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Single- and Two-Phase Pressure-Driven Flow Transport Dynamics in Micro-Channels

Permanent Link: http://ufdc.ufl.edu/UFE0021411/00001

Material Information

Title: Single- and Two-Phase Pressure-Driven Flow Transport Dynamics in Micro-Channels
Physical Description: 1 online resource (125 p.)
Language: english
Creator: Xiong, Renqiang
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: driven, dynamics, flow, microchannel, phase, pressure, single, transport, two
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The pressure-driven flow in a micro-channel is an important component of the micro-scale fluid dynamics and widely applied in many fields such as cooling of IC chips, micro-fuel cell fluid transport, and lab-on-a-chip. To enrich the current fundamental knowledge of micro-scale fluid dynamics, some experimental and numerical investigations were performed. The pressure drops of liquid flow in straight and serpentine micro-channels with hydraulic diameters of 0.209 mm, 0.412 mm, and 0.622 mm were evaluated. To segregate the bends and entrance effects individually from the total pressure drop, for each size, three types of micro-channels: straight short, straight long, and long serpentine, were fabricated. An in-house micron-resolution particle image velocimetry system (micro-PIV) was built at the University of Florida and used to obtain the detailed velocity vector field in micro-scale channels. The friction factor result shows that the conventional theory is still valid under the current channel size. The additional pressure drop is consistent with the flow structure around the bend measured by the micro-PIV. Adiabatic nitrogen-water flow patterns and void fractions in straight micro-channels were experimentally investigated. Gas and liquid superficial velocities were varied from 0.06-72.3 m/s and 0.02-7.13 m/s, respectively. The instability of flow patterns was observed. Four groups of flow patterns including bubbly-slug flow, slug-ring flow, dispersed-churn flow and annular flow were observed in micro-channels of 0.412 mm and, 0.622 mm while in the micro-channel of 0.209 mm, the bubbly-slug flow became the slug-flow and the dispersed-churn flow disappeared. The current flow regime maps showed that the transition lines shifted to a higher gas superficial velocity due to a dominant surface tension effect as the channel size was reduced. The void fractions hold a non-linear relationship with the homogeneous void fraction as oppose to the relatively linear trend for the mini-channels. A new correlation was developed to predict the non-linear relationship that fits most of the current experimental data within ?15%. Bubble generation in a simple co-flowing micro-channel with a cross-section area of 1.69*0.07 mm2 was also investigated. Mixtures of water-glycerol and water-Tween 20 were also used to obtain the effects of viscosity and surface tension. The break-up dynamics can be predicted using a three dimensional incompressible two-phase flow numerical model based on the volume of fluid (VOF) method. The bubble length L is dependent on the liquid flow rate Ql and gas flow rate Qg. Further more the ratio of L to the channel width w is a function of the ratio of gas and liquid flow rates Qg/Ql which is similar to that previously used in the T-junction case. The bubble frequency is found to be related to w, channel depth h, and QlQg/(Qg+Ql*pi/4), and shows a good agreement with the experimental data at the low frequency region. Different bubble shapes can be obtained at different liquid viscosities and surface tensions. The ratio L/w can still be predicted by a modified equation which uses the real bubble width wb or an equivalent bubble length Le.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Renqiang Xiong.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Chung, Jacob N.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021411:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021411/00001

Material Information

Title: Single- and Two-Phase Pressure-Driven Flow Transport Dynamics in Micro-Channels
Physical Description: 1 online resource (125 p.)
Language: english
Creator: Xiong, Renqiang
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: driven, dynamics, flow, microchannel, phase, pressure, single, transport, two
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The pressure-driven flow in a micro-channel is an important component of the micro-scale fluid dynamics and widely applied in many fields such as cooling of IC chips, micro-fuel cell fluid transport, and lab-on-a-chip. To enrich the current fundamental knowledge of micro-scale fluid dynamics, some experimental and numerical investigations were performed. The pressure drops of liquid flow in straight and serpentine micro-channels with hydraulic diameters of 0.209 mm, 0.412 mm, and 0.622 mm were evaluated. To segregate the bends and entrance effects individually from the total pressure drop, for each size, three types of micro-channels: straight short, straight long, and long serpentine, were fabricated. An in-house micron-resolution particle image velocimetry system (micro-PIV) was built at the University of Florida and used to obtain the detailed velocity vector field in micro-scale channels. The friction factor result shows that the conventional theory is still valid under the current channel size. The additional pressure drop is consistent with the flow structure around the bend measured by the micro-PIV. Adiabatic nitrogen-water flow patterns and void fractions in straight micro-channels were experimentally investigated. Gas and liquid superficial velocities were varied from 0.06-72.3 m/s and 0.02-7.13 m/s, respectively. The instability of flow patterns was observed. Four groups of flow patterns including bubbly-slug flow, slug-ring flow, dispersed-churn flow and annular flow were observed in micro-channels of 0.412 mm and, 0.622 mm while in the micro-channel of 0.209 mm, the bubbly-slug flow became the slug-flow and the dispersed-churn flow disappeared. The current flow regime maps showed that the transition lines shifted to a higher gas superficial velocity due to a dominant surface tension effect as the channel size was reduced. The void fractions hold a non-linear relationship with the homogeneous void fraction as oppose to the relatively linear trend for the mini-channels. A new correlation was developed to predict the non-linear relationship that fits most of the current experimental data within ?15%. Bubble generation in a simple co-flowing micro-channel with a cross-section area of 1.69*0.07 mm2 was also investigated. Mixtures of water-glycerol and water-Tween 20 were also used to obtain the effects of viscosity and surface tension. The break-up dynamics can be predicted using a three dimensional incompressible two-phase flow numerical model based on the volume of fluid (VOF) method. The bubble length L is dependent on the liquid flow rate Ql and gas flow rate Qg. Further more the ratio of L to the channel width w is a function of the ratio of gas and liquid flow rates Qg/Ql which is similar to that previously used in the T-junction case. The bubble frequency is found to be related to w, channel depth h, and QlQg/(Qg+Ql*pi/4), and shows a good agreement with the experimental data at the low frequency region. Different bubble shapes can be obtained at different liquid viscosities and surface tensions. The ratio L/w can still be predicted by a modified equation which uses the real bubble width wb or an equivalent bubble length Le.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Renqiang Xiong.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Chung, Jacob N.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021411:00001


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76903aabc8c53a265d3e10fba7520b67a7490598







SINGLE- AND TWO-PHASE PRESSURE-DRIVEN FLOW TRANSPORT DYNAMICS IN
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By

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A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2007

































@2007 Renqiang Xiong









ACKNOWLEDGMENTS

I would like to express my sincere appreciation to my advisor, Dr. Jacob N Chung, for his

invaluable patience, support and encouragement. Without his direction and support, this work

would not go further. Many thanks go to Dr. Steve Wereley from Purdue University and Dr.

Lichuan Gui from University of Mississippi for helping me to build the Micro-PIV system and

tutorials in this research.

Drs. S.A. Sherif, Corin Segal, William E. Lear, Jr, and Jason E. Butler were extremely

helpful in several aspects of this research while serving on my supervisory committee. Their

suggestions and encouragement have shaped this work considerably.

My fellow graduate students, Kun Yuan, Yunwhan Na, Yan Ji and Mo Bai, have

graciously given their time and experience. Finally, I would like to thank my parents and my

elder brother' s family for the most needed encouragement to finish my studies. Special thanks

are given to my wife, Xiaoxing Feng, for years of support. Without her sacrifice, it would have

been impossible for me to complete this work.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............3.....


LIST OF TABLES ................ ...............6............ ....


LIST OF FIGURES .............. ...............7.....


NOMENCLATURE .............. ...............9.....


AB S TRAC T ............._. .......... ..............._ 12...


CHAPTER


1 INTRODUCTION ................. ...............14.......... ......


1.1 Research Background ................. ...............14.......... ....
1.2 Research Obj ectives ................. ...............16...............
1.3 Research Overview............... ...............16


2 ENTRANCE FLOW AND BEND EFFECT............... ...............18.


2. 1 Introduction and Background ................. ...............19.......... ....
2.2 Experimental Setup............... ... ...............22
2.2.1 Micro-Channels Fabrication............... ..............2
2.2.2 Apparatus................ ...............2
2.3 Data Reduction and Analysis............... ...............24
2.4 Results and Discussion .............. ...............28....
2.4.1 Friction Factor .............. ...............28....
2.4.2 Bend Loss Coefficient ................. ...............28................
2.5 Summary ................. ...............30................


