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2/05 p:/ClRC/DateDuerindd-p.1

An Experimental Study of Pressure- and
Electroosmotically-Driven Flows in
Microchannels with Surface Modiﬁcations

By

Chee Leong Lum

A Dissertation

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

Doctor of Philosophy
Department of Mechanical Engineering

2005

Abstract

An Experimental Study of Pressure- and Electroosmotically-Driven Flows

in Microchannels with Surface Modiﬁcations

By

Chee Leong Lum

Researchers investigating pressure-driven flows within microchannels have
reported a discrepancy with classical theory. These discrepancies were attributed to
various reasons; notably entrance effects, electroviscous effects, early transition to
turbulence, surface roughness effects, etc. These measurements were all performed
using bulk ﬂow measurement techniques such as pressure drop and ﬂow rate
measurements. To investigate if deviations from classical theory do exist, the friction
factor obtained from the current study was compared to classical theory for
microchannels with a characteristic size of 300nm. The determination of the friction
factor in this study differs from other researchers as it is derived from local
measurements of the velocity proﬁle using the Molecular Tagging Velocimetry (MTV)
technique. This is the ﬁrst time that a local measurement of the velocity proﬁle has
been used to derive the friction factor. Local measurements are advantageous as
entrance effects do not affect it and it does not suffer from the high order dependence
on diameter (D4) when relating pressure drop to volume flow rate. The microchannels
used in this study were coated with polymer brushes (HEMA) and octadecyl-
trichlorosilane (OTS) to investigate if the added hydrophobicity of these coatings would
affect the pressure-driven ﬂow.

The second part of this study relates to electroosmotically-driven flows within

microchannels. Electroosmotically-driven ﬂows are of interest as pressure-driven ﬂows

become increasingly ineffective in transporting ﬂuid due to the increase in surface to
volume ratios in smaller microchannels. The electroosmotic velocity’s dependence on
temperature and the applied electric potential was studied using a simultaneous
velocity and temperature measurement technique (Molecular Tagging Velocimetry 81.
Thermometry, MTV&T). The estimation of the electroosmotic velocity based only on the
Helmholtz-Smoluchowski equation was found to be inadequate due to the presence of
Joule heating and showcases the need for a simultaneous local measurement of both
the velocity and temperature to resolve the flow physics. This local measurement
technique is also used to obtain local zeta potential (9 measurements of the different
surfaces. Zeta potential information is important in designing microfluidic devices to
improve mixing characteristics within microchannels. An added capability of the
measurement technique to reveal zeta potential dependence on temperature is also
presented. To further our understanding of the spatio-temporal evolution of
temperature within the microchannel during electroosmosis, a numerical simulation

(FLUENT) was employed with boundary conditions similar to our experimental studies.

Dedication

This thesis is dedicated to my parents for all the love and support throughout
the years, without which I would not have come so far in my education. I am also
eternally grateful to my ﬁance for being by my side throughout this journey which made

it more bearable at times of difﬁculties.

iv

Acknowledgements

This work would not have been possible without the help and support of many
people. I would ﬁrst like to thank my primary advisor Dr. Manoochehr Koochesfahani
for the excellent guidance that culminated in the work done in this thesis. Throughout
the years. it has been a privilege to work under his tutelage. I am also grateful for the
kind advice from my other thesis committee members; Dr. Ahmed Naguib, Dr. Merlin
Bruening and Dr. Andre Benard. Their help have been instrumental in the completion
of this thesis.

I would also like to thank my colleagues for all the assistance and discussions
that helped in the work presented in this thesis. I would like to speciﬁcally thank Doug
Bohl (for the help and guidance when I ﬁrst came in as a Masters student). Behshad
Shaﬁi (for the stimulating discussions on our projects and creating a lively environment
in the lab). Laura Hudy (for being there as a friend. basketball and football fan, phD
student. all rolled into one). Shahram Pouya (for his dependability and inherent strive
for perfection) and Jill Drexler (for her endless enthusiasm and hours of conversation
which kept boredom away).

This work would also not have been possible without support from the National
Science Foundation (NSF). the Center for Sensor Materials at Michigan State University
(Ann Kirchmeier, Darla Conley and Keri Marchand were amazingly helpful) and Mike

McClean for his help in creating the experimental setups in this work.

Table of Contents

Abstract .................................................................................................................. ii
Dedication ................................................................................................................. iv
Acknowledgements ........................................................................................................ v
List of Tables ................................................................................................................ ix
List of Figures ................................................................................................................ x
Nomenclature ............................................................................................................. xvi
Chapter 1 Introduction .................................................................................................. 1
Chapter 2 Experimental Setup & Measurement Techniques ........................................ 10
2.1 Optical Setup .............................................................................................. 10

2.2 Imaging System .......................................................................................... 12

2.3 Microchannels ............................................................................................ 13

2.3.1 Channel Construction .................................................................. 13

2.3.2 Preconditioning and Surface Modiﬁcations .................................. 15

2.3.3 Surface Roughness Measurements .............................................. 18

2.4 Flow Setup ................................................................................................. 21

2.4.1 Pressure-Driven Flows ................................................................. 21

2.4.2 Entrance Length .......................................................................... 24

2.4.3 Electroosmotic Flow Setup ........................................................... 25

2.5 Molecular Tagging Velocimetry ................................................................... 27

2.5.1 Velocity Correlation Technique .................................................... 32

2.5.2 Taylor Dispersion ......................................................................... 33

2.6 Molecular Tagging Thermometry ................................................................. 35
Chapter 3 Pressure-Driven Flows ................................................................................. 39
3.1 Equations of Motion ................................................................................... 39

3.2 Friction Factor ............................................................................................ 42

3.3 Results & Discussion for Pressure-Driven Flows ........................................ 48

3.3.1 Comparison of the Rectangular Channel Series Solution to

the 2-D Flow Parabolic Solution .................................................. 52
3.3.2 Determination of Friction Factor from Experiments ..................... 53
3.3.3 Experimental Results for Non-Coated Quartz Microchannels ....... 56
3.3.4 Extended Range of Re # for Non-Coated Microchannels ............... 62

3.3.5 Experimental Results for HEMA coated Quartz

Microchannels ............................................................................. 67

3.3.6 Experimental Results for 0T8 coated Quartz Microchannels ....... 71

3.3.7 Limit of Slip Detection ................................................................. 77

3.3.8 Electroviscous Effects .................................................................. 79

3.3.9 Contributions and Conclusions ................................................... 80

3.3.10 Future Work .............................................................................. 82
Chapter 4 Electroosmotic-Flow in Microchannels ........................................................ 83
4.1 Electric Double Layer ................................................................................. 84
4.1. l Debye-Hﬁckel Approximation ...................................................... 87

4.2 Principles of Electroosmosis ....................................................................... 88
4.2. 1 Factors Affecting Zeta Potential .................................................... 90

4.2.2 pH Stability .................................................................................. 92

4.2.3 Equation of Motion for EOF ......................................................... 94

4.2.4 Time Response of Electroosmotic Flows ....................................... 95

4.2.5 Surface Conduction Effects .......................................................... 96

4.2.6 Factors Affecting Electroosmosis .................................................. 97

4.3 Results and Discussion for Electroosmotic Flows ..................................... 100
4.3.1 Debye Length ............................................................................. 100

4.3.2 Conductivity of Solutions ........................................................... 101

4.3.3 Electrophoretic Mobility of MTV Triplex Solution ....................... 102

4.3.4 Experimental Results for Time Evolution of Electroosmotic

Velocity with Joule Heating ....................................................... 107

Vii

4.3.5 Temperature Variation along Height (Z-axis) of
Microchannel ............................................................................ l 18

4.3.6 Computational Solution of Electroosmotic Flow in the

Microchannel ............................................................................ 1 19

4.3.7 Zeta Potential Measurements ..................................................... 128

4.3.8 Contribution and Conclusions ................................................... 132

4.3.9 Future Work .............................................................................. 133

Appendix A: Lens Setup for Imaging .......................................................................... 135
Appendix B: Effective Magniﬁcation of Cameras ......................................................... 136
Appendix C: Intensiﬁer Characteristics of Dicam Pro ................................................. 138
Appendix D: Laser and Camera Synchronization Setup ............................................. 141
Appendix E: Pressure Drop within Microchannel ....................................................... 143
Appendix F: Spatial Resolution of Measurements ...................................................... 145
Appendix G: Velocity Proﬁles within commercial microchannels ................................ 147
Appendix H: Description of Single Line Velocity Proﬁle Labview Program ................... 149

Appendix 1: Methodology for Deposition of Polymer-brushes on Quartz Substrates... 156
Appendix J: Calibration of Phosphorescent Chemicals for Temperature
Measurements ....................................................................................... 1 58

Appendix K: Accuracy in the Temperature Measurements with the MIT technique 160

Appendix L: Equations of Motion with Slip Derivation ............................................... 161
Appendix M : Error Analysis for Pressure Driven Flows ............................................. 165
Appendix N: Determination of the Slip Detection Limit .............................................. 169
Appendix 0: Derivation of Equations for Molecular Tagging Thermometry ................ 172
Appendix P: User Deﬁned Functions (UDF) ................................................................ 175

viii

List of Tables

Table 2- 1. Surface roughness values for various surfaces ............................................ 19
Table 3- 1. Experimental data for pressure driven ﬂows in non-coated

microchannels with Reynolds number based on hydraulic diameter ......... 61
Table 3-2 Experimental data for pressure driven ﬂows in non-coated

microchannels with extended Reynolds number range based on

hydraulic diameter .................................................................................... 66
Table 3-3. Experimental data for pressure driven flows in HEMA coated

microchannels with extended Reynolds number range based on

hydraulic diameter .................................................................................... 70
Table 3-4. Experimental data for pressure driven flows in OTS coated

microchannels with extended Reynolds number range based on

hydraulic diameter .................................................................................... 74
Table 4-1. Elution time for MTV Triplex (Neopenthanol) ............................................. 103
Table 4-2. Elution time for Mesityl Oxide (neutral marker) ......................................... 104
Table 4-3. Elution time for MTV Triplex (cyclohexanol) .............................................. 104

Table 4-4. Electroosmotic velocity corrected for temperature effects at different
applied electric potential ......................................................................... 117

Table 4-5. Properties of Quartz .................................................................................. 122

List of Figures

(Images in this dissertation are presented in color)

Figure 1-1. Normalized friction constant plot with data from various

researchers. (Sharp et. a1. 2002) ................................................................. 3
Figure 2-1. Optical setup for experiments .................................................................... 11
Figure 2—2 Coming 7980 Transmission Spectra (Corning Inc.) ..................................... 14
Figure 2-3. Schematic of a completed rectangular quartz channel. .............................. 15

Figure 2-4. Comparison of hydrophobicity between uncoated, polymer brushes
and OPS coated quartz surfaces (liquid used is water). ............................. 17

Figure 2-5. Scanning electron microscope (SEM) images of polymer brushes

before and after laser irradiation (after ~9000 laser pulses). ..................... 18
Figure 2-6. AFM scan of uncoated quartz .................... . ............................................... 19
Figure 2-7. AFM scan of OTS coated quartz. ................................................................ 20
Figure 2-8 AFM Scan of HEMA Coated Quartz ............................................................. 20
Figure 2-9 Experimental Setup for Pressure Driven Flow (side view. X-Z plane) ........... 22
Figure 2-10. Setup for Pressure Driven Flows with Syringe Pump (X-Z Plane) .............. 22
Figure 2-11 Illustration of test section (syringe pump setup) ....................................... 23

Figure 2—12 Schematic of experimental interrogation location (top view. X-Y

plane) ....................................................................................................... 23
Figure 2- l3 Schematic of EOF setup ........................................................................... 26
Figure 2-14. Current measurement setup .................................................................... 26

Figure 2- 15 Chemical structure of Phosphorescent Supramolecule used here

for M'IV ..................................................................................................... 27
Figure 2-16 : Typical MTV image pairs and the corresponding correlated

velocity vector ﬁeld. (Gendrich. et. 31., 1997) After 8ms. the tagged

regions are imaged again to yield a distorted image due to the

velocity of the ﬂuid. Correlation of these images resulted in a

velocity vector ﬁeld as shown in the last image. ........................................ 29
Figure 2-17. Image of plume during uni-directional solidiﬁcation ................................ 29
Figure 2-18. Total phosphorescence emission from 1-Ber.GB-CD.ROH for

three different types of alcohol at ﬁxed concentrations of l-BrNP

and GB-CD and at 308nm wavelength laser excitation. (Plotted

from Gendrich et. a1.. 1997) ...................................................................... 31
Figure 2—19. Spectraphotometer Scan of Relative Absorption of

Bromonapthalene ..................................................................................... 3 1
Figure 2-20. Uncertainties of correlated single tagged lines at different signal to

noise ratios and line widths (full width at 1/e2). ....................................... 33

Figure 2-21 Undelayed (left) and delayed (right) images with line proﬁles drawn

across the center of the image for electroosmotic ﬂow ............................... 34
Figure 2-22 Comparison of line proﬁle for undelayed and delayed images. .................. 35
Figure 2-23 Exponential decay of phosphorescence intensity ...................................... 36
Figure 2-24. Normalized lifetime of both chemicals ...................................................... 38
Figure 3- 1 . Coordinate system for capillary ................................................................. 40
Figure 3-2. Schematic of channel geometry .................................................................. 42
Figure 3-3. Fanning friction factor for different geometries .......................................... 44
Figure 3-4. Series solution of velocity proﬁle. u(y,z), within a square channel .............. 48
Figure 3-5 Series solution of velocity proﬁle, u(y,z), within a 5:1 channel .................... 49

Figure 3-6. Change of velocity near the channel wall (Y -axis); aspect ratio of

84.67 ........................................................................................................ 50
Figure 3-7. Normalized velocity gradients (du/ dz) as a function of distance from

walls ......................................................................................................... 5 1
Figure 3—8 Umean/Umax for different channel aspect ratios ............................................. 51
Figure 3-9 Comparison of parabolic proﬁle solution to the numerical

computation of the series solution ............................................................ 53

xi

Figure 3- 10. Images of tagged molecules for pressure driven ﬂows. ............................. 54
Figure 3- l 1 Velocity proﬁle from correlation of initial and delayed images ................... 55
Figure 3— 12 Central Ditferencing Technique for obtaining Slope .................................. 55
Figure 3- 13. Images of tagged ﬂuid for different ﬂow velocities for uncoated

microchannels .......................................................................................... 58
Figure 3- 14. Velocity proﬁles at different Reynolds numbers (Re #: 11.23 -

43.07) ....................................................................................................... 59
Figure 3-15. Velocity proﬁles at different Reynolds numbers (Re #: 53.22-

84. 12) ....................................................................................................... 60
Figure 3- 16 Normalized friction factor based on deﬁnitions of Reynolds

number ..................................................................................................... 62

Figure 3-17. Images of tagged ﬂuid for different ﬂow velocities (Re # : 0.32-

10.86) ....................................................................................................... 63
Figure 3- 18 Plot of velocity at different pressure gradients (Re #: 0.33) ........................ 64
Figure 3- 19. Plot of velocity at different pressure gradients (Re #2 1.37- 137.98) ........... 65

Figure 3-20. Images of tagged ﬂuid for different ﬂow velocities for HEMA coated
microchannels (Re # : 2.19-65.05). ........................................................... 67
Figure 3-21 Plot of velocity at different pressure gradients for HEMA coated
microchannels (Re #: 2. 19-4.28). .............................................................. 68
Figure 3-22. Plot of velocity at different pressure gradients for HEMA coated
microchannels (Re #: 997-6505). ............................................................ 69
Figure 3-23. Images of tagged ﬂuid for different ﬂow velocities for OTS coated
microchannels (Re # : 2.42-10.58). ........................................................... 71
Figure 3-24. Images of tagged ﬂuid for different ﬂow velocities for OTS coated
microchannels (Re # : 13.48—138.44). ....................................................... 72
Figure 3-25. Plot of velocity at diﬁerent pressure gradients for OTS coated

microchannels (Re #: 242-13844). .......................................................... 73

xii

Figure 3-26. Comparison of normalized friction factor (Sharp et. al.. 2000) to

friction factor obtained from experimental results for uncoated.

OTS-coated and HEMA-coated quartz. ...................................................... 75
Figure 3-27. Zoomed-in view of normalized friction factor ............................................ 76

Figure 3-28. Comparison of theoretical velocity proﬁles near the wall with and

without slip ............................................................................................... 78
Figure 3-29. Central differencing technique for obtaining slope ................................... 78
Figure 4-1. Schematic of deprotonated silanol groups .................................................. 85
Figure 4-2. The diffuse electric double layer (Probstein. 1994) ..................................... 85

Figure 4-3. Schematic of a typical ion distribution in the vicinity of a charged

surface and the resultant electroosmotic velocity proﬁle and

surface potential (Probstein. 1994) ........................................................... 89
Figure 4-4. Schematic of velocity proﬁle within microchannel for electroosmosis ......... 89
Figure 4—5. Plot of zeta potential for various surfaces at different pH values. ............... 91

Figure 4-6. Schematic of a charged surface illustrating factors that affect zeta

potential ................................................................................................... 9 1
Figure 4—7. Change of pH of MTV Solution and Sodium Phosphate Buffer

Solution with increasing volume of Sodium Hydroxide .............................. 93

Figure 4-8. Plot of permittivity and viscosity of water vs. temperature (Wyman

et.al, 1930, Handbook of Chemistry and Physics, 85th Ed.) ....................... 98
Figure 4-9. Electrophoresis .......................................................................................... 99
Figure 4-10. Change of conductivity of various solutions with temperature ............... 102
Figure 4-11. Typical Capillary Electrophoresis Experimental Setup ........................... 103

Figure 4- l2. Detection peaks for the three chemicals separately tested and

combined. ........................................................................... 105
Figure 4-13. Plot of superposition of peaks ................................................................ 106
Figure 4-14. Image pairs at various potential gradients (74.7-234.9V/cm) ................. 108

xiii

Figure 4- 15. 'lypical electroosmotic ﬂow and temperature proﬁles showing

contamination of pressure gradient ........................................................ 109
Figure 4- 16. Non-linear increase in velocity at different electric potentials ................. 110
Figure 4- l7. Electroosmotic velocity at different temperatures for uncoated

quartz microchannels. ............................................................................ 11 1
Figure 4-18. Electroosmotic velocity corrected at different temperatures for

OTS coated microchannels ..................................................................... 112

Figure 4-19. Electroosmotic velocity corrected at different temperatures for

HEMA coated microchannels .................................................................. 112
Figure 4-20. Initial data and corrected data for electroosmotic velocity. ..................... 113
Figure 4-2 1. Plot of velocity increase with time for uncoated microchannels .............. 115

Figure 4-22. Plot of temperature increase with time for uncoated

microchannels ........................................................................................ l 15
Figure 4-23. Time evolution of temperature proﬁles within the microchannel at

18 1 .6V / cm ............................................................................................. 1 18
Figure 4-24. Schematic of microchannel in GAMBIT .................................................. 120

Figure 4-25. Schematic of end-view of microchannel with superposed wall

thickness ................................................................................................ 12 1
Figure 4-26. Boundary conditions applied to the geometry ........................................ 122
Figure 4-27. Plot of current rise with time at different applied voltage. ...................... 123

Figure 4-28. Temperature contour of the ﬂuid at 30 seconds after application

of the potential ........................................................................................ 125
Figure 4-29. Temperature proﬁle along X-axis at different times during

electroosmosis. ....................................................................................... 125

Figure 4-30. Temperature gradient along the Z-axis of the microchannel at X. Y

= 0 .......................................................................................................... 127
Figure 4-3 1. Zeta potential calculation from velocity vs. voltage plot at 28°C ............. 130
Figure 4-32. Plot of zeta potential of OTS vs. Temperature ......................................... 130

xiv

Figure 4-33. Plot of zeta potential of uncoated quartz vs. Temperature. ..................... 131

Figure 4-34. Plot of zeta potential of HEMA vs. Temperature ..................................... 131

Cf. theory

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RCCH
ReDH
RPE

Nomenclature

Description

half width (Y -axis)
cross sectional area
half width (Z-axis)
concentration of ions
friction factor (Fanning)
experimental friction factor (Fanning)
theoretical friction factor (Fanning)
charge distribution
Diameter
diffusion coefﬁcient
Hydraulic diameter
Dukhin number
applied electric potential per unit length
friction factor (Darcy)
Faraday's constant
gravity
current
emitted intensity
Initial intensity
total phosphorescence signal
Joules
bulk conductivity
surface conductivity
characteristic length (m)
Liter
pressure
power
volume ﬂow rate
heating rate
Radius
gas constant
Reynolds Number
Reynolds Number based on Characteristic Height
Reynolds Number based on Hydraulic Diameter
relative perturbation error
theoretical velocity ratio

Ieo
Ixy
Iyz

sz

circumference
time
temperature
ﬁnal temperature
initial temperature

sectional mean velocity

Sectional mean velocity (theory)

microchannel mean velocity
peak velocity
radial velocity
axial velocity
velocity in the Y-axis
velocity in the Z-axis
azimuthal velocity
voltage
ﬁnal velocity
initial velocity
electric potential energy per mole of counter ions
charge number
slip length
pressure differential
delay time
roughness (standard deviation)
permittivity
permittivity of vacuum
relative permittivity
zeta potential
angle
Debye length
dynamic viscosity
density
electric charge density
lifetime
double layer response time
electroosmotic response time
shear stress (X-Y)
shear stress (Y -Z)
shear stress (Z-X)
wall potential

xvii

Line thickness
Initial line thickness

xviii

Chapter 1 Introduction

For many years, researchers involved in the engineering ﬁeld were focused on
the macro scale as most applications that demanded our attention were macro in size.
The need for a wind tunnel to better simulate real world conditions. for example.
eventually led to the creation of an 80x120 feet wind tunnel at NASA Arnes. Other
instances of similar use of macro-sized test facilities can be observed. Biologists and
chemists, on the other hand. are mainly interested in cell structures, chemical
reactions and the like. which operate at micro or even nano-scales. In recent years.
however, miniaturization has become more important for engineers in efforts to build
smaller devices that have a smaller footprint with similar or better characteristics
compared to their macro-sized counterpart. Miniaturization holds many promises but
as yet not fully realized as our understanding of the ﬂow physics within micro scale
structures are not fully developed. One of the obvious advantages of miniaturization is
size. Smaller sized pumps. engines, chemical detectors. etc. utilize space constraints
more efﬁciently. A miniaturized chemical detector, for example, could in theory be ﬁtted
on a wrist watch and help warn the user of chemical exposure. Costs could also be
signiﬁcantly reduced as the use of material decreases. The miniaturization of a heat
transfer device increases the surface to volume ratio available for heat transfer thus
improving the performance of cooling and heating mechanisms. A cooling performance
increase in a small package would beneﬁt the cooling requirements of a personal
computer, for example. These advantages and many more have created a need to fully
understand the physical implications of miniaturization.

Coinciding with this need, this study speciﬁcally investigates methodologies
currently used to move ﬂuids within microchannels through experimental study and
comparing with known theories. Biologists and chemists have traditionally used

pressure driven ﬂows within capillaries for analyte separation analyses. Pressure driven

ﬂows. however, cause the separated analytes to spatially spread out or broaden as they
are advected downstream of the capillary for detection due to the presence of shear.
Band broadening of the separated analytes causes a reduced detection sensitivity.
Electroosmotically driven ﬂows (EOF). conversely. do not cause band broadening due to
the uniform ﬂow characteristics across the entire capillary. The surface charge present
on most surfaces, coupled with an ionized ﬂuid (e. g. aqueous solutions of an electrolyte)
within the capillary and an electric ﬁeld applied parallel to the surface causes EOF to
occur. This technique is essential in capillary electrochromatography (CEC). CEC
combines the advantage of chromatography (separating uncharged analytes possessing
different adsorption characteristics), and separation of charged analytes through
electrophoresis (variation in analyte velocity due to charge differences).

As much as pressure driven ﬂows and EOF have been utilized in biochemistry
and engineering. certain issues related to the ﬂow transport within micro- and nano-
sized channels need to resolved. Researchers over the years have compiled a large
amount of data that showed inconsistencies between experimental results and theory
for pressure driven ﬂows within microchannels. A representative data set for friction
factor was presented by Sharp et. al. (2002) and replotted in Figure 1-1. Agreement with
theory requires that the data in Figure 1—1 have a normalized friction constant of unity.
All the data sets showed large variations from theory except data from Sharp et. al.
(2000). These anomalies were attributed to surface roughness effects, electroviscous
effects. micro-rotational effects of individual fluid molecules. early transition to
turbulence, entrance effects. non-local ﬂow measurement techniques and inaccuracies
in measuring channel dimensions. Coincidentally. the data sets that showed variations
from theory were all acquired with bulk ﬂow measurements like measurement of ﬂow
rates and pressure drops. Data from Sharp et. al. (2000) were acquired using a
combination of pressure drop measurements and a local measurement technique called
Particle Image Velocimetry (PIV) and showed agreement with theory (Reynolds number.

Re: 100-2000). Transition to turbulence was observed at Reynolds number (Re) ~ 2000

2

which is consistent with general ﬂow theory. PIV is a measurement technique that uses
particles to track ﬂow movement but care is needed to ensure that the particles used do
not interfere with the ﬂow and that ﬂocculation (coalescing of particles) does not occur.
Above all. it is important that the particles used for ﬂow tracking do indeed follow the
ﬂow ﬁeld faithfully. Density mismatch with the working ﬂuid or the interaction of the

charged surfaces of the particles with the microchannel could cause errors in the

 

 

 

 

 

 

 

measurements.
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Figure 1-1. Normalized friction constant plot with data from various researchers. (Sharp
et. al. 2002)

More recently. Brutin et. al. (2003). through pressure drop measurements.
suggested that the observed deviations from classical theory for round glass capillaries
(as large as 530m) in their experiments are due to the ﬂuids ionic composition and its
interaction with the charged microchannel wall to cause an added viscosity near the

wall. This phenomenon is called electroviscous effects and is known to only affect the

ﬂow ﬁeld when the electric double layer (EDL) is comparable in height to the
microchannel dimensions (Rice and Whitehead. 1965). This phenomenon will cause an
added viscosity-like effect on the bulk ﬂow. thus causing a deviation from classical
theory. Phares and Smedley (2004). however. stipulated that electroviscous effects do
not affect the ﬂow ﬁeld for smooth capillaries >100um in diameter. As the channel size
decreases (<50um). the inconsistencies with theory become more pronounced. Their
measurement range was from a Re of 0.0001-1. Other causes of discrepancies with
classical theory have also been attributed to surface roughness. Phares and Smedley
(2004) measured deviations of up to 17% from classical theory for rough tubes
(roughness values (e/ D. roughness in relative to diameter) of 2% were observed). The
tubings that were used were made of stainless steel and the roughness characteristics
were noticeably higher than that of glass capillaries.

In any experiment. the appropriate use of experimental techniques plays a very
important role in determining its effectiveness. Pressure drop and volume ﬂow rate
measurements are suitable in providing bulk or averaged ﬂow information across the
entire ﬂow setup but entrance effects need to be decoupled from the measurement. An
local measurement technique is thus needed to resolve unambiguously the ﬂow physics
within microchannels.

