field is pseudo-colored and the color
map is shown in Figure 4-1.
4 mm
x = 3.5 mm

y
x
Flow
direction

x = 32 mm

C * ( x, y , t )
P

Figure 4-1. Instantaneous normalized product concentration field C * (x, y, t ) of
P
unforced flow at midspan (z = 0).
28

The unforced flow shown in Figure 4-1 has such a low velocity that the chemical
product appears as a thin straight line at the interface of two co-flowing streams. The
chemical product formed at the interface is solely due to the diffusion mechanism.
Although the chemical product thickness increases with downstream distance, very little
molecular mixing is seen for unforced flow.
Figures 4-2 and 4-3 depict the instantaneous normalized chemical product field of
forced flow at midspan for different forcing frequencies. The forced wake at forcing
frequency 2 Hz shows the interface being stretched and folded along and across the width
of channel with the chemical product being formed at the interface. The interfacial
structure formed due to forcing appears to maintain its overall shape, with longer tails
near the wall region as it progresses downstream. As expected, due to increase in the
forcing frequency, the mixed fluid structures formed at 4 Hz forcing frequency are
smaller in size compared to 2 Hz, and they appear to be more tightly arranged within the
channel. In general, for 2 Hz and 4 Hz forcing cases, the interfacial structures appear to
become thicker with more chemical product as the flow moves in the streamwise
direction. The mixing structures formed for 8 Hz case are periodic thin striations which
spans across the width of the test section. As the flow moves downstream, this thin
striation becomes smaller in size. Apart from thin striations of mixed fluid, a dense region
of mixed fluid is seen on the side of the flow stream which is being forced.
A dramatic increase in mixed fluid is seen for higher forcing frequencies (10, 12, 18,
19, 20 Hz) except for 15 and 25 Hz. The enhancement in mixedness for these forcing
frequencies is so high that the whole height and the width of the test section is filled with
mixed fluid and a large amount of chemical product is observed at a very early

29

streamwise location. Unlike lower forcing frequencies, unmixed fluid region was not
seen for the higher forcing frequency forced flow which also indicates the level of
molecularly mixed fluid in the test section. Such a complex mixing field is best
understood and quantified by spanwise images of the flow taken at various streamwise
locations which will be discussed in the Chapter 4.1.2.
Forcing frequencies of 15 and 25 Hz also show an increase in the mixedness compared
to low forcing frequencies. Unlike the other higher forced frequency cases it shows
regions with low levels of mixed fluid within the test section.

30

F = 2 Hz

F = 4 Hz

F = 8 Hz

F = 10 Hz

F = 12 Hz

F = 15 Hz

F = 18 Hz

F = 19 Hz

C * ( x, y , t )
P

Figure 4-2. Instantaneous normalized product concentration field C * (x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A3 = 60 µm).
31

F = 20 Hz

F = 25 Hz

C * ( x, y , t )
P

Figure 4-3. Instantaneous normalized product concentration field C * (x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A3 = 60 µm).

32

4.1.1. Chemically reacting spanwise LIF measurements
(A3 = 60 µm, F = 0 - 25 Hz)
In order to quantify the extent of mixedness, the chemical product area is calculated by
utilizing the spanwise chemical product concentration field C * ( x, z , y , t ) . Note that, the
P
chemical product referred in this dissertation relates to a chemical reaction described by
Figure 3-2 and Figure 3-3. The average chemical product area was calculated at four
different streamwise locations (x = 4.2, 9, 15 and 25 mm). The chemical product area at
each of the streamwise locations is the span-averaged data obtained from 1900
instantaneous normalized chemical product concentration fields C * ( x, z , y , t ) . If we
P
define A as the measure of the total area at streamwise location x mm (A = 4 mm × 9
mm), then the normalized product area ratio AP A represents the measure of the
chemical product area per unit cross sectional area (A) of the test section. This can also
be interpreted as the mixing efficiency.
Figure 4-4 depicts the normalized chemical product area measured at four different
streamwise locations (x = 4.2, 9, 15 and 25 mm) over a range of forcing frequency F = 0 25 Hz and for a fixed forcing amplitude A3 = 60 µm. In the following section, figure 4-4
will be utilized to discuss the amount of chemical product area formed at each forcing
frequency and at different streamwise locations. The instantaneous normalized product
concentration field C * ( x, y, z , t ) and average normalized product concentration field
P
C * ( x, y , z ) of unforced and forced cases are shown in Figures 4-5 to 4-15. For each
P
forcing frequency, the instantaneous and average normalized chemical product

33

concentration field measured at x = 4.2, 9, 15 and 25 mm will be utilized as qualitative

Normalised Chemical Product Area (AP/A )

and quantitative result.

1.0
x = 4.2 mm
x = 9 mm
x = 15 mm
x = 25 mm

0.8
0.6
0.4
0.2
0

0

5

10

15

20

25

F (Hz)
Figure 4-4. Normalized chemical product area for range of forcing frequencies measured
at four different streamwise locations (U = 20 mm/s and A3 = 60 µm).
The effect of forcing on the mixedness is apparent in Figure 4-4 as the normalized
chemical product area at any given forcing frequency was found to be greater than that of
unforced flow. This is mainly because in case of unforced flow chemical product is
limited and found only at the thin interfaces separating the two free stream fluids. This
result is seen in both streamwise and spanwise concentration fields shown in Figure 4-1
and 4-5 respectively.

34

Unforced flow

y

9 mm

z

4 mm
x = 4.2 mm, Unforced flow
C * ( y, z , t )
P

Figure 4-5. Instantaneous normalized chemical product concentration field at x = 4.2 mm
of unforced flow.
Figure 4-6, 4-7 and 4-8 highlight the spanwise chemical product concentration field at
four different streamwise locations for forcing frequencies 2, 4 and 8 Hz respectively.
The visual inspection of the forced flow at frequencies 2 and 4 Hz from streamwise and
spanwise concentration fields showed chemical product formed at the interfacial structure,
and the amount was seen to increase in the streamwise direction. As a result, the
normalized chemical product area for the forcing frequencies 2 and 4 Hz obtained from
spanwise concentration fields show an increasing trend with respect to streamwise
direction (Figure 4-4). The same conclusion is not applicable to 8 Hz forcing case, since
the chemical product area at x = 15 mm is smaller than x = 9 mm, which might be due to
change in the mixed fluid composition. However the chemical product area at the farthest
location x = 25 mm is greater than that measured at x = 4.2 mm. From the spanwise
35

concentration field, it can be observed that each forcing frequency creates a unique
interfacial structure. These interfacial structures typically maintain their shape, and they
become thicker as they travel in the downstream direction. For 8 Hz forcing case, higher
amount of chemical product was formed at the very earliest streamwise location
compared to 2 and 4 Hz, but as the flow moves downstream, relatively lower chemical
product was measured.

36

F = 2 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 2 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-6. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 2 Hz, U = 20 mm/s and A3 = 60 µm).

37

F = 4 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 4 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-7. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 4 Hz, U = 20 mm/s and A3 = 60 µm).

38

F = 8 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 8 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-8. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 8 Hz, U = 20 mm/s and A3 = 60 µm)
Although the forced cases (2, 4 and 8 Hz) produce more chemical product than an
unforced flow, they still show the presence of unmixed fluid within the channel. The
unmixed fluid information can be obtained through the probability density function (pdf)

39

of chemical product. The pdf of chemical product is calculated from the entire spanwise
concentration field, over the time period corresponding to the data acquisition time (1900
imgaes at 30 Hz). Thus, the pdf is spatially averaged pdf over the cross section area of
test section. A pdf of chemical product for all of the forcing frequencies at four different
streamwise locations are shown in Appendix C. Each pdf was obtained from spanwise
chemical product concentration field with bin size of C * ≈ 0.1 . The pdf shown in
P
Appendix C indicates that there is always an occurrence of unmixed fluid in the channel
for 2, 4 and 8 Hz forcing cases. For the 8 Hz forcing case, there is a low probability of
unmixed fluid and a larger distribution of mixed fluid probabilities compared to 2 and 4
Hz at the earliest streamwise location (x = 4.2 mm). This highlights the possible local
splitter plate tip flow dynamics which increases the contact area between the two streams
and thus, as a result, we observe more chemical product at the very early streamwise
location (Figures 4-6, 4-7 and 4-8).
The spanwise instantaneous and average normalized product concentration fields
corresponding to forcing frequencies in the range 10 to 25 Hz are shown in figures 4-9 to
4-15. The chemical product area for each forcing frequency at four different streamwise
locations is depicted in figure 4-4. From figure 4-4, it could be observed that the forcing
frequencies 10,12,18,19 and 20 Hz represent the highly mixed fluid cases. The forcing
frequencies 15 and 25 Hz show relatively lower amount of chemical product at any
streamwise location. This observation is consistent with the streamwise concentration
fields shown in figures 4-2 and 4-3.
Although 15 Hz forcing case provides lower chemical product compared to some of
the other higher forcing frequencies, it shows an interesting flow feature in the spanwise