3 FLOW STRUCTURES AROUND A BEND............... ...............36..


3.1 Introduction and Background .............. ...............36....
3.2 Micro-PIV System ................. .......... ...............39.....
3.2.1 Laser Beam Alignment............... ...............3
3.2.2 Timing Scheme............... ...............40.
3.2.3 Fluorescent Particles Image ................. ...............42........... ...
3.2.4 Measurement Depth............... ...............43.
3.3 System Validation............... ...............4
3.4 Results and Discussion ................. ....... ..... .. ..........4
3.4. 1 Flow Structures Around The Miter Bend ................. ...............45...........
3.4.2 Circulation Calculation............... ..............4
3.4.3 Shear Strain .............. ...............47....
3.5 Summary ................. ...............47.......... .....












4 ADIABATIC GAS-LIQUID TWO-PHASE FLOW ................. .............. ......... .....62


4.1 Introduction and Background .............. ...............62....
4.2 Experimental Apparatus .............. ...............66....
4.3 Results and Discussion .............. ...............68....
4.3.1 Two-Phase Flow Patterns ................. ...............68........... ..
4.3.2 Flow Regime Maps............... ....... ..... ... .......7
4.3.3 Comparison With Prior Mini-Channel Flow Map............... ...............73..
4.3.4 Time-Averaged Void Fraction .............. ...............74....
4.3.5 Frictional Pressure Drop ................. ...............77........... ..
4.4 Summary ................. ...............77.......... ......

5 MICRO-BUBBLE DISPENSER............... ...............9


5.1 Introduction and Background .............. ...............91....
5.2 Experimental Setup............... ...............94.
5.2. 1 Dispenser Fabrication ................. ...............94........... ...
5.2.2 Apparatus............... ...............9
5.3 Numerical Simulation ................. ...............96........... ...
5.4 Results and Discussion .............. ...............98....
5.4. 1 Bubble Break-Up ................... ........ .... ...............98.....
5.4.2 Bubble Distribution and Bubble Size ................ ...............99........... ..
5.4.3 Bubble Frequency................ ... ............10
5.4.4 Effect of Viscosity and Surface Tension ................ ...............102.............
5.4 Summary ................. ...............103................

6 CONCLUSIONS AND RECOMMENDATIONS ................ ...............................115


6. 1 Accomplishments and Findings ................. ...............115........... ...
6.2 Future Research ................. ...............116................
6.2. 1 Experimental Study ................. ...............116......... .....
6.2.2 Numerical Study ................. ...............117................

APPENDIX TIMING PROGRAM FOR MICRO-PARTICLE IMAGE VELOCIMETRY ...118


LIST OF REFERENCES ................. ...............119................


BIOGRAPHICAL SKETCH ................. ...............125......... ......










LIST OF TABLES


Table page

2-1 Dimensions of three groups of micro-channels ................ ...............31..............

2-2 Comparison of current pipe lengths with those of entrance regions ................. ...............31

3-1 Specification of the Nd:YAG laser (Continuum Minilite II) ................. .....................48

3-2 Calculated vortex circulation ................ ...............48................

4-1 Generalized two-phase frictional pressure-drop correlations. ............. .....................7

4-2 Non-dimensional parameters for a macro-channel and micro-channels ................... .........80











LIST OF FIGURES


Figure page

2-1 Three groups of fabricated micro-channels ........._..__.......___....._ ...............32

2-2 Exp erim ental pre assure drop measurement app aratu s ................ ............... 33...........

2-3 Pressure drop defect K(x /) vs x' ............. ...............33.....

2-4 Experimental pressure gradients without removing the entrance effect
(AP1-APsh)/(L-Lsh) VS Re number. ........._._ ....___. ...............34...

2-5 Experimental friction factor vs. Re number in straight micro-channels............._._._..........34

2-6 Bend additional pressure drops vs. Re number in serpentine micro-channels ................35

2-7 Bend loss coefficients vs Re number in serpentine micro-channels............... .............3

3-1 Top view of the optical layout of the laser beam alignment ................. ......................49

3-2 Timing diagram for the two lasers and CCD camera .............. ...............49....

3-3 Fluorescent images at straight and serpentine micro-channels............... .............5

3-4 Schematic of micro-PIV system ........._._._......_._ ......_ ......_ ..............50

3-5 Photo of the optical subsystem .............. ...............51....

3-6 Photo of the laser beam alignment component ...._ ......_____ ...... ....__........5

3-7 Micro-PIV results for low speed flow. ............. ...............52.....

3-8 Typical velocity vector in the serpentine micro-channel at Re = 500............... ................53

3-9 Flow structure at the outer wall and at the inner wall ...._.._.._ .... ... .... ........._.._.....54

3-10 Streamlines at different Re numbers ........._._. ...._... .. ...............57..

3-11 Total vortex circulation vs. Reynolds number. .............. ...............59....

3-12 Distribution patterns of shear strain rates .............. ...............60....

4-1 Schematic of the flow visualization apparatus and the mixer..........._.._.._ ......_.._.. .....81

4-2 Photograph of micro-channels and schematic of the micro-channel ........._.._... ..............83

4-3 Typical flow patterns in the micro-channel. ............. ...............83.....











4-5 Flow regime maps for three micro-channels .............. ...............85....

4-6 Flow map comparison between micro-channel and mini-channel predicted by the
Weber number model ................. ...............87........... ....

4-7 Measured time-averaged voi d fracti on results vs two previ ous correl ati ons ................... ..8 7

4-8 Comparison between the new correlation and experimental data .............. ...................88

4-9 Ratio of predicted and experimental time-averaged void fraction vs. homogeneous
void fraction P............. ............8

4-10 Comparison between the experimental data and the models (Dh = 0.412mm) .................. 89

5-1 Schematic of the co-flowing micro-channel ................ ...............104..............

5-2 3-D image and depth measurement by the optical profiler............... ...............10

5-3 Schematic of the experimental flow visualization apparatus ................. ............... ....105

5-4 Schematic of micro-PIV measurement for micro-bubble dispenser................. .... ...........105

5-5 Schematic of 3D CFD mesh .............. .....................106

5-6 Time evolution of the periodic bubble generation process (Qg = 6.3ml/h, Qz = 21ml/h,
Air+Water) and the prediction by CFD simulation .............. ...............106....

5-7 Unsteady break-up process at different flow rates ................. .............................107

5-8 Instantaneous micro-PIV measurements around the barrier (Qz 21ml/h, Qg
6.3 m l/h) ................ ...............107......... .....

5-9 Bubble distribution along the channel at different flow rates ................. ............... ....110

5-10 Dependence of the bubble length L on the gas flow rate (Qz = 18ml/h) and liquid
flow rate (Qg = 5ml/h) .........._._ ...... .___ ...............110...

5-11 Dimensionless ratio (L w) with the ratio of gas and liquid flow rates ..........................11 1

5-12 Bubble frequency with different liquid and gas flow rates (Air +water). ................... .....112

5-13 Bubble shapes at different viscosities and surface tensions ................. .....................113

5-14 Dimensionless ratio (L/i .) with the ratio of gas and liquid flow rates ........._._................112

5-15 Dimensionless ratio (Le w) with the ratio of gas and liquid flow rates.............._._. .........1 14









NOMENCLATURE


A Area [m2]

A, Area of interrogation window [Clm2]

B Coeffcient in Eq. 2-6

Bo Bond number

C Coeffcient in Eq. 4-4

C, Volumetric concentration [lm-3]

Co Coeffcient in Eq. 4-1

Ca Capillary number

dP/dz Pressure gradient [Pa/m]

D Diameter [mm]

f Fraction factor

fr~e Frequency [1/s]

g Gravity acceleration [m/s2]

j Superficial velocity [m/s]

K Pressure drop defect

Kb Bend loss coeffcient

L Length [mm]

Ld Entrance length [m]

m Mass transfer rate [g]

n Refraction index

N Total number

NA Numerical aperature









P

Q

Re

S

T

u

U

Vg,



We

X

x




y

Z,,,

Greek letters

A


Pressure [Pa]

Flow rate [ml/min]

Reynolds number

Depth of micro-channels [mm]

Time [s]

Local velocity at x direction [m/s]

Mean velocity [m/s]

Mean drift velocity [m/s]