In this study. an in-situ technique is utilized to determine the velocity and
estimate the wall friction factor. Molecular Tagging Velocimetry (MTV) is a local
measurement technique similar in implementation to PIV but uses “tagged” molecules
instead of particles to track the ﬂow. The utilization of molecules ensures that some of
the constraints (particle density. ﬂocculation. etc.) related to the use of PIV are not
present in MTV. A more detailed discussion of the MTV technique is presented in § 2.5.
Previous work by Maynes et. al. (2002) used the M'IV technique to provide mean ﬂow
characteristics within a 0.705 mm circular tube but did not utilize the velocity proﬁles
to derive friction factor information as is being done in this study. For each set of

experimental conditions. the velocity proﬁle. the pressure drop and the mass ﬂow rate

4

were quantiﬁed. The velocity proﬁle was measured using the MTV technique but only
the mean velocity information was derived from it. Volume ﬂow rate, however. was
measured by collecting the ﬂuid at the channel exit over a period of time. The two
measurements were compared to determine any discrepancies from theory. These
experiments were performed over a Reynolds number range of 500-2500 and the
friction factor derived from pressure drop measurements showed agreement with the
standard friction factor deﬁnition of f=64/ Re for a Poiseuille ﬂow in round capillaries. It
is intended in the current study to improve upon the measurements made by Maynes
et. al. (2002) by focusing on smaller channel sizes (300um) where a deviation from
theory (if any) is more likely, lower Reynolds numbers (1-100) and a higher
measurement resolution. Also. the ﬁiction factor will be derived from in-situ
measurements of the velocity proﬁle and not bulk ﬂow measurements as in the case of
Maynes et. al (2002) and Sharp et. a1. (2000). This is expected to provide higher
accuracy measurements as ambiguities like entrance length issues which are related to
bulk ﬂow measurement techniques are not present.

Maynes et. al. (2002), Sharp, et. a1 (2000) and our own experiments to date were
all performed using water as the ﬂowing medium but it is worth noting that some of the
data from Figure 1.1 was obtained using non-polar ﬂuids. Non-polar ﬂuids like silicon
oil and kerosene. for example. do not contain ions and their interactions with surfaces
are different from ionic ﬂuids. The difference in molecular forces present in each
material or ﬂuid causes surface tension when two different materials come in contact
(Adamson. et. al. 1997). An example of surface tension is illustrated in the beading of
water droplets into spheres to reduce the surface area exposed to air. Non-polar ﬂuids
have a lower surface tension caused by the absence of ions and any purported
interaction of ions between the ﬂuid and the microcharmel as a source of discrepancy in
friction factor (Ren et. a1 (2001) and Brutin et. al. (2003)) will be a non-issue in this
case. Nevertheless. experimental results from Pfahler et. al. (1990) with N-propanol and

silicone oil as the ﬂowing medium still showed a consistent deviation from theory which

5

could be due to other unknown factors or simply an error in measurement. The
discrepancies in the literature clearly indicate that there is a need to resolve some of
these issues.

Another prevalent issue in ﬂuid ﬂow in microchannels is the possibility of slip.
The typical no-slip boundary condition. whereby the ﬂuid ﬂow decelerates to zero
velocity at a solid boundary. holds for macro scales as the shear stress is considerably
lower than that present within microchannels. Navier. in 1823 proposed a slip
boundary condition with the slip velocity proportional to the velocity gradient at a

surface and a proportionality constant. B. as the slip length.
Bu
U = ,6— 1-1
By

To date. molecular dynamics simulations (Jabbarzadeh. et. al. (1999)) and
experiments (Pit et. al. (2000) and 'I‘rethaway. et. al. (2002)) have been performed to
estimate the slip length with varying results. Slip lengths on the order of nanometers to
1 micron have been reported on treated microchannels. Microchannels are typically
treated with octadecyl-trichlorosﬂane (UPS) to render the channel surface hydrophobic
(hydrophobicity is a tendency for a surface to repel water. hence the term hydro). An
increased hydrophobicity will typically increase slip lengths. Shear stress
measurements by itself do not reveal any information about slip as it is not affected by
its presence. However. the normalization of the shear stress to obtain friction factor
utilizes the mean velocity which increases with the presence of slip. The equations of
motion with slip velocity are derived in Appendix L.

Experimental techniques used to measure slip typically measure the increased
ﬂow rate within 3 treated microchannel or zoom in on the solid-liquid interface to locally
measure the slip length. The use of bulk ﬂow measuring techniques is usually plagued

with uncertainties as it is difﬁcult to attribute a measured increase in ﬂow rate to be

6

due to the presence of slip alone. An increased ﬂow rate could potentially be caused by
a change in channel size. an error in pressure drop measurements, etc. A local
measurement of the slip length on the other hand. although appealing since it removes
any ambiguities associated with bulk ﬂow measurements. is very difﬁcult since it
requires a high resolution measurement technique.

As the dimensions of our ﬂow device become smaller. pressure becomes less
effective in moving ﬂuids. The following expression. showing the relation between Ap

and Q. illustrates this for ﬂow within capillaries.

_ 128mg

”D, 1-2

AP

where Apis the pressure drop required. ﬂ is the dynamic viscosity. Q is the volume

ﬂow rate and. l and D is the length and diameter of the ﬂow device respectively. The
pressure drop scales inversely with the 4th power of diameter. As the ﬂow device
diameter becomes smaller. the pressure drop needed to move ﬂuid within
microchannels becomes very large. For example. a 10X reduction in diameter requires a
10,000X higher pressure drop to maintain the same volume ﬂow rate. Conversely, EOF
is an elegant way of transporting ﬂuid within microchannels without the need for high
pressure. A byproduct of EOF. however. is heat generation through Joule heating.
Excessive heat generation can affect electroosmotic ﬂow and cause problems with
analysis of separated analytes. To better comprehend the effects of Joule heating.
temperature measurements within the microchannels would be useful. Ross et. al.
(2001) managed to measure whole ﬁeld temperature distributions within acrylic
microchannels using a temperature dependent emission of a ﬂuorescent dye. The
precision with which the measurements were made were low and the technique did not
take into account the spatial inhomogeneity of the excitation laser nor curvature of the

microchannel. Thomson et. al. (2001). conversely, used a phosphorescent dye whereby

the emission intensity of the dye alone is used to infer the temperature. An
improvement to the techniques used by Thomson et. al. (2001) and Ross et. al. (2001).
as documented in Hu et. al. (2003), will be used for the ﬁrst time to measure
temperature and velocity simultaneously within microchannels in EOF. The
characterization of both temperature and velocity simultaneously will allow us to draw a
direct consequence of temperature change to velocity change due to physical changes of
the ﬂuid properties. A temperature gradient that develops along the length of the
microchannel as electroosmosis occurs may cause additional errors in measurement of
the electroosmotic velocity for bulk ﬂow measurements.

Another aspect of interest in EOF is the determination of the zeta potential of a
surface. Oftentimes. a surface is coated to change its charge characteristics (to prevent
ﬂocculation of particles. for example). The interaction of the surface coating with the
ﬂuid is not directly known and measurements of the zeta potential of the surface need
to be made. The zeta potential is a characteristic observed from the combination of the
interaction of the surface charge and the ﬂuid characteristics within the channel and is
one of the factors that affect electroosmotic velocity. A typical method for determining
the zeta potential of a miCrochannel is to observe the movement of a neutral particle
during electroosmosis. The Helmholtz-Smoluchowski equation is then used to calculate
the zeta potential from a measured electroosmotic velocity. The use of particles to
measure zeta potential within a microchannel, however. is cumbersome as the
electrophoretic contribution of the particle has to be taken into account. Sze et. al.
(2003) measured the averaged electroosmotic velocity within a microchannel and in
turn inferred a zeta potential. Through the in-situ measurement capability of the MTV
technique and charge neutrality of the tracers, part of this study addresses the
measurement of zeta potentials of various surfaces. Knowledge of the zeta potential will
help us in designing ﬂow control within microchannels.

The layout of the rest of this thesis is as follows. Chapter 2 describes in detail

the diagnostic techniques and instrumentation used to measure velocity and

8

temperature. For velocity measurements, the MTV technique (Gendrich et. al.. 1997) is
utilized while for temperature measurements. the phosphorescence characteristics of
the chemicals used for MTV are exploited to yield temperature information (Hu et. al.
(2001). This technique is termed Molecular Tagging Therrnometry (MIT). The
experimental setup for both electroosmotic and pressure driven ﬂows is described next
as well as the surface modiﬁcations performed on the microchannels. Chapter 3
introduces pressure-driven ﬂows and the various issues pertaining to it with results
and discussions at the end of the chapter. Chapter 4 delves into the intricacies of
electroosmotic ﬂow. The electric double layer and principles of electroosmosis are

initially described followed by the experimental results.

Chapter 2 Experimental Setup & Measurement
Techniques

In this chapter, the various experimental setups needed for experiments in
pressure-driven and electroosmotically-drivem ﬂows are described. The optical setup for
MTV and the imaging system are initially presented. Next the construction and surface
modiﬁcations of the microchannels are described followed by the ﬂow setup. The

chapter concludes with presentation of the MTV and MTI‘ techniques.

2.1 Optical Setup

The use of MTV in this study warrants the use of a UV laser and a range of
optics to shape the laser beam. Traditionally. a 308mm wavelength laser was used for
tagging of the ﬂow. In this study. however, a different wavelength was used due to beam
focusing issues. This is the ﬁrst implementation of the MTV technique with a 266nm
wavelength laser. The laser utilized is a Continuum© Powerlite 9030 running at a
wavelength of 266nm with peak emery levels of 115mJ / pulse and a repetition rate of
30Hz. The laser beam is circular in shape (~8mm diameter) and has a nearly Gaussian
enery distribution. To ensure a symmetric proﬁle of the laser beam, the laser is usually
ﬁring at high enery levels. However. due to the low energy requirements of these
experiments at micro scales. a large amount of the laser enery has to be removed
before allowing the beam to impinge on the experimental setup. A high enery level is
known to damage the quartz walls of the microchannels and could also cause excessive
bleaching of the MTV chemicals.

The laser enery is initially set to an estimated enery level of 50mJ/pulse. The
laser beam is subsequently passed through a 99.9% beam splitter to reduce the enery
to 0.1%. At 0.1% of the initial emery. the enery per pulse of the laser beam is

estimated at 0.05mJ/pulse. A spatial ﬁlter is added to the optical setup to improve the

10

beam quality. Spatial ﬁltering is achieved by two 50mm spherical lens and a pinhole.
Mer improvements to the beam quality can be achieved with smaller focal length
lens and a smaller pinhole. Eventually. a 12.7mm focal length lens is used to focus the
beam into a thin line. All optics used were UV grade synthetic fused silica acquired from

CV1 Laser LLC with a damage threshold of 10J/cm2.

50mm
spherical lens

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phOSphorescent "7':E..?::f°..f° microchannel
triplex \ v ';;.;".”.L5-1:*.::.if}I"I.
Quartz walls

Zoomed-up view

Figure 2-1. Optical setup for experiments

The current setup has been able to create laser lines as thin as 13pm (full width at half
maximum, FWHM) although most of the experimental results were obtained with a
25m line width. The minimum line width is not always achievable depending on how
accurately the optics were aligned. At the focal spot size of 13mm, the enery density
has increased to 37J/cm2 which is beyond the damage threshold of the best UV lenses
(due to the limits of the damage threshold on the anti-reﬂection coating) and near the
limits of quartz. Through experimentation with the beam enery and the focal spot size.
a realizable working condition is achieved for tagging of the MTV triplex. The optical
setup described is shown in Figure 2-1. The optical setup is common between the

pressure driven and electroosmotic ﬂow experiments.

11

2.2 Imaging System

Low light levels of phosphorescent chemicals used here for MTV require the use
of intensiﬁed cameras. Two different cameras were utilized. A Xybion ICCD (Xybion
Corp.) camera was used speciﬁcally for velocity measurements in the pressure driven
ﬂow studies due to its high gain. The image acquisition rate at full frame (640x480
pixels) is 30Hz. A Mutech M-Vision 1000 PCI Bus Frame Grabber was used to acquire
images to a PC. For simultaneous measurements of electroosmotic velocity and its
corresponding temperature proﬁle. a Dicam Pro (PCO AG) intensiﬁed camera was used.
An acquisition rate of 7Hz at full frame (1280x1024 pixels) is achievable. This camera
has the capability of imaging two full frame images (double-shot mode) successively in a
short time frame (as fast as 500ns between 2 frames) and its gain stability makes it
suitable for temperature measurements. Gain stability is an added beneﬁt as the
charging characteristics of the intensiﬁer on the camera does not need to be accounted
for in the temperature measurements. The measurements of gain stability and charging
capability of the camera in the double-shot mode are documented in Appendix C. For
the Xybion ICCD. the two consecutive images required for velocity measurements were
acquired separately under the assumption that the ﬂow ﬁeld does not change with time.
This is a good assumption since the ﬂow is steady. fully developed and laminar. In an
electroosmotic ﬂow setup. the temperature and velocity changes with time and the pair
of images need to acquired consecutively.

A 10X Mitutoyo (Inﬁnity Corrected M Plan Apo Long Working Distance) objective
was used in all the experimental work presented here. This apochromatic lens is
aberration corrected for red, blue and yellow. It has a working distance of 33.5mm and
a depth of focus of 3.5m with a numerical aperture of 0.28. Since the objective is
inﬁnity corrected. a Mitutoyo tube lens (MT-40) is needed after the objective to focus the
image at the imaging plane of the camera. A distance of 170mm between the tube lens

and the camera is required for the correct magniﬁcation of the image. Further details of

12

the lens setup are provided in Appendix A Although the objective is rated at 10X. the
effective magniﬁcation observed by the cameras is less due to the optical systerm within
the camera. An effective magniﬁcation of 6.6x was observed for the Dicam Pro and 5.9x
for the Xybion ICCD. The magniﬁcation calibration of the camera is provided in
Appendix B.

For synchronization of the Xybion ICCD camera to the laser. the internal timing
of the camera was used as the trigger source while for the Dicam Pro. an external delay
generator was used. Digital delay generators from Stanford Research Systems Inc. (DO-
535) and Berkeley Nucleonics (BNC 555) were used in the setup. The full description of

the various timing and cable connections are provided in Appendix D.

2.3 Microchannels

2.3.1 Channel Construction

The microcharmels used for ﬂow measurement are homemade and are
nominally 300m in height. 25.4mm in width and 63.5mm in length. For electroosmotic
ﬂow studies. a 5mm channel width was used instead. The width for EOF was reduced
due to the available electric current used to transport ﬂuid in an electroosmotic
experiment and the length is designed to allow for a sufﬁcient entrance length and other
optical access issues. Beam steering effects and optical distortion due to the curvature
when using capillaries can cause a misrepresentation of the results. This is shown in
Appendix G for a commercial quartz microchannel. Although software techniques can
be used to correct for some of these effects. it is a tedious effort. The microchannels
used in this research are all rectangular channels with ﬂat sides to eliminate any of
these effects.

Molecular tagging techniques usually require an excitation laser to “excite” the

lumophore. In this study. a UV laser is utilized and regular channels made of

13

borosilicate or Pyrex absorb part of the emery of the incident laser. This is due to
reduced optical transmission and higher absorption at deep UV wavelengths and
increases the possibility of damage to the channels. The absorption also reduces the
amount of enery that is available for excitation of the lumophore. Synthetic fused silica
(hereafter referred to as quartz). which has a higher purity than natural fused quartz. is
being used throughout this research as it exhibits high transmission and lower UV
absorption levels. Figure 2-2 illustrates the transmission spectra of the particular type
of quartz (Coming 7980) used in all the channel fabrication. The absorption at 248nm
is listed as 0.2% while at 198nm. the absorption is only 1% for a 10mm thick specimen.
This material exhibits excellent transmission characteristics in the Deep UV (DUV)
range. Since all the microchannels are made of quartz glass thinner than 5mm,

absorption is minimal.

Internal Transmittance: Code 7980 Standard Grade

1500 2000 2500 3000 3500
wavelength [nm]

 

Figure 2-2 Coming 7980 Transmission Spectra (Corning Inc.)

To make a microchannel. 4 pieces of quartz ﬂats are used. For the top and
bottom walls of the rnicrocharmel. quartz ﬂats l” x 1/8” x 3" (w x h x l) in size were
used and separated by a gauge block to space out the microchannel height. The gauge
block (Mitutoyo Corporation) has an uncertainty of 60.96nm and is NIST traceable. This
assembly of a gauge block sandwiched between two quartz ﬂats is secured and two

additional quartz ﬂats 6.35 x l x 76.2mm (w x h x l) are glued in place as the side walls.

14

The glue used is RTV Silicone. The silicone glue is allowed to cure for 24 hours before
the microchannel is handled.

For the pressure driven ﬂow setup. the microchannels are mated to Plexiglas
adapters which are ﬁtted with hose barbs. The hose barbs are connected with tubing to
the constant head reservoirs or the syringe pump. This is shown in Figure 2-3. The
materials chosen for the setup is known to be inert to the working ﬂuid and the

chemicals slated for use in this research.

Plexiglas adapter
Hose barbs Quartz J

\ channel

Flow _______________ __-_ ..........
direction » C ------ 53---- t ......... D

 

 

 

 

 

 

 

 

 

 

Figure 2-3. Schematic of a completed rectangular quartz channel.

The investigation of electroosmotic ﬂows requires the use of a different setup.
The quartz channels are still used but reservoirs are attached directly to the inlet and

outlet of the channels. The setup is shown in § 2.4.3.

2.3.2 Preconditioning and Surface Modiﬁcations

Glass surfaces usually exhibit a negative surface charge when exposed to
aqueous solutions. The adsorption of impurities on the surface. however. creates non-
uniforrnities in this surface charge. Quartz channels which are untreated have varying
levels of uniformity of surface charge and this can cause experiments to be inconsistent
and surface coatings to be non-uniform. To eradicate this problem, preconditioning of
quartz channels is crucial.

Methods employed by other researchers (Faller et. al.. 1999. Raber et. al.. 2000.

Dabek-Zlotorzynska et. al.. 2001) for preconditioning channels essentially reduces to

15

the rinsing of the channels in either an acid or a basic solution for an amount of time.
followed by a rinse in water and a buffer solution. Different methods of pretreatment
were used for detection of different chemicals. The use of hydrochloric acid for
preconditioning, for example. caused problems for detection of certain chemicals as
trace amounts of chloride ions remain in the channel. This resulted in spurious results
due to cross contamination. The method utilized here. since we are not concerned with
cross contamination. involves exposing the microchannels to a 1M solution of NaOH
and 1M solution of HCl separately for 1 hour each and then rinsing with deionized
water. The technique described here is similar to that described in Hau et. al. (2003)
and further details of the chemical reaction that deprotonates the silanol groups are
explained in the paper.

In this study. the microchannels are coated with different surfaces and the ﬂow
physics within these microchannels are then studied. The treated microchannel with a
uniform surface charge is coated with polymer brushes or a hydrophobic monolayer.
Surface modiﬁcations with OTS increases the hydrophobicity of quartz channels. while
growing polymer brushes modiﬁes the surface charge and the morpholoy of the quartz
channels. These surface modiﬁcations can affect the ﬂow ﬁeld within channels and it is
these aﬁ'ects that would be studied in this research. The OTS monolayer is typically
prepared by immersing the channel within a 2mM solution of OTS in dicylcohexyl for a
few hours. The charmels are then rinsed with chloroform and dried. The channel is
baked at 100°C overnight to crosslink the OTS molecules to form a robust layer. The
polymer brush derivatization on a silicon surface is complicated and involves many
steps and the details are provided in Huang et. al. (2002) and Kim et. al. (2000). A brief
description of the technique is provided in Appendix I. All surface modiﬁed channels
used in this research were made by Dr. Matt Miller at the Department of Chemistry at
Michigan State University.

Surface characteristics of channels are expected to affect the ﬂow ﬁeld due to a

change of zeta potential. The ﬂow may exhibit a higher ﬂow rate or a deviation from

16

standard fully developed ﬂow proﬁles under different surface conditions. Hydrophobicity
is the tendency for a surface to repel ﬂuid due to surface tension. Material that has a
tendency to attract ﬂuid and causes a blob of water to spread out when placed on the
surface is considered hydrophilic while the opposite is true for hydrophobic surfaces.

Figure 2-4 below shows the relative surface tension of the polymer brush coating
compared to the OTS—coated and uncoated quartz. These images show that the OTS
treated surface exhibited the highest surface tension while an untreated quartz surface
is more hydrophilic than quartz treated with polymer brushes. The polymer brushes

can be grown to increase or decrease the hydrophobicity of the surface.

A

 

Uncoated quartz Surface Quartz coated with OTS-coated Surface
polymer brushes (hydrophobic surface)

Figure 2—4. Comparison of hydrophobicity between uncoated. polymer brushes
and OTS coated quartz surfaces (liquid used is water).

The use of the MTV technique requires the use of a high enery laser to tag the ﬂuid
within the channel. The amount of enery used to tag the ﬂuid may also ablate the
surface modiﬁcations performed on the quartz surfaces. This is a concern if the treated
surface is damaged due to the tagging laser. The typical beam size (diameter) currently
used is approximately 25pm. focused down from an original beam size of approximately
8mm. This translates to an enery density of ~10J/cm2. Tests with a lOOmJ/pulse
laser with an enery density of ~0.2 J /cm2 did not indicate any damage to the polymer
brushes coating. Considering that 9000 pulses of the laser beam irradiated the sample.

this enery density is deemed sufﬁcient to investigate the possible damage on the

17

coatings. The following ﬁgure illustrates a scanning electron microscope (SEM) image of

the quartz channel coated with polymer brushes before and after laser irradiation.

   

Before Laser Irradiation After Laser Irradiation

Figure 2—5. Scanning electron microscope (SEM) images of polymer brushes before and
after laser irradiation (after ~9000 laser pulses).

2.3.3 Surface Roughness Measurements

Surface rouglmess of the various surfaces used in this work is quantiﬁed with
atomic force microscopy (AFM) scans. All the scans were performed at the W.M. Keck
Microfabrication Facility (Michigan State University) with the assistance of Dr. Baokang
Bi. A Dirnensiom 3100 Scanning Probe Microscope (SPM) with an active AFM probe
(Veeco Instruments Inc.) was used in the measurements. Three circular quartz samples
(1 inch diameter): one coated with OTS, one with polymer brushes (hereafter referred to
as HEMA) and one left uncoated were scanned. Figure 2-6. Figure 2-7 and Figure 2-8
illustrate the surface scans of the various surfaces and their corresponding roughness
values. The uncoated quartz surface illustrated in Figure 2-6 has a relatively low
surface roughness at 0.87nm. The surface rouglmess values are presented in Table 2-1.
Relative roughness values are usually quoted relative to the characteristic length of the
microchannel. For round capillaries. the diameter is used but in this case. the 300m

height (H) or the hydraulic diameter (DH) can be used interchangeably.

18

Standard Devlation (z - nm) = 0.870 (mm

 

2 [nm]

 

Figure 2-6. AFM scan of uncoated quartz

 

 

 

 

 

Relative Relative
Surface R Shunrfacemm) roughness, e/H lroughness, e/DH
oug 93$ (1 04,) (106)
Quartz 0.8705 2.9 1.47
OTS 4.743 15.81 7.99
HEMA 5.949 19.83 10.03

 

 

 

Table 2-1. Surface roughness values for various surfaces

19

 

Standard Deviation [Z - nm) = 4.743nm A

   

Figure 2-7. AFM scan of OTS coated quartz.

Standard Deviation (Z - nm) a 5.949nm z

 

Figure 2-8 AFM Scan of HEMA Coated Quartz

20

From the ﬁgure. the roughness in the HEMA coated quartz is of a lower spatial
frequency than the OTS coated quartz although the roughness values are higher. The
high frequency roughness displayed in OTS coated quartz may be the reason slip occurs
due to a higher probability of trapped bubbles and the reduction in contact between the
moving ﬂuid and the microcharmel surface. Even with the different coatings (OTS and
HEMA). the roughness values are about 3 orders of magnitude lower than that
measured by Phares and Smedley (2004). Thus the experimental results presented in

this work can be considered to be in the limit of a smooth surface.

2.4 Flow Setup

2.4.1 Pressure-Driven Flows

The ﬁrst experimental setup was initially created to provide for very accurate
control of ﬂow rates with minimum costs. Two constant head reservoirs were placed at
the inlet and outlet of the microchannel and the vertical traverse of one of these
reservoirs would vary the pressure drop across the microchannel. This setup is shown
in Figure 2-9. The reservoirs were each made of Plexiglas and connected to the quartz
microchannel assembly through Teﬂon tubing. For each reservoir. a pump is used to
continuously provide an overﬂow to maintain a constant head on each end of the
microchannel. The overﬂow from the two reservoirs is channeled into a larger reservoir.
Some of the data presented in this study were obtained with this experimental setup.
One disadvantage to varying the pressure gradient with this technique is the large
range of height needed to create different ﬂow rates (the velocity is proportional to the

square root of height).

21

overﬂows to create constant head 4’ Spherical Lens

    

 

RCSCTVOil’ 266nm Teﬂon Tubing

\ Teﬂon Tubing / laser \

is adjusted V/l/l//////////////////////////////////////

vertically to
vary the
elevation
head

Reservoir

7//////7///////////ﬂ/////////////////////A

‘

v a Rectangular quartz diannel i 9

.E Z (0.3 X 25.4 X 76.2mm) .

Quartz Channel (Aspect Ratio=84.6)
- Phosphorescent Triplex

x 0 Pump

Figure 2-9 Experimental Setup for Pressure Driven Flow (side view. x-z plane)

 

To circumvent this difﬁculty while still maintaining ﬂow rate accuracy. a syringe
pump (Harvard Apparatus pHD 22/2000) is utilized to provide a larger range of ﬂow
rates. The syringe pump is rated with an accuracy of i 0.35% of the reading with a
reproducibility of 0.05% and a minimum achievable ﬂow rate of 0.0001uL/hour. For the
ﬂow rates in this study (0-310mm/s peak velocity), the syringe pump causes a

maximum ﬂuctuation of only _-i; 0.35ml/s.

Quartz Channel
I/////////////////////////////////////, A (Aspect Ratio=84.6)
'///////////////////'////////A7////////1

  

I MTV Triplex

   

Syringe pump Side View of Channel

Figure 2-10. Setup for Pressure Driven Flows with Syringe Pump (x-z Plane)

The syringe pump is initially preloaded with the phosphorescent triplex solution before
the start of an experiment. The syringe pump is preprogrammed for a particular ﬂow

rate and a given time for any ﬂow transients to dampen out before the start of any

22

experiments. At the other end of the experimental setup (Figure 2—10). the ﬂow
discharges into a beaker. The syringe used is a 100ml stainless steel syringe which is
reﬁlled from a beaker aﬁer each run. In both experimental setups. care is taken to
ensure that while the microchannel is ﬁlled. no bubbles are trapped. Any trapped

bubbles could potentially cause the ﬂow ﬁeld to be aﬁected. An illustration of the

general experimental setup for pressure-driven ﬂows is provided in Figure 2-11.

   

.\\Im.ri . ,. ~ ,. ‘ j '
(.mn'iui k - _ . ' View Of test
‘ ‘ “ section : enlarged

   

\\l‘lll:(
|>lllll]i

Figure 2-11 Illustration of test section (syringe pump setup)

Interrogation region y

 

 

10x objective / a

Figure 2-12 Schematic of experimental interrogation location (top view. x-y plane)

23

All the measurements were performed near the edge of the side walls (-11.2 < y <
-9.7mm. -5mm < x < 5mm) where the signal to noise of the acquired images is better
compared to the center of the channel. The determination of the interrogation region is
based on calculations of the entrance length and the analytical solution of the ﬂow ﬁeld
within a rectangular microchannel at the x and y location selected for the experiments.
The velocity proﬁle and its corresponding shear stress are found to be insensitive
towards changes in Y-axis locations (only in the region of -12.2mm < y < 12.2mm in the
microchannel). An illustration of the interrogation region is provided in Figure 2-12. All
measurements were performed in the range of 1.5-3mm away from the wall (y-axis) in

the center of the microchannel (-5mm < x < 5mm).

2.4.2 Entrance Length

The analytical results used to compare with the experiments are computed for
the fully-developed region. For any duct ﬂow experiments. it is important to establish
the entrance length to obtain the propagation length of inviscid behavior. This is
irnportamt so that the interrogation region for any experiments is in the fully-developed
region. For micro scaled ﬂows. however. the characteristic lengths involved are much
smaller than macro scaled ﬂows and it is expected that the entrance length be short.

This is estimated by the following equation (White. 1991).