40

images (see Figure 4-11). At x = 4.2 mm, an inverted C-shaped interfacial structure is
seen such that chemical product is observed within the region which is bounded by this
structure. The mixed fluid found near the wall is connected to this inverted C-shaped
structure. The unmixed fluid is found outside of the inverted C-shaped structure which is
quantified in the pdf of chemical product shown in Appendix C. As the forced flow
moves downstream to x = 9 mm, more amount of chemical product is seen within the
inverted C-shaped structure. At this location, the chemical product appears such that the
inverted C-shaped structure is not clearly recognized because of the increase in the
amount of chemical product as well as the increase in the size of the structure. Also, it
should be noted that, the maximum chemical product is seen near the wall region. At x =
15 mm, the inverted C-shaped structure becomes bigger in size, but there is a decrease in
the amount of chemical product and thus as a result we measure lower normalized
chemical product area (Figure 4-4). The lowering of the chemical product may be
because of the change in the mixed fluid composition within the inverted C-shaped
structure and the mixed fluid near the wall. Continuing on to x = 25, a large increase in
the amount of chemical product is also observed. From the pdf of chemical product
corresponding to 15 Hz forcing frequency, it is observed that the amount of unmixed
fluid decreases in the streamwise direction.
At the early streamwise location x = 4.2 mm, for 10, 12, 18, 19 and 20 Hz forcing
cases (see Figures 4-9 to 4-14), the cross section of the test section is filled with the
mixed fluid. As a result, the pdf shown in Appendix C indicates zero probability of
finding unmixed fluid. This also defines the level of increase in the molecularly mixed
fluid. As the flow moves downstream (x = 9, 15, and 25 mm), an increase in the amount

41

of chemical product is seen for 10 and 12 Hz forced cases while a small variation is
observed for 18, 19 and 20 Hz cases. The three-dimensional nature of the forced flow
continues to occupy the whole cross section of the test section, and it remains complex.
The pdf of chemical product corresponding to forced cases 10,12,18,19, and 20 Hz show
a wide distribution of probabilities of the chemical product. The peak probability of nonzero chemical product is found around C * ≈ 0.5 − 0.55 . The distribution of chemical
P
product greater than 0.5 is due to the mixed fluid which is typically observed away from
the center of the channel and near the wall region.
In case of 25 Hz forcing frequency (see figure 4-15), an inverted C-shaped interfacial
structure is formed similar to the structure seen for 15 Hz forced case. Compared to 15
Hz case it does not show a significant increase in the amount of chemical product in the
streamwise direction.

42

F = 10 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 10 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-9. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 10 Hz, U = 20 mm/s and A3 = 60 µm).

43

F = 12 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 12 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-10. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 12 Hz, U = 20 mm/s and A3 = 60 µm).

44

F = 15 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 15 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-11. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 15 Hz, U = 20 mm/s and A3 = 60 µm).

45

F = 18 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 18 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-12. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 18 Hz, U = 20 mm/s and A3 = 60 µm).

46

F = 19 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 19 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-13. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 19 Hz, U = 20 mm/s and A3 = 60 µm).

47

F = 20 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 20 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-14. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 20 Hz, U = 20 mm/s and A3 = 60 µm).

48

F = 25 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 25 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-15. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 25 Hz, U = 20 mm/s and A3 = 60 µm).

49

4.1.2. Non-reacting spanwise LIF measurement
(A3 = 60 µm, F = 12 and 19 Hz)
All the results in section 4.1.1 are from chemically reacting LIF experiments
performed at one fixed value of the reactant stoichiometric ratio ξs = 0.065. To obtain
information on the entire composition distribution of the mixed fluid, a non-reacting LIF
(i.e. standard LIF) experiment was performed. In non-reacting LIF experiment,
fluorescein dye molecules were seeded in one of the two flow streams and the mixed
fluid composition was quantified by examining the concentration of the dye molecules.
Although non-reacting LIF is known to provide an upper bound to the actual amount of
molecular mixing (See Breidenthal 1981 and Koochesfahani and Dimotakis 1986), it still
remains the simplest diagnostic technique to estimate the entire mixture composition in a
single experiment. Thus, a non-reacting LIF experiment was performed for 12 and 19 Hz
forcing cases in the spanwise direction at x = 25 mm to quantify mixed fluid composition.
For non-reacting LIF, the experimental facility and instruments were same as used for
chemically reacting LIF experiments. For the forcing frequencies 12 and 19 Hz, 1900
images were acquired to monitor the spatio-temporal evolution of the mixed fluid
concentration field. The steps for processing the fluorescence intensity data are described
in detail by Koochesfahani and Dimotakis (1986) and thus they are not repeated here.
The normalized concentration ξ is related to local instantaneous dye concentration C d
and the free stream dye concentration C 0 as

C
ξ= d

(1)

C0

50

Here, the normalized concentration is defined such that ξ = 1 indicates the unmixed fluid
from the right-side stream seen in the image which was premixed with the dye while ξ =
0 indicates the unmixed fluid from the other stream (the one which had pure fluid). Thus,
the normalized concentration in the range 0 < ξ < 1 indicates the mixed fluid
concentration.
Figure 4-16 depicts the instantaneous normalized concentration field ξ (y,z) obtained
from non-reacting LIF experiment for 12 Hz and 19 Hz forcing frequency. The mixing
field is obtained at x = 25 mm over the y-z plane. Pseudo colors are assigned to the
different mixed fluid concentration levels in order to aid the interpretation of data. The
concentration ξ = 0 and ξ = 1 are assigned black color which indicates the unmixed
fluid from the two different flow streams. From 1900 normalized concentration

F = 12 Hz

F = 19 Hz

(a)

(b)

y
z

ξ ( y, z, t )

Figure 4-16. Instantaneous normalized concentration field ξ ( y , z ) from non-reacting LIF
experiment corresponding to 12 and 19 Hz forcing frequency at x = 25 mm.
(U = 20 mm/s, A3 = 60 µm, spanwise imaging)
51

fields ξ ( y , z ) , a total probability density function (pdf) is constructed using the entire y-z
plane data at x = 25 mm for 12 and 19 Hz forcing frequency (see Figure 4-17a and b).
Each pdf is calculated with the bin size as ε = 0.05. It is observed from figure 4-17a and b
that the maximum probability corresponds to mixed fluid concentration ξ = 0.5 i.e. there
is maximum occurrence of symmetric mixed fluid composition. The total pdf of the
mixed fluid composition is asymmetric as it is biased towards the dye bearing stream i.e.
the right-side fluid stream which is being forced. This indicates that the mixing field for
the highly mixed fluid cases has asymmetric mixing characteristics.

52

Figure 4-17(a). Total pdf of mixed fluid concentration from non-reacting LIF experiment
(F = 12 Hz, A3 = 60 µm, x = 25 mm, Spanwise imaging)

Figure 4-17(b). Total pdf of mixed fluid concentration from non-reacting LIF experiment
(F = 19 Hz, A3 = 60 µm, x = 25 mm, Spanwise imaging)

53

z = -3.5 mm
P (ξ)

P (ξ)

z = -1.5 mm

ξ

ξ
z=0
P (ξ)

P (ξ)

z = 1.5 mm

ξ

ξ

P (ξ)

z = 3.5 mm

ξ
Figure 4-18. Pdf of mixed fluid concentration from standard LIF experiment at various
span locations and fixed streamwise location x = 25 mm.
(F = 12 Hz, A3 = 60 µm, x = 25 mm, Spanwise imaging)
Unlike the pdf of concentration field shown in Figure 4-17(a), Figure 4-18 shows the
pdf at five different span locations (z = 0, 1.5, 3.5,-1.5 and 3.5 mm) and a fixed
54

streamwise location x = 25 for 12 Hz forcing frequency. It is observed that the functional
form of the pdf of concentration field along the span is same except at location z = -3.5
mm. At z = -3.5 mm, there is a more occurrence of mixed fluid with concentration in the
range 0.5 < ξ < 0.95 compared to other span locations. This means that along the span, at
position z = -3.5 mm, the mixed fluid composition is more asymmetrically mixed and is
in favor of dye bearing fluid stream.
Figure 4-19 shows the pdf at five different span locations and a fixed streamwise
location x = 25 mm for 19 Hz forcing frequency. The 19 Hz forced case has non-uniform
mixed fluid composition as the functional form as well as the width of pdf distribution
show noticeable difference at all of the five span locations. For the 19 Hz forced case, the
biased nature of the mixed fluid composition is towards the dye bearing fluid which is
seen on the positive side of the z-axis unlike to 12 Hz case. This means that, although the
highly mixed forced cases (12 and 19 Hz) provide the same amount of maximum
normalized chemical product area, its lateral uniformity of mixed fluid composition
varies.

55

z = - 1.5 mm

P (ξ)

P (ξ)

z = -3.5 mm

ξ

ξ
z=0

P (ξ)

P (ξ)

z = 1.5 mm

ξ

ξ

P (ξ)

z = 3.5 mm

ξ
Figure 4-19. Pdf of mixed fluid concentration from standard LIF experiment at various
span locations and fixed streamwise location x = 25 mm.
(F = 19 Hz, A3 = 60 µm, x = 25, Spanwise imaging)

56

4.1.3. Streamwise velocity measurement of the unforced and forced flow
(A3 = 60 µm, F = 0 - 25 Hz)
Molecular Tagging Velocimetry (MTV) technique was used to measure the
streamwise velocity at the mid-span of the mixing layer facility. MTV experiments were
performed for unforced and forced flow. A typical undelayed and delayed image obtained
from an MTV experiment is shown in Figure 4-20. The results obtained from the MTV
experiments are discussed in the following section of this chapter while the details of the
MTV experiment are provided in chapter 2.

Channel
wall

5 mm

(a) Undelayed image

Flow direction
(x mm)

(b) Delayed image (∆t = 10.25 ms)

Figure 4-20.Undelayed and delayed MTV image of an unforced flow.