Width [mm]

Weber number

Martinelli parameter

The coordinate along the length

Dimensionless entrance length

The coordinate along the width

Measurement depth [Clm]



Variable difference

Aspect ratio

Homogeneous void fraction

Circulation [mm2/S]

Differential value

Wavelength of light in a vacuum [Clm]

Viscosity [kg/m-s]














o

Subscripts

b

c

dev

exp

fd

G/g

GS

h



io

L/

LS

1

m

p

s

sh


Light collection angle

Density [kg/m3]

Surface tension [N/s]



900 bend

Cross-section

Developing and developed flow

Experimental result

Fully developed

Gas

Superficial gas

Hydraulic diameter

Particle image

Inlet and outlet

Liquid

Superficial liquid

Long straight micro-channel

Other type of flow patterns

Fluorescent particles

Serpentine micro-channel

Short straight micro-channel









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SINGLE- AND TWO-PHASE PRESSURE-DRIVEN FLOW TRANSPORT DYNAMICS IN
MICRO-CHANNEL S

By

Renqiang Xiong

August 2007

Chair: Jacob N Chung
Maj or: Mechanical Engineering

The pressure-driven flow in a micro-channel is an important component of the micro-scale

fluid dynamics and widely applied in many Hields such as cooling of IC chips, micro-fuel cell

fluid transport, and lab-on-a-chip. To enrich the current fundamental knowledge of micro-scale

fluid dynamics, some experimental and numerical investigations were performed.

The pressure drops of liquid flow in straight and serpentine micro-channels with hydraulic

diameters of 0.209 mm, 0.412 mm, and 0.622 mm were evaluated. To segregate the bends and

entrance effects individually from the total pressure drop, for each size, three types of

micro-channels: straight short, straight long, and long serpentine, were fabricated. An in-house

micron-resolution particle image velocimetry system (micro-PIV) was built at the University of

Florida and used to obtain the detailed velocity vector Hield in micro-scale channels. The friction

factor result shows that the conventional theory is still valid under the current channel size. The

additional pressure drop is consistent with the flow structure around the bend measured by the

micro-PIV.

Adiabatic nitrogen-water flow patterns and void fractions in straight micro-channels were

experimentally investigated. Gas and liquid superficial velocities were varied from 0.06-72.3 m/s

and 0.02-7.13 m/s, respectively. The instability of flow patterns was observed. Four groups of









flow patterns including bubbly-slug flow, slug-ring flow, dispersed-churn flow and annular flow

were observed in micro-channels of 0.412 mm and, 0.622 mm while in the micro-channel of

0.209 mm, the bubbly-slug flow became the slug-flow and the dispersed-churn flow disappeared.

The current flow regime maps showed that the transition lines shifted to a higher gas superficial

velocity due to a dominant surface tension effect as the channel size was reduced. The void

fractions hold a non-linear relationship with the homogeneous void fraction as oppose to the

relatively linear trend for the mini-channels. A new correlation was developed to predict the

non-linear relationship that fits most of the current experimental data within 15%.

Bubble generation in a simple co-flowing micro-channel with a cross-section area of

1.69x0.07 mm2 was also investigated. Mixtures of water-glycerol and water-Tween 20 were also

used to obtain the effects of viscosity and surface tension. The break-up dynamics can be

predicted using a three dimensional incompressible two-phase flow numerical model based on

the volume of fluid (VOF) method. The bubble length L is dependent on the liquid flow rate Q1

and gas flow rate Q,. Further more the ratio of L to the channel width w is a function of the ratio

of gas and liquid flow rates Qg/Q1 which is similar to that previously used in the T-junction case.

The bubble frequency is found to be related to w, channel depth h, and Q1Q,/(Q,+Q1-x/4), and

shows a good agreement with the experimental data at the low frequency region. Different

bubble shapes can be obtained at different liquid viscosities and surface tensions. The ratio L/w

can still be predicted by a modified equation which uses the real bubble width wb Of an

equivalent bubble length Le.









CHAPTER 1
INTTRODUCTION

Micro-scale fluid dynamics usually refers to the dynamics of fluid flow in the devices with

length scales less than one millimeter. Studies of such fluid-related phenomena have long been

an important part of the fluid mechanical component (Batchelor 1977). Due to the availability of

MEMS fabrication methods (Ho and Tai 1998; Stone & Kim 2001), methods for fabricating

individual and integrated flow configurations with length scales on the order of tens and

hundreds of microns and smaller, micro-scale fluid dynamics research has received enormous

recent attention and been widely applied in many fields such as biotechnology (Beebe et al.

2002), cooling of IC chips (Zhang et al. 2002), micro-fuel cell (Heinzel et al. 2002) and lab on a

chip (Erickson and Li 2004). In many applications, a valuable feature of microflows is that the

dynamics in a single channel can be replicated in many channels, so understanding the

fundamental knowledge of fluid motion and associated transport processes in micro-channels is

quite important for the micro-scale fluid transport system design.

In this study, we experimentally and numerically investigated many flow features of

pressure-driven single- and two-phase flow in micro-channels to enrich the current fundamental

knowledge of micro-scale fluid dynamics.

1.1 Research Background

Micro-scale flows can be manipulated using many kinds of external fields such as pressure,

electric, magnetic, capillary, etc. Pressure-driven flow is an indispensable component in

micro-scale fluid dynamics research. It is widely used in micro-heat exchanger (Brandner et al.

2000), and the pressure drop is a critical parameter to design the micro-pumps. For single phase

liquid flow in straight micro-channels, many scientists have published numerous papers on the

relationship between the friction factor and Re number in the past fifteen years. Some of them









found for a liquid flow an increase of the friction factor with the Re number including Wu and

Little (1983), Peng and Peterson (1996), Mala and Li (1999), Qu et al. (2000), and Li et al.

(2003). They attributed it to surface roughness effect or the early transition to turbulent flow

(Re=300-500) in straight micro-channels. However, recent studies showed general agreement

with theoretical macro-scale predictions for friction factors including Judy et al. (2002), Wu and

Cheng (2003), Hetsroni et al. (2005), and Kohl et al. (2005). They attributed the deviation from

the theoretical prediction in the previous literatures to the size measurement uncertainties and

neglect of the entrance effects. Hence, the relationship is not clear yet. The studies for liquid

flow in serpentine micro-channels just started (Lee et al. 2001; Maharudrayya et al. 2004). It is

of concern in the field of micro-fuel cell.

Most measurements of microflows have been performed with optical microscopes. An

adaptation of particle image velocimetry known as micro-PIV can yield a spatial resolution of

the flow field of approximately one micron (Santiago et al. 1998). Due to the high expense of

purchasing such a commercial system, around $500,000, building an in-house micro-PIV system

became timely to speed up the progress of micro-scale fluid dynamics research at the

University of Florida.

Two-phase flow in micro-channels is also a major research subj ect in micro-scale fluid

dynamics. Recent researches show that the surface tension becomes dominant when the channel

size decreases which may result in a big change in the flow pattern and flow map, even the void

fraction (Kawahara et al. 2002). A study of the size effect on those flow features need to be

performed to provide a clear image of the micro-scale two-phase flow.

Micro-bubble dispenser is one of the fundamental elements in a lab-on-a-chip system. It

can be integrated with other microfluidic components including valves, pumps, actuators,










switches, sensors, mixers, filters, separators, heaters, etc. to succeed with chemical synthesis,

analysis, and reactions using only very small fluids volumes (Stone et al. 2004). Recent studies

have reported several bubble dispensers but with complex structures (Ganan-Calvo and Gordillo

2001; Garstecki et al. 2004). New dispensers with simple structures that are easy to be scaled up

or multiplexed need to be designed and tested.

1.2 Research Objectives

This research is performed to provide fundamental understanding for the following flow

features in micro-scale:

* Friction factor, entrance effect and bend effect for a liquid flow in micro-channels.

* Flow structure around the bend and its correspondence to the additional pressure drop.

* Flow patterns, time-averaging void fraction and two-phase frictional pressure drop for
gas-liquid two-phase flow in micro-channels

* Micro-bubble dispenser with a simple structure to generate uniform micro-bubbles.

To reach the above obj ectives, several micro-channels and bubble dispensers need to be

fabricated and a micron-resolution particle image velocimetry system needs to be built to obtain

the flow structure in micro-scale.