1,. = 0.04" H * Rec” 2-1

where la is the entrance length. H is the characteristic height of the microchannel and
the Reynolds number is based on the characteristic height. For the maximum Reynolds
number considered in this study. the entrance length for a 2-D microcharmel is < 1mm.
For our experiments, the measurement location is in the region of x = 15mm which is

well beyond the entrance region.

24

2.4.3 Electroosmotic Flow Setup

Two Plexiglas cylinders with a diameter of 84mm were used as reservoirs and
mated to the microchannel. The large diameter of the reservoirs was needed to minimize
the formation of an elevation head which would cause a pressure gradient to
contaminate the electroosmotic ﬂow ﬁeld. The consideration of this problem is outlined
in Appendix E. Platinum wires were placed in each cylindrical reservoir near the
channel inlet and outlet to act as electrodes. A high voltage potential is applied across
these electrodes. A schematic of the electroosmotic ﬂow setup is illustrated in Figure
2-13. The ﬂuid used as the ﬂowing medium is the phosphorescent chemical mix added
with sodium phosphate as an electrolyte and buffer. More details on the use of sodium
phosphate are discussed later.

A Wavetek Programmable ﬁrnction Generator (Model 275) was used to provide a
DC signal to a high voltage DC ampliﬁer (Trek Model 609C-6) which ampliﬁes the input
by 1000x before applying it to the electrodes. This creates an electric potential across
the length of the microchannel needed for electroosmosis. The high voltage setup ﬁxes
the voltage but the electric current may vary due to changes in conductivity of the ﬂuid
within the microchannel. The actual current is monitored during the experiment by
measuring the voltage drop across the inline resistor as shown in Figure 2-14.

For the setup shown in Figure 2-14. the resistor contributes to the overall
current of the circuit. Experiments with a voltage of 2000V have yielded a current of
2mA. This essentially indicates a resistance of IMO present in the ﬂuid circuit through
Ohm's Law. At this resistance level. the relative perturbation error (RPE) of the added
resistor is computed and shown in equation 2-2. This level of perturbation will only
increase the current within the circuit by 0.328%. For the range of voltages (560V-
1963V) and current (0.5-2mA) in this experiment, the perturbation error from the

current monitoring resistor is negligible.

25

High voltage
Platinum electrodes power supply
Plexiglas ﬂuid reservoir

. f - - H ‘
.' 1 ‘
o--.-_' . ‘ '
1 ' ._’,r ‘ _- .
1 ‘ -| ;-'
r -.
u .
1’ .1
.
.-
z ,.
1
.

      

 

300nm

microchannel

Figure 2-13 Schematic of EOF setup

 

    
  
 

 

 

 

 

 

 

 

 

 

 

 

 

electrode
\ microchannel
3.28 k!)
High Voltage 2% Tolerance

Current

DAQ monitor

System resistor

Figure 2-14. Current measurement setup
R 2
% RPE = ——1-—x100 = 3 80 x100 = 0.328% 2-2
Rc + R1 1x10

26

2.5 Molecular Tagging Velocimetry

Molecular Tagging Velocimetry (MTV) is an optical technique for obtaining whole
ﬁeld velocity information in a plane. The current implementation of the technique is
based on excitation of long lifetime molecular tracers that phosphoresces, ﬂowing
within the experiment of interest. by a laser at a suitable wavelength. These molecular
tracers move with the ﬂow and continue to emit light after the laser is turned off. The
tracking of these tracers would then yield velocity information.

The long lifetime tracers used in this implementation of MTV is a

phosphorescent chemical triplex. l— Ber - MﬂCD - ROH. with typical molar

concentrations of 1x10-4M Maltosyl-B-cyclodextrin, 0.055M neopenthanol and a
saturated amount of l-bromonaphtalene (approx 1x10-5 M). Figure 2-15 illustrates the
schematic of the chemical conﬁguration that allows the tracer to achieve long

phosphorescent lifetimes (The particular capping alcohol used in this ﬁgure is tert-

    
 

 

     

butyl).
A B
3

H

H3C\ /.
H30 K.
hV H30 r—-

ROH
___.’
hv

hv _o 0‘

\

(9 08) Hag/[c H H (5 ms)

Figure 2- 15 Chemical structure of Phosphorescent Supramolecule used here for MIV

Bromonaphtalene is the chemical that luminesces upon excitation by a UV

laser. This chemical goes into the “cup” structure of cyclodextrin in a dynamic way and

27

while it is interspersed within cyclodextrin, cyclohexanol attaches to the “lip” of the
“cup”. The capping efﬁciency of cyclohexanol determines the degree of oxygen
quenching. As oxygen. among others. quenches the phosphorescence emission of the
chemical. a reduction in quenching causes an increase in lifetime of the emission.
Figure A in Figure 2-15 illustrates the reduced lifetime (9ns) when dissolved oxygen is
allowed to enter the “cup” structure of cyclodextrin. Figure B illustrates how alcohol
attaches to the “lip” of the “cup” to shield bromonaphtalene from being quenched by
oxygen to yield a resultant increase in lifetime to 5ms. The addition of these chemicals
to water. due to the low concentration used. does not affect the general characteristics
of water as the viscosity and density of water remains the same.

These long lifetime tracers are “excited” to a higher quantum state by an
ultraviolet laser and the subsequent decay to a lower state produces emission in the
visible wavelength. Typically. a pulsed laser (20ns or less pulse width) in the UV
wavelength range is used to “tag” or “excite” the molecules in the region of interest.
These “tagged” molecules are imaged at two successive instances. one right after the
laser pulse and the second within the lifetime of the emission.

The delay time between the two images is dependent on the signal level of the
intensiﬁed camera and the time required for a sufficient amount of pixel displacement
between the tagged lines. The pair of images is then correlated to obtain velocity
information. The measured Lagrangian displacement vector provides the estimate of the
velocity vector. In Figure 2-16. two sets of laser lines were aligned orthogonally and
used to excite the chemicals to form a grid pattern of “tagged” ﬂuid.

The MTV technique has been continuously varied based on the nature of the
problem involved to suit the application at hand. Single line tagging is by far the easiest
implementation of MTV. This method provides a single component of velocity within the
ﬂow ﬁeld. The drawback to this method is that knowledge of the ﬂow ﬁeld is needed a
priori as single line tagging can only resolve 1 component of velocity perpendicular to

the tagged line. For example. single line tagging was applied to the measurement of the

28

initial velocity within a plume during a solidiﬁcation process due to its unidirectional

velocity ﬁeld (Figure 2-17).

 

 

 

L L
I l
20cm/s
“.I.'.I'I,I"’ -447.
t 1 1 r 1 v I '
\ I 1 1 1 I I ' ‘,‘_
"i‘lll'llil'x'r" ' ‘
1 . . , . I , -
\{:.‘;..fl;/’./// ‘
. , . ' ,,V, \
lll'l‘tjljl'Iﬂ fr‘ ‘r‘
lt'oLrlvly'j‘lj j.
llflflvﬁllllli‘m;,~‘1
1"; 4:13;"- ~‘.‘\‘.- , ,
{lilv'l‘o‘h\x‘\v‘\‘—c’ .
,I , .i \. z.. a r
:rll'bl‘\.\:\j‘\f‘*‘."- _’_
Tagged regions imaged Tagged regions The velocity ﬁeld derived using
right after the laser pulse imaged 8 ms later a spatial correlation procedure

Figure 2-16 : Typical MTV image pairs and the corresponding correlated velocity vector
ﬁeld. (Gendrich. et. al., 1997) After 8ms. the tagged regions are imaged again to yield a
distorted irmage due to the velocity of the ﬂuid. Correlation of these images resulted in a
velocity vector ﬁeld as shown in the last image.

 

Figure 2—17. Image of plume during uni-directional solidiﬁcation

(red line indicates single component velocity proﬁle. Lum et. al.. 2001)

29

Laser line tagging. as illustrated in Figure 2-16. is commonly used to obtain 2
components of velocity in a plane and has been applied to the measurement of velocity
very near the surface of a stalling airfoil (Gendrich. 1998). among others. In this same
multi-line conﬁguration, images obtained from a pair of cameras aligned at an angle
with respect to the tagged line allow us to obtain the 3rd component of velocity in the
out of plane direction. This technique. called stereoscopic imaging. was recently applied
to the study of the 3-dimensional structure of a concentrated line vortex array (Bohl et.
al.. 2001). Detailed discussions of the planar 2-D technique applied to various ﬂows are
provided in Koochesfahani et. al. (1996). Gendrich and Koochesfahani (1996). Gendrich
et. al. (1997) and Koochesfahani (1999).

In this research, single line tagging is utilized as it is expected that the ﬂow ﬁeld
within microchannels would be unidirectional and fully developed. The assumption of
fully developed ﬂow is acceptable within microchannels as long as the interrogation
region is sufﬁciently downstream of the channel inlet to avoid any entrance length
issues. Only one component of velocity is needed to resolve the ﬂow physics under these
conditions. Flows within microchannels with recirculating features. however, would
require the use of 2-component MTV.

The reduced area of laser illumination and the imaged ﬁeld of View causes the
amount of light collected by the imaging system to decrease compared to macro-scaled
ﬂows. The lower amount of light limits the delay between the two images needed for
detection of slow moving ﬂows. Neopenthanol is used to replace cyclohexanol (typically
used due to its low cost) as the capping efficiency of neopenthanol is higher and causes
a further reduction in oxygen quenching resulting in a higher emission. The relative
intensity of phosphorescence emission by using neopenthanol compared to
cyclohexanol and other available alcohols is provided in Figure 2-18. The use of a
different laser wavelength in this study (266mm) compared to the typical 308nm
wavelength also improves the absorption of the MTV chemicals which in turn should

help increase the phosphorescence emission. Figure 2-19 illustrates the relative

30

absorption spectra of bromonaphtalene at different wavelengths. The relative absorption

at 266mm is 7 times higher than at 308nm.

Figure 2- 18.

N
O

.3
01

Phosphorescence Emission (relative intensity)
or 8

 

Y 7 T l

 

v— — -V t-butanol E f o
[3 — — {l cyclohexanol : ﬂ, _,. ,: 9‘ "‘
o— —o Neopenthanol l/G’ " ’j' E

/ l i 1

 

 

 

 

 

1 W/ /
732/
f i

/ I I
/ 1 : , _ 7 ; ______ 1*

l : 48"9.“ “““““ 1' - " '1

/ a 2'81? , z .
/ Fr I E ; : l ‘/j.v——-—"V

4’ : axe—arr"?
v/Vi/VV’V/l : 7 .
0 0.025 0.050 0.075 0.100 0.125 0,150

Alcohol Concentration, M

Total phosphorescence emission from 1-Ber.GB-CD.ROH for three
different types of alcohol at ﬁxed concentrations of l-BrNP and GB-CD and
at 308mm wavelength laser excitation. (Plotted from Gendrich et. al.. 1997)

Relative Absorptlon

 

 

 

 

 

 

 

 

 

 

 

1.5 1 f 1
1.0
1W 1 5, ,
. l : 1
266nm. relative 1 T .
absorption or 0.15 308nm._relauve
: E absoprtion of 0.02
220 240 260 280 300 320

 

Wavelength (nm)

Figure 2-19. Spectraphotometer Scan of Relative Absorption of Bromonapthalene

31

2.5.1 Velocity Correlation Technique

Previous procedures for correlating a single tagged line (Lum et. al., 2001)
utilized a peak detection algorithm. At the peak, a 2nd order ﬁt is used to obtain
subpixel accuracy of the measured displacement. The use of a peak detection algorithm.
although simple in implementation, is vulnerable to noise contamination. Sharp noise
spikes may affect the detection of the true line center and a high signal to noise is
required to obtain accurate results. A higher order ﬁt may also be necessary whenever
the line proﬁle does not appear to be Gaussian. In the current research, the accuracy of
the single line velocity correlation technique was improved upon by using a spatial
correlation technique and a 7th order polynomial ﬁt to locate the center of the displaced
lines. This is the l-D implementation of the original 2-D correlation technique used for
processing 2-component M'IV data (Gendrich et. al.. 1997)

The image pair obtained from the MTV technique. one imaged right after the
laser pulsed and the other after a given delay, is spatially correlated. row by row, to give
velocity proﬁle information. Each row of pixel from each image is extracted and a
convolution procedure applied to obtain the position of highest spatial correlation
coefficient. The spatially correlated peak is ﬁtted with a 7th order polynomial to obtain
subpixel position accuracy. The spatial correlation technique is more impervious to
noise spikes in the tagging line and would provide a better control on the accuracy of
the correlations. The correlation program was written in Labview due to its friendly
graphical user interface (GUI) and ﬂexibility. The program was written to accommodate
correlation of the whole image, or regions of interest only. in order to reduce processing
time. The correlation data set is exported to a text ﬁle and subsequently read into a
plotting program for data analysis. A description of the source code and the graphical
user interface is provided in Appendix H.

The program was tested with images of known signal to noise ratios to determine

the accuracy of the correlation procedure. Typical results yielded a displacement RMS

32

of < 0.1pixels. Figure 2-20 illustrates the RMS from the correlation of single tagged lines

with different signal to noise (S/ N) ratios at different line thicknesses.

 

 

 

 

 

 

 

 

0.5 V f ﬁr /- ‘:‘~- .;_ Y
+~\ / \ ,/
/ i \/
0.4 --------- « -------------------------- j» ------------------------- -
¥ G
:7; +— — + SN=2
.2 ﬂy ewe”; SN=4 . : t
v 0.3 r--__.- I—— I SN=6 t ... , 7', .. .. , ,. . ----l
8 o—-c SN=8 . 1
g v——-v SN=12 ;
g B-—£} SN=14 f
8 A E . . I:
0 0.2 """"" LL?” "2991‘“ ""7??- r"""""“ ":35: """"" :'""V;.‘:TV"‘V """""""" "
°\° j; ..~J I \‘~ 7‘} #_. ﬁ: r’” “
m I
O) .
' /” I -“ ..'I- -’ .— ’. ~‘ I.— .4 : — a- .
0.1' '.’,/‘.“‘-‘ .L'” _‘_"’_’."._.Z;-'--."/" :“<. """" ‘
-_‘_ ,%—____...—-_.l _ _:—ET:W:—::h:m
0 l L l
10 15 20 25

Line Width (pixel)

Figure 2-20. Uncertainties of correlated single tagged lines at different signal to noise
ratios and line widths (full width at 1 /e2).

2.5.2 Taylor Dispersion

Taylor dispersion can be induced by a combination of molecular diffusion and ﬂow
convection and is a phenomena that manifests itself in this study by broadening the
tagged fluid. In a capillary, a dispersion coefﬁcient is used to describe the extent of
dispersion and is given to be proportional to the ratio of the axial convection to the
radial molecular diffusion. This effectively represents the rate at which material spreads
out axially in the system. For MTV experiments, if broadening of the tagged ﬂuid occurs.
the signal to noise ratio could decrease in the delayed image and may cause a higher
RMS error in the correlation. Thus it is of interest to estimate the level of dispersion.

At the small time scales utilized in this study, however (which usually translates to
low convective velocities). dispersion is dominated by molecular diffusion only and the

convective velocity is not an issue. Longer time scales would cause the convective term

33

to dominate. The effects of diffusion can be estimated by calculating the broadening of

the tagged line over time. This is represented by equation 2-3. (Miles et. al. 2000)

(1)2 = (002 + 81n(2)DAt 2-3

where a: is the resultant thickness of the line. 00 is the original width of the tagged line.
D is the diffusion coefficient and At is the time delay across which the broadening is
calculated for. For a representative diffusion coefficient of 5x10-6 cm2/s (fluorescein), a
line width, at, of 25mm and a delay time, At, of 4ms. the eventual line width becomes
25.22pm. Thus a negligible amount of broadening is brought upon by molecular

diffusion.

 

Figure 2—21 Undelayed (left) and delayed (right) images with line proﬁles drawn across
the center of the image for electroosmotic flow

To further investigate the effects of dispersion. a line proﬁle is drawn across an
undelayed and a delayed image (average of 30 images) and is shown in Figure 2-21 and
Figure 2-22. Again, the results illustrate that over a timescale of 4ms. the broadening of

the tagged line is negligible.

34

 

 

 
   

 

1.00 ~ - f V - -
b ﬁ (
l G- — -Ci Delayed Image ‘
’ O- -O Undelayed Image

 

1
1

 

o

F‘n
8‘13.

~11;
3-3

max)
33%
—D’

0.50 i 6? I

Normalized Intensity (III

P
N
01

 

 

40 60 80 100
Spatial Location (pixels)

 

 

Figure 2-22 Comparison of line proﬁle for undelayed and delayed images.

2.6 Molecular Tagging Thermometry

The original implementation (Thomson et. al., 2001) of Molecular Tagging
Thermometry (MTD was based on the intensity decay of the phosphorescent emission of
the tagged molecules. This, however, could not correct for non-uniformities of the laser
beam which could introduce errors into the measurement. Hu et. al. (2003) improved
upon this technique by relying on the temperature dependence of the phosphorescence
lifetime of the triplex instead. Through a ratiometric method, any non-uniformities of
the laser beam or background are corrected for. The lifetime of the phosphorescent
triplex are calibrated and is used to provide temperature information.

For a typical M’IV application, the laser is used to create a 2-dimensional grid
pattern and two images are taken in quick succession. These images are spatially

correlated to obtain velocity information. The same images can yield temperature

35

information since the lifetime can be calculated from knowing the emission intensity
decrease at a spatial location at two different times.
According to quantum theory, the emission decay of ﬁrst-order

photoluminescence is exponentially based. This is expressed by the following equation.

[em = IOe-t/T 2'4

where t is the time constant used to define a 37% drop from the initial intensity
or the emission lifetime. lo and [em is the emitted intensity. The region of interest 81 and

82 in Figure 2-23 represents an area averaged to yield temperature information.

Initial tagged region

Channel
wall

A Intensity, I

First Image. Si

 

\\\\\\\\\\\\
! 300un1

Second Image. 82

'5

 

limet
r

 

Tagged region 9ms later

Figure 2-23 Exponential decay of phosphorescence intensity

36

The phosphorescence emission decays exponentially and is depicted in the plot. It turns
out that the division of the intensity integrals at these two instances in time only
depends on the time delay between images and the phosphorescence lifetime. This is
shown in equation 2-5. Note that it is important to integrate the intensity of the same

molecules in both images for this relation to be true.
_S_2_ z e- 7 2-5

where At is the time delay between the two images. For the current work, both
undelayed and delayed images have the same exposure times to yield equation 2-5. The
exposure times can be set differently to increase the dynamic range of the
measurements.

This method, coupled with the calibrated phosphorescence dependence on
temperature, will give us temperature proﬁle information along the tagged laser lines.
This temperature ﬁeld is obtained simultaneously with velocity ﬁeld information. Since
the chemicals used by Hu and Koochesfahani (2004) are slightly different from that
used in this research (difference in the alcohol used) a recalibration of the chemical
lifetime dependence on temperature was performedUsing the double shot feature of the
Dicam Pro (PCO AG) camera, the lifetime variation with temperature was measured and
illustrated in Figure 2-24. When the calibration results for the two different chemicals
were normalized at the same temperature, the data points showed slight differences
accentuated at lower temperatures due to less sensitivity of the technique at lower
temperatures (Hu et. al. (2005)). To apply the technique during an experiment, the
initial temperature of the ﬂuid is recorded with a thermocouple. This gives a reference
point for the measured lifetime at room temperature which is used to ﬁt to the
calibration curve to obtain temperature information. Another important aspect in
implementing M'IT is background correction of the images. Since the technique is based

on intensity, any spurious contribution from the background could cause errors in the

37

measurements. All the measurements performed in this study were background

corrected to avoid this error.

 

 

 

 

zo -. . - -.- --. - f. l-x-- ---‘
: a Neopenthanol MTV Mix (Trial 2)

1-8 r o Neopenthanol MTV Mix (Trial 1) 1
E 3rd Order Fit

1.6 :

1.4 E

   
   

1.2'

1.0 '

0.8

AAAA-AA‘AAAAAAAAA‘AAA-AAAA-

0.6

Normalized lifetime (t/Taooc)

AAAA‘AAA

0.4

 

  

0.2

vvvv'v v VVﬁv'vvw—VVvvv
- AAA

 

 

Temperature (°C)

Figure 2-24. Normalized lifetime of both chemicals

38

Chapter 3 Pressure-Driven Flows

The solution for pressure driven ﬂows within round capillaries are well-known
and available in most ﬂuid mechanics textbooks. In this chapter, the equations of
motion for capillary ﬂows are initially introduced and contrasted to the series solution
for rectangular channels. The three-dimensional velocity proﬁle for a rectangular
channel is numerically computed to illustrate the differences. A measure of deviation
from classical theory is the friction factor and this is computed for comparison with
other researchers. The derivation of the friction factor for rectangular channels is
presented along with the required experimental measurements to obtain the normalized
friction factor. The “Results and Discussion” section ﬁrst explores the errors involved in
pressure drop measurements due to uncertainties in the channel dimensions and
moves on to presenting the experimental results used to calculate the friction factor for
uncoated, OTS or HEMA-coated microchannels. The friction factor results are then
compared with theory and results from other researchers. Other factors that could

affect the friction factor are also presented.

3.1 Equations of Motion

The exact solution for a fully-developed pressure driven laminar ﬂow within a
capillary (i.e. Poiseuille ﬂow) is well known. The Navier-Stokes equations in combination
with the conservation of mass equation, fully characterizes the ﬂow of incompressible
Newtonian ﬂuids. The full N avier-Stokes equation in cylindrical polar coordinates can

be written as follows, using (w, ue, L1,.) as the three components of velocity.

39

 

 

 

Figure 3-1. Coordinate system for capillary

 

 

 

3.7+” a. 73?“.— x3;
3-1
zﬂa 1% 9i)_i+iazur__2_ilﬁ 321.,
8r rar 8r r2 r2 392 r2 39 8x2
Lao; 92a Bialﬂ_iu_d 39g)
p[at +ur3r+r 39 r +uxax
2 2 3-2
__13_P ii M_EQ_1_3U€_2_ﬂg_au0
_ r86+pgg+ﬂ[r8r[r 8r] r2+r2 662 +r2 86 + 8x2
aux aux £01311 aux]
p( at + 8r + r 86+ux 8x
3-3
__§£+ +ﬂli[raux]+i82ux+82uX
8x pgx rar 8r r2 392 6x2

where p is density, t is time and p is pressure. Equations 3-1, 3-2 and 3-3 are

representations of the Navier Stokes equations along the different axes. For a steady.

incompressible, fully-developed laminar ﬂow within capillaries, the velocity proﬁle is

characterized by an exact solution to the Navier-Stokes equations. Under these

conditions, the three equations of motion simplify to

8p
O=—— 3-4
8r
oz—la—p 3-5
r 86
O=—— —— — -
8x+ﬂ[r ar[r 8r ] 36

40

Integrating Equation 3—6 results in a paraboloid velocity distribution
ux :_L(a_p.)(r2 _R2) 3_7

where R is the radius of the capillary. Physically, the velocity distribution within a
capillary is a paraboloid and the volume ﬂow rate is given by

R
Q = 27: qu r dr 3-8
0

In order to obtain a relationship between volume ﬂow rate, Q, and pressure gradient,

Equation 3-8 is integrated to give

 

_ n04 8p
Q — 128,u( 8x) 39

Note that ﬂow rate scales with the 4th power of diameter. This condition has a
signiﬁcant impact on the accuracy of measurements of friction factor using bulk ﬂow
measurement techniques. An uncertainty of 2% in determination of the diameter, D.
results in an uncertainty of 8% in the ﬂow rate.

The fully-developed ﬂow within a rectangular channel is also based on the

solution of the Poisson's equation (V211 x = 1/y(8p/ax) but its solution is complicated by

the geometry. This is provided in the form of a series solution. The series solution is
depicted in the following equation for a rectangular section: -a _<_ y g a, -b g z 5 b.

(White, 1991).

2 °° , . .
Ux(y»Z) : 16a (_ E) Z (_ 1)(l_1)/2[1 _ cosh(uzz/2a)] cos(uzy/2a) 340

i=l,3,5... cosmmb/ 2“) l

41

 

 

 

_.’ X > y-axis 2b
ﬂow

 

 

 

’I/I/I/I/I/III/III/II/Illlllllillla

4)
v

2a

Side view End view

Figure 3—2. Schematic of channel geometry

where uly,z) is the velocity proﬁle within the rectangular channel, a and b are the half
width and half height respectively, dp/dx is the pressure gradient along a speciﬁed
length of the channel and u is the dynamic viscosity. Integration of this equation over

the channel cross section yields the overall volume ﬂow rate equation.

3-11

 

 

4ba3(_£12)1_192a i tanh(isz/2a)

Q = ——
5 5
3” dx ” b i-l,3,5... ‘

At any given y-location, the mean velocity is needed for comparison of the experimental
results to theory. This is given in the following equation by integrating equation 3-10 in

the z-axis.

3—12

 

2 °° , -
Edy) = 32a3 [ 3:) Z (_ 1)(l_1)/ 2(1) _ 2a sinhétmb/Za)) cos(ijrg /2a)
l1” i=l,3,5.. ‘

3.2 Friction Factor

Friction factor is a non-dimensionalized representation of wall shear stress. For
any viscous ﬂuid ﬂow, once the ﬂow is fully developed (i.e. no acceleration), the shear
stress counterbalances the pressure force. The shear stress for incompressible

Newtonian ﬂuids is linearly related to the rate of deformation and can be expressed in

42

Cartesian coordinates (refer to Figure 3-2 for axes designation) as shown in the

following equations.
aux +8uy
Txy— — Tyx— [U [_+ By ax J 3'13
Bu 3“
Tyz — 72y: # [ azy+ Tyz] 3-14

3 a
sz=oa= #[5—f+ 3:17") 3-15

where y is the dynamic viscosity. Lbr. Hg and Ma are velocity components in the x, y and
2 directions respectively. For a fully-developed ﬂow within a rectangular duct, equations

3-13, 3-14 and 3-15 simplify to

 

It will be shown later that only sz needs to be considered as the experimental data

were obtained in the central region of the microchannel. The friction factor or

sometimes referred to as the Fanning friction factor is deﬁned as a normalized shear

stress in Equation 3-17.

_xz__|__2_wall

f:% Pux2

where 5,, is taken to be the local mean velocity at any given x—z plane in our

measurements. For laminar round capillary ﬂows. it can be shown that the Darcy

43

friction factor is deﬁned by f=64/ Re (the Fanning friction factor, Cf, only differs from the

Darcy friction factor, f, by a factor of 4).

25

2O

Cf/ Re

16

10

Figure 3—3. Fanning friction factor for different geometries
(White, 1991: data from Shah and London, 1978)

 

 

    

 

 

 

Concentric annulus
... circle \
l Circular sector
. r i l l _._. i . l
0.0 0.2 0.4 0.6 0.8 1.0
b/a

The Fanning friction factor for various geometries are shown in Figure 3-3 where b/ a is

the aspect ratio and Re is based on the hydraulic diameter. For a rectangular channel.

as the aspect ratio increases, the ratio b/ a decreases and approaches a strictly 2-D ﬂow

with a Cf shown in Equation 3-18.

96
Re

44

3-18

To calculate the friction factor for a rectangular channel with a different aspect
ratio. the series solution needs to be employed. The derivative of Equation 3-10.

evaluated at the wall gives

 

aux 16a2[ dp) 0° i—l)/2[ . Ur ] cos(r‘zzy /2a)
—-(y)= —-—-— (— l)( tanh(Utb/2a)‘— —— 3-19
az ””3 dx tags... 2“ ‘3

Substitution into Equation 3-17 yields the friction factor at the wall for a given x-z

plane for rectangular channels with an arbitrary aspect ratio.