UNFORCED FLOW CHARACTERISTICS
Figure 4-21 shows the measured streamwise velocity profile across the test section at
three downstream locations (x = 3, 4.55, 6.86 mm). The flow valves (upstream and end
section valves) were adjusted such that the maximum mean streamwise velocity of both
of the flow stream was U1 = U2 = 20 mm/s at x = 3 mm. Unlike the typical velocity
profile of a wake flow, it can be observed from Figure 4-21 that there is no region across
the channel width with uniform streamwise velocity.
57

The velocity defect, which is caused due to presence of the splitter plate wake, is
apparent in Figure 4-21. The strength of this defect at x = 3 mm is such that the minimum
velocity of the wake Umin is 15% less than Umax = 20 mm/s. As the flow progresses
downstream, decay in the velocity defect is observed such that at x = 6.86 mm zero
velocity defect is measured (Figure 4-22). The Reynolds number for the experiments
discussed in this dissertation is defined based on the width (w) of the channel.
Re =

ρU M w
µ

(2)

The value of UM at the midspan is chosen to be the average velocity across the width of
the test section at x = 3 mm. Based on this definition the Reynolds number is Re ≈ 75.

58

x = 3 mm
x = 4.55 mm
x = 6.86 mm

2

y (mm)

1

0

-1

-2
0

10

20

30

U (mm/s)
Figure 4-21. Mean streamwise velocity profile of unforced wake flow at midspan.
-0.20

(Umin- Umax)/Umax

-0.15

-0.10

-0.05

0

2

3

4

5

6

7

8

x mm

Figure 4-22. Evolution of the wake velocity deficit of unforced wake flow in the
streamwise direction at midspan.
59

FORCED FLOW CHARACTERISTICS
As shown in the Figure 4-21, due to the small size of the test section no “free stream”
region exists in the unforced wake flow. Thus, the normalized average RMS streamwise
velocity magnitude for each forcing frequency is calculated by spatially averaging the
RMS velocity over the width of the test section and normalizing it with respect to the
spatially averaged streamwise velocity. Normalized average RMS streamwise velocity is
calculated to provide label for each forcing frequency in terms of perturbation velocity
amplitude.
The normalized average RMS streamwise velocity can be written as,

 U RMS ( y )dy 
∫



w
U RMS 

=
UM
UM

,

(3)

where U M is the spatially average streamwise velocity across the width of the channel at
the midspan and w is the width of the channel. Figure 4-23 shows the normalized
average RMS streamwise velocity calculated for various forcing frequencies. Figure 4-23
will be utilized in the following section while discussing the RMS velocity magnitude for
each forcing frequency.

60

8
7
6

UURMS/UM
RMS/U M

5
4
3
2
1
0

0

4

8

12

16

20

24

28

F (Hz)
F (Hz)
Figure 4-23. Normalized average RMS streamwise velocity for various forcing
frequencies and for a fixed perturbation amplitude A3 = 60 µm measured at x = 3 mm.
Figures 4-24 to 4-29 depicts the streamwise velocity measured at x = 3 mm and z = 0
(midspan) for various forcing frequencies (F = 0 to 25 Hz). For each forcing frequency,
mean, phase resolved ( φ1 = 0 , φ2 = 0.25 , φ3 = 0.50 , φ4 = 0.75 ) and the RMS streamwise
velocity are highlighted. It is observed that 2 Hz and 4 Hz forcing frequencies have
similar mean streamwise velocity profile showing a parabolic functional form with the
maximum velocity near the center of the channel (see Figure 4-24). One important aspect
of this forced flow is that the signature of the wake flow (velocity deficit) which is seen
in the unforced flow (Figure 4-21) is completely absent. Although both the frequencies
have similar looking mean streamwise velocity profile, 4 Hz forcing case has higher
61

2
1
0
-1
-2

2

Mean
velocity

y (mm)

y (mm)

2 Hz

Φ1
Φ2
Φ3

20

40

60

0
-1
-2

Φ4

0

1

0

80

20

40

60

80

URMS(mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2

y (mm)

y (mm)

4 Hz

Φ3
Φ4

0

25 50 75 100

2
1
0
-1
-2
0 20 40 60 80 100
URMS(mm/s)

U (mm/s)

Figure 4-24. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 2 and 4 Hz forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm).
RMS velocity compare to 2 Hz forcing frequency. Also it could be observed that for 4 Hz
case, a negative velocity is seen in one of the phase resolved velocity profiles near the
wall of the channel. This indicates that during the time period of perturbation, forced flow
has reverse flow near the wall. The reverse flow characteristic is absent in 2 Hz forcing
case. The mean streamwise velocity profile for 8 Hz forcing case has a lateral variation
and also its shape is much different from the 2 Hz and 4 Hz case (see Figure 4-24 and 4-

62

25). Unlike 2 and 4 Hz cases, the phase resolved velocity profiles for 8 Hz case shows the
reverse flow behavior near the center as well as near the wall. The RMS velocity for 8 Hz
case is also larger than 4 and 2 Hz forcing frequencies.

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2

y (mm)

y (mm)

8 Hz

Φ3
Φ4

2
1
0
-1
-2
20 40 60 80 100

-40 0 40 80 120160

URMS(mm/s)

U (mm/s)

Figure 4-25. Mean, phase resolved and RMS streamwise velocity profile of 8 Hz forcing
frequency at midspan (U = 20 mm/s, A3 = 60 µm).

63

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2
Φ3

y (mm)

y (mm)

10 Hz

Φ4

2
1
0
-1
-2
0 20 40 60 80 100

-80 -20 40 100 160

URMS(mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2

y (mm)

y (mm)

12 Hz

Φ3
Φ4

2
1
0
-1
-2
0

-70 10 90 170

40

80

120

URMS(mm/s)

U (mm/s)

Figure 4-26. Mean, phase resolved and RMS streamwise velocity profile of 10 and 12 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm).

64

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2

y (mm)

y (mm)

15 Hz

Φ3
Φ4

2
1
0
-1
-2
0

-100 -20 60 140 220

40

80

120

URMS(mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2
Φ3

y (mm)

y (mm)

18 Hz

Φ4

2
1
0
-1
-2
0

-100 -20 60 140 220

40

80 120

URMS(mm/s)

U (mm/s)

Figure 4-27. Mean, phase resolved and RMS streamwise velocity profile of 15 and 18 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm).

65

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2
Φ3

y (mm)

y (mm)

19 Hz

Φ4

2
1
0
-1
-2
0 30 60 90 120150

-100 0 100 200

URMS(mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity
Φ1

y (mm)

y (mm)

20 Hz

Φ2
Φ3
Φ4

-80 40 160 280

2
1
0
-1
-2
0

50 100 150 200
URMS(mm/s)

U (mm/s)

Figure 4-28. Mean, phase resolved and RMS streamwise velocity profile of 19 and 20 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm).

66

2
1
0
-1
-2
-50

Mean
velocity
Φ1
Φ2

y (mm)

y (mm)

25 Hz

Φ3
Φ4

0

2
1
0
-1
-2
0 20 40 60 80 100

50 100

URMS(mm/s)

U (mm/s)

Figure 4-29. Mean, phase resolved and RMS streamwise velocity profile of 25 Hz
forcing frequency at midspan (U = 20 mm/s, A3 = 60 µm).
The forcing frequency cases in the range 10 Hz to 25 Hz exhibit a very large velocity
dynamics (Figure 4-26 to 4-29). A reverse flow and a forward flow behavior is observed
for the high forcing frequency cases within a single cycle of forcing. The reverse flow is
seen across the whole width of the channel unlike the low forcing frequency cases. The
phase resolved velocity profiles of all of the high forcing frequency cases highlight that
the stream which was forced (y > 0) has always a large negative velocity compare to the
other co-flowing stream.
The maximum normalized average RMS streamwise velocity was measured for 12, 19
and 20 Hz, while among the high forcing frequency cases, 15 and 25 Hz are the forcing
frequencies with lower RMS velocity (see Figure 4-23). This also explains the reason for
15 and 25 Hz cases showing lower chemical product. It should be noted that although a
fixed bellows amplitude was used, depending upon the frequency different level of RMS
velocity is measured for each forcing frequency.

67

4.2.

CHEMICALLY REACTING STREAMWISE AND SPANWISE LIF

MEASUREMENTS (U = 20 mm/s, A2 = 40 µm, F = 2 – 25 Hz)
Instantaneous normalized concentration fields shown in Figure 4-30 and 4-31
correspond to the forced flow at lower forcing amplitude A2 = 40 µm and over the range
of forcing frequencies 2 to 25 Hz. The streamwise LIF measurements are performed at
midspan over the x-y plane (along the flow direction). To quantify the chemical product
across the cross section of the channel (y-z plane), spanwise LIF measurements are
performed at four different streamwise locations (x = 4.2, 9, 15 and 25 mm).
Figure 4-32 to 4-41 represents the collage of normalized product concentration fields
of forced flow obtained from spanwise LIF measurements. For each forcing frequency
instantaneous and average normalized concentration field is highlighted. Average
spanwise normalized concentration field is calculated from 1900 LIF images. The
average spanwise normalized concentration field is utilized to calculate the chemical
product area (Ap). Figure 4-42 depicts the chemical product area for each forcing
frequency at four different streamwise locations. To find the probability of unmixed fluid,
a spatio-temporal probability density function (pdf) is calculated from 1900 LIF images.
The pdf for each forcing frequencies at four different streamwise locations is shown in
Appendix D. Figures 4-30 to 4-42 will be utilized in the following section to discuss the
effect of lower forcing amplitude A2 = 40 µm on mixedness over the range of forcing
frequencies (2 to 25 Hz).