1.3 Research Overview

Chapter 2 presents the flow characteristics of liquid flow in straight and serpentine

micro-channels including the friction factor and bend loss coefficient. The entrance effect and

bend effect are discussed. This chapter can also refer to Xiong R. and Chung J.N., "Flow

characteristics of water in straight and serpentine micro-channels with miter bends",

Experimental Thermal and Fluid Science, Vol 3 1(7), pp. 805-8 12, 2007.

Chapter 3 describes an in-house micron-resolution particle image velocimetry system

(Micro-PIV) used to measure the velocity profile in microscale and discusses the flow structure










around the bend in a serpentine micro-channel. This work has been submitted as Xiong R. and

Chung J.N., "Effects of miter bend on pressure drop and flow structure in microfluidic channels",

International Journal of Heat and Ma~ss Transfer, 2007.

Chapter 4 presents an experimental study of two-phase flow features in straight

micro-channels including flow patterns, flow map, time-averaged void fraction and two-phase

frictional pressure drop. This chapter can also refer to Xiong R. and Chung J.N., "An

experimental study of the size effect on adiabatic gas-liquid two-phase flow patterns and void

fraction in micro-channels", Physics ofFluids, Vol. 19(3), 033301, 2007.

Chapter 5 describes a simple co-flowing micro-bubble dispenser which can be used in a

lab-on-a-chip system. A VOF model is used to predict the bubble motion. Bubble size, bubble

distribution, bubble frequency, and effects of viscosity and surface tension have been

investigated in details. This chapter can also refer to Xiong R. and Chung J.N., "Formation of

bubbles in a simple co-flowing micro-channel", Journal of2~icromechanics and'

M~icroengineering, Vol. 17(5), pp. 1002-1011, 2007.

Chapter 6 concludes the research with a summary of the overall work and suggests future

work.









CHAPTER 2
ENTRANCE FLOW AND BEND EFFECT

Flow characteristics of pressure-driven de-ionized water were investigated in straight and

serpentine micro-channels with miter bends. The micro-channels had rectangular cross-sections

with hydraulic diameters of 0.209 mm, 0.412 mm and 0.622 mm. To evaluate bend loss

coefficient in the serpentine micro-channel and micro-scale size effect on it, the additional

pressure drop due to the miter bend must be obtained. This additional pressure drop can be

achieved by subtracting the frictional pressure drop in the straight micro-channel from the total

pressure drop in the serpentine micro-channel. Since currently there still has a debate on the

relationship between the friction factor and Re number in the straight micro-channel, the

frictional pressure drop had to be obtained experimentally here. Three groups of micro-channels

were fabricated to remove the inlet and outlet losses. The experimental results show that after

considering the measurement uncertainties the experimental Poiseuille number can be well

predicted by the conventional laminar incompressible flow theory when Re number is less than

some value around 1500, the discrepancy observed by the former researchers can be attributed to

not accounting for the additional pressure drop in the entrance region. The onset of transition to

turbulence might be at 1500-1700. For serpentine micro-channels, the additional pressure drop

can be divided into two regions. One is Re<100. It' s very small since no circulation exists. The

other one is Re larger than some value in 100-200. At this time the circulation appears and

develops at the inner and outer wall of the bend. The additional pressure drop increases sharply

with Re number. The bend loss coefficient was observed to decrease and tend to be a constant

with decreasing Re number. It' s found to be larger than the predicted value for macro-channel

turbulent flow and related with the channel size when flow separation appears, namely

Re>100-200.









2.1 Introduction and Background

In recent years, the proliferation of MEMS and micro-fluidic devices has resulted in the

use of micro-channels in many applications including propulsion and power generation of micro

air vehicles, micro-scaled cooling systems of electronic devices, micro satellites, etc. Because of

the wide range of uses for micro-channels, it is important to be able to well predict their behavior

which requires a good knowledge of flow characteristics in straight and serpentine

micro-channels (Ho and Tai 1998).

Flow characteristics in circular and non-circular macro-ducts with curved bends have been

extensively studied (Humphrey et al. 1981; Berger et al. 1983; Bradshaw et al. 1987) in the past

years. However, there were limited literatures on single phase flow characteristics in the

channels with miter bends in the past. Streeter (1961) reported the bend loss coefficient for miter

bend was taken to be around 1.1 for engineering applications, which was usually for turbulent

flow. Yamashita et al. (1984, 1986) and Kushida et al. (1985) studied three-dimensional flow and

heat transfer in miter-bend experimentally and numerically. They found a decreasing trend of the

bend loss coefficient with Re number in laminar and turbulent flow region and analyzed the

effects of Re number and aspect ratio on the flow structures. Though significant attention has

been paid to the flow in macro-systems with bends, research on flow characteristics in

micro-systems with bends has recently been started. In most practical applications the

micro-channels are not straight due to required turns and sometimes it is complicated and

expensive to keep the micro-channel straight. To minimize the pressure losses in the flow

through the micro-channels for optimum design, flow characteristics in serpentine

micro-channels with miter bends must be also well understood. Lee et al. (2001) researched on

the gas flow in micro-channels having the dimensions 20xlx5810Clm3 with bends of miter,









curved and double-turn. They found the flow rate through the channel with the miter bend was

the lowest at a certain inlet pressure and the largest drop was found in the miter bend with the

lowest flow rate. They also found the secondary flow could develop in micro-channels, contrary

to expectations. Maharudrayya et al. (2004) studied the pressure losses and flow structures of

laminar flow through serpentine channels with miter bends by a CFD code but they didn't

consider the micro-scale effect. After literature review, it can be seen that the experimental work

of liquid flow in serpentine micro-channels with miter bends and the micro-scale size effect on

flow characteristics have never been reported before.

As we know, the additional pressure loss due to the miter bend in serpentine channels was

usually related with the flow separation and reattachment around the bend. To evaluate the bend

loss coefficient, the additional pressure drop must be achieved. It can be calculated by

subtracting the frictional pressure drop of straight micro-channels from the total serpentine

micro-channel pressure drop. Hence, the issue of frictional pressure drop in straight

micro-channels was involved in this work too.

For recent 15 years, many scientists have published numerous papers on the flow

characteristics in straight micro-channels. Some of them found flow characteristics in the straight

micro-channel were quite different with those predicted by the conventional laminar flow theory.

One of the important flow performances was the relationship between the friction factor and Re

number. For liquid flow in straight micro-channels, an increase of friction factor with Re number

under certain conditions was found by the scientists including Wu and Little (1983), Peng and

Peterson (1996), Mala and Li (1999), Papautsky et al. (1999), Qu et al. (2000), Pfund et al.

(2000), and Li et al. (2003). Wu and Little's (1983) friction factor measurements appear to

correlate with surface roughness, as the results agreed well with theory for smooth channels, but









the agreement decreased as the roughness increased. In an effort to understand the influence of

geometrical parameters specificallyy, hydraulic diameter and aspect ratio) on flow resistance,

Peng et al. (1994) considered water flows in rectangular machined steel grooves enclosed with a

fiberglass cover. A large range of Re were obtained (50 to 4000), and a geometrical dependence

was observed. For the most part, the friction factor increased with increasing H/W and also with

increasing Dh (holding H/W constant). Nonlinear trends between pressure drop and flow rate

were observed for Re as low as 300 by Mala and Li (1999), specially for water flowing through a

0. 13mm diameter stainless steel micro-tube. At small Re number (Re<100) the measured friction

factors were consistently higher in stainless steel and fused silica micro-tubes. Measured flow

friction for trapezoidal channels was 8 to 38% higher than macroscale predictions for the range

of parameters studied by Qu et al. (2000), and a dependence on Dh and Re was also observed.

However, there were some other scientists finding general agreement with theoretical macroscale

prediction for friction factor including Flockhart and Dhariwal (1998), Jiang et al. (1995), Sharp

et al. (2000) and Wilding et al. (1994), Xu et al. (2000), Judy et al. (2002), Wu and Cheng (2003),

Hetsroni et al. (2005), and Kohl et al. (2005). Jiang et al. (1995) got a linear relationship between

flow rate and pressure drop in micro-channels with various cross-sectional shapes. In the circular

case, the friction factor matched theoretical predictions within 10%-20%. Wilding et al. (1994)

found the result for water flowing in silicon micro-machined channels agreed well with theory

for at least the lower Re number (Re around 17 to 126) tested. Flockhart and Dhariwal (1998)

found a good agreement between the numerical calculations for flow in trapezoidal channels and

the experimental results for Re<600. Sharp et al. (2000) found the microscale measurements of

the friction factor generally agree with the macroscale laminar theory to within +2%

experimental error over all Re numbers up to transition (around 50








through circular fused silica micro-channels with hydraulic diameter 0.075 to 0.242 mm. This

group attributed the deviation from the theoretical prediction in the previous literatures to the

size and measurement uncertainties. Hence, the relationship between the friction factor and Re

number in straight micro-channels is not clear yet. The frictional pressure drop in straight

micro-channels can't be calculated by a universal formulation and need to be achieved

experimentally here.