 

2 m e a
_ 32a dp {_1)/2 . , u: cos(my/2a)
Cf(y)- {—J 2 (—1)‘ [tanmmb/za) —]———-——— 3-20
—2
P“ ”3 ‘dx i=1.3.5... 2a ‘3

Investigation of ﬂow physics and friction factor within microchannels are
typically performed through the determination of the overall volume ﬂow rate, Q. and
pressure drop (Ap) measured across the length of the entire microchannel. Equation
3-18 is used to represent the theoretical friction factor with the Reynolds number
derived from the volume ﬂow rate measurements. Equation 3-21 is typically used by
other researchers to derive the experimental friction factor from pressure drop and ﬂow

rate measurements, where land D represents the length and hydraulic diameter of the

channel respectively, p is density of the ﬂuid and [7 is the mean velocity averaged over

the entire cross section of the microchannel.

p172
2

3-21

 

l
APT-f3

One major drawback to using the pressure drop to measure friction factor, apart
from measuring bulk ﬂow quantities, is the difficulty in accounting for the contribution

of entrance effects (multiple experiments have to be performed to estimate the

45

contribution of entrance effects for a particular channel geometry). Recall that entrance
effects cause a higher pressure drop to occur. Also, as noted previously (Equation 3-9).
the D4 dependence of volume ﬂow rate, Q. could cause signiﬁcant errors in the
measurement of bulk ﬂow quantities due to uncertainties in knowing the actual value of
D (errors as large as 20% in friction factor due to a 5% uncertainty in channel
dimensions). The combination of all these factors has motivated the current in-situ
measurements for friction factor. In this study, the MTV technique is utilized to obtain
local measurements of friction factor within a rectangular quartz rrricrochannel with a
nominal height of 300m. The ability of the technique to measure spatially resolved
velocity proﬁles across the height of the microchannel result in the determination of the
local friction factor.

The measured experimental friction factor (equation 3- 17) is then compared with
the theoretical friction factor (equation 3-20) to illustrate any deviations from classical

theory. This is illustrated in Equation 3-22 where the pressure drop, dp/dx. is

substituted with the experimental mean velocity (equation 3-12).

 

 

 

 

 

i (_ 1)(i-1)/2[ b _ maximum/2.1)] cos(iny/2a)
_ ' 3
C f ,exp = 2“theory (it) t=l,3.5.. U: i 3-22
f.th€0ry uexp Z exp 2 (— Iii—n/2l— (Mb/2a) . Z] COS(iﬂy/2a)
rm“ 2a _—"‘-3
. i=l,3.5. . l i

The series in equation 3-22 is numerically computed for a given height and width of the

microchannel although computation of ammry requires the peak velocity measured

from the experiments. The velocity gradient, (LU) , and the mean velocity, aexp, are all

82 /exp

obtained from experiments. The velocity proﬁles obtained from the experiments are

integrated and the local mean velocity calculated. The theoretical mean velocity, gammy.

is obtained from integration of a parabolic proﬁle at the interrogation location. This will

46

be shown in § 3.3 where the experimental results are presented. The parabolic proﬁle
matches the theoretical solution of ﬂow in the central region (—12.2mm < y < 12.2mm) of
a rectangular microchannel (25.4mm wide in the y direction) and is thus used for ﬁtting

of the velocity proﬁles obtained from the experiments.

47

3.3 Results & Discussion for Pressure—Driven Flows

To better illustrate the fully developed ﬂow ﬁeld within a rectangular channel. a
computation of the series solution (Equation 3-10) was performed for various aspect
ratios. Figure 3—4 illustrates the computational results obtained from the exact solution
of the series solution for a channel of aspect ratio of l. The color bar represents the
normalized velocity, Ll/Umax where Umax is the overall maximum velocity across the cross
section). Notice that the velocity proﬁle resembles a paraboloid except near the wall

boundaries where it tapers out to conform to the square boundaries of the channel.

0.8
0.6
0.4

U/Umax

0.2

   

 

Y-Axis

 

 

 

   

Y-axis Z-Axis

Figure 3-4. Series solution of velocity proﬁle, u(y,z). within a square channel
(refer to Figure 3—2 for axes designation)

With the current experimental setup, the width of the channel is 25.4mm and the
height is 0.3mm. This translates to an aspect ratio of 84.667. For this aspect ratio, the
flow ﬁeld is parabolic only in the X—Z axis while in the Y-Z axis. the velocity proﬁle is ﬂat

over most of the channel. To visualize the velocity proﬁle within a channel of high

48

aspect ratio, Figure 3-5 is illustrated for a channel of aspect ratio of 5. The differences
between the velocity proﬁle within a microchannel with an aspect ratio of 5 and 84.667

lies only in the length of the central ﬂat region.

 

 

 

 

 

 

. .8
ii
E . .8
20.4 0.4
D
0.2
-5 0 5 - 5
Y-Axis Z—Axis

Figure 3-5 Series solution of velocity proﬁle, u(y,z). within a 5:1 channel.

For the high aspect ratio channels used in this research, the proﬁle along the Y—axis is
almost ﬂat While the proﬁle along the Z-axis still maintains a parabolic proﬁle across
most of the width of the channel. This is in contrast to Figure 3—4 where a parabolic
proﬁle was observed along both axes of the channel. The computation of the series
solution (Equation 3-10) allows us to predict a priori the expected ﬂow ﬁeld for our
experimental tests and is the basis for our comparisons with classical theory. The
comparisons with experiments were made at speciﬁc y-locations selected by the optical
requirements of the imaging system.

Digressing, it is of interest to investigate the errors that may be involved in our
comparisons to theory due to uncertainty in the exact y-location of the experimental

interrogation regions. The normalized velocity computed from the series solution is

49

shown in Figure 3-6 for a microchannel with an aspect ratio of 84.67 (this is the
rrricrochannel used in the experiments). The data points are plotted along the yards in
the center of the channel (Z20). The velocity at different y-locations is normalized with
the peak velocity at the center of the microchannel and the distance from the wall refers
to the side walls of the microchannel in the Y-axis. The ﬁgure shows that the
normalized velocity is close to unity as close as 0.5mm from the wall. Close inspection
of this ﬁgure at 0.5mm reveals that the discrepancy in velocity from the center of the
channel is less than 0.1%. Figure 3-6 illustrates that for a microchannel width of

25.4mm. u(y,z =0) does not deviate signiﬁcantly in the range of ~12.04 < y <

+12.04mm. As long as the interrogation regions of the experiment are within this range.
the velocity can be considered a constant. The velocity gradients at the wall also show
the same trend. This is illustrated in Figure 3-7. This allows the experiments to have

more ﬂexibility given that the range of interrogation locations is not too constrained.

 

 

1.00
0.75

0.50

 

 

 

utheory(Y)/u1heo,y(y=o))

 

 

 

 

0.25 ..

 

 

 

0 0.5 1.0 1.5 2.0
Distance from Wall (mm)

Figure 3—6. Change of velocity near the channel wall (Y -axis); aspect ratio of 84.67

50

O/o

 

  

 

   

 

 

 

 

 

 

 

2 . 1.2
i 1
H 0 1 1.0 1 ------------------------------------------------------
0:, i
'6 I I
S 2 .03 i
(D + . }
g 1
8 i >
75 -4 . 0 6
> » o—-e du/dz(y)w
“o > —— % Change in Velocity Gradient
:1 ’ from Center of Channel
:T-U '6 ’ 0.4 ’ 1
E ’ ‘
o 1
Z ’ 1
-8 10.2 .
-10 . o ----------------------- A ...........

0 0.25 0.50 0.75 1.00 1 .25 1 .50 1.75 2.00

Distance from wall (mm)

Figure 3—7. Normalized velocity gradients (du / dz) as a function of distance from walls

 

 

 

 

 

 

 

 

 

 

 

0.70 ....... - - , - , - _ _ -
C Mo—eoeuw—o—o—e-o—e-e—eo—eo—o-o—o—e—o—o-t
0.65 ’ f? ‘
“a * .
D Z ‘
:35 0.60 » I ‘
\= ' A 1
g 1 p
E ’ 1
3 0.55 1 2b >y .
E Z, .
.9 ‘
0 ‘ _’
5 2a 1
8 0.50 +
O \ i
0.45 ASpect ratio of j
microchannels for j
pressure-driven ﬂows .
0.40 ““““ 44 .....................
0 50 100 150 200 250 300
Aspect Ratio (a/b)

Figure 3—8 Umean/Umax for different channel aspect ratios

51

An interesting observation of the series solution is that in order to achieve a
strictly 2-D ﬂow, a very high aspect ratio for a rectangular channel is needed. This is
shown in Figure 3—8. As the aspect ratio becomes large enough, the ﬂow ﬁeld becomes
more two-dimensional and thus yield a ratio of Umcan/Umax that asymptotically
approaches a constant value where Um... is the overall channel mean velocity and Umam
is the maximum velocity. For a 2-D ﬂow, the ratio Umcan/Umax would be 2/3. The
microchannel used in this study (aspect ratio of 84.667) would not yield a strictly 2—D

ﬂow geometry.

3.3.1 Comparison of the Rectangular Channel Series Solution to the 2-D
Flow Parabolic Solution

For pressure driven ﬂows within round capillaries, a steady, laminar and fully-
developed ﬂow would produce a paraboloidal ﬂow ﬁeld. If a cross section of the ﬂow is
taken along the diameter of the capillary, a parabolic velocity proﬁle results. For ﬂow in
rectangular channels, cross sections of the ﬂow ﬁeld along the X-Z plane (refer to Figure
3-2) also produce parabolic proﬁles but as the side walls (y=112.7mm) are approached,
the velocity proﬁle starts to deviate. This causes a change in the velocity gradient (slope,
Us) at the wall. This is shown in Figure 3—9 where around 0.2mm from the edge of the
microchannel, the series solution starts to deviate from the parabolic proﬁle. It is worth
noting that the the numerical computation of the series solution is the exact solution of
the ﬂow ﬁeld within a rectangular channel. However, since the series solution in the
“central” region (-12.2mm < y < 12.2mm) of the microchannel matches the parabolic
proﬁle so well, the parabolic proﬁle is used to obtain the friction factor in our
experimental data sets. All the experimental data in this study were obtained from this
“central” region. At 1mm from the side wall. the percentage change in slope is only
0.03% from the centerline. Another technique of obtaining the friction factor without the

assumption of a parabolic proﬁle is also employed and is described later. If the

52

experimental data were obtained closer to the walls (< 1mm). the actual numerically

computed velocity proﬁle at that interrogation location would be used instead.

 

 

€131 .

Ag“
&‘

 

o—o Parabolic solution for slope
[Si—El Actual Rectangular Channel Series Solution 1

 

Normalized Slope

 

 

 

 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Distance from the wall (mm)

Figure 3-9 Comparison of parabolic proﬁle solution to the numerical computation of the
series solution

3.3.2 Determination of Friction Factor from Experiments

Experiments with pressure driven ﬂows were performed with a microchannel
fabricated from quartz ﬂats resulting in a channel width of 25.4mm and a channel
height of approximately 300m. The ﬂow facility was shown in Figure 2-9. Using the
MTV technique. a single laser line was used to “tag” the MTV chemical across the
300m height of the microchannel and its phosphorescence is tracked in time to obtain
velocity information. The images in Figure 3-10 illustrate the initial phosphorescence

image and the corresponding delayed image 3ms later (images are averages of 100

53

images). The width of the laser line in this case is 30pm (full width at half maximum)
and the interrogation region is y = 3mm from the side wall (y-axis, refer to Figure 3—2). A
correlation procedure. as described previously was used to process the images and
obtain velocity information. The central region of the tagged ﬂuid is thicker due to the
higher velocities present in the center of the channel and the long exposure times. This
could be reduced by lowering the exposure time at the expense of lower intensities in
the images. The size of the microchannel can be accurately determined because of the

reﬂection of the tagged ﬂuid.

Reﬂection of

/ upper wall

Channel
wall

300nm

   

Initial Image with 500us exposure Delayed Image 3ms later

Figure 3-10. Images of tagged molecules for pressure driven ﬂows.

Figure 3—11 illustrates the velocity proﬁle obtained from the correlation of Figure
3-10. The data points near the wall are seen to deviate from zero velocity as the poor
signal to noise near the walls resulted in 2-4 (~2um/pixel) pixels of unreliable data.
However, by curve ﬁtting the rest of the data to a parabolic curve. and extrapolating

based on the channel height, a nominally zero velocity was obtained at the walls.

54

 

100

 

@— —e Velocity Data Points
0 2nd Order Curve Fit

 

-100

 

 

Coordinate Along Channel Height (um, Z-axis)

 

 

Velocity (u. mm/s)

Figure 3-11 Velocity proﬁle from correlation of initial and delayed images

 

 

   
 

 

 

 

 

 

 

 

 

 

200 W
0 9°“, 0 M CD
0 00" U” CE 0
067100 00 a E“? D '5
—¢%-o.o o 051,11 i M
DD 0
A 1% 1
E
3
c
.9
‘16
8 0 Wall Locations
_1 D Slope from Central
8 Differencing
:- 0 Experimental Data
8 points
U) -1 00 . 4
000°“
$0 000 00°°° 0°
° 000 5:3me
3355?an g
-200
-5000 25008 0 2500 5000
1:31:32), 0 50 100 150 200

Shear rate We)

Figure 3- 12 Central Differencing Technique for obtaining Slope

55

There are two ways to obtain the local friction factor from the experimental data set.
The ﬁrst technique involves ﬁtting a parabolic curve and obtaining the velocity gradient
at locations of zero velocity. This however assumes the no-slip condition at the wall. The
derivation of slip velocity and the limitations of the current technique to measure slip
will be described in a later section. The second technique involves determining the slope
directly from the data. A 1st order central differencing procedure was performed on the
data points to obtain the slope. The key idea of this technique is to utilize the reﬂection
at the walls to determine the location of the walls and hence the slope at that location.
This is illustrated in Figure 3- 12.

Linear curves (blue lines) are ﬁtted to the data points near the reﬂection and the
location of zero slope (change of sign) is taken to be the location of the wall; illustrated
by the green horizontal lines in Figure 3—12. Another linear curve (black line) is ﬁtted to
the central region of the slope data and is extrapolated to intersect with the green
horizontal lines to obtain the slope at the walls. One advantage of this technique is that
no assumption about wall slip needs to be made a priori The two techniques were
compared and differences of less than 0.5% in the friction factor resulted. A discussion

of the uncertainties in the measurements is provided in Appendix M.

3.3.3 Experimental Results for Non-Coated Quartz Microchannels

The ﬁrst data set for pressure driven ﬂows was obtained with the setup as
shown in Figure 2-9 where the pressure gradient is varied by gravitational forces. This
resulted in measurements with Reynolds numbers in the range of 11.23 - 84.12 where
the Reynolds number was determined from the mean velocity at the interrogation

location and the hydraulic diameter as the characteristic length.

56

   

Re #: 11.23 Re #: 11.23
Undela ed (0.3ms Ex osure) Delayed 2ms (031115 E

  
  
  
 

 
 
 
 

Re #1 22.37 Re #2 22.37

Undela ed (0.3ms Ex osure) Delayed 2ms (0.3ms E osurc)

Re #2 32.84 Re #: 32.84

Undela ed (0.3ms E )osurc) Delayed 2ms (0.3ms E osurc)

Re #: 43.07 Re #2 43.07
Undela ed (0.3ms Ex )osure) Delayed 21115 (031115 E

Re # 53.22 Re #: 53.22
Undelayed (0.3ms Exposure) Delayed 2ms (0.3ms Exposure)

57

   

Re #: 63.89 Re #: 63.89
Undelayed (0.2ms Exposure) Delayed lms (0.2ms Exposure)

   

Re #: 74.11 Rc#: 74.11
Undelayed (0.2ms Exposure) Delayed lms (0.2ms Exposure)

   

Re #18412 Re #2 84.12
Undelayed (0.2ms Exposure) Delayed lms (0.2ms Exposure)

Figure 3— 13. Images of tagged ﬂuid for different ﬂow velocities for uncoated
microchannels
For the Reynolds number range of 11.23 — 53.22, the images were taken with an
exposure time of 0.3ms and a delay of 2ms. From Reynolds number of 63.89 - 84.12, a
0.2ms exposure and a lms delay was used. The use of shorter delays is warranted to
minimize the amount of pixel displacement while the lower exposure time is used at
higher velocities to minimize broadening of the tagged ﬂuid. Note that the thicker
central region of the tagged ﬂuid is not caused by dispersion but by the long exposure
time and the higher velocities in the center of the microchannel. Blemishes apparent on

the images are caused by dead pixels and dirt on the front face of the microchannel.

58

This affected the correlation procedure as apparent in the red curve (Re #: 43.07) in
Figure 3-14 where a bump in the proﬁle can be seen (highlighted by an arrow). This
caused a slight under prediction of the velocity for all the curves in the ﬁgure at the

approximate wall location of -70pm. This is illustrated by an arrow in the ﬁgure.

 

 

 

 

 

 

 

 

A — — - Wall Locations
g B- — -0 Re 11:43.07
m- .— —. Re if: 32.64
5 v— — V Re if: 22.37
'4' O— —0 Re it: 11.23
E 1
.9
a)
I
To
C
C
a
.C
O
------------------- d
0 50 100 150 200

 

Velocity (mm/s)

Figure 3-14. Velocity proﬁles at different Reynolds numbers (Re #: l 1.23 - 43.07)

However, when a parabolic curve was ﬁtted to the data points. the general trend of the
curve is negligibly affected by the anomaly. The velocity proﬁles for all the different flow

rates are shown in Figure 3-14 and Figure 3-15.

59

 
  
 

 

 

200 v - - - r

i r ‘
“Hi. Pl
C x ‘ —
' A

v - .. - . v v v v v ﬁ Tﬁ
‘n )1; . I"
‘.I' . U
u

 
  
   

1

 
 

1
------------------q

' r

   

v.._ t
1

 

. Wall locations

 
 
 
 
 

} 0 F16 it: 53.2 ‘
7 Re if: 63.89
0 Re #2 74.11 1
0 Re #: 84.12 J

  

 

Channel Height (Z-axis, rim)
0

-100 1

v

+44; A

 

 

 

 

§

0 ‘ 3 3 50 100 A 150
Velocity (mm/s)
Figure 3-15. Velocity proﬁles at different Reynolds numbers (Re #: 53.22-84.12)

The imaging system has difﬁculties resolving the ﬁne detail near the wall due
probably to parallax issues. This causes the velocity to have an apparent non-zero value
at the walls. As the velocity increases, the data points at the walls seem to measure a
higher non-zero velocity. This is an artifact of the imaging issues and could potentially
be improved upon by using a higher magniﬁcation objective for imaging near the walls.
A parabola is curve ﬁtted to the rest of the data points away from the wall and
extrapolated to the location of the walls to obtain the slope and thus the friction factor.

Table 31 details the experimental results obtained from the correlated images.
The ﬁt coefﬁcients for the parabolic curve ﬁt for all the data sets are shown and the
“lower” and “upper” positions designate the wall locations. The two techniques
described in § 3.3.2 are then used to obtain the slope (shear rates) at the wall locations.
Minimal deviations were observed and the easier technique of ﬁtting a parabolic curve

to the data points is henceforth used.

60

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61

One disadvantage of using a high aspect ratio microchannel is that the
hydraulic diameter, DH. is biased by the width of the channel and the Reynolds number
computed from the hydraulic diameter (Rena) may not be representative. Table 3- 1 adds
a column for Reynolds number computed from the characteristic height (Recn,
301.4pm) and this results in a Reynolds number range that is about a factor of 2 lower

than that computed previously. The differences are illustrated in Figure 3-16.

 

 

 

 

 

 

 

 

E‘ 1
g .

5 1.03 . =1

0": L D FieCH

\% . 0 FleDH *
..- 1. 2 ’ i

O 0 .

.5

g 1.01

Ll.

c

.9

:5 1.00 ’

Lt .

'8 -

.5 0.99 r I

'6

g :

o 0.98 ' 4

5 10 20 50 100
Reynolds Number (Re)

Figure 3- 16 Normalized friction factor based on deﬁnitions of Reynolds number.

3.3.4 Extended Range of Re # for Non-Coated Microchannels

More experiments were performed with the non-coated microchannels to try and
extend the range of the Reynolds number. From our experiments, as the Reynolds
number becomes lower. the amount of displacement achievable while maintaining

sufﬁcient signal to noise becomes smaller. Due to the reduced signal to noise at long

62

delay times. a Reynolds number, Rem. lower than 0.32 was not achievable. A
representative set of images is shown in Figure 3— 17 and by correlating the images, the
velocity proﬁles are obtained. The velocity proﬁles for the lowest Reynolds numbers are
shown in Figure 3—18. Note that from Figure 3-17. the images for a Reynolds number of
0.32 had very small displacements (1 pixel or less) and this contributed to the level of
noise when the images were correlated. This effect is demonstrated in the normalized
friction factor shown in Table 3-2. Comparing the normalized friction factor in Table 3-2
to Table 3-1, a noticeable difference in friction factor is present. At the lowest Reynolds

number. the deviation from a normalized friction factor of 1 is higher.

   

Re #: 0.32 Re #: 0.32
Undela ed Ima e Dela ed lma e

  
 

 

Re #2 1.37 Re. #1 1.37
Undela ed [1118 e Dela ed [Ina e

 

Re #2 10.86 Re #1 10.86
Undelayed Image Delayed Image

Figure 3-17. Images of tagged ﬂuid for different flow velocities (Re # : 0.32- 10.86)

63

Velocity proﬁles obtained from the different images in Figure 3-17 are shown in Figure
3-19. One of the differences with this set of data is the interrogation location (1mm from
the side wall) and the shorter reﬂection at the upper and lower walls. The closer the
interrogation region is to the side walls. the shorter the reﬂection will be. However. the

intensity of the images increases due to a shorter path length.

 

0.3

0.2

Channel Height (Z-axis, mm)

0.1

 

 

 

 

Velocity (mm/s)

Figure 3— 18 Plot of velocity at different pressure gradients (Re #1 0.33)

64

 

 

 

 

 

A — — - y=-142.29

e ‘00 -— -- y=146.7

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.3 A—A Re#:95.58
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Velocity (mm/s)

Figure 3-19. Plot of velocity at different pressure gradients (Re #: 1.37- 137.98)

65

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66

3.3.5 Experimental Results for HEMA coated Quartz Microchannels

The experimental results for HEMA coated microchannels echo the results from

the non-coated microchannels.

 

Re # : 2.19
Undela ed lma e (lms ex )osure)

    
 
 

Re # : 12.93
Undela ed Ima ye

Re # : 32.59
Undelayed Ima e (0.51115 exposure)

Re # : 65.05
Undelayed Image (0.2ms exposure)

 

Re # : 2.19
Dela ed [ma e (Sins delay)

   
 
 

Re # : 12.93
Dela ed Ima e

Re # : 32.59
Dela ed Ima e (2ms delay)

Re # : 65.05
Delayed Image (lms delay)

Figure 3—20. Images of tagged ﬂuid for different ﬂow velocities for HEMA coated

microchannels (Re # : 219-6505).

The image pairs obtained from the experiments are illustrated in the Figure 3-20.

The images in Figure 3—20 are slightly different in appearance from previous line
tagging images. Due to the different intensity variations. some images illustrate a
thicker tagged line in the middle due to the higher exposure times. Another aspect of
the tagged lines which is also inherent in the previous set of images is the curvature
present in the undelayed images. The curvature becomes more apparent as the ﬂow
velocity increases. This is caused by the amount of delay between the ﬁring of the laser
and the time when the image was taken. If the delay is reduced. this effect will also be
reduced. However, since the velocity correlation technique is based on the correlation of
the undelayed with the delayed image. the curvature of the undelayed image did not
cause any problems with the correlation technique. The velocity proﬁles obtained from

the pair of images are shown in Figure 3-21. The full experimental data set is shown in

 

 

 

 

 

 

Table 3—3.
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10 15 20 25

Velocity (mm/s)

Figure 3-21 Plot of velocity at different pressure gradients for HEMA coated
microchannels (Re #: 2.19-4.28).

68

 

100

- Wall Locations
: 9.97
: 12.93
0 : 15.23

: 32.59
: 65.05

 

Channel Height (Z-axis, pm)

-100

 

 

 

Velocity (mm/s)

Figure 3- 22. Plot of velocity at different pressure gradients for HEMA coated
microchannels (Re #: 9. 97 65.50 ).

69

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3.3.6 Experimental Results for OTS coated Quartz Microchannels

For the OTS coated quartz microchannels, a similar experimental procedure was
performed. Notice that the tagged ﬂuid in Figure 3-23 and Figure 3-24 exhibits a
thinner region in the middle of the microchannel. The laser beam is at its focal point in
the middle of the microchannel which caused the narrower beam. An artifact of a more

focused beam is the higher energy levels present which cause bleaching effects.

 

Re # : 2.42
Dela ed [ma 6. (3ms delay)

   
 

Re#:4.51 Re#:4.5l
Undela ed [ma 6 (lms ex )osure) Dela ed Ima e (3ms delay)

 

Re #2 10.58 Re #2 10.58
Undelayed Image (lms exposure) Delayed Image (3ms delay)

Figure 3-23. Images of tagged ﬂuid for different ﬂow velocities for OTS coated
microchannels (Re # : 2.42-10.58).

71

   

Re #: 13.48 Re # : 13.48
Undela ed Ima e (lms ex )osure) Dela ed Ima e (3ms delay)

  
 

 

Re # : 36.98 Re # : 36.98
Dela ed Ima e (lms delay)

Re #2 138.44 Re #2 138.44
Undelayed Image (0.1ms exposure) Delayed Image (lms delay)

Figure 3-24. Images of tagged ﬂuid for different ﬂow velocities for OTS coated
microchannels (Re # : 13.48-138.44).

This is illustrated in Figure 3-24 where the central region of the tagged ﬂuid has a lower
intensity. The intensity levels. however, were sufﬁcient in performing the velocity
correlation. The last image set in Figure 3-24 illustrates a thicker central region in the
delayed image due to the longer exposure time necessary for a good signal to noise

ratio. This is not caused by dispersion.

72

 

 

    

 

 

  

 

g- _ - Wall Locations
.2 A Re : 138.
3 I Re a : 36.98
5 0 Re a : 13.48
.. 7 Re I: : 10.58
£3 a Re a : 4.51
O .

I 0 Re x 2,42
3

C

5

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o

 

 

 

 

Velocity (mm/s)

Figure 3—25. Plot of velocity at different pressure gradients for 018 coated
microchannels (Re #: 242-13844).

The images from Figure 3-24 are correlated to obtain the velocity profile for each
individual syringe pump setting. These velocity proﬁles are shown in Figure 3-25 and
illustrate a representative set of the data taken for this experimental setup. The full
experimental data set is provided in Table 3-4 and illustrates similar results obtained
for the non—coated and HEMA coated microchannels. The normalized friction factor
displays excellent agreement with classical theory. The normalized friction factor for all
the different surfaces is plotted against the results from other researchers and is shown
in Figure 3-26. A zoomed-up view of the experimental results is provided in Figure 3—27
along with the calculated error bars. The error bars signify the uncertainties in

determining the friction factor.

73

 

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76

3.3.7 Limit of Slip Detection

The possibility of ﬂuid slip at a boundary was proposed by Navier in 1823. The
slip velocity at the boundary is assumed to be proportional to the shear stress at the
surface. This is shown in equation 3-23 where ,8 is the slip length and u: is the slip

velocity.

_X 3-23

Results from Tretheway et. al. (2002) reported a slip length as large as lm for
ﬂuid ﬂows within a 30m x 300m microchannel coated with OTS. The measurements
were made using ﬂuorescent particles 300nm in diameter with the velocity proﬁle
measured along the 300nm height of the microchannel with an integrated depth of
30m. From the experimental results presented in previous sections for pressure driven
ﬂows within microchannels with different coatings, the normalized friction factor yielded
a deviation from theory of only i 0.5%. It is thus of interest to investigate the slip
detection limit of the in-situ measurement techniques that were applied in comparison
with the reported lum slip length.