68

F = 2 Hz

F = 4 Hz

F = 8 Hz

F = 10 Hz

F = 12 Hz

F = 15 Hz

F = 18 Hz

F = 19 Hz

C * ( x, y , t )
P

Figure 4-30. Instantaneous normalized product concentration field C * (x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A2= 40 µm).
69

F = 20 Hz

F = 25 Hz

C * ( x, y , t )
P

Figure 4-31. Instantaneous normalized product concentration field C * (x, y, t ) of forced
P
flow at midspan (U = 20 mm/s and A2= 40 µm).
The low forcing frequency cases 2, 4 and 8 Hz show a unique interfacial flow
structure formed in the channel which is observed in both streamwise and spanwise LIF
measurements (Figures 4-30, 4-32, 4-33 and 4-34). The interfacial structures are formed
such that the chemical product is found on these structures. As the forced flow moves in
the downstream direction, the chemical product found on the interfacial structures
increases, which is also depicted in the normalized product area versus forcing frequency
plot (Figure 4-42). It is interesting to note that, the maximum chemical product is
typically observed near the wall region. The forced flow has a very high shear near the
wall. Thus, due to the shear in the velocity and large residence time for the diffusion near
70

the wall, maximum chemical product is typically seen on the interfaces which are closer
to the channel wall (see Figure 4-32, 4-33 and 4-34).
Although an increasing trend in the chemical product is seen in the streamwise
direction, unmixed fluid is always found in the channel which is quantified in the pdf
plots shown in Appendix D (Figures D-1, D-2 and D-3). Unlike the higher forcing
amplitude A3, the interfacial structures seen for 2, 4 and 8 Hz at lower forcing amplitude
A2 = 40 µm are less tightly wound. Thus, as a result due to a lesser interfacial contact
area for A2 = 40 µm, a lower amount of chemical product is seen compared to A3 = 60
µm.

71

F = 2 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 2 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-32. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 2 Hz, U = 20 mm/s and A2 = 40 µm).

72

F = 4 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 4 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-33. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 4 Hz, U = 20 mm/s and A2 = 40 µm).

73

F = 8 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 8 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-34. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 8 Hz, U = 20 mm/s and A2 = 40 µm).

74

F = 10 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 10 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-35. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 10 Hz, U = 20 mm/s and A2 = 40 µm).

75

F = 12 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 12 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-36. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 12 Hz, U = 20 mm/s and A2 = 40 µm).

76

F = 15 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 15 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-37. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 15 Hz, U = 20 mm/s and A2 = 40 µm).

77

F = 18 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 18 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-38. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 18 Hz, U = 20 mm/s and A2 = 40 µm).

78

F = 19 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 19 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-39. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 19 Hz, U = 20 mm/s and A2 = 40 µm).

79

F = 20 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 20 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-40. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 20 Hz, U = 20 mm/s and A2 = 40 µm).

80

F = 25 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 25 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-41. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 25 Hz, U = 20 mm/s and A2 = 40 µm).

81

Among the high forcing frequency cases between 10 to 25 Hz, 12 Hz forcing case
shows the maximum amount of chemical product formed in the channel (see Figure 4-42).
The level of mixedness for 12 Hz forcing case is so high such that chemical product
occupies the whole width and the height of channel as observed in streamwise and
spanwise concentration fields. Thus, for the 12 Hz forcing case a zero probability of
unmixed fluid is measured (see Appendix D, Figure D-5). This means that within one
forcing cycle there is always a passage of mixed fluid in the channel. From the spanwise
concentration field it can be observed that at any streamwise location the maximum
chemical product is typically seen near the wall. Similar observation was also made for
higher forcing amplitude.
The forcing frequency cases 10,15,18,19 and 20 Hz, show different levels of chemical
product but they have similar looking mixed fluid structure. At the earliest streamwise
location x = 4.2 mm, an inverted C–shaped structure is observed in the channel (Figures
4-35, 4-37, 4-38, 4-39 and 4-40). The arms of the inverted C-shaped structure are
connected to the mixed fluid appearing near the wall. The thickness of the inverted Cshaped structure i.e. the amount of chemical product varies depending upon the forcing
frequency. The maximum chemical product is found in the mixed fluid region which
connects the arm of the inverted C-shaped structure with the wall. Unlike 12 Hz forcing
case, 10,15,18,19 and 20 Hz forcing cases show the presence of unmixed fluid (see the
pdf of chemical product in Appendix D; Figures D-4 to D-9). The unmixed fluid region is
generally found outside of the inverted C-shaped structure. As the flow moves
downstream in the channel, by x = 25 mm, an increase in the chemical product area is
measured with maximum chemical product appearing near the wall.

82

For 25 Hz forcing case a ‘mini’ inverted C-shaped interfacial structure is observed at
any streamwise location (Figure 4-41). A very small amount of chemical product is
measured as the chemical product is limited to the ‘mini’ inverted C-shaped structure

Normalised Chemical Product Area (AP/A )

which occupies a small area within the test section.

1.0
x = 4.2 mm
x = 9 mm
x = 15 mm
x = 25 mm

0.8
0.6
0.4
0.2
0

0

5

10

15

20

25

F (Hz)
Figure 4-42. Normalized chemical product area for range of forcing frequencies
measured at four different streamwise locations (U = 20 mm/s and A2 = 40 µm).

83

Normalized Chemical Product Area (AP/A)

1.0

A2 = 40 µm
A3= 60 µm

0.8
0.6
0.4
0.2
0

0

5

10

15

20

25

F (Hz)
Figure 4-43. Normalized chemical product area for range of forcing frequencies
measured at x = 4.2 mm for two different forcing amplitudes.
Figure 4-43 depicts the normalized chemical product area versus forcing frequency for
two different forcing amplitudes (A2 = 40 µm and A3 = 60 µm) measured at earliest
streamwise location x = 4.2 mm. It is interesting to note that for both of the forcing
amplitudes A2 and A3, the forcing frequencies 12 Hz and 19 Hz provides the maximum
amount of chemical product area. The direct relation between the normalized chemical
product area and the forcing amplitude is also apparent from Figure 4-43. For any given
forcing frequency in the range 2 - 25 Hz, the maximum chemical product area is always
found for the highest forcing amplitude. Thus, as we lower the forcing amplitude, lower
chemical product area is measured in the channel at any forcing frequency.
84

4.2.1. Streamwise velocity measurement of the forced flow
(A2 = 40 µm, F = 2 - 25 Hz)
In this section, streamwise velocity results will be discussed corresponding to forced
flow of forcing amplitude A2 = 40 µm and over a range of forcing frequencies (2 - 25 Hz).
To measure the streamwise velocity, MTV experiments were performed at x = 3 mm and
z = 0 (midspan). As mentioned in section 4.1.3, the main motivation of velocity
measurement is to find the forcing amplitude in terms of velocity. A spatially averaged

8
7

URMS/UM

6
5
4
3
2
1
0

0

5

10

15

20

25

30

F (Hz)
Figure 4-44. Normalized spatially averaged RMS streamwise velocity for various forcing
frequencies and for a fixed perturbation amplitude A2 = 40 µm measured at x = 3 mm
and z = 0.
RMS streamwise velocity ( U RMS ) is normalized by spatially-averaged streamwise
velocity ( U M ) to define the forcing amplitude in terms of velocity. Figure 4-44 shows
85

the normalized streamwise RMS velocity for each forcing frequency measured at x = 3
mm corresponding to forcing amplitude A2 = 40 µm. The normalized streamwise RMS
velocity results shown in figure 4-44 will be utilized in discussing the streamwise
velocity measurements of each forcing frequency in the following section.

2
1
0
-1
-2

Mean
velocity

y (mm)

y (mm)

2 Hz

Φ1
Φ2
Φ3
Φ4

0

20

40

60

2
1
0
-1
-2
0

80

20

40

60

80

URMS (mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity

y (mm)

y (mm)

4 Hz

Φ1
Φ2
Φ3
Φ4

0

25 50 75 100

2
1
0
-1
-2
0 20 40 60 80 100
URMS(mm/s)

U (mm/s)

Figure 4-45. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 2 and 4 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm).

86

Mean
velocity

2
1
0
-1
-2

y (mm)

y (mm)

8 Hz

Φ1
Φ2
Φ3
Φ4

-20 10 40 70 100

2
1
0
-1
-2
0 20 40 60 80 100
URMS(mm/s)

U (mm/s)

Figure 4-46. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 8 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm).
Figure 4-45 and 4-46 depicts the mean, phase resolved ( φ1 , φ 2 , φ 3 , φ 4 ) and RMS
streamwise velocity for 2, 4 and 8 Hz forcing frequency at x = 3 mm. The mean
streamwise velocity profile of 2 Hz and 4 Hz forcing case has a parabolic functional form
while 8 Hz forcing case has a unique profile which was also observed for forcing
amplitude A3 = 60 µm (see Figures 4-25). From the phase resolved velocity profiles it
can be observed that the reverse flow behavior is absent for 2 Hz forcing case while 4 and
8 Hz case highlights the reverse flow characteristics away from the center and near the
wall region. Among 2, 4 and 8 Hz forcing cases, the maximum normalized spatially
averaged RMS velocity is measured for 8 Hz which is depicted in Figure 4-44. As
expected, the RMS velocity of 2, 4 and 8 Hz forcing frequencies in case of forcing
amplitude A2 is smaller than the corresponding cases of forcing amplitude A3. It is
interesting to note that, the RMS velocity profiles of 2, 4 and 8 Hz cases have same
functional form for forcing amplitudes A2 and A3 (see Figures 4-24,4-25,4-45 and 4-46).
87

2
1
0
-1
-2
-50

Mean
velocity

y (mm)

y (mm)

10 Hz

Φ1
Φ2
Φ3
Φ4

0

2
1
0
-1
-2
0

50 100 150

40

80

120

URMS(mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity
Φ1

y (mm)

y (mm)

12 Hz

Φ2
Φ3
Φ4

-100 -30 40 110 180

2
1
0
-1
-2
0

50 100 150 200
URMS(mm/s)

U (mm/s)

Figure 4-47. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 10 and 12 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm).