In our research, three groups of micro-channels were fabricated. Each group has three

micro-channels with the same size: straight long, straight short and single serpentine with miter

bends. The straight long and straight short micro-channels were used to achieve the reliable

frictional pressure drop in straight micro-channels, and the serpentine micro-channels were used

to get the additional pressure drop due to the miter bend. The main obj ective of this study is to

achieve this additional pressure drop and bend loss coefficient to evaluate flow characteristics in

serpentine micro-channels, and compare it with the bend loss coefficient in macro-channels. The

Poiseuille number for straight micro-channels can also be achieved experimentally and compared

with the previous conclusions.

2.2 Experimental Setup

2.2.1 Micro-Channels Fabrication

Fig. 2-1 a) to d) shows the photographs of straight and serpentine micro-channels and

schematic of the straight micro-channel used in this work. The micro-channel was laser etched in

a silicon plate and then a Pyrex thin cover glass plate was anodically bonded on the top of the

plate. The micro-channel plates have two dimensions of 30xl2x2 mm3 (Straight long and

serpentine) and 11xl2x2 mm3 (Straight short). Two small connection tubes which can be inserted

into the inlet and outlet assembly were connected with the small reservoirs. Each of the










serpentine micro-channels had Hyve straight micro-channels with the same size and eight miter

bends. A microscope (Olympus BX50), a 10x obj ective lens and a CCD camera with pixel size

6.45 Clm were used to measure the dimensions of the micro-channels' rectangular cross-sections,

which were listed in Table 2-1.

2.2.2 Apparatus

Fig. 2-2 shows schematic and 3-D assembly drawing of the experimental apparatus used to

investigate the pressure-driven de-ionized water flow in straight and serpentine micro-channels.

It includes a syringe infusion pump (Cole-Parmer Instrument), 60ml syringe (Mcmaster),

micro-filter (Swagelok), pressure transducers (Kavlico), straight and serpentine micro-channel

test sections and computerized data acquisition system. The de-ionized water at the flow rate

from 0.1Iml/min to 70ml/min, which can be set on the panel of the infusion pump with an

accuracy of f0.5%, was driven to the micro-channel test section. The 2Cpm micro-filter can

remove any particles or bubbles which may block the micro-channel before the flow enters into

the test section. Owing to the unavailability of appropriate internal pressure sensors which would

allow in situ measurements, two pressure transducers with f0.5% F S accuracy were installed at

the inlet and outlet of the micro-channel to measure the upstream and downstream pressure and

then sent to the data acquisition system. To get the accurate pressure at the upstream, two

pressure transducers with different measurement range were used. The one with large

measurement range (0-150PSI) was used for smaller micro-channels/larger flow rates, and the

other one with small range (0-15PSI) were used for larger micro-channels/smaller flow rates.

The data started recording when the pressures didn't change heavily for some time, which can be

considered as steady state. The digital pressure output signals (0.5V-4.5V) were collected by an

A/D data acquisition board (Measurement Computing PCI-DAS6034). This board has 16 single









ended or 8 differential channels, 16 bits resolution and the maximum sampling rate can be 200

KS/s. For the signal range of 5V, the absolute accuracy is 10.9 LSB. A Labview program can

read the signals from the board, show the pressure data in real time and save them to a data file.

The test sections were placed horizontally, and all experiments were conducted at room

temperature. Since the pressure measurements were made between the inlet and outlet, which is

beyond the actual length of the micro-channel, there should be contraction and expansion losses

in pressure drop from the inlet to micro-channel and micro-channel to the outlet. In our work, the

pressure drops for the short and long straight micro-channels were measured separately. The

short micro-channel has the entrance effect while the long micro-channel has the entrance effect

and the friction effect, so the difference of these two pressure drops can be considered as the

pressure drop due to the straight friction factor. Besides these two effects, the serpentine

micro-channel has one more effect, bend effect. This effect is introduced by the flow separation

around the corner and will be evaluated individually at the late section.

2.3 Data Reduction and Analysis

For a laminar flow in a macro-scale rectangular channel, the length of the developing flow

in the entrance region can be estimated by the following equation given by Shah and London

(1978):


Ld = 0.06 + 0.07a -0.04a )Re D, (2-1)

Table 2-2 shows the minimum and maximum Ld/Dh for the flow rate range in our

experiment and the L/Dh for the current short and long channels. It is clear that for a substantial

number of cases, the flows are not fully developed under the current experimental conditions.

The follow addresses the estimation of the friction factor for both entrance and fully developed

flows.









For a fully developed laminar flow in a macro-scale rectangular channel with an aspect

ratio ce, Shah and London (1978) used a power series for the friction factor and fitted the

coefficients using their experimental data as below:


( f Re)I, = 96(1-1.3553a +1.9467a' -1.7012a3 + 0.9564a4 0.2537a') (2-2)

This empirical equation can approximate the two-dimensional theoretical exact solution (Nguyen

and Wereley 2006) for the fully developed friction factor with an error less than 0.05%. For the

current micro-channels, the aspect ratio range is from 0.9 to 0.97, so the corresponding

theoretical Poiseuille numbers (fRe)fd for the fully developed flow are around 57. However, the

current micro-channels may not be long enough for the flow to become fully developed under

laminar flow conditions. Actually in many practical applications, flows generally can not reach

the fully developed state in micro-channels as they are relatively short due to space limitations in

micro-systems.

For a developing flow, its pressure drop is higher than the fully developed flow. As a result,

the pressure drop from the inlet of the channel to a downstream location x in the entrance region

is the sum of the fully developed pressure drop and the pressure drop defect given by the

equation below (Kakac et al. 1987):


Ms =( f e) x +K x(2-3)

x =~ (2-4)
Re- D,,

where K(x ) is the pressure drop defect given by:


K x' )= J Re-(f Re)i x (2-5)










f~ Re= '13.44 K(ao) ~4x )+ ( fRe), 4 -3.44'j xO 26
x1+ B x'-

where fa,, is the apparent friction factor and Eq. (2-6) is given in Kalkac et al. (1987). According

to White (1991), the constant B in Eq. (2.6) is equal to 2.93x10-4. As plotted in Figure 2-3, the

pressure drop defect K(x ) for the current micro-channels begins at the value of 0 for x+ = 0 and

increases asymptotically to the fully developed constant value K(co) which has a dependence

upon the channel aspect ratio for rectangular channels as suggested by Shah and London (1978).


K(o) = 0.6796 +1.2197a + 3.3089a' 9.5921a' + 8.9089a" 2.9959a' (2-7)

Eq. (2-7) determines the fully developed K(co) for a rectangular channel with an uncertainty of

0.04%. So the pressure drop for the straight short, AP,, and straight long channel, F can be

expressed as:

B;h = R~o + Ries. (x = L,,,) (2-8)
M,= Ro~ + Ries.(x = L, ) (2-9)

where APio is the inlet and outlet assembly losses due to changes in tubing diameter, tees and

elbows as indicated in Figure 2-1(e). Straight short and straight long micro-channels have the

same channel size but different channel length.

Since the inlet and outlet pressure losses are proportional to U2, the inlet and outlet losses

are the same for both lengths of the channels under a given Re number because that both have

two ends placed in the same inlet and outlet assembly. APs,h and AP1 are the measured pressure

drops for the straight short and straight long channels, respectively. Hence, the experimental

friction factor that takes the entrance effect into consideration is estimated by the following

equation:









APr AP D,
fexp pl 2" K(L)-K(,,,] L ,,,(2-10)


For the serpentine micro-channels, the measure pressure drop can be expressed as:

APS = Aio +A ar,(x =Lg)+ N -AP, (2-11)

where APs is the measured pressure drop for the serpentine channel and APb is the additional

pressure drop due to the miter bend. N is the number of miter bends. So APb and the bend loss

coefficient, K,, can be written as:


AP, AB AP A L, L,
pU / 2 pU / 2 L, L,,,
AP, = (2-12)


AP, Ag AP-A Ls L O)XT
[K (L, ) -K (L,rh )1 L L
pU / 2 pU / 2L -L,
K, =(2-13)

According to the error propagation analysis, the uncertainty of the friction factor and bend

loss coefficient can be expressed as:


3( f Re) iD,D, i A +O (A /AL
fRe D AI Q / L

=K 2l +l6~L 2 +sM, (2-15)
K, AP,

The uncertainty range of the friction factor and bend loss coefficient can be calculated to be

f10.2-f15.1%/ and fl2.3%-f l6.1%/.