In the presence of slip within a microchannel an offset is imposed on the
parabolic ﬂow proﬁle (derivation of the equations are presented in Appendix L). For a
1m slip length, a wall velocity with a magnitude of 1.325% of peak velocity is observed
(Figure 3-28). In order to understand the slip detection limit of the in-situ measurement
technique, the error margin from the experimental results is used as a starting point.
Although the errors were obtained for the normalized friction factor measurements (the
slip imposes an offset and there is no change in shear stress although the friction factor
will decrease due to a higher mean velocity), the errors from the measurements are an

indication of how well the technique can resolve differences in velocity near the wall.

77

Figure 3-29 is a more detailed version of Figure 3-12 and is used to illustrate how the

error margin is utilized to obtain the slip detection limit.

 

 

   
   

— - - x=1.325°/o
Proﬁle with No-Slip
— Profile with 1pm Slip

 

 

 

 

 

 

Spatial location (z-axis, mm)

Normalized velocity (ulum)

Figure 3-28. Comparison of theoretical velocity proﬁles near the wall with and without

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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0.1 at:
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-5000 -2500 0 2500 5000

Velocity
(mm—50 o 50 100 1 50 200

Shear rates (1/s)

Figure 3-29. Central differencing technique for obtaining slope

78

The linear curve ﬁt (black line) in Figure 3-29 is used to obtain the slope at the
wall and the upper wall is taken as an example. The wall location (347.7um) is plugged
into the linear curve ﬁt equation to obtain the slope at the upper wall. Since the friction
factor measurements typically yield an uncertainty of < 0.5% and assuming that in the
worst case scenario that all the errors are attributed to the determination of the slope
(although in reality, the uncertainty of 0.5% is cause by the combination of the
uncertainty in determination of the wall locations an_d the ﬁt). the slope at the wall is
determined to be -2570.82 1 12.85 US. The shearing rate of 2570.82 US is the highest
shear rate measured in this study. The spatial locations within this slope range are
determined and the corresponding velocity differences at these two locations are
compared. At a slope of -2570.82, the velocity is zero while the velocity is 1.897mm/s at
a slope of (-2570.82+12.85). Note that this uncertainty in velocity is dependent on the
gradients at the wall (higher gradients will result in a higher uncertainty in velocity).
Since the minimum shift in velocity that can be measured is 1.897mm/s in this case, it
translates to a minimum detectable slip length of 752nm. This value. however. is close
to the reported value of 1pm by Trethaway et. al. (2002) and it is inconclusive if the

present technique will be able to resolve the slip lengths.

3.3.8 Electroviscous Effects

The electroviscous effect is based on the presence of ions in a ﬂuid made to
move relative to a charged surface by an induced pressure gradient. For a charged
surface. ions of opposite charge to the surface are preferentially attracted to it. A
pressure gradient within the microchannel would tend to move the ions near the walls
and thus create a streaming potential. This potential opposes the motion of the ﬂuid in

the direction of the pressure gradient by inducing back conduction by ion diffusion and

79

electroosmotic ﬂow (Probstein. 1994). The resultant pressure driven ﬂow would
effectively demonstrate a higher ‘viscosity’ due to this added resistance.

The streaming potential created is limited to the interaction between the Debye
layer and the charged surface. The Debye layer is a layer primarily composed of ions
opposite in charged to the surface (more details in § 4.3.1) and is usually on the order of
less than 100nm. Rice and Whitehead (1965) consider the electroviscous effect to be
negligible when k >> 1 where k is the ratio of the capillary radius to the Debye layer
thickness. Brutin and Tadrist (2003), however. measured discrepancies with classical
Poiseuille ﬂow for capillaries as large as 539.69um and attributed it to electroviscous
effects. Note that the k value is 13,500 which is expected to have negligible
electroviscous effects. The experimental data illustrated in the present study for
pressure driven ﬂows have been shown to be highly consistent with classical theory and
no discrepancies have been found for microchannels 300m in height. This further

proves that discrepancies from classical theory at this level are highly unlikely.

3.3.9 Contributions and Conclusions

The present study illustrates a marked improvement over previous diagnostic
techniques used by other researchers (Maynes et. al. (2002) and Sharp et. al. (2000)) to
measure ﬂow characteristics within microchannels. Maynes et. a] (2002) utilized the
MTV technique to measure the velocity proﬁle within a 705m diameter capillary but
the quality of the images were not sufﬁcient to resolve the velocity gradients at the
walls. Surface curvature issues of the round capillaries used in their study also
impeded the measurements at the walls. Multiple smoothing algorithms were needed to
improve the signal to noise characteristics of the images but were only used to yield ﬂow

rate information. Sharp et. al (2000) also measured the ﬂow rate but utilized a particle

80

tracking technique instead. Although these measurement techniques were local in
nature, it was used to measure bulk ﬂow properties. The implementation of the MTV
technique in this study. however, managed to resolve the velocity proﬁles near the
channels walls to provide a local measurement of friction factor that is not
contaminated by entrance effects.

Apart from an improvement in the measurement technique. one obvious
discrepancy between local measurements (Maynes et. al. (2002), Sharp et. al. (2000)
and the present study) and bulk ﬂow measurements are deviations from classical
theory. Other researchers (Wu and Little (1983). Pfahler (1990), Choi (1991). Wilding
(1994), Yu (1995), Jiang (1995)) have advocated a deviation from classical theory within
microchannels as large as 500m in size under high shearing rates (~2000 l/s).
Various reasons for the deviations that were proposed include increased roughness.
electroviscous effects, entrance effects, an early transition to turbulence and
inaccuracies in measuring the dimensions of the channel.

This study, however, has proven conclusively that at similar shearing rates and
even with hydrophobic microchannels 300m in size, classical theory still holds. One of
the primary advantages in this study is the ability of the experimental technique to
measure the velocity proﬁles locally. This essentially removes the contribution of
entrance effects and any uncertainties of the dimensions of the microchannel. Thus
more accurate measurements of the velocity gradients are possible. The accuracy of this
measurement is also utilized to determine the limit of slip detectability. The analysis
showed that a minimum slip length of 752nm is detectable. It is concluded that slip
lengths of > 752nm were not measured in the present study. Previously reported slip
lengths of 1m by Trethaway et. al. (2002) may have been caused by the interaction
between the tracer particles used for velocity measurements and the microchannel

walls.

81

3.3.10 Future Work

Currently, the measured velocity proﬁles have unreliable data points near the
walls. This is due to the combination of the large physical size of a pixel and the
thickness of the laser line. To be able to use a higher magniﬁcation objective to resolve
the velocity proﬁle close to the walls. a diffraction grating can be used to create fringes
and use it for tagging the ﬂuid. The fringes are expected to be much thinner than the
tagging lines used in the present study. This is expected to provide a more resolved
velocity proﬁle. Another plausible technique for measuring slip lengths at these scales is
a combination of the MTV technique with total internal reﬂection (11R).

As the mean velocity of the measured velocity proﬁles increases. the “measured”
velocity at the wall seems to increase accordingly. This is an artifact of the
measurement technique as it is not able to resolve at sub-pixel levels. However, this
value may be an indication of the increase in shearing rates as the mean velocity
increases. A closer look at this problem may yield a novel way of measuring shearing

rates.

82

Chapter 4 Electroosmotic-Flow in Microchannels

Microchannels experience large pressure drops as the large surface to volume
ratio causes an increased frictional resistance to ﬂuid movement. To create a ﬂow speed
comparable to macro ﬂow phenomena within microchannels would require a prohibitive
amount of pressure. Microchannels in the tens of microns in diameter would require an
alternative method of ﬂuid transport. An elegant way of moving ﬂuid within
microchannels, albeit not without its own challenges. is through electroosmosis.
Electroosmosis is the movement of an ionized ﬂuid relative to a charged channel due to
an induced electric potential. The Helmholtz-Smoluchowski equation is used to relate
the electric potential, Ex. to the resultant velocity ﬁeld, u... and is given in the following

equation.

86‘ E
ux: or; X 4-1

,u

where so is the permittivity of vacuum given by a constant, 8r is the relative
permittivity of the ﬂuid, 5 is the zeta potential and u is the viscosity. For a given ﬂuid
temperature. the electroosmotic velocity linearly increases with electric potential. A by-
product of moving ﬂuid with electroosmosis. however. is Joule heating. As
electroosmosis progresses. the temperature of the ﬂuid increases which causes the
relative permittivity and viscosity to change (the temperature dependence of these
properties will be discussed later). A higher electric potential also causes a higher
heating rate. This causes a non-linear increase in electroosmotic velocity. To correctly
determine the electroosmotic velocity dependence on electric potential, the temperature
and velocity of the ﬂow needs to be measured simultaneously to account for changes of
the ﬂuid properties. Thus. the Molecular Tagging Velocimetry and Thermometry
(MTV&T) technique is simultaneously applied to the measurement of electroosmotic

ﬂows within microchannels. The time evolution study of electroosmotic velocity is

83

presented in § 4.3.4. An added advantage of being able to measure temperature and
velocity simultaneously is the determination of the zeta potential dependence on
temperature. This is illustrated in § 4.3.5.

Due to the constraints of the experimental setup, the imaging system can only
image the center of the channel. As electroosmosis causes heating of the ﬂuid within
the microchannel, it is of interest to determine the temperature proﬁle within the entire
microchannel as it undergoes a gradual increase. This was investigated through a
computational solution (FLUENT).

In the coming sections. the surface charge of quartz is initially discussed
followed by its effect on the ﬂuid adjacent to its surface. This sets the basis for
discussion of the principles of electroosmosis and the variables that affect it. The
equation of motion for electroosmosis is subsequently presented. This chapter
concludes with results and discussions from the present work. focusing on the
importance of measuring electroosmotic velocity and temperature simultaneously and
the ability to indirectly measure zeta potential and its temperature dependence. The
computational solution will provide further details on the temperature characteristics of

electroosmosis within a microchannel.

4.1 Electric Double Layer

Most surfaces exhibit a charged surface when exposed to an aqueous polar
medium (electrolyte). In the case of glass or quartz. deprotonated (lacking in protons)
silanol groups (Figure 4-1) naturally occur and cause the surface to assume a negative
charge. The presence of the surface charge, however, affects the ionic distribution
within the electrolyte because the negatively charged surface preferentially attracts
positively charged ions (counter-ions) within the ﬂuid. Coupled with the random

thermal motion of the ions. an exponential distribution of ions is exhibited near the

84

surface (Probstein. 1994). Figure 4-2 illustrates the distribution of counter-ions and co-

ions and the corresponding potential distribution at the surface.

 

O - 0'
.I l
81 Si

 

 

 

Figure 4—1. Schematic of deprotonated silanol groups

    
 

 

   

 

 

 

Concentration. c Potential. <1)
ll
(bw
Counterions
Co
Coions
L $7 1
0 AD 0 AD
Distance from Distance from
surface, x surface. x

Figure 4-2. The diffuse electric double layer (Probstein. 1994)

One deﬁning feature of the ion distribution is the Debye length (110). The thickness of
this layer can be estimated through the application of the Poisson equation. The
electrodynamic problem may be considered electrostatic assuming that there are no
magnetic ﬁelds induced by the current. The Poisson equation (equation 4-2) can thus
be utilized to relate the spatial variation of the charge distribution for a medium of

constant permittivity. (Probstein, 1994)

V2¢= ii:- 4-2
6‘

where ¢ is the electric potential. 8 is the permittivity and pr: is the electric charge

density deﬁned as

85

pE =FZZiCi 4’3

where F is Faraday’s constant, 2 is the charge number (valency). c is the concentration
of ions and iis summed for all the ionic species in the solution. Assuming that there are
no co-ions present near the surface, the Poisson equation can be simpliﬁed to equation

4-4.

(12¢ cm
axz :7:— 4-4

 

where x is deﬁned as the distance from the surface. Integrating the equation twice. the

electric potential is given as

cmx2
= 26

4-5

 

(1’

Note that the concentration, c is the concentration of the bulk ﬂuid. To obtain the
Debye length, the electric potential is equated to the electric potential energy per mole

of counter-ions which is deﬁned to be

W:_Fz¢ 4-6

As mentioned before. the random thermal motion of the ions caused a decaying
distribution of counter-ions near the surface. At the Debye distance. the electric
potential energy is approximately equivalent to the thermal energy (RT/ 2 per mole per
degree of freedom; where R is the gas constant and T is the temperature). In a strictly 2-
dimensional setting (assuming that the other dimension is uniformly distributed). the

thermal enery needed to overcome the potential energy (AW) is RT.

2 2 2
sz—F 2 ex
2!:
F222 2
=__2£CX 4-7
,1 _ 2£RT
x— D Fzzzc

86

In equation 4-7. it is shown that the Debye length is proportional to the square root of
temperature and inversely proportional to valency and the square root of concentration.
As the electrolyte increases in valency or concentration. the Debye length becomes
shorter due to the increased amount of ions present to neutralize the effects of the

surface charge.

4.1. l Debye-Hﬁckel Approximation

The estimation of the Debye length presented in the previous section from a
thermal energy stand point does not yield the ion distribution near the walls. If the
distribution at the wall is taken into account. the Poisson’s equation would look slightly
diﬁerent. The ions near the surface have a Boltzmarm distribution given as

3FzF¢

 

ct = coe RT 4‘8
where c -) coas ¢ -> O. From equation 4-3, the charge density is modiﬁed to become
.52 3’1":
pE =ch0 8 RT —eR’T
4-9

. zF¢
=—2cm s —
PE 0 1111){ RT]

substituting the charge density back into equation 4-2. the Poisson equation becomes

2
d ¢ = ZZFCO sinh[—ZF¢] 4-10
dx2 8 RT

For small potentials, zF¢ << RT and Equation 4-6 can be simpliﬁed to become

 

d_2¢:__¢_
dxz [102 4-11

This is the Debye-Hilckel approximation which is applicable for surfaces with small
potentials. The integration of equation 4-11 with the boundary conditions of ¢ = ¢w at

x=0 and d¢/dx = 0 as x -) oo results in

87

X

¢ = (blue-71’: 4‘ 12
This equation illustrates that the electric potential is exponentially decaying from the

charged surface and the Debye length. AD, is the l/ e decay distance of the potential.

4.2 Principles of Electroosmosis

At the ionic level (see Figure 4-3), a single layer of ions with an opposite charge
to that of the surface, called the Stern layer. is strongly attracted to the surface charge
(opposite charges attract) and largely remains immobile. Beyond this layer. the Debye
layer. which is a layer consisting on average of ions opposite in charge to the surface
charge is present. This layer. depending on the concentration of the ionized ﬂuid
present, could range in the order of angstroms to nanometers. When an electric ﬁeld is
applied parallel to the negatively charged surface, the positively charged Debye layer is
attracted to the negative electrode. This induces motion and through the action of
viscous forces, this motion is transferred from the Debye layer to the bulk ﬂuid (ionized
but neutral). One can perceive the Stern layer as a no-slip surface and the movement of
ﬂuid above this layer to resembles a boundary layer type ﬂow. The ﬂow proﬁle is
described in diagram (a) of Figure 4-3. The induced motion caused by the movement of
ions at the shear surface (between the Stern and Debye layers) results in a perceived
“plug” ﬂow as the Debye layer is so thin (refer to equation 4— 1 for the uniform plug ﬂow
velocity). Plug ﬂow is characterized by a uniform velocity proﬁle across the whole

microchannel. This is illustrated in Figure 4-4.

88

  
   

 

   
   

Neutral Bulk Fluid (8) lb)
Debye

Ionic Cloud —

(+) net Layer

charge
Electroosmotic
Velocity g
Proﬁle

 

 

Figure 4-3. Schematic of a typical ion distribution in the vicinity of a charged surface
and the resultant electroosmotic velocity proﬁle and surface potential (Probstein. 1994)

Electrode Quartz walls

9 O

‘ velocity goes to
zero very near
the walls. Debye

layer on the
115 order of 30nm

Figure 4—4. Schematic of velocity proﬁle within microchannel for electroosmosis

Diagram (b) in Figure 43 illustrates the change in potential with distance from

the surface. The surface potential, 6150. is dictated by the amount of deprotonated silanol

89

groups that are present. The potential drops at the Stern layer due to the presence of
ions of opposite charge. At the interface of the Stern and Debye layer. the potential is
called the zeta potential. _Z, The zeta potential is an important aspect of electroosmosis

because it is this potential that the rest of the ions within the ﬂuid are affected by.

4.2.1 Factors Affecting Zeta Potential

The uniformity of the formation of deprotonated silanol groups and thus the
consistency of surface charge for different microchannels. however, depends on the pH
value of the aqueous solution it is exposed to. At a lower pH. less silanol groups are
deprotonated which causes a reduction in surface charge. Figure 4-5 illustrates the zeta
potential for various surfaces at different pH values. The potential at the shear surface
is deﬁned as the net addition of the surface charge and the charge present in the Stern
layer. At a particular electrolyte concentration, reducing the pH causes a reduction in
zeta potential. The reduction in zeta potential is due to the reduced presence of
deprotonated silanol groups. The zeta potential can even be made to change sign at very
low pH (sapphire, for example). When an electric ﬁeld is applied within the
microcharmel over time. positive ions tend to accumulate at the anode and negative
ions at the cathode. Positive ions contribute to the basicity whereas negative ions to the
acidity of the solution. This essentially creates a pH gradient within the electroosmotic
ﬂow setup and may ultimately affect the uniformity of the zeta potential. One way to
limit the change of pH is by using a buffer solution which is discussed further in § 3.3

when results for electroosmotic ﬂows are presented.

90

~150

 

-1OO b ' 00
a- ~ . ‘ . C ‘
E A D D ‘ A ‘ ‘ ‘ ‘
v ‘ . 0
g -50 E Latex .
c
3 L 0
8 t
a, L . Sapphire
33 o - - ._ .
N f v r v
f
F o
F o
O P .
5 ° ' I,A:conventional cell

 

 

2 3 4 5 6 7 8 910
pH

Figure 4-5. Plot of zeta potential for various surfaces at different pH values.
(Ohshirna. et. al.. 1998)

(a) Less Surface Charge (b) More Surface Charge

O; O: Q it: HO O: } Deprotonated

:. silanol group

         

Ions from electrolyte

\r@--@-l :© @636) Sternl.ayer
3°:QIOIQIO Charged
010.0:01010. Surface

(c) Low electrolyte concentration ((1) High electrolyte concentration

       

 

 

Figure 4-6. Schematic of a charged surface illustrating factors that affect zeta potential

Figure 4-6 further explores other factors that affect the zeta potential of a
surface. For a surface that has less deprotonated silanol groups as in Figure 4—6(a). the

zeta potential will be less compared to Figure 4-6(b) which has a higher surface charge.

91

Figure 4-6(c) on the other hand illustrates a high surface charge but a low
concentration of electrolytes. Since the zeta potential is the net addition of the surface
charge and the charge in the Stern layer. Figure 4—6(c) would have a higher zeta

potential compared to Figure 4-6(d).

4.2.2 pH Stability

During electroosmosis. when ﬂuid is transported within the channel. electrolysis
is occurring simultaneously. The electrolysis of water causes a pH gradient to form. The
following reaction balance details electrolysis of water and the formation of ions which

causes the pH gradient (Skoog et. al.. 1997).

2H20 —) o2 +4H+ +4e‘
4H20+4e' -—>2H2 +4OH‘

4-13

As electrolysis of water progresses. oxygen and hydrogen gases are created at
the anode and cathode respectively but the amount of hydrogen gas created is two
times that of oxygen gas. Positive ions and negative ions are also created and this
causes a pH imbalance. To counter this, a phosphate buffer solution is used to buffer
the additional ions present at each electrode and maintain the pH level. The following

reaction balance details the workings of the buffer. (Skoog et. al.. 1997)

H2PO4‘ + OH“ —> HPO42’ + H20

2_ _ 4-14
HPO4 + H30+ —+ H2P04 + H20

Phosphate ions (H 2PO49 react with hydroxide ions to form a different phosphate ion

2— . . .
(HPO4 ) and water when there IS an excess of hydroxrde ions. ’llre converse occurs

when there are excess hydronium ions. Hydroxide and hydronium ions cause a change

92

in pH and by balancing the amount present in the ﬂuid through the use of a buffer. the
pH stays essentially constant.

Figure 4-7 illustrates the measured change of pH with an increased volume of
sodium hydroxide within the sodium phosphate buffer solution. The plot illustrates
plateaus of nearly constant pH values and once the buffering capability of the buffer
solution is exceeded. a sudden jump to the next plateau is observed. The electroosmotic
experiments will be conducted at a pH of 7 where any addition of pH contributing ions
should not affect the overall pH signiﬁcantly.

During the course of an electroosmotic experiment. the amount of additional
ions accumulated at each electrode is assumed to be small. The amount of sodium
hydrordde added to the buffer to cause the pH to cross the plateaus of almost constant
pH is considerably larger than what is expected from a short electroosmotic experiment.

Thus an essentially constant pH value can be assumed.

 

12 WW.
This is the pH of the MTV + phosphate solution
- when the phosphate was initially mixed with the
MTV solution

 

10‘

pH

 

 

A A A A A A A A A A A A A

140 ‘ 15 20 25
Volume of NaOH (ml)

A A A

 

 

Figure 4-7. Change of pH of W Solution and Sodium Phosphate Buffer Solution with
increasing volume of Sodium Hydroxide.

93

An essentially constant pH also translates to a constant zeta potential (refer to section
2.3). The zeta potential. as explained previously. is also affected by the concentration of
the electrolyte. At a higher concentration. the amount of ions within the Stern plane

increases and neutralizes the surface charge further. This creates a lower zeta potential.

4.2.3 Equation of Motion for EOF

The equation of motion for electroosmosis is based on the momentum equation
with modiﬁcations to include the Lorentz forces caused by the presence of an electric
ﬁeld. The Lorentz relation is used to relate the forces on the ions and the bulk ﬂuid ﬂow

in the system. This relation is shown in equation 4- 15 (Probstein. 1994).

f =PEE 4-15

where j is the force on an ion, pE is the charge density (equation 4-3) and E is the

electric ﬁeld. It is worth noting that since equation 4-3 sums the valence number and
concentration of each ion species, an electrolyte is necessarily electrically neutral
unless an electric ﬁeld is present. The momentum equation is shown in equation 4- 16.

I21; =-Vp+,uV211+p§ 4-16

 

,0

Assuming steady. fully developed unidirectional ﬂow. neglecting any pressure gradients
and gravitational effects while adding the contribution of the Lorentz forces, the

momentum equation becomes
szﬂ = -pEE 4-17
Substituting the Poisson equation (equation 4-2) for the charge density and
integrating twice. the resultant electroosmotic velocity is

a e E
ux —_-__9_i_£ 4-18
,1:

where 5 is the zeta potential, ,1: is the viscosity of the electrolyte and Ex is the applied
electric potential. This is the Helmholtz-Smoluchowski equation used to characterize

94

electroosmotic velocity. This equation, however is valid only when the Debye length is
signiﬁcantly smaller than the size of the channel. For a Debye length that is comparable
to the channel size. the Huckel-Onsager relation should be used instead (Probstein.
1994). The present study only deals with the former case and the Helmholtz-
Smoluchowski equation proves to be adequate. A comparison of the Debye length to the
channel size is presented in a later section.

Traditionally. the Helmholtz-Smoluchowski equation was used to determine the
velocity component given an electric potential. This. however, can prove to be
inaccurate since a signiﬁcant amount of heat can be generated at high electric
potentials. The rise in temperature of the ﬂuid from heating will cause the relative
permittivity and viscosity to change and result in a non-linear increase in velocity. This
gives rise to the importance of measuring temperature and velocity simultaneously with

the MTV&T technique so that the changes in the ﬂuid properties can be accounted for.

4.2.4 Time Response of Electroosmotic Flows

The inertia of ﬂuid ﬂows in response to an electric ﬁeld is largely disregarded for
equilibrium ﬂows. However, a ﬁnite time is needed for the ions within the ﬂow to
response to the applied potential. For electroosmotic ﬂows, the two characteristic time
scales are polarization of the double layer and viscous diffusion. Double layer
polarization is dependent on the ions present in the ﬂuid while viscous diffusion is
dependent on the size of the channel. The time scales involved in the polarization of the

double layer, rat is estimated to be on the order of

rd, = 0(23, / D) 4-19

where 20 is the Debye length, and D the diffusion coefficient of ions within the ﬂuid

(Minor et. al. (1997)). The viscous diffusion time scale. tea on the other hand is on the

order of

95

T... = 0(DlP/ﬂ) 4-20
where Dr. is the hydraulic diameter or characteristic length. p is the density and u is the
viscosity of the ﬂuid. The larger the characteristic length, the longer the time scale
would be. In the present study, the time scales are all in the sub-microsecond scales
and are not expected to cause issues with measurement of the uniform velocity proﬁle.
The time scales are only important if the start-up phenomena of electroosmotic ﬂow is

being investigated. It is presented here for completeness.

4.2.5 Surface Conduction Effects

The Helmholtz-Smoluchowski equation given in equation 4- 18 is a simpliﬁcation
as only the M conductivity of the ﬂuid is taken into account in its derivation. One
other factor that affects electroosmotic velocity is surface conduction. Surface
conductivity is an excess quantities and is a second order effect. This phenomenon
occurs because of an excess of ions constituting the countercharge. To quantify this
effect relative to the bulk conductivity. the applied potential. E, is related to the current.

I as in equation 4-21 (Lyklema, 1995).
I L 0’
E = AK + SK 4-21

where I represents current, E the electric potential, A the cross—sectional area of the
channel, KL the bulk conductivity S is the circumference of the channel and K0 the
surface conductivity. The bulk conductivity contribution, AKL, is Ohm's law and is the
leading term in the equation. Comparison of equations 4-18 and 4-21 and eliminating E

reduces the equations to the following.

_ £08,; I
U" u [AKL+SK"] 4'22

 

When 8K0 << AKL, the equation reduces to the standard Helmholtz-Smoluchowski

equation. Experimental values (Bikerman (1935)) have shown that surface

96

conductivities do not exceed 10-8 S (Siemens) while present experimental bulk
conductivities are easily two orders of magnitude higher (152 x 10-6 S). A measure of the
relative importance of surface conductivity in electroosmosis is given by the Dukhin
number (Du).

K0
[KL

Du : 4-23

 

where l is the characteristic length (typically the height or radius of the channel). When
the characteristic length is large. the Dukhin number becomes negligibly small as does

the contribution from surface conduction to electroosmotic ﬂow (Lyklema, 1995).

4.2.6 Factors Affecting Electroosmosis

The Helmholtz-Smoluchowski equation gives a relation for electroosmotic
velocity that allows a simpliﬁed view of the factors that affect electroosmosis. The
permittivity. a. (dielectric constant) is the capability of the ﬂuid to hold charge and is the
product of the permittivity in vacuum. 80. and the relative permittivity. 8,. The
permittivity of free space or vacuum, 80, is a constant given by 8.854 x 10-12 C2N'lm'2.
where C is Coulomb and N is Newtons. while the relative permittivity of the ﬂuid. 8,, is
taken to be that of water. The relative permittivity of the ﬂuid is assumed to be the
same as water as the concentration of the buffer and the added phosphorescent
chemicals are low.

Figure 48 illustrates the temperature dependence of the relative permittivity of
water. Its temperature dependence needs to be taken into account since the
temperature of the ﬂuid changes with time during the course of electroosmosis due to
Joule heating. As the temperature increases. the permittivity decreases. This is due to

the increased mean free path between water molecules which causes a reduced ability

97

to conduct electricity. For example. as water evaporates and transitions to the gas
phase, the permittivity drastically drops to unity.

The viscosity of the electrolyte is also changing with temperature (Figure 4—8).
Thus it is imperative that both the temperature dependence of viscosity and the relative

L‘A r‘ I L

permittivity is taken into account when using the i' ‘ wuski equation to

predict electroosmotic velocity.