88

2
1
0
-1
-2

Mean
velocity

y (mm)

y (mm)

15 Hz

Φ1
Φ2
Φ3
Φ4

2
1
0
-1
-2
20 40 60 80 100

-10 30 70 110 150

URMS(mm/s)

U (mm/s)
18 Hz

y (mm)

1

Φ1

0

Φ2

-1

Φ3

y (mm)

Mean
velocity

2

Φ4

-2
-100 -20

60

2
1
0
-1
-2
0

140

40

80 120

URMS(mm/s)

U (mm/s)

Figure 4-48. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 15 and 18 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm).

89

2
1
0
-1
-2

Mean
velocity
Φ1
Φ2
Φ3

y (mm)

y (mm)

19 Hz

Φ4

2
1
0
-1
-2
0

-100 -30 40 110 180

50 100 150 200
URMS(mm/s)

U (mm/s)

2
1
0
-1
-2

Mean
velocity

y (mm)

y (mm)

20 Hz

Φ1
Φ2
Φ3
Φ4

-150 -50 50 150 250

2
1
0
-1
-2
0

50

100

150

URMS(mm/s)

U (mm/s)

Figure 4-49. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 19 and 20 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm).

90

2
1
0
-1
-2

Mean
velocity

y (mm)

y (mm)

25 Hz

Φ1
Φ2
Φ3
Φ4

0

50 100 150

2
1
0
-1
-2
0

50

100

150

URMS(mm/s)

U (mm/s)

Figure 4-50. Mean, phase resolved and RMS streamwise velocity profile corresponding
to 25 Hz forcing frequency at midspan (U = 20 mm/s, A2 = 40 µm).
Figures 4-47 to 4-50 depicts the mean, phase resolved ( φ1 , φ 2 , φ3 , φ 4 ) and RMS
velocity of a forced flow corresponding to forcing frequencies 10, 12, 15, 18, 19, 20 and
25 Hz and forcing amplitude A2 measured at x = 3 mm. Similar to higher forcing
amplitude A3, a large velocity dynamics is also seen for lower forcing amplitude A2 in
case of each forcing frequencies within one forcing cycle. For each forcing frequency, the
phase resolved streamwise velocity profiles show forward and reverse flow behavior in
the channel. It is interesting to note that, although the forced flow in case of higher
forcing frequencies show a large velocity dynamics, the functional form of the phase
resolved streamwise velocity profiles ( φ1 , φ 2 , φ3 , φ 4 ) remains same with respect to the
mean streamwise velocity profile.
Among the high forcing frequency cases, 12 and 19 Hz case depict the maximum
normalized spatially average RMS streamwise velocity (see figure 4-44). The RMS

91

streamwise velocity profile of high forcing frequency cases has same functional form.
Similar result was also seen in case of higher forcing amplitude A3. As expected, the
normalized spatially averaged RMS streamwise velocity for each forcing frequency
corresponding to forcing amplitude A2 is always smaller than that of forcing amplitude
A3 (see figure 4-23 and 4-44).

4.3.

CHEMICALLY REACTING STREAMWISE LIF MEASUREMENTS

AT LOW FORCING AMPLITUDE (A1 = 25 µm, F = 2 - 25 Hz)
A streamwise chemically reacting LIF measurement was perform at forcing amplitude
A1 = 25 µm to qualitatively study the effect of a very low forcing amplitude on
mixedness. Figure 4-51 and 4-52 shows the instantaneous normalized streamwise
concentration field C * (x, y , t ) at midspan for a forcing amplitude A1 = 25 µm and for
P
few selected forcing frequencies in the range F = 0 - 25 Hz. The effect of lower forcing
amplitude is such that, no forcing case is observed with the large increase in the
mixedness which was typically observed for forcing amplitudes A2 = 40 µm and A3 = 60
µm. Since a very small amount of chemical product was observed for forcing amplitude
A1 = 25 µm in the streamwise LIF measurements, the detail spanwise chemically reacting
LIF and MTV measurements were performed only for A2 = 40 µm and A3 = 60 µm
forcing amplitudes.

92

F = 2 Hz

F = 4 Hz

F = 8 Hz

F = 12 Hz

C * (x, y , t )
P

Figure 4-51. Instantaneous normalized product concentration field C * (x, y , t ) of forced
P
flow at midspan (U = 20 mm/s and A1 = 25 µm).

93

F = 15 Hz

F = 18 Hz
C * (x, y , t )
P

F = 20 Hz

Figure 4-52. Instantaneous normalized product concentration field C * (x, y , t ) of forced
P
flow at midspan (U = 20 mm/s and A1 = 25 µm).

94

4.4.

STATIONARY FLOW BEHAVIOR OF MIXED FLUID

Instantaneous Average

Instantaneous Average

F = 4 Hz

F = 8 Hz

C * ( x, y , t ) , C * ( x, y )
P
P

Figure 4-53. Instantaneous and average normalized product concentration field of forced
flow at midspan (U = 20 mm/s and A3 = 60 µm).
Figure 4-53 depicts the instantaneous and average normalized product concentration
field of forced flow at midspan corresponding to forcing amplitude A3 = 60 µm and
forcing frequencies 4 and 8 Hz. In general, the averaging of the instantaneous normalized
concentration field provides a smoothing effect on the flow structure. In other words, this
means that the mixed fluid structures observed in the instantaneous normalized product
concentration field are smeared out in the average normalized product concentration field.

95

It is interesting to note that, the average normalized concentration field of 4 and 8 Hz
forcing case does have a smoothing effect but it also shows a presence of a well-defined
mixed fluid structure which is observed in the instantaneous normalized concentration
field. This phenomenon is also noticed in the spanwise LIF measurements highlighted in
figures 4-7 and 4-8. To better understand this effect, the streamwise instantaneous
normalized concentration fields (1900 LIF images) were phase ordered such that it
described the flow structure behavior for one complete forcing cycle. The instantaneous
normalized concentration fields obtained from streamwise LIF measurements were phase
ordered such that 95 phase ordered normalized concentration fields represented one
complete cycle of forcing. Each concentration field out of 95 phase ordered concentration
fields is an average of 20 instantaneous normalized concentration fields.
From the phase-ordered streamwise images, it was found that, within the time period
of one forcing cycle the flow structures showed stationary and reverse flow behavior for a
certain fraction of a forcing cycle. As a result, the averaging of the instantaneous
normalized concentration field showed both, a smoothing effect as well as a well-defined
pattern of mixed fluid structure wherein the well-defined mixed fluid structure
corresponds to the phases where the flow exhibits stationary flow behavior. To find the
phase duration for which the flow exhibits stationary behavior within one complete
forcing cycle, an in-house correlation program was used made by D. Olson. This program
calculates the phase resolved displacement and the velocity of a mixed fluid structure
utilizing the phase ordered streamwise LIF images. For each forcing frequency, the
location of the structure whose displacement is measured is shown by its respective x and
y co-ordinates (see figure 4-54). Although the displacement of the mixed fluid structure

96

F = 4 Hz

F = 8 Hz
A3

F = 8 Hz

F = 4 Hz
A2

Figure 4-54. Position of the mixed fluid structure whose displacement is measured
throughout a complete forcing cycle is marked by a solid circle.
will vary across the whole test section, the displacement measured here corresponds to
only a portion of mixed fluid structure defined by x and y co-ordinates. Note that, this
analysis is performed just to provide an estimate of the time period for which the flow
exhibits stationary behavior.
Figure 4-55(a, b) depicts the phase resolved displacement and velocity of the mixed
fluid structure for one complete forcing cycle corresponding to 4 and 8 Hz forcing case.
In this analysis, each phase resolved displacement refers to the actual distance travelled
by the mixed fluid structure over the phase duration ∆ϕ = 0.052. From figure 4-55(a, b), it
is observed that forced flow at 4 Hz and 8 Hz forcing frequency exhibits stationary flow
behavior such that mixed fluid structure remains stationary for 15.7 % of the forcing
cycle. This means that, mixed fluid structure has zero displacement for 39 ms and 20 ms
97

Interface displacement (mm)

8 Hz (x = 11.5 mm, y = - 0.6 mm)
4 Hz (x = 6.8 mm, y = 0.6 mm)

0.8
0.4
0
-0.4

Reverse flow
behavior

Stationary
flow structure

-0.8
0

0.2

0.4

0.6

0.8

1.0

Phase (φ)

Velocity (mm/s)

Figure 4-55(a). Phase resolved displacement of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A3 = 60 µm and forcing
frequency 4 and 8 Hz.

100
80
60
40
20
0
-20
-40
-60
-80
-100

8 Hz (x = 11.5 mm, y = -0.6 mm)
4 Hz (x = 6.8 mm, y = 0.6 mm)

Reverse flow
behavior

Stationary
flow structure

0

0.2

0.4

0.6

0.8

1.0

Phase (φ)

Figure 4-55(b). Phase resolved velocity of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A3 = 60 µm and forcing
frequency 4 and 8 Hz.