2.4 Results and Discussion


2.4.1 Friction Factor

Fig. 2-4 shows the comparison between the experimental pressure gradients without

removing the entrance effect, (AP1-APsh)/(L1-Lsh), and theoretical results for the current

micro-channels. The dot lines represent the pressure gradients predicted by the 2-D conventional

laminar incompressible flow theory, which shows a linear relationship with Re number

theoretically. However, as the Re number increases, the measured pressure gradients shows a

non-linear relationship with Re number. Some former researchers attribute it to the early

transition to turbulence at Re=700. However, from Fig. 2-5, we can conclude it doesn't result

from the early transition to turbulence but may from not accounting for additional pressure drop

in the entrance region of the channel.

Fig. 2-5 shows the comparison between the experimental friction factor calculated by Eq.

(2-10) and theoretical results predicted by Eq. (2-2). The solid line represents the predicted

friction factor for fully developed flow, and the vertical bars denote the measurement uncertainty.

From Fig. 2-5, we can see after the experimental uncertainties are considered, the experimental

results show agreement with standard laminar incompressible flow predictions when Re<1500.

It' s believed that the consistent offset observed by the previous researchers is the result of

unaccounted for bias in experimental setups. When Re equals to 1500-1700, fRe begins to

deviate from the theoretical value which may suggest the transition to turbulence.

2.4.2 Bend Loss Coefficient

For laminar flow, the additional pressure drop is related with the flow separation which

need energy to be maintained and results in an additional pressure drop not associated with

frictional losses. As we know, in micro-channels, the flow usually keeps in laminar flow region,

so the flow pattern along the miter bend affects the additional pressure drop pretty much.










Maharudrayya et al. (2004) used CFD simulation and obtained the flow pattern along a miter

bend at different Re numbers. When Re = 100, there are no eddies around the inner and outer

wall. While Re = 210, significant recirculation at the inner and outer wall appears. The size and

intensity of both vortices increase with increasing Re number.

Figure 2-6 shows the experimental additional pressure drop under different Re numbers. It

can be divided into two regions. One is Re<100. There is no eddies and the additional pressure

drop is very small for all of the channels. The other one is the circulation appears on the inner

and outer wall and develops with increasing Re number. The critical Re number is in the range

100-200. At this time the additional pressure drop increases sharply. The experimental results

also show the additional pressure drop increases with decreasing hydraulic diameters. From Fig.

2-6, the additional pressure drop of the micro-channel with hydraulic diameter 0.209 mm is

around 0.5atm when Re number reaches around 850, which is approximately equal to the

frictional pressure drop of the same size straight micro-channel with 23.7 mm length, 101% of

the current total length. Hence, the additional pressure drop due to the miter bend is also a big

source of the micro-channel pressure drop, especially for small size and short length

micro-channels.

Since the pressure drop for channel 1 is pretty high, Re number can only reach around 850

and the upstream pressure will exceed the measurement range of the transducer. Here the bend

loss coefficients are calculated by using Eq. (2-13) and compared at Re number from 47-2268,

which is shown in Fig. 2-7. The solid line represents the bend loss coefficient of the miter bend,

1,1, reported by Streeter (1961). From Fig. 2-7, we can see bend loss coefficients of the

micro-channels are all larger than 1.1. It is a similar conclusion with that of Yamashita et al.

(1984), the bend loss coefficient in laminar flow region is larger than that in turbulent region.










The second characteristic is it' s dependent of Re number and decreases with increasing Re

number, which is also different with turbulent flow. For macro-channel turbulent flow at larger

Re number, Kb almOst won't change with Re number. When Re is larger than some value in

1300-1500, Kb almOst keeps constant and changes in the range of +10%. The last characteristic is

the size effect on Kb. It's larger for smaller channel when there is flow separation, namely

Re>100-200. After considering the measurement uncertainty, these two curves still have

difference. The quantitative relationship needs more experiments and simulation to be

determined.

2.5 Summary

The investigation of a pressure-driven water flow in straight micro-channels and in

serpentine micro-channels with miter bends was conducted experimentally. A short straight and

a long straight micro-channel with the same channel size were fabricated and used to isolate the

inlet and outlet assembly extra pressure losses. The following conclusions were obtained:

* The experimental friction factors show good agreement with the classical laminar
incompressible flow predictions after considering the measurement uncertainties when the Re
is less than 1500. When the Re is larger than 1500, the onset of transition to turbulence may
take place. For laminar flows in micro-channels, the frictional pressure drops in the
developing entrance region can still be predicted by the classical macro-scale equations for
developing flows. In general, the frictional pressure drop in a micro-channel can be estimated
by macro-scale theories and correlations.

* In serpentine micro-channels, the additional pressure drop due to miter bends can be divided
into two groups. The first group is for Re<100 where there is no eddies and the additional
pressure drop is very small for all of the channels. The other group is for flows with the
Reynolds numbers exceeding the threshold values that are in the range of 100-300. When the
Reynolds is higher than the threshold value, we found the flow separation and formation of
vortices that appear on the inner and outer wall around the miter bend. These vortices
increase in strength with increasing Re number that causes the bend pressure drop to increase
sharply with the Re number. The experimental results also show the bend pressure drop
increases with decreasing hydraulic diameters. Bend loss coefficient Kb is a, function of the
Re number only when Re<100, a function of the Re number and channel size when Re>100,
and almost keeps constant and changes in the range of +10% when Re is larger than some










value in 1000-1500. The trend of the experimental pressure drop is consistent with the flow
structure change.

The flow structures around the serpentine micro-channel can also be achieved by a relatively

new laser diagnostic technique micron-resolution particle image velocimetry (Micro-PIV),

which is present in Chapter 5 in details.


Table 2-1. Dimensions of three groups of micro-channels
Channel Width Depth Hydraulic Total length of the micro-channels LA 0.3mm
group No. Wi2Cpm Si2Cpm Diameter
Dh (mm) __,_ .__+_


onglf ~lannelC ortV ~lannelC erpentne
Li (mm) Lsh (mm) Channel Ls (mm)
213 206 0.2094 23.6 4.1 118
419 406 0.4124 23.5 4 117.5
630 615 0.6224 23.8 4.2 119

Comparison of current pipe lengths with those of entrance regions.
Ld/Dh L/Dh (Straight short) L/Dh (Straight long)
Channel 1 Channel 2 Channel 3 Channel 1 Channel 2 Channel 3
4.23
19.58 9.70 6.74 112.7 56.98 38.24
204.12


Channel 1
Channel 2
Channel 3

Table 2-2.
Re

47

2268





Dt




Pyex glass cover


Micro-channel


Connection tube


Figure 2-1. Three groups of fabricated micro-channels: A) Photograph of a group of
micro-channels (Dh = 0.209 mm) B) Dh = 0.412 mm C) Dh = 0.622 mm D) Schematic
of the straight micro-channel E) Schematic showing inlet and outlet elbows.










Inlet Pressure Outlet Pressure
Filter Transdrucer Transdlucer

Miicrochann~el
Syringe Prunp


m


Pir esiu e
1 ineie


MirchnEl


li~J~


Data Acquisition System


Figure 2-2. Experimental pressure drop measurement apparatus


1E-7 1E-6 1E-5 1E-4 1E-3 O 01 0.1 1 10 100
X+


Figure 2-3. Pressure drop defect K(x ) vs x .













100


-a- Channel 1
--+- Channel 2.
-o- Channel 3
Theoretical values


1000


2000


Figure 2-4. Experimental pressure gradients without removing the entrance effect
(AP1-APsh)/(L-Lsh) VS Re number.