 

 

 

 

 

 

Viscosity
(Ns/m‘)
2.0xio’3 r 90
Exponential Curve Fit
2nd Order Curve Fit
El Viscosity of Water
0 Relative Permittivity (Wyman (1930))
- 1.5x10'3

    

 

1.0xio’3

Relative Permittivity, e

0.5x10'3

 

 

 

 

20 30 40 50 60 70 80

Temperature (°C)

Figure 4—8. Plot of permittivity and viscosity of water vs. temperature (Wyman et.al,
1930. Handbook of Chemistry and Physics, 85‘h Ed.)

Joule heating is an integral part of electroosmosis as it is a by-product of ﬂuid
transport by an electric ﬁeld. Factors that contribute to the signiﬁcance of Joule heating
include duration and magnitude of applied electric ﬁeld. concentration and conductivity
of electrolyte. As an electric ﬁeld is applied for electroosmosis. a subsequent rise in
temperature is observed. The power dissipated within the ﬂuid due to the electric ﬁeld

is governed by the following equation.

98

P 2 IV 4-24

where P is the power in watts. I is the current and V. the applied voltage. A more
detailed calculation of Joule heating is provided in Grushka et. al.(1989). The
temperature rise within the channel is due to the inability of the setup to dissipate the
amount of heat generated. For electroosmosis within a microchannel at low current and
voltage, the heat is dissipated through conduction and convective currents outside the
channel. At a higher applied voltage. the heat generated is not dissipated at a high
enough rate and results in a temperature increase of the ﬂuid within the microchannel.
The increase in temperature is known to cause an increased amount of dispersion and
results in band broadening in analyte separation analyses.

Another phenomenon that could occur during electroosmosis is electrophoresis.
Electrophoresis is deﬁned as movement of a charged surface or particle relative to a
ﬂuid (Probstein. 1994). When using the PIV technique. electrophoresis adds complexity
to the technique as the electrophoretic velocity contribution of the particles need to be
taken into account (i.e. measured particle velocity is due both to the ﬂuid velocity and

electrophoretic response of the particle). Figure 4-9 illustrates this.

Injected sample Buffer

At ’7/////////./ﬂ’//////lW/Mﬂ/M//////////////////////A
- e
0. : . .
ﬂ : c e
0 0

    

7////////////////. WWW/”MW

    

WWW!

       

I)
A

WWWﬂW/l/Wz
I
' l

Il|l l||

High Voltage High Voltage

 

 

 

 

 

 

 

 

Figure 4-9. Electrophoresis

99

For example, imagine a slug of ﬂuid with three different particles (each with a different
surface charge and illustrated as different colors) is injected into a microchannel. Each
particle has a different velocity as the charge characteristics are different. The yellow
particles have an opposite charge compared to the red and blue particles and thus move
in an opposite direction. The blue particles, on the other hand, have a higher surface
charge and thus possess a higher electrophoretic velocity. To account for this. the

measured velocity (through PIV) needs to be corrected for by the following equation.

Unleasured : Uelectroosnvsis + Uelectrophrresis 4'25

In the case of the MTV technique. a tracer molecule is added to the ﬂuid and the
electroosmotic mobility of the tracers also need to be taken into account. §4.3.3 detail

the results on the electrophoretic mobility of the MTV triplex.

4.3 Results and Discussion for Electroosmotic Flows

4.3. l Debye Length

From equation 4-7. the Debye length can be estimated to be 9.105nm for a
buffer concentration of 1.12 milirnolar (equation 4—26). In contrast, for pure water, the

Debye length is several hundred nanometers thick.

 

/l — _ZeRT _ 2*78.3x8.854x10“202N‘1m‘2*8.314JK“mol"*300K
D F2220 (9.65x104Cmol"‘)2(—2)2(l.12moi/m3) 4%

1,, = 9.105nm

100

The Debye length of ~9mn is easily 4 orders of magnitude smaller than the
characteristic length of 300m for the microchannel used in this study. Thus the
Helmholtz-Smoluchowski equation is applicable.

Other factors that may affect the Debye length are valency. temperature and
permittivity. Recall that temperature plays a role in determining the Debye length (l/ e
decay of potential) as the thermal energy of the counter ions become higher as
temperature increases. This increase in thermal motion increases the distance at which
the 1/e decay is satisﬁed. However, this increase is countered by the lowering in
permittivity as temperature rises. A 2% reduction in Debye length is estimated for a 20
degree change in temperature. This change in Debye length due to the temperature

variance present in this study is considered negligible.

4.3.2 Conductivity of Solutions

For all electroosmotic ﬂow measurements. an aqueous solution of sodium
phosphate (NazHPO4.7HzO) with a concentration of l. 12 milirnolar was used. At this
concentration, the conductivity of the solution was measured to be 152 i 5 uS. The
conductivities were measured with an Oakton Con 110 conductivity meter. Plotted in
Figure 4-10 is the change of conductivity with temperature for various solutions. For
pure water (reverse osmosis. RO). pure water with the M'IV Cyclohexanol mix and pure
water with the MTV Neopenthanol mix. the measured conductivities are low ranging
from 1-3 uS across a temperature change of 50 degrees. The rates of change of the
three curves are also comparable. For the aqueous solution of sodium phosphate with
the MTV Neopenthanol mix. the rate of change of conductivity is also comparable but
the conductivity values are much higher. The values of conductivity are used to
determine the rate of heat generation in the electroosmotic process. It was determined
that the rate of change of conductivity with temperature is consistent with the increase

in the measured current.

101

 

 

 

 

 

 

 

 

 

250 r -
200 > 3
150 .
’5‘ 2
E
.9
3):; 50 .
E 1
a o -
‘3’ / 0 MTV Neopenthanol with 1.12 miliMolar Sodium
: -50 . Phosphate Pentahydrate (Na HPO .7H 0)
o 1 2 4 2
O y = +3.56x +739 0
v MTV Cyclohe1xano|
-100 ~ y = +0.0426x +0627
[1 MTV Neopenthanol
_150 . y = +0.0352x +0918
0 no Water 1 '1
y = +0.0303x +0.353
-200 -

 

 

O 20 4O 60

Temperature (°C)

Figure 4— 10. Change of conductivity of various solutions with temperature

4.3.3 Electrophoretic Mobility of MTV Triplex Solution

As mentioned in § 4.2.6, the MTV triplex may exhibit electrophoretic mobility.
The term electrophoretic mobility applies to the movement of the tracer molecules
relative to the electrolyte when under the inﬂuence of an electric ﬁeld. This has the
detrimental effect of causing the measured velocity to be a combination of the tracer
and solvent velocity and not solely that of the solvent. To investigate this. the
electrophoretic velocity of the MTV triplex was measured.

A capillary electrophoresis experiment was setup with a buffer concentration of
10 milimolar at a pH of 7. Figure 4—11 illustrates a typical capillary electrophoresis

setup.

102

High Voltage

. II L
r
I Electroosmotic
——-'>ﬂow direction

 

 

    

capillary Laser
Buffer Sample detector

Reservoir injected

Figure 4-11. Typical Capillary Electrophoresis Experimental Setup

A sample of the MTV triplex is injected into the capillary initially and the elution time is
tracked. The capillary used had a length of 34.1cm and the high voltage source was set
at 15,000 V which is equivalent to 439.88 V/cm. For the given capillary length and

applied voltage, the results are shown in Table 4-1.

 

 

 

 

 

 

l Neopenthanol MTV - Detected at 212 nm - No Dilution
Retention Time Retention Apparent

(min) Time (s) Mobility(cm2N/s)
Run 1 2.096 125.76 4.700E-04
Run 2 2.014 120.84 4.891 E-04
Run 3 2.116 126.96 4.656E-04
Average 4.7E-04

StDev 1E-05

 

 

 

 

Table 4-1. Elution time for MTV Triplex (Neopenthanol)

The apparent mobility of the M'IV triplex is on average 4.7 x 10-4 cm2/(V.s). To
determine the measurement accuracy of the technique, the elution time of mesityl oxide
is measured. Mesityl oxide is a neutral marker that is regularly used as a reference
neutral marker to determine electroosmotic mobility. The results are shown in Table

4-2.

103

 

 

 

 

 

 

Mesityl Oxide (Neutral Tracer Molecule) - Detected at 195
nm - 1 uL r1 mL 01 Butter
Retention Time Retention aren
(min) Time (s) Mobility(cm2N/s)
Run 1 1.951 117.06 5.049E04
Run 2 1.915 114.9 5.144E-04
|Run 3 1.949 116.94 5.054E-04
Average 5.08E-04
StDev 5E-06

 

 

 

 

Table 4-2. Elution time for Mesityl Oxide (neutral marker)

Note that the averaged electroosmotic mobility for mesityl oxide is larger than that for
the MTV triplex which would indicate an apparent negative mobility. To investigate the
validity of the results. the elution time for a standard MTV triplex with cyclohexanol was
also measured. The electroosmotic mobility of this mixture should be of the same sign
since both triplex have alcohol groups that should display similar pKa values. The

results for the MTV triplex with cyclohexanol are shown in Table 4-3.

 

 

 

 

 

 

Cyclohexanol + MTV - Detected at 195 nm - Diluted 1:10
in Butler
Retention Time Retention Apparent
(min) Time (s) Mobility(cm2N/s)
Run 1 1.864 111.84 5.28604
Run 2 1.877 112.62 5.25E-04
Run 3 1.861 111.66 5.29E04
I Average 5.28E-04
StDev 2E—06

 

 

 

 

 

Table 4-3. Elution time for MTV Triplex (cyclohexanol)

Contrary to what was expected. the elution time for the MTV triplex with cyclohexanol
indicated a positive electroosmotic mobility. A last experiment was performed where all
three solutions were mixed together to investigate if three separate peaks could be

resolved. The capillary electrophoresis technique could not resolve three separate peaks

104

although the peak when all three chemicals were tested together appeared wider. This is

shown in Figure 4- 12.

 

 
  
 
    

 

0—-»—0Mesiiy10)dde
V -—~v NeopenthanolMTV
El ----- U CyclohexanolMTV
O——0 Alladremicals

20

 

 

Relative Absorbance

 

 

 

 

1.8 2.0
Elution Time (minutes)

Figure 4-12. Detection peaks for the three chemicals separately tested and combined.

The fact that when all three chemicals were tested together that only a single
peak was detected illustrates that the discrepancies from the individual testing are
caused by errors in the measurement and the MTV triplex is essentially neutral with no
electroosmotic mobility. The wider peak however allows the investigation of the

measurement resolution. The resolution is deﬁned as

Rs : At /(0.5 * (FWHMl + FWHM2)) 4-27

where At is the time that separates two peaks and FWHM signiﬁes the width of each
peak (in time scale) at half maximum. It is commonly accepted that the resolution needs
to be more than 1 in order for a peak to be resolved. Figure 4-13 illustrates a basic

Gaussian curve displaced 0.45‘FWHM to each side and superposed together.

105

 

1.0 ~ -

f v v v v

 

— Averaged superposition
of all three curves
— Averaged superposition
of the two displaced l
curves

1 —— Baseline displaced 1.5
(0.45 FWHM) to the right
0.6 - — Baseline displaced 1.5
(0.45 FWHM) to the left

Y=exp(-((x-10)/2)2

  
  
   
   

 

 

 

0.2

 

 

 

 

5 10 15 20 25

Figure 4-13. Plot of superposition of peaks

The superposed curve displays a noticeable dip in the center and is beginning to show
separation between the two curves. When all three curves (basic and displaced curves)
were superposed. a ﬂatter peak is observed. The ﬂatter peak has similar likeness to the
peak observed in Figure 4- 12 when all three chemicals were simultaneously measured.
It can be concluded that although no peak separation is observed. an uncertainty due
to the ﬂatter peak of the combined measurement is present. This uncertainty is
approximately 0.5“ FWHM and in the case of the peak width of mesityl oxide in Figure
4-12, this corresponds to 1.38 seconds. Thus the electrophoretic mobility of the MTV
triplex is 0 i 1.4135 " 10-5 chWs) The uncertainties in determining the mobility is at
least an order of magnitude better than the electrophoretic mobility of rhodarnine B.
ﬂuorescein and other dyes. To put the uncertainty in determining the electrophoretic
mobility in perspective. for a 200V/ cm (typical for the experiments in this study)

potential gradient. a velocity uncertainty of 28um/s is present.

106

4.3.4 Experimental Results for Time Evolution of Electroosmotic Velocity
with Joule Heating

Simultaneous velocity and temperature measurements were performed for
different electric potential along the microchannel using the MI‘V&T technique. The
velocity information obtained is useful in determining the evolution of electroosmotic
velocity in time as Joule heating becomes more of an issue. The temperature
information on the other hand. is used in analyzing the degree of Joule heating involved
and decoupling the effects of temperature on the determination of electroosmotic
velocity. The experiment was performed on three different surfaces; uncoated quartz.
OTS-coated quartz and HEMA-coated quartz microchannels and the electric potential
was varied from 560V-1963V (74.7V/cm - 234.9/cm) in increments of ~200V. Figure
4-14 illustrates the undelayed and delayed images for electroosmotic ﬂow within
uncoated quartz nricrochannels. Similar image pairs were also obtained for the other
coated microchannels and are not shown here.

In Figure 4-14. the undelayed images are all arranged on the left side while the
delayed images (5ms delay) are to the right. The images are averaged over 25
instantaneous images. The dashed line in each delayed image signiﬁes the location of
the undelayed tagged ﬂuid before any displacement has occurred. As the applied
potential increases. the separation between the tagged ﬂuid and this dashed line
increases denoting a higher electroosmotic velocity as potential increases.

Recall from § 4.3.1 that the Debye length is short (~9nm) relative to the
characteristic height (300um) of the microchannel. With reference to Figure 4-3. the
velocity proﬁle measured with the MTV technique will only reveal the velocity proﬁle
within the “neutral bulk ﬂow" region which is uniform in nature. Inspection of the data
set however. indicated a non-equilibrium starting condition for each experiment and the

electroosmotic velocity proﬁles were contaminated by a pressure gradient.

107

   

74.7 V/ cm Delayed Image (5ms delay)
Undelayed Image

 

127.9 V/cm Delayed image (5ms delay)
Undela ed lrna e

 

181.6 V /cm Delayed Image (5ms delay)
Delayed Image

   

234.9 V/cm Delayed Image (5ms delay)
Undelayed Image

Figure 4- 14. Image pairs at various potential gradients (74.7-234.9V/cm)

108

This is due to the heights of the two reservoirs in the experimental setup not
being at equilibrium before the start of the experiment. This is illustrated in Figure
4-15. The pressure gradient was acting against the direction of ﬂow for electroosmosis
and had to be taken into consideration to accurately account for the velocity
component. Note that this set of conditions were only apparent for the initial uncoated
quartz microchannel dataset. More care was taken with subsequent results to avoid this
pressure gradient contribution.

An example image pair of the presence of a pressure gradient is shown in Figure
4—15. The undelayed image.(a), in Figure 4—15 is an average of 25 images while the

delayed image ((b). 5ms later) is an instantaneous realization.

(a) Undelayed Image

 

 

 

 

 

 

 

 

 

 

1963V (234.9 V/cm)
1 00 I
A I
g I
Z
a I
“3 Vel i
O O
3 ix: Temperature
.72
g I
a) I H Velocity (mm/s)
—— 2nd Order Fit
-100 I e—e Temperature (°C)
—- x=35.8
I
o 2‘ 4 6
Temperature 30 3A4 38 42
(°C)
I .
(b) Delayed Image Ve OCItY(mm/S)
1963V (267 V/cm) (C)

Figure 4— 15. Typical electroosmotic ﬂow and temperature proﬁles showing
contamination of pressure gradient

109

Cross correlation of these images produced the red data points in (c). From
Chapter 3. the velocity proﬁle for pressure driven ﬂows is necessarily a parabolic. Thus
a 2nd order curve (green curve, symmetric) is ﬁtted to the proﬁle and the curve’s
intersection with the channel walls is taken to be the actual electroosmotic velocity
(dashed line). For this case. an electroosmotic velocity of 2mm/s and an average
temperature of 358°C is obtained. Note that the temperature proﬁle is uniform along
the height of the microchannel. This procedure was applied to the whole data set to
correct for the added pressure gradient. The temperature results, as shown in (c) of
Figure 4-15. are not affected because the correlation program tracks the correct region
of ﬂuid for calculation of temperature. The correlation program calculates the velocity
(red data points) and simultaneously obtains the lifetime of the tagged ﬂuid to give
temperature information. In this case where pressure gradient contribution is present,
post-processing of the data is needed to extract the electroosmotic velocity.

Figure 4-16 illustrates the electroosmotic velocity at diﬁerent applied electric

potentials and a non-linear increase in velocity is observed.

 

 

 

 

 

 

 

 

2.5 ~ - - - . - - - . 0
Linear Fit to 1st Data Point
2nd Order Fit ‘

1,7 2 0 i 0 Velocity Data Points extracted at ‘
E ' . 4OSeconds into the experiment .
E.
g .
‘2’ 1.5 >
a) ’ .
> I o 1
.9 4
8 l
E 1.0 ’ i
(D ' t
o
9 l
‘33, l
a 0.5 t 1

' l

’ l

0 - - A - A A g A A A A A A A A A A - A
O 500 1 000 1 500 2000

Applied Potential (V, Volts)
Figure 4— 16. Non-linear increase in velocity at different electric potentials

110

These data points were taken 40 seconds after the electric potential was turned on.
Recall from the Helrnholtz-Smoluchowski equation (4—18) that the electroosmotic
velocity is linearly dependent on the applied electric potential with all else being
constant. This is shown by the black curve ﬁtted to the ﬁrst data point. A large
discrepancy between the measured and calculated electroosmotic velocity is observed.
When the electroosmotic velocity was plotted at the same temperature. the data points

collapsed on a straight line as shown in Figure 4-17.

 

 

 

 

 

 

 

 

 

 

 

2.5 - - -
v Temperature = 28°C .
Linear Fit
2_o » 0 Temperature = 31°C .
Linear Fit j
,5 0 Temperature = 35°C
E 1.5 ’ Linear Fit
3
2‘
.5 ‘
2 1.0 > .
m t
> 1
0.5 ' .
0 _ A L .
0 500 1000 1500 2000

Applied Potential (V, Volts)

Figure 4-17. Electroosmotic velocity at different temperatures for uncoated quartz
microchannels.
The non-linear increase in velocity is clearly caused by temperature affecting the other
variables (viscosity. u and relative permittivity. e.) in the equation. The different curves
illustrate that the same linear dependence is observed at different ﬂuid temperatures
but with a slope that is temperature dependent. As the temperature of the ﬂuid
increases. the slope of the straight line increases due to the combined change of
viscosity and permittivity with temperature. Similar experiments were also performed

with microchannels coated with OTS and HEMA and the corresponding plot of

111

electroosmotic velocity against the applied electric potential are shown in Figure 4—18

and Figure 4—19.

 

 

 

 

 

 

 

 

 

 

2.5
0 Temperature = 34°C
Linear Fit
2_0 0 Temperature = 30°C 0
Linear Fit
A v Temperature = 26°C
3 Linear Fit
2 1.5 .
g /
g 1 0
a /
0.5 1
0 A
0 500 1000 1500 2000

Applied Voltage (V)

Figure 4-18. Electroosmotic velocity corrected at different temperatures for OTS coated

 

 

 

 

 

 

 

 

 

microchannels
2.5
0 Temperature = 31°C
Linear Fit
2.0 0 Temperature = 29°C
Linear Fit
’g v Temperature = 27°C
E 1 5 Linear Fit
E, .
.é‘
o .
g 1.0 /
> /
0.5
0
0 500 1000 1500 2000

Applied Voltage (V)

Figure 4-19. Electroosmotic velocity corrected at different temperatures for HEMA
coated microchannels

112

The slopes for all three plots are different due to the differences in zeta potential.
This will be discussed in further detail in the next section. Consequently. correct
electroosmotic velocity measurements cannot be made without local temperature
information or some temperature control mechanism to prevent Joule heating from
being a problem. The MTV&T technique is advantageous in this respect to sort out the
rise in temperature and its effect on increasing the electroosmotic velocity.

As the electroosmotic ﬂow continues. the temperature of the ﬂuid will rise and
causes a rise in velocity due to a change in viscosity and permittivity of the ﬂuid. The
initial data set with no correction and the subsequent corrected data are shown in
Figure 4-20. Every velocity proﬁle at different times with no pressure correction as
shown in Figure 4—15 (red data points) is averaged and is represented by a single data
point (in pink) in Figure 4-20.

Temperature
(°C)

 

      
      
 

 

 

 

 

 

 

:Electroosmotic
:Velocity
42 2 ' \
E 38
E
2. 1
8 34 »
T)
> Temperature
30 A—A Initial Data
0 0—0 Electroosmotic Velocity
. (3—5] Temperature (°C)
: —— Linear Fit
26
g 10 20 30
Electric ﬁeld Time (seconds)

is turned on

Figure 4-20. Initial data and corrected data for electroosmotic velocity.

113

Before the electric potential was turned on, the “initial data” set showed a negative
averaged velocity indicating that a pressure gradient is present. As the data points are
corrected, it is illustrated that the initial velocity correctly assumes a zero value. The
sudden increase in velocity thereafter is due to the imposed electric potential. The
velocity is seen to continually rise as Joule heating becomes prevalent.

All the electroosmotic velocity plots at different electric potentials were corrected
for the added pressure gradient and plotted in Figure 4-21. Recall from Figure 4-8 that
the dependence of viscosity and permittivity with temperature is non-linear. However.
over the temperature range investigated in this study. a linear dependence can be
assumed with minimal errors. Thus the velocity plots in Figure 4-21 were all ﬁtted to a
linear curve. Note that at lower applied potentials, the velocity is constant and does not
vary with time. The heat generated at this applied voltage is dissipated and does not
contribute to an increase in temperature of the ﬂuid. As the applied electric potential
increases, the velocity magnitude increases although the plot is seen to appear noisier.
This increase in ﬂuctuations in the velocity proﬁle is mainly caused by the decrease in
signal to noise of the experiments as temperature increases. Recall from Figure 2-24
that the lifetime decreases as the temperature rises.

The plot of temperature with time is shown in Figure 4-22. At an applied
potential gradient of 74.67V/cm and 101.2V/cm. the increase of temperature with time
is minimal resulting in a non-varying velocity plot in Figure 4-21. As the electric
potential increases. the heating rate increases as well contributing to a higher
temperature rise. The data set for different applied electric potentials is shown in Table
4-4. The ﬁrst set of data illustrated in the table is the initial data where 110 is the
electroosmotic velocity right after the application of the electric potential and u; is the
ﬁnal velocity measured before the potential was turned off. These values for U0 and u;
were obtained from the linear ﬁt to the curves in Figure 4-21. The corresponding

temperature were obtained from Figure 4—22 and listed as To and T; in the table.

114

 

 

 

o—e 74.7V/cm
B—E] 101.2V/cm
v--—v 128.0V/cm
e——o 154.8V/cm
[3——€l 181 .6V/cm
e———e 208.1V/cm
+—+ 234.8V/cm
o—e 261.7V/cm

 

Velocity (mm/s)

 

 

 

 

 

 

Time (seconds)

Figure 4-21. Plot of velocity increase with time for uncoated microchannels

 

 

4o .
o— —e 74.7V/cm .f'
e - —o 101.2V/cm o.
v— -v 128.0V/cm ’J'
I3— —£l 154.8V/cm

35 * El— —El 181.6V/cm

A—A 208.1V/cm
+— -+ 234.8V/cm

 

O — -0 261.7V/cm
-

 

Temperature (°C)

 

 

  
  
  
 
 
   

 

 

 

 

20

Time (seconds)

30

Figure 4—22. Plot of temperature increase with time for uncoated microchannels

115

 

Given the temperature rise during a particular experiment (for a given electric
potential), the theoretical change in velocity was computed from the combined change of
viscosity. u. and relative permittivity. 8r with temperature (refer to Figure 4-8 for
dependence of viscosity and relative permittivity on temperature). The ratio, uo/ur. is a
measure of the increase of electroosmotic velocity due to heating. Note that without any
change in temperature, this ratio would be unity.

The initial data set included an opposing pressure contribution and thus yielded
a lower ratio of uo/ur. When compared against the theoretical change in velocity. a
higher discrepancy was observed. When a symmetric parabolic proﬁle was ﬁtted to
account for the pressure gradient contribution. the experimental data matched well
with theory and were within i 3.5%. If velocity and temperature were not
simultaneously measured. the determination of the electroosmotic velocity based only
on the Helmholtz-Smoluchowski equation (4- 18) at room temperature would be 24%

lower. This is a signiﬁcant underestimation of the velocity component.

116

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4.3.5 Temperature Variation along Height (Z-axis) of Microchannel

Researchers (Ross et. al.. 2001) have measured a large temperature gradient
across the width (z-axis) of the microchannel. Ross et. al. measured a temperature
gradient of 3°C in quartz capillaries and as large as 10°C in a prismatic acrylic
microchannel using a ﬂuorescent thermography method. These microchannels were
approximately 50pm in size. Although these two microchannels were similar in size and
were subjected to the same level of heating, a surprisingly large temperature gradient is
present in the prismatic microcharmel. Beam steering effects due to the high amount of
curvature could be the cause of these discrepancies (The author did not detail the
inaccuracies caused by the presence of curvature). The MIT technique was utilized in
this study to measure the local temperature within a 300mm microchannel and no
signiﬁcant temperature gradient was observed along the height of the microchannel (z—
axis, refer to Figure 3-2). The plot of temperature along the height of the microchannel

with time is shown in Figure 4—23.

I- —I t: 803
e—0 t: 603
v— v t= 408
D- -D t=2OS
.— a t: Os

4O

30

Temperature (°C)

20

 

-150 -100 -50 0 50 100 150
Height of Microchannel (Z-axis, pm)

Figure 4—23. Time evolution of temperature proﬁles within the microchannel at
18 1 .6V/ cm

118

Note that the tagging laser and the viewing camera are perpendicular to each other and
no beam steering effects are present due to the use of a rectangular channel. The
temperature proﬁle in the ﬁgure has an average RMS of 021°C. The error analysis is

provided in Appendix K.

4.3.6 Computational Solution of Electroosmotic Flow in the Microchannel

The experimental setup for electroosmotic ﬂow was illustrated in Figure 2-13.
Optical access issues constraint the velocity and temperature measurements with the
MTV&T technique to the central part of the microchannel (x-axis, i 15mm). This
constraint is caused by obstruction from the reservoirs and the physical size of the
objective lens.

It is hypothesized that at the inlet of the microchannel, the temperature would
be lower due to the intake of ﬂuid from the reservoir with an ambient temperature.
From § 4.3.4, the experimental results showed that the electroosmotic velocity is
dependent on temperature. If the ﬂuid at the inlet of the microchannel has a lower
temperature, the resultant electroosmotic velocity at the inlet is necessarily lower. To
compensate for the higher electroosmotic velocity in the center of the microchannel
where the temperature should be higher (continuity). a pressure gradient should
develop. To check this hypothesis, the heat diffusion characteristics of electroosmotic
ﬂow within a microchannel were computed numerically with FLUENT. The thermal
development length and the temperature proﬁle along the streamwise direction (x-axis)
are of interest to better understand the ﬂow characteristics of electroosmotic ﬂow. Also,
as mentioned in the previous section. some researchers have reported a high
temperature gradient along the height of the microchannel (z-axis). The numerical

solution would help in understanding if a temperature gradient exists.

119

The geometry of the microchannel is replicated in a grid generation package
(GAMBIT) and solved numerically in a CFD software (FLUENT) with the boundary
conditions of our experiments. The schematic of the microcharmel reproduced in
GAMBIT is shown in Figure 4—24. The middle of the channel is outlined in red and
denotes the ﬂuid within the microchannel. The volumes above and below the ﬂuid
depict the upper and lower walls of the microchannel while the inlet is deﬁned at the

positive end of the x-axis.