98

of the time period corresponding to 4 and 8 Hz forcing frequencies. In addition to
stationary flow behavior, 8 Hz forced flow also exhibits the reverse flow behavior for 21 %
of the time period i.e. 26 ms.
Similar analysis was also performed for lower forcing amplitude A2 = 40 µm. Figure 456 (a, b) depicts the phase resolved displacement and velocity of the mixed fluid structure
for one complete forcing cycle corresponding to 4 and 8 Hz forcing case and forcing
amplitude A2 = 40 µm. Due to lower forcing amplitude, 4 Hz forcing case shows
stationary flow behavior for smaller amount of time period i.e. 26 ms. In case of 8 Hz
forcing frequency, unlike to higher forcing amplitude, stationary flow behavior is
observed for larger time period compared to reverse flow. Although a reverse flow is
seen for 8 Hz forcing case, but a very small displacement is measured compared to the
reverse flow displacement seen for higher forcing amplitude. Thus from figure 4-55 and
4-56 it could be observed that the stationary and the reverse flow behavior characteristics
changes with forcing frequency and forcing amplitude.

99

Interface displacement (mm)

8 Hz (x = 9.75 mm, y = - 0.7 mm)
4 Hz ( x = 8 mm, y = 0.36 mm)

0.8
0.4
0

Stationary
flow structure

-0.4

Stationary
flow structure
Reverse
flow
behavior

-0.8
0

0.2

0.4

0.6

0.8

1.0

Phase (φ)

Velocity (mm/s)

Figure 4-56(a). Phase resolved displacement of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A2 = 40 µm and forcing
frequency 4 and 8 Hz.

100
80
60
40
20
0
-20
-40
-60
-80
-100

8 Hz (x = 9.75 mm, x = - 0.7 mm)
4 Hz (x = 8 mm, y = 0.36 mm)

Stationary
flow structure

0

0.2

Stationary
flow structure

0.4

0.6

Reverse
flow
behavior

0.8

1.0

Phase (φ)

Figure 4-56(b). Phase resolved velocity of mixed fluid structure of forced flow at
midspan corresponding to forcing amplitude A2 = 40 µm and forcing
frequency 4 and 8 Hz.

100

4.5.

REVERSE FLOW CHARACTERISTICS

It was shown earlier in section 4.1.4 (see figure 4-26 to 4-29) that the higher forcing
frequencies (10 to 25 Hz) exhibit very large streamwise RMS velocity corresponding to
forcing amplitude A3 = 60 µm. Such is the RMS velocity that the phase resolved
streamwise velocity profiles showed the forward and the reverse flow characteristics.
This means that the chemical product formed in the test section travels in reverse and
forward direction (negative and positive x direction) within one forcing cycle. Thus it is
possible that the chemical product travels even upstream of the splitter plate tip. This
could be easily verified by imaging the chemical product in the upstream of the splitter
plate. But due to limited optical access to the upstream of test section, a different
approach was used to verify the presence of chemical product in the upstream of the
splitter plate tip. An experiment was performed wherein during the data acquisition time,
the forced flow (F = 12 hz, A3 = 60 µm) was transitioned to unforced flow condition i.e.
the forcing mechanism was stopped during the data acquisition. The recorded images
during the data acquisition time monitored the time required by the forced flow
concentration field to revert back to the unforced flow concentration field.

101

x = 3.5 mm

Flow
direction
x = 17.5 mm
(a)
Forced flow

(b)
t=0
Unforced

(c)
t=2s

(d)
t = 10.4 s

Figure 4-57. Streamwise chemically reacting LIF image sequence at midspan showing
the transition of forced flow (F = 12 Hz and A3 = 60 µm) to unforced flow condition.
Figure 4-57 highlights the LIF streamwise time series images which depicts the
transition of the forced flow (F= 12 Hz and A3 = 60 µm) to unforced flow condition.
Note that the chemical product concentration field shown in figure 4-57 has arbitrary
units since the concentration field is not normalized by the concentration field
corresponding to stoichiometric ratio ξs.
Figure 4-57(a) shows the highly mixed forced flow corresponding to forcing
frequency F = 12 Hz and forcing amplitude A3 = 60 µm at the midspan. The chemical
product at the time instant when the forcing mechanism is stopped is highlighted by
figure 4-57 (b). This LIF image will be referred as t = 0 since it marks the beginning of
the transition of the forced flow to unforced flow. The subsequent LIF images at t = 2 s
and t = 10.4 sec from the beginning of transition event is shown by figure 4-57(c) and 4-

102

57(d). It could be observed from figure 4-57(c) that, although the forcing mechanism has
been stopped, a large amount of chemical product is still found entering the test section
from the flow stream which was forced. The inflow of chemical product in the test
section after 2 seconds from stopping the forcing condition indicates the presence of the
chemical product in the upstream of the channel. The occurrence of chemical product in
the upstream of channel is due to the reverse flow behavior of the forced flow wherein
chemical product travels upstream of the channel and once the forcing mechanism had
stopped, it travels in the forward direction i.e. downstream of channel. At t = 10.4 sec
(see figure 4-57(d)), if we neglect the near wall chemical product, almost zero product is
seen on the forced flow stream and the concentration field appears similar to the unforced
flow concentration field. Considering the time as t = 10.4 sec for the flow to revert back
to unforced flow concentration field and the maximum streamwise velocity as U = 5.5
mm/s in the contraction chamber, the approximate upstream distance travelled by the
chemical product from the splitter plate tip is 5.4 cm. Thus, the results presented above
suggests that the highly mixed fluid forced cases exhibit reverse flow to such an extent,
that the chemical product is found in the far upstream location from the splitter plate tip
location.

103

4.6.

MIXING PERFORMANCE CORRESPONDING TO VARIOUS FORCING
FREQUENCIES AT FIXED VELOCITY AMPLITUDE

The results discussed in sections 4.1 and 4.2 relate to two different forcing amplitudes
A3 and A2 over a frequency range 2- 25 Hz. Thus, by utilizing the database of the forced
flow results obtained from the above mentioned conditions, the normalized RMS
streamwise velocity is shown in figure 4-58 for each forcing frequency. In addition to A3
and A2, the normalized RMS velocity is also shown for two forcing frequencies (12 and
18 Hz) corresponding to forcing amplitude A1. From figure 4-58, it can be observed that,
forcing frequencies 8, 10, 12, 15, 18 and 22 Hz have the same velocity perturbation

30
Forcing Frequency (Hz)

A1 = 25 µm

25

A2 = 40 µm
A3 = 60 µm

22 hz

20
18 hz

15

15 hz

10

12 hz
10 hz
8 hz

5
0

0

1

2

3

4

5

URMS/UM
Figure 4-58. Normalized spatially averaged RMS streamwise velocity for various forcing
frequencies and for a three different forcing amplitudes measured at x = 3 mm and z = 0.
104

amplitude

U RMS
= 1.45 . Thus, these forcing cases will be utilized to discuss the
UM

mixing performance of mixing layer facility at fixed velocity perturbation amplitude.

Normalised ChemicalProduct Area (A(A/A)
Normalized Chemical Product Area P P/A)

1.0

x = 4.2 mm
x = 9 mm
x = 15 mm
x = 25 mm

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

3

6

9

12

15

18

21

24

Forcing Frequency (F Hz)
Forcing Frequency (F Hz)
Figure 4-59. Normalized chemical product area for range of forcing frequencies
measured at a fixed velocity perturbation amplitude URMS/UM = 1.45 (U = 20 mm/s).
Figure 4-59 depicts the normalized chemical product area corresponding to forcing
frequencies 8, 10, 12, 15, 18 and 22 Hz and fixed velocity perturbation amplitude

U RMS
= 1.45 obtained from spanwise chemically reacting LIF measurements. For each
UM
forcing frequency the chemical product area is measured at four different streamwise
locations (x = 4.2, 9, 15 and 25 mm). The instantaneous and average normalized chemical
product concentration field of forcing frequencies 8, 10, 12, 15, 18 and 22 Hz is

105

highlighted in figures 4-8, 4-35, 4-60, 4-11, 4-61 and 4-62. Unlike figure 4-43, the
change in chemical product with respect to forcing frequency for fixed velocity amplitude
is shown in figure 4-59. It is observed that within the range of forcing frequency 8 to 22
Hz, the maximum chemical product is measured for 15 and 22 Hz while the lowest
corresponds to 12 and18 Hz. In general, for the above mentioned forcing frequencies an
inverted C-shaped mixed fluid structure of different size is observed. A larger size
inverted C-shape structure is associated with the higher chemical product. Thus, as a
result 15 Hz and 22 Hz cases show increased amount of chemical product compared to
any other forcing frequency. One common feature among all of the forcing frequencies is
the presence of unmixed fluid region. At URMS/UM = 1.45 all of the forcing frequencies
show the occurrence of unmixed fluid. The unmixed fluid region is apparent in the
average normalized concentration fields highlighted in figure 4-8, 4-35, 4-60, 4-11, 4-61
and 4-62. Thus figure 4-58 depicts the selective behavior of mixing layer facility in
enhancement of mixing with respect to forcing frequency at fixed velocity perturbation
amplitude.

106

F = 12 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 12 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-60. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 12 Hz, U = 20 mm/s and A1 = 25 µm).

107

F = 18 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 18 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z , t ) , C * ( y, z )
P
P

Figure 4-61. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 18 Hz, U = 20 mm/s and A1 = 25 µm).