SChannell
o Channel 2
o Channel
-- Th eo retic al frictio n fa cto r


0 500 1000 1500 2000


Re


Figure 2-5. Experimental friction factor vs. Re number in straight micro-channels





































I I I I I I I I I I 1 11I
100 1000

Re


Bend additional pressure drops vs. Re number in serpentine micro-channels


ul'l" ",I,,, I,,,I ,,, I,,, I,
0 500 1000 1500 2000 2500

Re


Bend loss coefficients vs Re number in serpentine micro-channels


60 -



50 -






;30

2-


- ~-Channel l
S-+- Cha nn el 2
_o~-Channel 3


Figure 2-6.


-n- Channel 1
-+~- Channel 2
- *- Channel 3
-K~ fo r turbule nt flow (Streete r 1 961 )


Figure 2-7.









CHAPTER 3
FLOW STRUCTURES AROUND A BEND

From chapter 3, we know the bend additional pressure drop is related to the flow structure

around the bend, here a micron-resolution particle image velocimetry (micro-PIV) system was

built and used to obtain the detailed velocity vector field in a serpentine micro-channel. The

micro-PIV system was verified first by the velocity profile in a straight micro-channel of 0.209

mm. It was found that the vortices around the outer and inner walls of the bend do not form when

Re<100. Those vortices appear and continue to develop with the Re number when Re>100, and

the shape and size of the vortices almost remain constant when Re is larger than a value in

1000-1500. The results are compatible with those in chapter 3.

3.1 Introduction and Background

In curved channels, the centrifugal force drives the more rapid fluid toward the concave

part of the curved channel while the fluid in the convex part is slowing down causing a

secondary flow at a right angle to the main flow. The magnitude of the secondary flow increases

with a decreasing bend radius and increasing fluid velocity. As expected, the curved channel will

cause a much higher friction loss than that of the corresponding straight tube for both laminar

flow and turbulent flow. In previous works, the researchers used computational method or color

dye to visualize the flow structure. Here a relatively new experimental technique, microscopic

particle image velocimetry (micro-PIV) was used to measure the velocity field. The

micron-resolution Particle Image Velocimetry (CLPIV) system was first developed by Santiago et

al. (1998) to investigate microscale fluid flow. He used an epi-fluorescent microscope with a

continuous Hg-arc lamp, and a Princeton Instruments' intensified CCD camera to record the flow

around a nominally 30Cpm diameter cylinder in a Hele-Shaw flow cell. A bulk velocity of 50Cpm/s

was measured with a spatial resolution of 6.9pmx 6.9pmx 1.5Cpm, based upon the size of the first









correlation window and the depth-of-field of the microscope. Later, the system was modified by

Meinhart et al. (1999) to measure higher speed flow using the pulsed laser. It is becoming one of

the most versatile experimental tools in microfluidic research. Though CLPIV has evolved from

conventional PIV, there are several important factors which differentiate CLPIV from

conventional PIV.

One hardware difference is the method of illumination in CLPIV, i.e. volume illumination.

The conventional PIV used a light sheet to illuminate a single plane of the flow with the

thickness less than the depth of field of the image recording system. Volume illumination is an

alternative approach, whereby the test section is illuminated by a volume of light. This

illumination model may be necessary for obtaining two-dimensional measurements when optical

access is limited to only one direction or in micro-scale geometries in which alignment of the

light sheet is difficult. It is advantageous when one is interested in measuring flows through

micro electromechanical systems for which optical access is limited to one direction and the

length scale is of the order of micrometers (Meinhart et al. 2000a). The small length scales

associated with microfluidic devices require that the thickness of the measurement plane should

be only a few micrometers. Since it is difficult to form a light sheet that is only a few

micrometers thick and virtually impossible to align such a light sheet with the optical plane,

volume illumination is the only feasible illumination method for most micro-PIV applications.

One shortcoming for volume illumination is it causes significant background noise and limits the

particle concentration by reducing the signal to noise ratio (Gui et al. 2002; Meinhart et al.

2000b).

Image processing and advanced interrogation algorithms can be used to enhance image

quality and to increase the signal-to-noise ratio. The images taken in micro-PIV are usually in









worse condition, i.e. lower signal-to-noise ratio, than those in the conventional PIV. Errors in

PIV measurements can be reduced by improving the experimental conditions and by using

advanced interrogation algorithms such as the average correlation method. Ensemble average

correlation method is a time-averaged PIV algorithm developed by Meinhart et al. (2000b) to

improve the signal to noise ratio, especially in case of the volume illumination. This algorithm

can only be applied to steady or periodic flow fields. Since most typical microfluidic devices are

working in steady flow conditions, the time averaged velocity field is sufficient to resolve the

micro-scale flow. The central difference image correction algorithm (Wereley and Gui 2003) is a

very effective and accurate method, especially for making measurements in regions of high

velocity gradient. This method is a combination of the central difference interrogation algorithm

developed by Wereley and Meinhart (2001), the continuous window shifting technique

developed by Gui and Wereley (2002) and the modified image correction algorithm originally

introduced by Huang et al. (1993). This central difference image correction method shows the

significant reduction in the evaluation error, i.e. the bias and random errors, when compared to

other more traditional methods.

Another important difference is the size of seed particles. Since a seed particle should be

small enough compared to the dimension of the microfluidic device not to disturb the flow

pattern, relatively small seed particles are required in CLPIV. However, when the particle diameter

is much smaller than the wavelength of the illumination light, scattering from the particles is too

weak to image them using elastic scattering, i.e. the frequency of the scattered light is the same

as that of the incident light. An inelastic scattering technique such as fluorescence can be used to

increase the signal-to-noise ratio by filtering the background light.









Brownian motion is another factor to be considered in CLPIV since Brownian motion

becomes significant when the particle or the flow velocity is very small, and eventually causes

errors in the velocity measurement and increases the uncertainty in the particle location.

Brownian motion has two maj or effects on CLPIV measurements. One effect decreases the

accuracy in estimating the particle displacement between the two light pulses, i.e. the time

interval. Brownian motion also can cause errors in estimating the particle location during the

illumination exposure. The latter problem can be solved readily by using pulsed lasers which

reduce the exposure time so significantly (to 5 ns) that Brownian motion has no effect (Nguyen

and Wereley 2002). The former error can be reduced by increasing the time interval. Though

long time interval values generally have been avoided in PIV evaluation because of the larger

evaluation error associated with the longer time interval, this problem can be minimized with

advanced interrogation algorithms such as the central difference interrogation. Also the

Brownian motion error is further reduced by a factor of 1/~N when Ni particle images are

averaged in a single interrogation spot.

In this chapter, the main obj ective is to 1) build an in-house micro-PIV system and 2)

achieve the flow structures under different Re numbers to explain the pressure drop data in

chapter 3.

3.2 Micro-PIV System

3.2.1 Laser Beam Alignment

Two Nd:YAG laser machines(Continuum Minilite II) were used to create the illumination

source. Some useful information of the laser is listed in Table 3-1. To make the two lasers

illuminate approximately the same region, a laser beam alignment component is constructed to

combine these two lasers in the same optical axis. Fig. 3-1 shows the top view of the optical










layout of the laser beam alignment component. A half waveplate (Newport) changes the vertical

polarization of laser B to be horizontal polarization while laser A still keeps the vertical

polarization. The beam merger, a dielectric polarizer (Newport), reflects the laser with vertical

polarization, namely laser A and transmits the laser with horizontal polarization, namely laser B.

A beam stop absorbs the light that transmits the beam merger. A linear and rotation stage A with

high precision was fixed beneath the beam merger and another linear high precision positioning

stage B was fixed beneath the laser B output. Rotate stage A to change the incline angle of laser

A and make the intensity of the reflection beam maximum. After that, adjust stage B to make

laser B merge into the optical axis of laser A. A beam expander including two spherical concave

and convex lenses (Newport) expands the size of the laser beam after the beam merger.

Adjusting the distance between these two lenses can change the expanded laser beam size. The

reason why the spherical lenses were used here is to create volume illumination for micro-PIV

measurement.

3.2.2 Timing Scheme

Since the laser beams are pulsed and the pulse width is so short, 3-5 nsec from Table 3-1,

the CCD camera shutter is required to keep open to make the frame exposed during the pulse

width. And one frame is required to be exposed once. Hence a timing scheme is required to

externally control the two lasers and CCD camera.