 

Figure 4-24. Schematic of microchannel in GAMBIT

The side walls (1mm) are not depicted in the schematic as GAMBIT allows for boundary
conditions of wall thickness and thus the physical geometry does not have to be
reproduced. This wall thickness boundary condition is applied on all side walls. Figure
4-25 illustrates the wall thickness boundary condition superposed on the end-view of
the microchannel. In GAMBIT. the type of boundary conditions is deﬁned for the inlet,
outlet and walls of the microchannel. A “VELOCITYJNLET” boundary condition was

speciﬁed at the inlet while an “OUTFLOW‘ condition was speciﬁed for the outlet.

120

Outﬂow boundary conditions are used when the ﬂow velocity and pressure are not

known prior to solution of the problem. (FLUENT Manual)

ql mrlz

300nm

 

Figure 4-25. Schematic of end-view of microchannel with superposed wall thickness

The mesh needed to compute the solution was created in GAMBIT. For the ﬂuid.
a ﬁne grid was employed along the 300m height (z-axis) of the microchannel to resolve
the temperature gradients that may exist. An “successive ratio" condition was set for
the grid size where a higher density of grids are present near the interface of the ﬂuid
and the quartz walls. A minimum grid interval of 7.5m was used. For the walls of the
microchannel. a coarse grid interval was used to minimize computation time while
maintaining grid independence of the solution.

The mesh from GAMBIT was imported into FLUENT to compute the solution.
Within FLUENT. the properties of the ﬂuid and quartz. and the speciﬁc boundary

conditions were assigned to each face or volume in the geometry. The properties of

121

water were used for the ﬂuid and is provided from the built-in database within FLUENT.

The properties of quartz are detailed in Table 4-5.

 

Progrties
Density, p

Specific Heat, C ,,

Thermal conductivity, k

  

770J/(kg.K)
1.3W/ m.

    

 

 

Table 4-5. Properties of Quartz

The boundary conditions imposed on the geometry are illustrated in Figure
4—26. The heat transfer coefﬁcient. havg. used here is a typical value used for free
convection in external ﬂows (Incropera. 1996). This boundary condition was applied to
all external surfaces except the inlet and outlet faces of the microchannel which are
exposed to the ﬂuid in the reservoir. The walls at these locations were subjected to a
constant temperature of 300K.

One of the difﬁculties encountered while specifying the boundary conditions was

that FLUENT did not have provisions for computations of electroosmotic ﬂows.

Patm=101.325kpa

 

x avg = 1T5W/m2K .. = T=300K
.222..._. \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
3...... \\

Figure 4—26. Boundary conditions applied to the geometry

122

This resulted in an ad-hoc modiﬁcation of the inlet velocity. u... and heating rate. Q.
based on the experimental results to simulate the effects of electroosmotic ﬂows.

The initial velocity, u... was set at 1.75mm/s, similar to the initial electroosmotic
velocity measured within the microchannel at an applied electric potential of
261.7V/cm (refer to Figure 4-21). The experimental data from this particular applied
electric potential was used as it represents the highest heating rate measured by the
experiments. Any temperature gradient that may develop within the microchannel
should manifest itself under these conditions. The rate of increase of velocity measured
through the experiments was also incorporated into the increase of the inlet velocity.
The user-deﬁned function (UDF) used to modify this property is detailed in Appendix P.
To create a uniform velocity proﬁle within the microchannel. a zero shear stress
condition was set for all internal walls.

During electroosmosis, a constant voltage was applied along the length of the
microchannel. From measurements of the current required to maintain this voltage. a

linear increase in current was observed (Figure 4-27).

 

T v V T

 

  

 

 

 

 

 

 

 

Initial current ##de
m”
0.002 .
2
I," 0.001 »
c
2
8 e ----- e 760V
(3 ----- El 960V .
0 ~ v—-—v 1161V .
1" H" + G—-£'l 1361V
r3 — —— E] 1560V
Electric Potential Applied —- ”a 176W
+—- -—+ 1962V
O 10 20 30 4O 50 60

Time (seconds)
Figure 4—27. Plot of current rise with time at different applied voltage.

123

The rate of increase is consistent with the change of conductivity with temperature as
shown in Figure 4-10. This indicates that the rise in current is solely caused by the
change in conductivity with temperature. The slope of the current measurements at
261.7V/cm was used to obtain the rate of increase of the heating rate. The initial
heating rate. 90, is computed in Equation 4-28 from the initial measured current (red
circle in Figure 4-27. The UDF for speciﬁcation of this property is provided in Appendix

P.

P = IV = 1.7695x10'3A ‘1962V = 3.472 watts

4-28
A = (5x10'3 x 300x10‘6 x 63.5x10‘3lrn3 = 9.5x10'8m3
O = ﬂea—3 = 3.6451x107 watts/m3
9.5x10’ m

This heating rate, however, caused a higher rise in temperature in the numerical
simulations compared to the temperature measurements performed with WT (Figure
4-22). An approximate factor of 3 lower heating rate was observed in the experiments.
Notice that in Equation 4-28 that the ﬂuid volume used represents only the internal
volume of the microchannel. Since the electrodes were not placed directly at the inlet
and outlet of the microchannel, the actual volume is difﬁcult to measure. Thus a
heating rate that resulted in a temperature increase consistent to the MIT
measurements was selected for the computation instead.

For the aforementioned boundary conditions. Figure 4-28 illustrates the
temperature contours of the ﬂuid. The ﬁgure is scaled independently on each axis and
is not shown in correct proportions. The width (Y-axis) is 5mm, the height (Z-axis) is
300m and the length (X-axis) is 60mm. From the computation. at the inlet of the
microchannel, the ﬂuid has a temperature of 300K which steadily increases as it moves
along the channel culminating in a region of high temperature in the center. The outlet

of the microchannel sees a reduction in temperature as it is cooled by the other end of

124

the reservoir. A plot of the temperature proﬁles along the X-axis in the center of the

channel is shown in Figure 4-29 at different times during electroosmosis.

 

Temperature: 301 303 305 307 309 311 313

Figure 4-28. Temperature contour of the ﬂuid at 30 seconds after application of the

 

 

 

 

 

 

 

 

 

 

potential
315 l
| N

l I
: g i
.2 310
g i . . i
7; j I l 1
‘5 I l
E f | l
0
g 305 I : Vii

I
l9 ' 3—9 10 seconds '

— — x=0.015
| — — x=-0.015 l
| o— —o 30 seconds I
300 ‘ '
0.030 0.015 0 -0.015 -0.030
Inlet Outlet
X-axis (m)

Figure 4-29. Temperature proﬁle along X—axis at different times during electroosmosis.

Comparison of the temperature evolution for an electric potential gradient of
261.7V/cm in Figure 4-22 to the temperature proﬁle in Figure 4-29 shows that the
peak velocity at 30 seconds do not match. The peak velocity from the numerical
simulation yielded a value of 413°C while the measured temperature was 36.7°C. It
should be noted that the heating rate used in the computation was selected to give an
approximate solution since the actual ﬂuid volume affected by heating is not known. A
trial and error and iterative modiﬁcation of the heating rate to match the exact peak
temperature could be done but was not performed as the qualitative results from the
computation were deemed more important.

One key observation from Figure 4-29 is the presence of a temperature gradient
along the length of the microchannel. Since electroosmosis is dependent on
temperature. as detailed in § 4.3.4. each section of the microchannel would essentially
have a different uniform velocity although the volume ﬂow rate would still be constant.
For capillary electrophoresis or other techniques utilizing the measurement of averaged
ﬂow rates to determine zeta potential, signiﬁcant errors could result based purely on the
assumption that the electroosmotic velocity is constant. To accurately measure the zeta
potential in these setups. careful control of Joule heating is needed to minimize the
differences in temperature gradient or an in-situ technique like the one applied in this
study is required.

Another observation from the temperature proﬁles in Figure 4-29 is the thermal
development length. As the temperature gradient along the length of the microchannel
increases. the thermal development length increases accordingly. The vertical lines in
this plot indicate the range of interrogation locations that were physically possible with
the current experimental setup due to space constraints. If the MIT technique was used
to measure the temperature proﬁle within this range, no temperature gradient along the
length of the microchannel would be measured for experimental times of < 30 seconds

at this particular applied electric potential.

126

Temperature proﬁles along the z-axis were also obtained from the computation
to investigate the temperature gradients along the 300m height of the channel. Figure
4-30 illustrates the temperature proﬁle along the z-axis at 30 seconds in time. Within
the ﬂuid (2 = ilSOum). a parabolic temperature proﬁle is observed with a maximum
temperature gradient of only 032°C. For the measurement resolution of the MIT
technique. a 032°C temperature gradient is at the threshold of its measurement limits
and may not be detectable in the measurements. This is in contrast to the large

measured gradients reported by other researchers (Ross et. al.. 2001).

 

 

f I’ v f

— - =-0.00015
AT = 032°C — -— z=0.00015
314 ’ o— —0 Temperature Profile

’ {I at 1962V
’ l

I“

313

312

Temperature (Kelvin, K)

—> C—Fluid ‘

ﬁ—J L—Douartz Wall

l - l -
0 0.0025

 

311'

  

 

 

 

Spatial Location (Z-axis, meter)

Figure 4-30. Temperature gradient along the Z-axis of the microchannel at X. Y = 0

127

4.3.7 Zeta Potential Measurements

The zeta potential of surfaces is usually measured with streaming potential.
electroosmosis or electrophoresis experiments (Hunter (1981), Overbeek (1952).
Erickson. et. al. (2000)). The streaming potential method measures the potential drop
between two ends of the measuring region. This potential drop is caused by the
transport of ions within the double layer due to the ﬂow ﬁeld created with a pressure
gradient. The relationship between the imposed pressure gradient and the resultant
potential measured is used to calculate the zeta potential. In electroosmosis, a potential
gradient is applied along the length of the channel and the resultant ﬂow rate is
measured. The ﬂow rate can be used to indirectly calculate zeta potential.
Electrophoresis techniques are similar in approach.

The need to fully characterize the geometric size of the microchannel. the
conductivity characteristics of the ﬂuid and possible surface conduction effects and
hydrodynamic considerations, however, complicates the use of these bulk
measurement techniques. Surface conduction effects. although second order in nature.
can signiﬁcantly affect zeta potential measurements for capillary sizes on the order of
the Debye length. All the measurement techniques described are useful but the
measurements are averaged along the length of the measurement region and does not
provide local zeta potential measurements. Although averaged measurements of zeta
potential are important in obtaining general properties of materials. local
measurements of zeta potential is critical for analysis of microchannels or labs-on-a-
chip devices with non-uniform coatings. The different coatings can be utilized to induce
better mixing characteristics within microchannels. (Stroock. et. al.. 2000; Biddiss. et.
al., 2004))

The molecular tagging velocimetry technique applied in this study is unique in
that it provides a measure of the local electroosmotic velocity. When the contamination

of the velocity proﬁle (if any) is corrected for any pressure driven ﬂow contribution and

128

temperature changes, the Helmholtz-Smoluchowski equation can be used to calculate
the zeta potential. The zeta potentials for uncoated. OTS-coated and HEMA-coated
quartz microcharmels were measured and are shown in Figure 4-31. The zeta potential
of HEMA was the lowest at -65.3mV while that of OTS is highest at -93.6mV and the
value for an uncoated quartz microchannel is in between at -84.5mV. These values
were averaged over multiple electric potentials.

Some researchers have documented a zeta potential in the -l25 mV range
(Ohshima et. al., 1998) for quartz although it should be kept in mind that the value of
the zeta potential is dependent upon the concentration of the electrolyte and the non-
uniforrnity of the surface charge may cause differing results. Thus it is usually difficult
to match the exact zeta potential for different experiments. even for the same type of
surface. In microchannels with non-uniform coatings (to induce additional mixing), the
use of a predetermined zeta potential for a particular coating may wrongly predict the
local zeta potential. This is an additional reason why in-situ measurements are
advantageous. The measurements shown in Figure 4-31 were obtained with a 1.12mM
buffer solution. Recall that the higher the concentration, the lower the zeta potential as
more ions are available within the Stern layer to neutralize the surface charge. The plot
illustrates velocity vs. volts at a given temperature (28°C).

Since the MTV&T measurement technique measures velocity and temperature
simultaneously, it is now possible to prepare plots similar to Figure 4-31 at different
temperatures to yield zeta potential information as a function of temperature. An
example of this capability is shown in Figure 4-34. The red dashed line plotted in the
ﬁgure illustrates the zeta potential of HEMA at 28°C while the other data points
illustrate the measured zeta potential at different applied voltages along the length of
the channel. A buffer maintains the pH levels within the microchannel and this slight
variation in zeta potential may be due to the inadequacy of the buffer to maintain a
stable pH as temperature rises. Nevertheless. this illustrated a measurement technique

for obtaining zeta potential variance with temperature for different surfaces.

129

 

 

 

 

 

 

 

 

2.5
’5? 20 o OTS
5 a Uncoated Quartz
E 15 V HEMA
E
'6 1.0
2
a)
> 0.5

0

0 100 200

of OTS = -93.6mV

of Uncoated Quartz = -84.5mV

Zeta Potential (Q)

of HEMA = -65.3mV

 

0 100 200 300
Applied Potential Per Unit Length (V/cm)
Figure 4-31. Zeta potential calculation from velocity vs. voltage plot at 28°C

 

 

 

 

 

200
— §=-94.4mV

A 150
>
E
E
g 100 o a .. - -
8 V v v 0 O
Q
(U
E

50

0

24 26 28 30 32 34

Temperature (°C)

Figure 4—32. Plot of zeta potential of OTS vs. Temperature

130

 

 

 

 

 

 

 

 

200 - - ~
. — l;=-84.6mV]
A 150 » .
> i
g . .
a I
8 100 » i
‘6 r r - - - - - - r ..
a j - - - - - - - - -
g i
lg], .
50 . .
l
O a A - - A
26 28 30 32 34 36

Temperature (°C)

Figure 4-33. Plot of zeta potential of uncoated quartz vs. Temperature.

 

 

 

 

 

 

 

200 ~ - ~ - - - - - - - ~
—r;=es.3va
A 150» f f l
> l
g l
.72 .
g 100»
‘5 i
a. l
E ’ A A A A n
:31 ' U .. - - V
50» l
O - - A a - A - A A A - A L A A
26 28 30 32 34

Temperature (°C)

Figure 4-34. Plot of zeta potential of HEMA vs. Temperature

131

4.3.8 Contribution and Conclusions

This study has demonstrated that simultaneous measurements of
electroosmotic velocity and temperature of the ﬂuid is crucial in understanding the
physics involved in such a ﬂow. Without temperature compensation. the measured
electroosmotic velocity can deviate signiﬁcantly from the Helmholtz-Smoluchowski
equation. When the in-situ temperature of the ﬂuid is measured through experiments.
the change of relative permittivity and viscosity with temperature can be taken into
account to reveal the actual increase in electroosmotic velocity with increasing
potential.

From the computational solution, Joule heating was found to cause temperature
gradients along the length of the microcharmel but the layout of the test section did not
allow validation of the results with in-situ measurements of the temperature ﬁeld at the
inlet and outlet of the microchannel. The MIT technique measured temperature proﬁles
along the z—axis and did not yield any temperature gradients but the numerical
simulations showed that a temperature difference of 032°C exists. This small difference
in temperature. however. is at the threshold of the MIT capability. Nevertheless. the
results presented here showed a much lower temperature difference compared to the
measurements performed by Ross et. al.. 2001.

An indirect method for measuring zeta potential is from the measurement of
electroosmotic velocity. The in-situ measurement of zeta potentials of three different
surfaces was presented. For microchannels with a non-uniform surface coating
(possibly to induce improved mixing), this technique allows the determination of the
local zeta potential at multiple locations and not as an averaged value measured along
the whole length of the microchannel. Since the simultaneous velocity and temperature
within the microchannel was measured at different applied potentials and temperature.
the temperature dependence of zeta potential can also be measured. The experiments in

this study. however, were conducted with a buffer solution and this limited the change

132

of zeta potential with temperature. The buffer solution essentially maintains the pH

levels within the test section.

4.3.9 Future Work

The temperature gradient along the length of the microchannel is mainly
concentrated near the inlet and outlet. Due to the way the microchannel was mounted
to the reservoirs and accessibility of the imaging system. only the central region of the
microchannel was accessible to the imaging system. Thus the temperature variations
along the length could not be measured here. To be able to measure these temperature
gradients. the microchannel needs to be mounted differently. These measurements
would provide further validation of the Fluent simulations and would provide a better
understanding of electroosmotic ﬂow in microchannels. Also. with the MTV&T
technique, the velocity at these locations can be measured. Since the simulations
showed that the inlet and outlet of the microchannel is at a lower temperature, the
electroosmotic velocity is correspondingly lower compared to the center of the channel
where a higher ﬂuid temperature exists. From continuity. in order to maintain the ﬂow
rate, a pressure gradient is naturally present at the inlet and outlet. Unfortunately. the
numerical simulations used a uniform inlet velocity. It would thus be of interest to
study the velocity proﬁle at different locations along the microchannel through
experimental measurements and investigate the pressure gradient distribution.

The in-situ techniques of MTV and MIT were utilized to provide simultaneous
velocity and temperature data. The velocity measurements indirectly provide zeta
potential measurements. Without the use of a buffer to control the pH. the zeta
potential can be systematically studied for variation with temperature and

concentration.

133

Appendices

134

Appendix A: Lens Setup for Imaging

The lens setup used for all the imaging in this study is shown in the ﬁgure.
Since a microscope was not utilized. due to space constraints and access limitations. an
objective needs to be arranged in the following manner for use with the intensiﬁed
cameras. The inﬁnity-corrected objective (10X) was connected to the tube lens which
directs the image to the image plane of the CCD. The working distance for the particular
objective used in this study has a working distance of 33.5mm. The distance between
the end of the tube lens and the CCD imaging plane is nominally 170mm. Within the
camera body itself. various optical elements are present which causes the actual

magniﬁcation to vary. The magniﬁcation calibration is provided in Appendix B.

Extension
Tubes

 

 

Tube lens

Inﬁnity-corrected
ohiective

 

I 33.5m
A Plane of focus

Working surface

/

Figure A- 1. Setup of Imaging Lens

135

Appendix B: Effective Magniﬁcation of Cameras

Optical elements in each of the intensiﬁed cameras used in this study caused a
lower magiiﬁcation when used with a 10X objective. This appendix details the

calibration of the two camera.

Xybion ICCD Camera:
An image of a high—resolution target (Max Levy Autograph Inc.) was imaged with the
camera using the 10X objective. Every line division in Figure B-l is 50m. A lmrn

physical length translated to 512 pixels on the CCD.

 

Figure B-l. High resolution target acquired with the Xybion ICCD (10X objective).

To convert this value to an effective magniﬁcation. the following calculation was done.

Width of CCD chip( physical units) = scaling * width in pixels

Width of CCD chip(physical units) = r 756 pixels = 1.47mm (1)

1mm
5 1 2 pixels

136

The camera manual indicates that the physical size of the CCD chip is 8.8mm (width) x
6.6mm (freight). Dividing the actual width with that of equation (1) results in a

magniﬁcation value of

8.8mm
M nyicatio = — = 5.96X
ag n 1.47mm (2)

Dicam Pro Camera:

 

Figure B-2. High resolution target acquired with the Dicam Pro camera (10x objective)

Similarly, .every line division in Figure B—2 is 50m. A 1mm physical length translated to

994 pixels on the CCD.

Width of CCD chip(physioa1 units) = scaling . width in pixels

lrnm (3)
Width CCD ical its = ———- 1280 ls = 1.288
of chip(phys un ) 994 pixels * pixe mm
For a CCD width of 8.52mm, the magniﬁcation is
8.52mm
M aiio = —— = 6.6X
ammo " 1.288mm 14’

137

Appendix C: Intensiﬁer Characteristics of Dicam Pro

An intensiﬁed camera has an added intensiﬁer to the CCD and typically exhibits
a non-linear gain response. This is especially a concern for the MIT technique where
the intensity decay of the image is used to infer temperature information. Thus.
characterization of the intensiﬁer is important. The gain linearity and fast charge
capability of the intensiﬁer are two aspects of the intensiﬁer that were studied. Gain
linearity pertains to the response of the intensiﬁer to a linear increase in incident light
and non-linearity results when a non—linear response is measured. In the double-shot
mode. images are taken in quick succession and the capability of the intensiﬁer to

charge rapidly for the second image is a concern.

Gain Linearity:
To measure gain linearity. the camera was setup to look at an intensity gradient
as shown in Figure 1. An intensity gradient allows a wide dynamic range of intensity

levels to be simultaneously imaged.

 

Figure C—l. Intensity Gradient

To ﬁll the whole dynamic range of the camera, the exposure time was also increased
with the assumption that the exposure time increases linearly with incident light.
Figure 2 illustrates a plot of the linearity of gain. The abscissa is the theoretical

intensity counts at a given exposure time while the ordinate is the measured intensity

138

from the camera. At low intensities. <1500 counts. the response of the camera is
linearly varying with incident light and a noticeable decrease in response in seen at
higher intensity counts. For the experiments performed in this study. all images were
obtained at an intensity level of <1000 to avoid this non-linearity. However. it should be
noted that as long as this non-linearity is characterized. the intensity levels in the

images can always be corrected to measure the right temperature.

 

 

 

 

 

 

 

 

 

4000
v— -v 800us exposure
9— —e 200us exposure
Y=X
3000 .
33
C
3
o
9
B“ 2000
‘6
C
2’.
E
1000 .
0 a r A
0 1000 2000 3000 4000

Theoretical Intensity (Counts)

Figure C-2. Gain Linearity at Gain Setting of 99%.

Fast Charge Capability:

Measuring the fast charge capability of the intensiﬁer requires the use of the
same gradient shown in Figure 1. The exposure time is set so that the gradient covers a
wide range of intensity levels. Figure 3 illustrates the intensity ratios of the ﬁrst and
second images. At 4ms delay and an initial intensity of 1000 counts in the ﬁrst image.

the ratio shows a 1.5% decrease in intensity in the second image while at 8ms. the

139

differences are negligible. This is factored into the measurement accuracy of the MIT

 

 

 

 

 

 

 

 

 

 

technique.

1.1
3
E
'5
c
a)
E
8
__r~_r 0.8
a :71.
E .

0.7 v-—-v 8ms

r3 ----- r3 4ms
0.6
0 1 000 2000 3000 4000

I1

Figure C-3. Intensity ratios in double-shot mode

140

Appendix D: Laser and Camera Synchronization Setup

Xybion ICCD Camera:

 

 

 

 

 

 

 

 

Continuum
Powerlite 9030

 

 

 

 

 

 

 

 

 

 

 

 

To ﬂash To Q-
lamp switch
VD Out
—_> Xybion [CCD Camera
External
Trigger In

 

 

 

 

 

 

i

   

L ILJ L

 

 

 

 

 

 

 

Trigger Trigger AB + CD + Trigger Trigger AB + CD +
In Out In Out
SRS D0535 SRS D0535
Digital Delay Generator #1 Digital Delay Generator #2
Delay Generator #1 Settings Delay Generator #2 Settings

Trigger: External Trigger: External
Trigger Threshold: +2V Trigger Threshold: +2V
Trigger Slope: (+) Trigger Slope: (+)
Trigger Termination: High 2 Trigger Termination: High Z
All output loads: High 2 All output loads: High 2
All output voltages: TI‘L/ Normal All output voltages: 'ITL/ Normal
Delay A: T0+0.022seconds Delay A: 10+0.0225econds
Delay B: A + IOus Delay B: A + lms

Delay C: A + 385us
Delay D: C + lOus

141

Dicam Pro Camera:

 

 

 

 

 

 

 

 

 

Continuum
Powerlite 9030

 

 

 

A
To flash
lamp

To Q-
switch

 

 

 

 

J lj

 

External

Dicam Pro Camera

 

Trigger In

 

L

 

In Out

ENC—555

 

Trigger Trigger AB + CD+

Digital Delay Generator

 

 

Delay Generator Settings

Trigger: Internal

__. _.....

h All output voltages: TTL/Normal
Channel A: 10us width. 0 delay
Channel B: lOus width. 0.13384 secs delay

142

 

Appendix E: Pressure Drop within Microchannel

This section describes the pressure drop within a microchannel and the height
difference in the reservoir for the electroosmotic velocity setup as illustrates in Figure
2.42 to cause a noticeable velocity within the microchannel. Figure 1 illustrates the
electroosmotic ﬂow setup while Equation 1 describes the factors that affect the pressure

drop within the microcharmel.

microchannel

Zl---

 

 

reservoir
Figure 1. Electroosmotic ﬂow setup
I V2 1
P—P=z—z+——+K—V2 (l)
1 2 7( 2 1) fdp 2 L2p

where P1 and P2 are the pressure above the reservoirs respectively (both are exposed to
atmospheric pressure), yis the product of density. p. and gravity. f is the friction factor.
1 is the length of the channel. d is the hydraulic diameter of the channel. V is the
velocity within the channel and K1. is the loss coefﬁcient. Since there are no external

pressure induced forces. the term on the left goes to zero.

1 V2 1
7121 ‘22)=f“P—+KL_PV2
d 2 2 (2)
961 V2 l 2
z -z =——— —+K — V
711 2) Redp 2 L2},

143

 

“21‘22’75'5 ‘2‘ Lap“ (3)
96 1V 1
7121‘ 2): DI: §+KL§ V2

For a rectangular channel with the dimensions 25.4mm X 0.3mm. the friction factor is

deﬁned as 96/ Re (note that for round capillaries. the friction factor is 64/ Re).

96 ‘1.12x10-3N.s/m2 .. 0.05m ' 0.01x10-3m/s +

 

 

 

r121 - 22) = 2
—3
2 . (0.5x10 m)
(4)
kg _3 2
0.4 * 999—? : (0.01x10 m /s)

m N I Nominally this value

M21 — 22) = 0.10752—N— + 3.99x10"8 _ -
m2 m

The ﬁrst term on the right is the dominant term. As an approximation. we only keep the

ﬁrst term.

y(zl - 22) .. 0.1075231”—2

O. 10752N / m2 (5)

22 z 3 2 = 1.097x10‘5m = 0.01097mm @V = 0.01mm/s
999kg /m “ 9.81m/s

 

Z]-

From the analysis above. a head difference of ~11um is all that is needed for a velocity
change of 0.01mm/s. From a constant head adjustment standpoint. 3 11pm head
adjustment is almost impossible to achieve as the ﬂuctuation of the reservoir surface is
easily more than llum. If the electroosmotic velocity that is induced is 2mm/s, the
volume flow rate is estimated to be 2mm/s*5mm*0.3mm = 3mm3/s. If we restrict the
height change at the reservoir to be 0.01097mm, this translates to an area of
3mm3/s/0.01097mm =273.5mm2/s. For a 50mm diameter reservoir. the time for a
0.01097mm change in height at the reservoir is: n(25mm)2/273.5mm2/s=7.2seconds.
By relaxing the criteria. a height change of 50m is probably the best a constant head
reservoir can achieve. This translates to a velocity of 0.05mm/s. The rate of change of

area is then 3mm3/s/0.05485=54.7mm2/s. For a 50mm diameter reservoir. the time we

144

can run the experiment for is increased to n(25mm)2/54.7mm2/s = 36 seconds. If the

velocity is 1mm / s. we can run the test for 72 seconds.

145

Appendix F: Spatial Resolution of Measurements

With a 10X magniﬁcation objective. the Dicam Pro camera has a magniﬁcation
of 6.6x while the Xybion ICCD exhibited a magniﬁcation of 5.96X. The line width
coupled with the total displacement of the tagged molecules between the “undelayed”
and “delayed” images determined the spatial resolution of the measurements. In the
worst case scenario where the image pairs have a signal to noise ratio of 4
(instantaneous images), the correlation software in Labview results in an RMS (95%

conﬁdence) of 0.2 pixel.