108

F = 22 Hz (Instantaneous normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

F = 22 Hz (Average normalized concentration field)

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

C * ( y, z, t ) , C * ( y, z )
P
P

Figure 4-62. Instantaneous and average normalized chemical product concentration field
at four different streamwise locations (F = 22 Hz, U = 20 mm/s and A2 = 40 µm).

109

5. CONCLUSIONS
The effects of the periodic forcing in the small mixing layer facility on one of the flow
streams were investigated. The mixing enhancement in the forced mixing layer facility
was studied over a range of forcing frequencies (2 - 25 Hz) and forcing amplitudes A1 =
25 µm A2 = 40 µm and A3 = 60 µm. The streamwise chemically reacting LIF technique
was used to visualize the mixed flow structure at center span. The detail mixedness in the
forced flow was quantified by performing spanwise (cross stream) chemically reacting
LIF measurements at four different streamwise locations. In addition to chemically
reacting LIF, non-reacting LIF (standard LIF) measurements were performed for few
highly mixed fluid cases to find the composition distribution (pdf) of mixed fluid. The
streamwise velocity dynamics within the forcing cycle was quantified by Molecular
Tagging Velocimetry (MTV) performed at midspan. Following is the summary of the
results:
1) The effect of forcing amplitude A3 = 60 µm over the range of forcing frequencies
(2-25 Hz) was such that it produces a unique interfacial mixed fluid structure for
each forcing frequency. For lower forcing frequencies (2, 4 and 8 Hz) chemical
product was found on the interfacial structures and it was observed to increase in
the streamwise direction. Although the lower forcing frequency cases show the
higher chemical product compared to an unforced flow, unmixed fluid was always
found in the test section which was quantified using pdf of chemical product.
Unlike the lower frequencies, a large amount of enhancement in the chemical
product was observed when the flow was forced at higher frequencies (10, 12, 18,

110

19 and 20 Hz). Such was the dramatic increase in the chemical product that, there
was no occurrence of unmixed fluid in the test section. The maximum chemical
product area measured at four different streamwise locations was typically in the
range 0.47 to 0.57. This defines the enhanced mixing efficiency of the mixing
layer facility corresponding to the high forcing frequencies. Unlike the above
mentioned high forcing frequencies, 15 and 25 Hz are other two high forcing
frequencies for which a very low mixedness was measured.
To quantify the forcing amplitude in terms of velocity, MTV experiments were
performed. Although the bellows amplitude was kept constant, as expected, each
forcing frequency was found to have different RMS velocity at the entrance of the
test section. A large RMS velocity was measured for higher forcing frequencies
which also correspond to the highly mixed fluid cases. The RMS velocity for
these cases was so large that a forward and a reverse flow characteristics were
measured within a forcing cycle. Among the high forcing frequency cases, a
lower RMS velocity was measured for 15 and 25 Hz forcing cases. This also
explains the reason for these frequencies yielding lower chemical product area.
The reason for selective increase of RMS velocity at the higher forcing
frequencies is not known yet.
2) The effect of lower forcing amplitude on the mixedness in the small mixing layer
facility was investigated by forcing the mixing layer at amplitude A2 = 40 µm. At
any given forcing frequency, the amount of mixing was found to be directly
connected to the forcing amplitude. The measured chemical product was lower
compared to the similar cases corresponding to higher forcing amplitude A3 = 60
111

µm. Among the higher forcing frequencies (10 to 25 Hz) corresponding to A2 =
40 µm, a lower amount of chemical product was measured for 15 and 25 Hz. The
selective behavior of the mixing layer facility in terms of enhancement of
mixedness at higher forcing frequencies was found to be consistent with forcing
amplitudes A2 and A3. MTV experiments were also performed to find the forcing
amplitude in terms of velocity. As expected, for any forcing frequency, a lower
RMS velocity was measured compared to the similar cases of A3 = 60 µm. As
observed for forcing amplitude A3, forward and reverse flow characteristics were
also measured for forcing cases of A2.
3) Non-reacting spanwise LIF measurements were performed for few selected
forcing cases. The total pdf of the mixed fluid concentration of highly mixed
cases showed asymmetric mixing characteristics such that it was biased towards
the stream which was forced. It was interesting to note that although the total pdf
was asymmetric, but the maximum occurrence of mixed fluid was measured for
50:50 mixed fluid compositions.
4) Stationary flow structure behavior was studied for certain forcing cases by
utilizing the phase resolved streamwise LIF concentration fields. From the phase
ordered sequence of concentration fields, it was found that, within the time period
of one forcing cycle the flow structure appeared to be stationary for a certain
fraction of the time period. As a result, an average concentration field showed a
strong presence of a flow structure in addition to a smoothing effect. Here, the
flow structure corresponded to the phases wherein the flow was stationary.
112

5) The database of forced cases obtained from forcing amplitudes A1, A2 and A3
over a range of forcing frequencies 2- 25 Hz was also utilized to study the effect
of varying forcing frequency and fixed forcing velocity amplitude on mixedness.
It was found that mixing layer facility showed an enhancement in mixedness for
only certain forcing frequencies. This shows the selective behavior of mixing
layer facility in terms of enhancement in mixing with respect to forcing frequency.

113

6. FUTURE DEVELOPMENTS
Following are some of the improvements and the ideas to be explored in future:
1) For the highly mixed cases, a large reverse flow was noticed within the forcing
cycle of perturbation. Such was the reverse flow behavior that chemical product
was found to travel upstream of splitter plate. The experimental facility (mixing
layer facility) has a limited optical access wherein flow cannot be imaged beyond
x = 3 mm. Thus, the facility should be modified such that flow can be visualized
near the splitter plate and in the contraction chamber. This will help to understand
the mixing process in the upstream of the channel.
2) One of the objectives of this research was to determine the operating conditions
and the characteristics of the highly mixed flow. It was found that a large amount
of mixedness can be obtained for high forcing frequency and amplitude. For such
highly mixed flow, although the total pdf was asymmetric, a maximum
occurrence of 50:50 mixed fluid compositions was measured. From an
engineering stand point, the highly mixed case might be very useful in a real
microfluidic mixing device. Thus, the next logical step would be to utilize similar
large forcing conditions to enhance the mixing in miniaturized devices. One such
microfluidic Y-channel is shown in figure 6-1.

114

Flow stream 1

Flow stream 2

60 deg Y channel
width: 1 mm
depth: 140 µm

Figure 6-1. A sample microfluidic Y-channel
3) Incorporating a high forcing mechanism (high frequency and amplitude) proposed
above might be very difficult in practical scenarios since microfluidic devices are
known for their difficulty in fabrication. As shown in this dissertation, one could
obtain appreciable amount of stretching and folding of interfacial structures even
at low forcing amplitudes and frequencies. But one problem in low forced cases
was that typically chemical product was seen to be ‘sticking’ near the wall and
thus limiting its ability to mix as the flow travelled downstream of the channel. As
a possible solution, it would be interesting to modulate the flow at low frequency
and amplitude in a “herringbone” type channel. Through this method, one would
not only increase the interfacial structures by forcing the flow but also allow the
flow to mix more efficiently throughout its travel in the flow channel. Thus, this
defines the hybrid approach wherein both active and passive mechanism would be
used.

115

APPENDICES

116

APPENDIX A. DELAY TIME BETWEEN UNDELAYED AND DELAYED
IMAGES USED FOR MTV EXPERIMENTS
Table A-1 depicts the delay and exposure time used for unforced as well as forced
cases. An MTV measurement provides the velocity which is actually an average velocity
over the delay time chosen for experiment. Thus, in general, smaller delay time was used
for higher forcing frequency cases.
Consider an example wherein a velocity signal is periodically varying with a
frequency of 25 Hz i.e. time period T = 40 ms. Figure A-1 and A-2 shows the filtering
effect on this signal using two different time delays i.e. td = 2 ms and td = 10 ms. It can
be observed from the figure that because of the larger time delay 10 ms (large time
average window span) the sampled data points have noticeable deviation with respect to
the original signal (blue solid line). While in case of 2 ms delay time, data points are
sampled with relatively good fit with respect to the original signal. The delay time was
chosen for all of the forced cases such that td/T ≤ 0.05, which provided a minimum
filtering effect of delay time on velocity measurement while performing MTV
experiments.