Line
width

./

(lisplzir‘vincnt

 

Figure E- l. Superposition of undelayed and delayed images

146

With reference to the largest (87 pixels) and smallest displacements (1 pixels) in this

study, the corresponding spatial resolutions are calculated.
(Spatial RESOIUtionharge = displacement(pixels)* scaling factor

(1)
= 87 * 1.95m =169.7/rm

(Spatial Resolution)smau = displacement(pixels)* scaling factor
(1)
=1 * 1.95pm =1.95,um

This result is applicable to both pressure driven and electroosmotic ﬂows.

147

Appendix G: Velocity Proﬁles within commercial
microchannels

Commercial quartz microchannels (Stama Cells) were initially used in the
experiments. Figure 1(a) below illustrates a cross-sectional view of the microchannel.
The height of the microchannel is 300m. Notice that the internal geometry of the
microchannel does not have square edges which would hinder viewing from the side. A
slight curvature is also present on the exterior. The combination of these anomalies
contributed to a spurious velocity proﬁle at different tilt angles relative to the imaging
system. Within a high aspect ratio rectangular microchannel. the velocity proﬁle should

resemble a parabola. This is exhibited in Figure 1(b).

300m.
152 pixels

 

(c) (d)

Figure 1. Velocity proﬁle within commercial microchannels

148

However. the velocity proﬁle is narrower (92 pixels) than the actual height of the
channel (152 pixels). Another artifact is the double velocity proﬁle seen in the image. At
different angles, Figure 1(c) and ((1) illustrates a completely different proﬁle. When the
microchannel was tilted to different angles, at no point did a single velocity proﬁle
match the dimensions of the microchannel while maintaining a parabolic semblance.
This was not investigated further. This difficulty resulted in the making of our own

rectangular channels from quartz ﬂats.

149

Appendix H: Description of Single Line Velocity Profile
Labview Program

This describes the working principle of the Labview program designed to give
simultaneous velocity and temperature proﬁles. Figure 1 illustrates the graphical user
interface (GUI) of the program. For temperature measurements. the calibration
constants of the MTV chemical have to be provided along with the lifetime of the

normalization point.

correlationapgm _fbrSingle‘ urgvéiaerryjairémpgranrié Profile

 

TWMCBIlbI‘atImW _ Wﬁm

- 4.1%me Twldtl’t.

  
 

 

Fm. .1325. 33%“ 4‘3;- gm.“
1 mama”... am-

Mm; .
iﬂu. 00475 $994 00' a :’2

   

 

 

 

   

0 - .' . .' .. .:-w
‘-i.a' 411a 0152605051,.mg. ,. .. _

 

 

Figure l. Graphical User Interface for Correlation Program.

150

The normalized calibration constants are shown in Figure 2. It was determined
that the MTV chemicals prepared on different days may differ in lifetime values but the
normalized lifetime always collapsed on a single curve. Thus a normalized calibration

curve was used in the program.

 

 

 

 

55 .
I — y=57-54.5x+37.9x2-15.4x3I

50

45 ' r
o
“L,
2 4o
3
E
3 35» .
E
Q)
|—

30

25»

20 - A

 

 

 

0.1 0.2 0:3 0:4 0:5 0:6 0:7 0:8 09 1.0 1.1 1.2
Normalized lifetime
Figure 2. Plot of normalized lifetime
The region of interest in the GUI pertains to the region within the images that
correlation is performed. The whole image can be selected but the correlation will take
longer to perform. Other input boxes include speciﬁcations for delay time between
images, scaling factor (pixels/mm). rows to average (temperature measurement only),
ﬁtting order for correlation. points for polynomial ﬁt. columns to average (temperature
measurement only) and image bit levels. Additional inputs are also needed to specify
the locations for ﬁle input output. The graphical display on the left illustrates the local
polynomial ﬁt along each line of pixel and its corresponding correlation coefﬁcient while

the display on the right illustrates the velocity proﬁle measured.

151

The following illustrations detail the inner workings of the program and are self

explanatory by reading the captions.

First step in structure

lam-ﬁl-Iguana-ﬂail:Imlﬁnﬁnmlﬁlmnmlﬁl?linalﬁlylr gnu-woulvlglﬂlilg

            

:1 [J [0.4] '
Deﬁne image as 8/16 bit and uses the
IMAQ function to prepare to open the ﬁle

Create the needed images

{32919.8 Imam? ITemEIate Image lHﬂO.
-}1_ r- j ..

“multlixuulxl rxlllxumtl‘

 

 

 

 

 

 

 

 

 

I,
F
I
L‘

mm‘rmlxmltzm _ . . - ' “rmrmmm _ _ _ _ _ . . ml

 

 

Outputs the image data to
other steps in the structure

Figure 3. First step in program is to open the images for correlation.

=‘oWuigEuﬁu'i‘ua‘.’It; nil-Infini-Ii. Iﬁllll'il‘l‘lgl

      

Iii-alar-.::a:i-'|il-Iil-l-i -:-'i-‘Iii’ii'l"“~""“‘f"“‘ :1:

MM WindToolsS elect Select IMAQ Windilove : IMAQ WindROlColor: set the
the first tool available Display the top-left ROI color to yelow.
corner of the image at :

 

tl'il'

 

 

 

 

 

 

it

Uses a rectangle tool to select Region of
Interest (ROI)

Figure 4. Setup the ROI operator

152

. . ZIEHI 'PF

 

 

 

 

 

 

   

 

 

 

   

 

  

 

 

 

 

 

 

 

 

 

b
:31 um
\ Inﬁnite loo - that runs until “return” button is clicked to sto n the 'Jrogram
................................... _m I" . . .. .. . . ..
6
o h I
I: F339 '5
@
Displays
image in
_H window
electFiOlinD.r
Load File path is
button deﬁned here
When "load” button is pressed. open the inage aid display it.
Figure 5. Loading of images and displaying it in window
lnputttng the
number of
rows and

columns \

Inputting the

data in
matrices

 

 

 

 

Calculation of
mean and
standard
deviation to
compute cross
correlation

Figure 6. Preparation of the data set and obtain mean of each row

153

 

 

 

 

 

 

 

Figure 7. Performs the cross correlation of the data

Conversion of
pixels to
physical units

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- !subEpixel determination and conversion to ghésical units! 4

Figure 8. Fits a polynomial around the peak of the cross correlation to obtain sub-pixel
accuracy

 

 

 

 

 

 

 

 

 

 

 

Mean Mean

{1
D

HIE
rif' ' T

i
- vera

ave Velocity
nfo to File?

Figure 10. Saves the dataset into text ﬁles

 

 

 

Each of the previous ﬁgures illustrates a core section of the program without going into
details the function of each icon. For completeness. the entire program is illustrated in

Figure 11.

155

Swamp—m Goad—8.80 “seasons—05 EHO 380:5 0:3 oQEw .8 8.0.930 wEooO .: PEME

 

156

Appendix 1: Methodology for Deposition of Polymer—

brushes on Quartz Substrates
(adapted from Miller et. al. (2004))

The rrricrochannels utilized in this study were constructed out of quartz ﬂats
and coated with polymer brushes. Each quartz ﬂat was initially washed for 1 hour with
1M of NaOH followed by a 5 minute rinse with deionized water. The substrate is then
rinsed for 1 hour with 1M of HCl and ﬁnally dried in 3 110°C oven overnight. Before
polymerizing the HEMA (2-hydroxyethyl methacrylate) on the substrate. a
trichlorosilane initiator, (11-(2-bromo-2-methyl)propionyloxy)undecyltrichlorosilane is
used. A solution containing IOuL of the initiator in 10mL of THF (2uM initiator) was
used to rinse the substrate for 5 minutes and then allowed to stand for 18 hours. The
substrates were then rinsed with THF for 10 minutes and dried with a ﬂow of nitrogen
for 10 minutes.

Before using HEMA, it needs to be prepuriﬁed with basic alumina.
Subsequently. 10mL of HEMA was added to 10mL of deionized water in a Schlenk ﬂask
and degassed via three freeze-pump-thaw cycles. Next. 55mg (0.055milimol) of CuCI.
36mg (0.16milimol) of CuBrz and 244mg (1.56mi1imol) of bpy were added to the
solution. The ﬂask was then sealed with a septum, purged with nitrogen for 2 minutes
to remove oxygen, and sonicated for 5 minutes to yield a homogeneous, dark brown
mixture. The substrate is allowed to stand in this mixture for l to 12 hours depending
on the coating thickness needed and eventually ﬂushed with DMF (2.3-
dichlorophenol,N,N-dimethylforrnamide) for 2 hours. The ﬁgure below illustrates the

chemical structure of HEMA

157

 

:S __ Cl

; I OH CI"S‘ \ 0))(Br
L1 CH ‘C' i:

i' r-OH =
rC

{Al—OH 18h

Figure 1. Schematic of the substrate surface initially, after treatment with the initiator

and HEMA

158

H0156:
H

:24“: ﬁx“
+oi°++o+§<ar

TONE) n O

 

 

$H0J><m
HO, OH H
Initiator Film

HEMA
CUCVCuBrz
bpy

Appendix J: Calibration of Phosphorescent Chemicals
for Temperature Measurements

Before the phosphorescent chemicals are used to measure the temperature of
the ﬂuid, it needs to be calibrated. The calibration relates the lifetime of the chemicals
to the temperature of the ﬂuid. To obtain the lifetime of the chemicals, the
phosphorescence emission of the chemicals at different times after the laser has ﬁred is
imaged. After background subtraction the averaged phosphorescence intensity is

plotted. A typical plot of the emission decay is shown in Figure I- l.

Intensity

it

 

 

’Qmei

Figure I- 1. Typical emission decay of phosphorescent chemicals.
This procedure of obtaining lifetime is repeated across the temperature range of interest

and plotted below. The coefﬁcients of the third order ﬁt to the data points are then

plugged into the image correlation program for calculation of the temperature.

159

 

 

 

 

 

 

 

 

2.0 . w
a Neopenthanol MTV Mix (Trial 2)
1.8 ' o Neopenthanol MTV Mix (Trial 1)
3rd Order Fit
A 1.6
00
O
\P‘” 1.4 »
£1 %%
w 1 2 . 0» .
é 33a!
,3 1 o “a .
v “a,
E 0-8 ' “a
a 33
g 0.6 33 as
o ..
2 0.4 . 3 ER .
as
o A n A n
25 30 35 40 45 50 55

Temperature (°C)

Figure 1—2. Normalized lifetime at different temperature for the phosphorescent
chemicals

160

Appendix K: Accuracy in the Temperature
Measurements with the MTI‘ technique

The analysis of the accuracy of the temperature measurements with the MIT
technique was previously described in Hu and Koochesfahani (2005). The accuracy of
the technique is directly inﬂuenced by noise in the two phosphorescence signals 81 and
82 (refer to Figure 2-23). The actual image noise at each pixel. characterized by the
standard deviation of the signal, is much higher and is in the 3% range. This noise
level is connected to the CCD depth of well and the intensiﬁer stage of the CCD. 'lhe

accuracy in calculating the phosphorescence lifetime can be estimated by the following

0': — 1 0,51 2 15$ 2
7"ln(sl/sz)\[[81] {3.) ’ (1)

This was suggested by Ballew and Demas (1999), where 051.052 and a, are the

equation.

 

 

standard deviations of 81.82, and t, respectively. The 3% phosphorescence signal at each
pixel will, therefore, result in a lifetime measurement accuracy of about 4% and an
instantaneous temperature error of 08°C (using the lifetime temperature sensitivity of
5% per 0C at 20°C for reference). Since this error is unbiased, it can be substantially

reduced by average over neighboring pixels. Assuming statistical independence, the
error can be reduced by the factor 1/ W , where N is the number of pixels in the

interrogation window. For the results given in the present study based on 32x32 pixel
interrogation windows, the instantaneous measurement error due to the noise in the

phosphorescence images is estimated to be less than 0. 1°C.

161

Appendix L: Equations of Motion with Slip Derivation

 

Figure J - 1. Coordinate system

The velocity proﬁle with slip in a 2-D geometry is derived. The slip boundary conditions

for this ﬂow are:

Uy=h =-ﬂ13y- . Uy=—h =-ﬂ2— (1)

(2)

l 8p 2
— =——h —Ch+C
hayy=_h 2;! 3x 1 2

where ﬂ: and ,82 are deﬁned as the slip lengths at the walls

Subtracting the two equations above.

8_u +ﬂ1§E = 2C1h
3yy=_h 3yy=h
C1= _aiu _aa_u
2h ayy=_h 2h ayyzh

(3)

Adding the two equations together.

2
Gregg. _aa_u _h_22

(4)
2 8yy=_h 2 ayyzh 2;: 8x

162

Again as in the case of a single slip length derivation, the slope needs to be substituted.

We know that the slope has the following general expression:

Bu 1 8p
— = —— (5)
By a 8x
substituting the results from above, we obtain
a_u =_l_a_py -2232 _aa_u
8y ,u 8x 2h 8yy=_h 2h ayyzh
Bu aph_ﬂ23_u _ﬂa_u (6)

l
ayyzh [1 8x 2"! 6yy=_h 2h ayy:h

consolidating the terms.

[1 ﬂijiu _£§£-&§£
_a_u_ = 2h2 12- +2 a_u
8yy=h p(2h+ﬂ1)ax 2h+ﬂ13yy=_h

[HQ—jit- _ nap ﬁlau

2h ayyz—h - _Za -Egyzh

(7)
a_u =.__2h2 22- m 22
ayy=_h ,u(2h+ﬂ2)8x 2h+ﬂ28yy:h

substituting into the equation for slope at y=h with the equation for slope at y=-h. the

following expression results:

 

 

 

 

:92 _ 2'12 a; +2 ~2h2 a_p_ m a

ayy=h’(2h+p1)ax 2h+ﬂ1(2h+2,62),u8x 2h+ﬂ28yy=h

[,_ 191/32 ]a_u z 2h2 92+ 232 21932
(211+;31X2hw2) ayy:h (2h+ﬂ1),uax 2mm (2h+,62)p8x

 

4h2+2hﬂ2+2hﬁ1[8u 2:12 3p[l+ [32 ]
— — (8)

(2h+ﬁ])(2h+ﬂ2) 8y]y=h=(2h+ﬂ1)p8x 2h+,62
(a = +91- [+1
3y y=h p(4h2+2hﬂ2+2hﬂ1) 3X 4h2+2hﬂ2+2hﬁ1 3x

 

[Lu] = 2h2l2h+ﬂ2) [11).][1+_/32_]
3y y=h y(4h2+2hﬂ2+2hﬂ1] ax 2h+,62

163

similarly. the slope at y=~h needs to be expressed in terms of the pressure gradient:

 

 

 

a_u -2h2 8_p .61 2h2(2h+ﬂ2) [0311+ .62 J

8yy=_h =(2h+,62);1 8x 2h+ﬂ2 ,u(4h2 +2t1ﬂ2+2hﬂ1) 8x 2h+ﬂ2

93 = —2h2 g H 51(2h+2/32) (9)
39 y=—h (2" + 52»! 3" 4h2 + 211,62 +2hﬁ1

9g _ —2hz(2h+2,61) 33

 

ayy=—h ,u(4h2 +2hﬂ2 + Zhﬂlj ax

substituting the values for slope at the walls into the general equation describing the

ﬂow velocity, U.

 

 

 

 

 

my )_;_a_p 2 __ﬂ2_ya_u _ﬂ_1y8u _ﬂ_2_8_u/910uh28p

2p3x 2h 8yy_ -—h 2h 8yy_ -h 2 egg. -—h 2 3yy_ -h Z—pax
u(y)=_y3_8£_ﬂy_ —2h2(2h+2ﬂ1) a_p _ﬂy 2h2(2h+ﬂ2) ap[1+ ,62 ]
_ﬂ 2h2(2h+ﬂ2) LIT” 52 ]+& —2h2(2h+2,61) 22 _Iﬁd—Q
simplifying, the following expression results:

2

y2 _E)_p+ 2h ap ___p

Ulyl= 2#ax+#(4r12+ +2hﬂlja" x-[lﬂz ﬁ1)y- h(ﬂ1+ﬂz)- ”1.621;“ 8x (11)

For veriﬁcation, we test the equation above for the conditions when the slip length is
zero or if the slip lengths are the same. For zero slip length, it is obvious that the

following expression results:

U ________ (12)
(y) 2/18x 2,118x

for same slip lengths,

164

 

 

Standard Slip
solution within velocity
2-D channel

165

(13)

(14)

Appendix M: Error Analysis for Pressure Driven Flows

This section of the appendix detail the uncertainties associated with
determination of the friction factor. The equation used to calculate the normalized

friction factor is repeated here

 

 

 

 

 

i (_ 1)(i—1)/ 2(1) _ 2a sinh(i7rb/2a)) COS(i”y/20)
_ . .3
cf,exp = 2utheory [1:] i=1,3.s.. m I (1)
C f ,theory L72 62 exp 0° ' ' .
exp 2 (—1)(l‘1)/2[tanh(i7rb/20)* 1] w.)
_ i=1’3,5-oe 20 i "

The terms within the square brackets in equation (1) only depend on the half height, b,
the half width, a, and the particular location along the y-axis, y. The determination of

the half height, b, will be discussed later when the uncertainties in the slope au /62 is

discussed. For the half width, a, the relative error (compared to the width dimension) in
determining its dimensions is small due to the use of a high aspect ratio microchannel
and is neglected in this analysis. The uncertainties in determining the interrogation
location along the y-axis is also neglected as Error! Reference source not found. and
Error! Reference source not found. demonstrated that the changes in velocity and the
velocity gradient at the wall is minimal in the center of the channel. All the experiments
in this study were conducted away from the wall so that this applies. Thus the errors in
determining the normalized friction factor reduce to the errors in measuring the mean
velocity and the velocity gradient at the wall.

The uncertainty in the mean velocity propagates from the uncertainty in
determining the velocity from the correlation program. Error! Reference source not
found. illustrates the uncertainty (95% confidence, 20). For the typical image pairs used
for correlation in this study, a 0.1pixel uncertainty in the velocity is assumed. The
determination of the errors in the slope, however, is more involved. The uncertainty in
the fit and the determination of the wall location both contribute to it. Figure 1

illustrates the velocity data points

166

obtained from the correlation of typical image pair. The 2nd order ﬁt to the velocity data

points is illustrated as a red continuous curve. The errors in this ﬁt is analyzed below.

 

0.4

   
  

 

 

 

 

 

 

 

 

 

 

 

0.3
E
E
E’ y=0.347648
.9 y=0.046248
g 02 0 Experimental Data points ,
o ' x=a +by+c;a=-8357. L7, ,1
j b=32a5, c=-132 "L.
g C! Slope from Central " 1’
8 Diﬂerencing 1 L 1 n
(I) y=-5.86E—5x +0.19? “‘3
0.1 'i. ‘ 0c:
‘ ‘rl
w°°° D ;. 2in
9953.33
-5000 -2500 0 2500 5000
Velocity
(”mm-50 0 50 100 150 200

Shear rates (1/s)

Figure 1. Central—differencing procedure for determining slope at the wall

The method used here for determining the uncertainty in the ﬁt is described in the book
“Data Reduction and Error Analysis for The Physical Sciences”, by Bevington and

Robinson (2nd Ed.) on page 125. The 2nd order ﬁt equation is described in equation (2).

ux=ax2+bx+c (2)

The uncertainty in the calculated value of ux results from the uncertainty in the

coefficients of the ﬁt. This is given by the following equation.

167

 

 

 

 

02 :[auxa)2+(8ux0_)2+(ﬂ_15_0)2+2(8ux auxa )2
“x an " ab " ac C an ab 0”

”(gang fwﬁaauxa )2 (3)
an ac “‘ ac ab 0"

a": = a” + x2622 + x4633 + 200912 + x2813 + x3823)

 

where aux. 0a, ab, ac are the uncertainties in determining the velocity and the

parameters a. b and c respectively. The 6 terms in the equation are the terms in the
error matrix. The error matrix was obtained from the matrix inverse of the symmetric

matrix, a which is deﬁned as follow

01+ = Z[;l;lexilfk(xil] (4)

for a quadratic ﬁt to the data set. we have 3 terms. The f terms in the above equation

resolves to the following:

f1(x1) = 1
f2(x1) = X. (5)
f3(x1) = x12

and the a matrix was computed for a typical data set.

a“ = 2—1— = 15500

 

(0.1)2

(x,
al2 = Z —-2— = 2831.4 =a2,

LO’,

(x2 (6)
a“, = Z —2] = 635.7728 =ar31 = 0122

LO',

((4
(233 = X :7 = 42.51779

1

K
by taking the inverse of this matrix, we obtain the error matrix. The error matrix is

shown below:

 

 

 

 

(AN-Ln

 

 

These values are plugged into the equation for 0'“)r and the uncertainty of the 2ncl order

ﬁt is obtained. The other contribution to the uncertainty is the error in the
determination of the wall locations. From Figure l, a blue curve was ﬁtted to the
central-differenced data points near the walls. A linear curve ﬁt was used to determine
the intersection of the data points with the location of zero shear rate. This would yield
the location of the wall. The uncertainty in ﬁtting this linear ﬁt would contribute to the
uncertainties in the measurement of the friction factor. A similar analysis as was
performed before for the 2nd order ﬁt was done here to determine the uncertainties of
the linear ﬁt. The combination of the three uncertainties adds up to give the overall

uncertainty associated with the determination of the friction factor, Cf. 02nd. Gist and a;

are the uncertainties associated with the 2nd order ﬁt, the linear ﬁt and the

determination of the mean velocity respectively.

 

0C = JOan + Ulst + 0'11“ (7)

The errors for all the friction factor measurements were calculated and shown in the

last column of the tables of results (Table 3-1Table 3-2. Table 3-3’1‘ able 3-4).

169

Appendix N: Determination of the Slip Detection Limit

The friction factor analysis shown in the main body of this thesis showed an
excellent agreement with classical theory. In this section of the appendices. the average
difference between the experimental friction factor and theory is used to investigate the
possibility of determining the slip length. This is done by attributing the average

uncertainty to be solely caused by the errors in the ﬁt to the data points in Figure L-l.

 

 

    
  

 

 

 

 

 

 

 

 

 

 

 

 

0.4
9 0°06, 1

0.3
E
E
‘C’ y:0.347648
,9 y=0.046248
‘6 0 Experimental Data points .
8 0'2 x=ay2+by+c;a=-8357. i.
1' 13:32:35, c=-132 1:. ~,
g D Slope from Central ' rim
3 Ditlerencing 1 ll '
(I) y=-5.86E~5x +0.197 ”1

0.1 M'- = no

000 D (5‘, .30
Wig
Jim-J
-5000 -2500 0 2500 5000

Velocity
(mm/9‘50 0 50 100 150 200

Shear rates (1/s)

Figure L- 1. Central differencing procedure for determining friction factor.

The linear ﬁt to the central-differenced data points (red) is investigated. The equation for

linear curve ﬁt is

y =—5.86*10'5x+0.197 (1)

by plugging in the upper wall location, the slope at the wall is determined.

x _ 0.34765mm —O. 197 _

5 —2570.819 (2)
— 5.86 " 10"

170

If the i 0.5% uncertainty in friction factor is attributed entirely to the determination of
the slope, 0.5% of the slope determined at the wall would be 12.85. At a slope of (-

2570.819+12.85), the spatial location is determined to be 346.9pm.

y = —5.86 *10'5 * (—2557.965) + 0.197 = 346.9,um (3)

The wall is located at 347.7um. By substituting the two spatial locations into the
parabolic curve ﬁt equation, the corresponding velocity can be determined. For the
0.347648mm spatial location, the calculated velocity is identically zero. The velocity at

the second spatial location is calculated as follows

x = —8357(O.346897)2 + 3285 (0.346897) — 132 = 1.8973mm/ s (4)

Thus the 0.5% uncertainty in friction factor translates to a 1.8973mm/s velocity
uncertainty at the wall for this particular case. To determine the slip length, the

following equation is used.

2
2
utyi=L[--a£ 1-[i] +% (5)
h h

At the wall, y = h and the ﬁrst two terms cancel out. This results in the following

equation.

U(h)=ﬂ[-33] (6,
p 8x

From the numerical simulation of pressure driven ﬂow within a 301.4um X 25.4mm
microchannel, the pressure drop would be 14,747.49 N /m3. Substituting this into the

equation,

171

 

 

u(hm _ 1.8973‘10‘3‘000088 =752nm

h(_ 93] - 0.1507 * 10‘3 (14,747.49) (7)
3x

ﬂ:

Thus, the slip length has to be more than 752nm to be detected.

172

Appendix 0: Derivation of Equations for Molecular
Tagging Thermometry

The basis of the Molecular Tagging Thermometry technique is the dependence of the
decay rate of phosphorescence emission of photoluminescent chemicals on
temperature. The total phosphorescence emission is generally described by the

following equation.
1,, = 1,. Ce (1) p (1)

where 1,. is the total phosphorescence intensity, IiiS the total incident intensity (which in
this case would be the laser excitation), C is the concentration of the photoluminescent
chemical. e is the absorption coeﬂicient and (DP is the phosphorescence quantum
efﬁciency. For all practical purposes, however. the concentration, absorption coefﬁcient
and phosphorescence quantum efﬁciency is unknown. To circumvent this problem of
unknowns, a ratiometric method is developed to avoid the use of these unknowns to
determine the lifetime of the chemicals.

Lifetime, I. which is deﬁned as the l/e decay rate of phosphorescence emission

can be expressed with regards to the initial intensity, I: by the following equation.

I = 1.19"”1 (2)

em I

where Iem refers to the intensity emission at a particular instance of time, t. after initial
excitation of the photoluminescent molecules. To physically image this emission, a
gated intensiﬁed camera is used. Since the camera is exposed to the phosphorescence
emission for a ﬁnite time, equation2 can be integrated over a gate period, ﬁt, to yield

equation 3.

173

to+6t
Iemﬁt = Julie-HQ“ (3)
t

O

The equations presented so far can be shown to yield equation E.4.

Iemﬂt = IiCe<bp(l — e‘at/T) e’t/T (4)

The ratiometric method involves the ratio of the integrated intensity at two time periods
as per equation 4. For the same gate or exposure time, the ratio of the two intensities
reduce to equation 5 since the initial excitation intensity, It. concentration, C.
absorption coefﬁcient, a, and the quantum efﬁciency, (b all remains the same.

_ A}:

18111.1 :8 1' (5)
Iem,2

 

This illustrates that by dividing the intensity of the ﬁrst image with the intensity from
the second image on a pixel by pixel basis, the lifetime of the phosphorescence emission
can be obtained as long as the time delay (At) between the two images is known.
However, the phosphorescence emission in the second image is usually much
lower and the constraint of the same exposure time with the initial image is sometimes

not met. The equation is rederived for the case where the exposure times are diﬂerent.

Ieml (l—e‘ﬁl/Tje-tJr (1_e—6t1/r) -91

rem ” (1—e‘59/Tje‘Q/T =(1-e-5e/r)e

 

 

(6)

To relate lifetime to temperature, a calibration is initially performed on the
photoluminescent chemicals in a range of temperature to obtain the respective lifetimes

at different temperatures. Normalized at room temperature, the dataset proved

174

consistently reproducible thus enabling the calibration to be done only once for each

type of photoluminescent chemical.

175

Appendix P: User Deﬁned Functions (UDF)

The following UDFs were written to specify a varying inlet velocity and a transient heat
source in FLUENT. The inlet velocity is varying with time due to the increase in
conductivity of the ﬂuid as temperature rises. The rising heat source is also a direct

consequence of a change in conductivity.

(a) Transient Velocity Magnitude:
DEFINE_PROFILE (ramp_velocity, thread, position)
{
face_t f:
real t = CURRENT_TIME;
begin_f_loop(f, thread)

{

F_PROFILE(f, thread, position) = 0.00175 + (0.00453614/30)‘t;

}
end_f_loop(f, thread)

(b) Transient Best Source:

DEFINE_SOURCE (q_source, cell, thread, dS. eqn)
{

real source;

real t = CURRENT_TIME;

source = 2"‘107 + (0.44395‘107/30)*t:

dS [eqn] = (0.44395‘107/30):

return source;

}

176

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