117

Filtered signal
( 2 ms delay time)
Filtered signal
(10 ms delay time)
Original signal
F = 25 Hz

Velocity Signal

1.0
0.5
0
-0.5
-1.0
0

0.01

0.02

0.03

0.04

t (sec)
Figure A-1. Filtering effect on high frequency periodic signal

Velocity Signal

1.0

0.5
Filtered signal
( 2 ms delay time)
Filtered signal
(10 ms delay time)
Original signal
F = 25 Hz

0

0.01
t (sec)
Figure A-2. Close-up view of filtering effect on high frequency periodic signal
118

Table A-1. Delay and Exposure time used for MTV experiments (U = 20 mm/s)
Frequency

Amplitude

Delay

Exposure Undelayed

Exposure Delayed

(ms)

(ms)

(ms)

10

1

1

40 µm

10

0.1

0.4

60 µm

10

0.1

0.6

40 µm

9

0.1

0.6

60 µm

10

0.1

0.6

40 µm

7

0.1

0.3

60 µm

4

0.1

0.3

40 µm

2.4

0.1

0.1

60 µm

1.6

0.1

0.1

25 µm

2.5

0.1

0.1

40 µm

1.5

0.1

0.1

60 µm

1.2

0.1

0.1

40 µm

2.8

0.1

0.1

60 µm

1.2

0.1

0.1

25 µm

2.5

0.1

0.1

40 µm

1.5

0.1

0.1

60 µm

1.0

0.1

0.1

40 µm

1.5

0.1

0.08

60 µm

1

0.1

0.08

(Hz)
Unforced

2

4

8

10

12

15

18

19

-

119

Table A-1 (cont’d)
20

40 µm

1.2

0.1

0.08

60 µm

1

0.1

0.08

22

40 µm

1

0.1

0.08

25

40 µm

1.7

0.1

0.08

60 µm

1.7

0.1

0.08

120

APPENDIX B. ESTIMATE OF PHOTOBLEACHING EFFECT
The model relating the number of active molecules (n) and the initial total number of
dye molecules (n0) after being exposed to light for a time (t) is given by (See
Koochesfahani (1984), and the references therein)

n = n0 exp(−t / τ b )

(B-1)

The bleaching time constant τ b is given as
−1
τ b = Qbφ pσ

(B-2)

Where

Qb - bleaching quantum efficiency (probability that a dye molecule will be bleached with
the absorption of a single photon)

φ p - laser photon flux

σ - dye absorption cross section
For the experiments described in this dissertation, bleaching time constant is 32 sec. This
means that only 37% of molecules will be absorbing after 32 sec. The bleaching time
2
constant is calculated based on Qb = 4 × 10 − 6 , φ p = 3.67 × 1019 photons/cm /sec,

corresponding to 15 watts/ cm power density at 488 nm and σ = 2.14 × 10 −16 cm
2

(calculated from attenuation of 2 × 10 − 7 M).

121

2

APPENDIX C. CHEMICAL PRODUCT HISTOGRAM
(U = 20 mm/s, A3 = 60 µm, F = 2 - 25 Hz, SPANWISE IMAGING)

2 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-1. Pdf of chemical product at four different streamwise locations (F = 2 Hz, U
= 20 mm/s and A3 = 60 µm).

122

4 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-2. Pdf of chemical product at four different streamwise locations (F = 4 Hz, U
= 20 mm/s and A3 = 60 µm).

123

8 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-3. Pdf of chemical product at four different streamwise locations (F = 8 Hz, U
= 20 mm/s and A3 = 60 µm).

124

10 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-4. Pdf of chemical product at four different streamwise locations (F = 10 Hz, U
= 20 mm/s and A3 = 60 µm).

125

12 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-5. Pdf of chemical product at four different streamwise locations (F = 12 Hz, U
= 20 mm/s and A3 = 60 µm).

126

15 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-6. Pdf of chemical product at four different streamwise locations (F = 15 Hz, U
= 20 mm/s and A3 = 60 µm).

127

18 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-7. Pdf of chemical product at four different streamwise locations (F = 18 Hz, U
= 20 mm/s and A3 = 60 µm).

128

19 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-8. Pdf of chemical product at four different streamwise locations (F = 19 Hz, U
= 20 mm/s and A3 = 60 µm).

129

20 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-9. Pdf of chemical product at four different streamwise locations (F = 20 Hz, U
= 20 mm/s and A3 = 60 µm).

130

25 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure C-10. Pdf of chemical product at four different streamwise locations (F = 25 Hz,
U = 20 mm/s and A3 = 60 µm).

131

APPENDIX D. CHEMICAL PRODUCT HISTOGRAM
(U = 20 mm/s, A2 = 40 µm, F = 2 - 25 Hz, SPANWISE IMAGING)
2 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-1. Pdf of chemical product at four different streamwise locations (F = 2 Hz, U
= 20 mm/s and A2 = 40 µm).

132

4 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-2. Pdf of chemical product at four different streamwise locations (F = 4 Hz, U
= 20 mm/s and A2 = 40 µm).

133

8 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-3. Pdf of chemical product at four different streamwise locations (F = 8 Hz, U
= 20 mm/s and A2 = 40 µm).

134

10 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-4. Pdf of chemical product at four different streamwise locations (F = 10 Hz, U
= 20 mm/s and A2 = 40 µm).

135

12 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-5. Pdf of chemical product at four different streamwise locations (F = 12 Hz, U
= 20 mm/s and A2 = 40 µm).

136

15 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-6. Pdf of chemical product at four different streamwise locations (F = 15 Hz, U
= 20 mm/s and A2 = 40 µm).

137

18 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-7. Pdf of chemical product at four different streamwise locations (F = 18 Hz, U
= 20 mm/s and A2 = 40 µm).

138

19 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-8. Pdf of chemical product at four different streamwise locations (F = 19 Hz, U
= 20 mm/s and A2 = 40 µm).

139

20 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-9. Pdf of chemical product at four different streamwise locations (F = 20 Hz, U
= 20 mm/s and A2 = 40 µm).

140

25 Hz

x = 4.2 mm

x = 9 mm

x = 15 mm

x = 25 mm

Figure D-10. Pdf of chemical product at four different streamwise locations (F = 25 Hz,
U = 20 mm/s and A2 = 40 µm).

141

BIBLIOGRAPHY

142

BIBLIOGRAPHY

Aref, H. (1984), “Stirring by chaotic advection.” Journal of Fluid Mechanics, 143:1-21.
Aref, H. (1990), “Chaotic advection of fluid particles.” Proc. R. Soc. Lond. A 434:273289.
Aref, H. (2002), “The development of chaotic advection.” Phys. Fluids, 14:1315-1325.
Bau, H. H., Zhong, J. and Yi, M. (2001), “A minute magneto hydro dynamic (MHD)
mixer.” Sensors and Actuators B, 79:207-215.
Breidenthal, R. (1981), “Structure in turbulent mixing layers and wakes using a chemical
reaction.” Journal of Fluid Mechanics, 109, pp. 1-24.
Campbell, C. J. and Grzybowski, B. A. (2004), “Microfluidic mixers: from
microfabricated to self-assembling devices.” Phil. Trans. R. Soc. Lond. A, 362:10691086.
Glasgow, I. and Aubry, N. (2003), “Enhancement of microfluidic mixing using time
pulsing.” Lab Chip, 3:114-120.
Koochesfahani, M. M. (1984), “Experiments on turbulent mixing and chemical reactions
in a liquid mixing layer.” Ph.D. Thesis, Caltech.
Koochesfahani, M. M. and Dimotakis, P. E., (1986), “Mixing and chemical reactions in a
turbulent liquid mixing layer.” Journal of Fluid Mechanics, 170, pp. 83-112.
Koochesfahani, M. M. and Dimotakis, P. E. (1989), “Effects of a downstream
disturbance on the structure of a turbulent plane mixing layer.”AIAA, 27, pp. 161-166.
Koochesfahani, M. M. and MacKinnon, C. G. (1991), “Influence of forcing on the
composition of mixed fluid in a two-stream shear layer.” Phys. Fluids A., 3(5), pp.
1135-1142.
Koochesfahani, M. and Nelson, R. (1997), “Molecular mixing enhancement in the
confined wake of splitter plate.” AIAA 97-2007.
Lin, K. W. and Yang, J. T. (2007), “Chaotic mixing of fluids in a planar serpentine
channel.” International Journal of Heat and Mass Transfer, 50:1269-1277.
Liu, R. H., Stremler, M. A., Sharp, K. V., Olsen, M. G., Santiago, J. G., Adrian, R. J.,
Aref, H. and Beebe, D. J. (2000), “Passive mixing in a three-dimensional serpentine
microchannel.” Journal of Microelectromechanical systems, 9, No.2, 190-197.
143

MacKinnon, C. G. and Koochesfahani, M. M. (1993), “Three-dimensional structure and
mixing of a forced wake inside a confined channel.” AIAA-93-0658.
Mengeaud, V., Josserand, J. and Girault, H. (2002), “Mixing processes in a zigzag
microchannel: Finite element simulations and optical study.” Anal. Chem., 74, 42794286.
Mensing, G. A., Pearce, T. M., Graham, M. D., and Beebe, D. J. (2004), “An externally
driven magnetic microstirrer.” Phil. Trans. R. Soc. Lond. A, 362:1059-1068.
Nelson, K. E. (1996), “Structure and mixing in a low Reynolds number forced wake in a
confining channel.” M.S. Thesis, Michigan State University.
Nguyen, N. T. and Wu, Z. (2005), “Micromixers- a review.” J. Micromech. Microeng, 15:
R1-R16.
Oster, D. and Wygnanski, I. (1982), “The forced mixing layer between parallel streams.”
Journal of Fluid Mechanics, 123, pp. 91-130.
Ottino, J. M. (1989), “The kinematics of mixing: stretching, chaos, and transport,
Cambridge University Press.
Roberts, F. A. (1985), “Effects of a periodic disturbance on mixing in turbulent shear
layers and wakes.” Ph.D. Thesis, Caltech.
Roberts, F. A. and Roshko, A. (1985), “Effects of periodic forcing on mixing in turbulent
shear layers and wakes.”AIAA-85-0570.
Squires, T. and Quake, S. (2005), “Microfluidics: Fluid physics at the Nanoliter scale.”
Reviews of modern physics, 77, pp. 977-1026.
Stone, H. A., Stroock, A. D. and Ajdari, A. (2004), “Engineering flows in small devices:
Microfluidics toward a lab-on-a-chip.” Annu. Rev. Fluid Mech, 36:381-411.
Strook, A. D., Dertinger, S. K.W., Ajdari, A., Mezic, I., Stone, H. A. and Whitesides, G.
M. (2002), “Chaotic mixer for microchannels.” Science, 295, 647 (2002).

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