To externally control the laser, tumn the real panel FLASHLAMP and Q-SWITCH switch

of the laser machine Minilite II from INT to EXT. It will disable the internally generated signals

which respectively fire the flash lamp and open the Q-switch. At the same time, these switches

let the Minilite II accept TTL signals into the FLASHLAMP TRIG IN and Q-SWITCH TRIG IN

BNC ports to trigger flash lamp firing and Q-switch opening. The Q-switch delay can adjust the

output pulse energy. For Minilite II, the delay of about 152 Cps yields highest energy laser pulse.









The time delay between the two lasers' firing the flash lamp is quite important and should be

chose carefully since it sets the interframing time.

A specialized CCD camera (Cooke Sensicam QE), 1376 x 1040 pixels, was used to record

the flow field. It uses thermo-electrical cooling to cool down to -120C, which lowers the readout

noise low to 4 e-rms so the weak fluorescent signal can be measured. The interframing time low

to 500 ns make it enough to measure the flow with high Reynolds number up to 2000. To

externally control the CCD camera, set the operation mode to double shutter in the software and

use a coaxial cable to connect the TRIG IN BNC ports with the timing controller. The double

exposure is controlled via an external TTL trigger signal from the controller.

A timing controller (Labsmith LC 880) was used to realize the timing scheme. It has 8

input and 8 output channels. It is also able to send a trigger-pulse delay from 50ns to 1370s and

trigger-pulse duration from 7.7ms to 1370s with the resolution of 10 ns. A RS232 interface

connects the controller with the computer to make remote control. Connect the two lasers (4

output ports) and the CCD camera (1 output ports) with the controller, and TTL trigger signals

can be sent to them via some coaxial cables. Fig. 3-2 shows the timing diagram for the two lasers

and CCD camera. How to program LC 880 to realize this time scheme refers to the Appendix.

When the shutter trigger signal falls, the shutter opens after a very short period. The

integration time for image one will be finished some time after the trigger signal rises again and

the integration time for image two starts. What we need control is to send two laser pulses by

setting a proper time delay from the trigger signal to make one pulse be in the integration time of

image one and the other pulse in the integration time of image two, so in each integration time

the image will be exposed once, which is called double frames double shutter. The interfaming

time can be shortened by sending the first pulse at the end of the image one' s integration time









and the second pulse at the beginning of the image two' s integration time. After testing the CCD

camera, we find the minimum interframing time for our CCD camera can reach 300ns which is

enough short for our experiment. Another important issue is the rising duration of the trigger

signal must be long enough for the CCD to read out the two images.

3.2.3 Fluorescent Particles Image

To visualize the flow field in the micro-channel, fluorescent particles, polymer

micro-spheres (Duke Scientific R500), are seeded in the flow. These micro-spheres have a

measured mean diameter of 0.49Cpm and approximate a number of 1.5x1011 per mL. They also

have the excitation maxima of 542 nm and the emission maxima of 612 nm with 70 nm stokes

shift. A filter cube (Olympus U-MWIG), assembled in the microscope (Olympus BX50), reflects

the light with wavelengths between 520 and 550 nm, exciting TMRM (maximum excitation at

548 nm), and transmits fluorescence through a high-pass filter (565 nm). The process of taking

fluorescent particles image was that the expanded laser beam was delivered into the microscope,

where the filter cube directs the beams to the objective lens. The obj ective lens relays the light

onto the micro-channel, where it illuminates the entire flow volume. Fluorescent particles in the

cone of illumination absorb the illumination light, h=532nm, and emit a distribution of red light,

h=612nm. The emitted red light can go through the filter cube and is recorded onto the CCD

camera while the reflected green light from the background is filtered out by the filter cube.

According to the timing scheme, the CCD camera shutter was opening when the lasers came.

Hence two consecutive fluorescent particles images were recorded. Fig. 3-3 (a) and (b) show the

real images and schematics of a straight micro-channel with the hydraulic diameter of 209Cpm

and a serpentine micro-channel having a rectangular cross-section 650Clmx100Clm with hydraulic

diameter of 0. 173 mm.









3.2.4 Measurement Depth

Fig. 3-4 shows the schematic of micro-PIV used to investigate the pressure-driven

de-ionized water flow in serpentine micro-channels. Fig. 3-5 and Fig. 3-6 show the photo of the

system and the laser beam alignment component. Firstly the fluorescent particles were seeded

into the de-ionized water flow. Two Nd:YAG lasers were directed to the same optical path by

optical lenses and expanded by a beam expander made up of a concave and a convex lens. The

0.69 Clm particles absorb green light (~542nm) and emit red light (~612nm). The emitted light is

imaged through a 10x obj ectives lens (NA=0.3) and passed to the fluorescent filter cube, where

the green light from background reflection is filtered out and the red fluorescence from the

sub-micron particles is passed to the 0.5x lens and recorded on the CCD camera. With the

micro-PIV technique, the depth of field is described by Meinhart et al. (2000a) as:


3nAl 2.16D
Z,+ P + Dp (3-1)
NA tan6 B

where n is the index of refraction of the immersion medium between the microfluidic device and

the obj ective lens, h is the wavelength of light in a vacuum, NA is the numerical aperture of the

obj ective lens, D, is the diameter of the PIV particle and 6 is the small light collection angle. In

our case, n was 1, h was 612 nm, NA was 0.3, d was 0.69 Clm and tan6 was 0.31. Therefore, the

depth of field was calculated to be 26.06 Clm. The concentration of the fluorescent particles

solution was prepared to ensure at least 5-10 seed particles in each interrogation volume. The

necessary minimum seed density was estimated using the equation (Li et al. 2006):


N, = C,A, (2z,,) (3 -2)

where N, is the desired minimum number of particles in each interrogation volume; Cv is the

volumetric concentration of the fluorescent particle solution; Ai is the area of each interrogation









window. The interrogation windows in current experiments measure 42Clm square. Adj acent

interrogation windows were overlapped by 50%, yielding a spatial resolution of 21Cm. To

achieve this spatial resolution required a volumetric particle concentration of approximately

0.0082%. This volume fraction of seed particles is small enough to neglect any two-phase effects,

and the working fluid can be considered a single-phase fluid. In this work, this time delay is set

to be 1-15 Cls for the micro-channel flow at different Re numbers, so the particles move

approximately 1/4th of an interrogation window between pulses. The interrogation windows

measure 32 camera pixels square, thus the particles moves approximately 8 pixels between laser

pulses. Assume that the measured velocity is accurate to within 1/5th of a pixel. It results in an

experimental uncertainty of less than +2.5% (Prasad et al. 1992).

3.3 System Validation

To validate the micro-PIV system, the velocity field is initially obtained at room

temperature in the straight micro-channel of 0.209 mm at low Re numbers. The time delay

between consecutive frames is 5ms. An interrogation window of 32x32 pixels and a grid size of

16xl6 pixels are used. The analytical solution for the velocity profile at the PIV measurement

depth can be formulated as:


W2 dPW 2 (3 (2 + 1)3 oshc s[z~)(2k +1) "'~~~ ~[6~,~ ~2 -W 3
W P y2 (- 1)k 2W (y-W
u(y) = cs(k133
2pu dx k=0 2 1)

where dp/dx is the pressure gradient, W and S are the width and depth of the micro-channel

respectively. Figure 3-7(a)-(b) shows the results of PIV analysis for the square micro-channel of

0.209 mm and comparison with the theoretical profile computed from Eq. (3-3). The average

discrepancy between our PIV measurements and the predicted velocities is averagely about 4%










for the center line + 70Cpm while about 10% for the measurements closet to the wall due to the

near-wall effect.

3.4 Results and Discussions

3.4.1 Flow Structures Around The Miter Bend

Figure 3-8 shows a typical image and velocity vector field generated by the micro-PIV

system. The focus of the flow field in Fig. 3-8 is the effects of the 90 degree turning on the flow

micro-structurees around the miter bend in the serpentine micro-channel at Re = 500. We note that

the main stream velocity increases while the flow is rounding the corner. It is also apparent that

micro-structures of flow recirculation have formed around the outer corner and immediately after

the inner corner (flow separation). A detailed visualization and discussion on the onset and

development of induced vortices around the outer and inner corners with the Re number are

given below. Fig. 3-9(a-e) shows the enlarged velocity fields at the outer corner for the Reynolds

numbers ranging from 100 to 1500. Fig. 3-9(f-j) shows the enlarged velocity fields at the inner

corner for the same Reynolds numbers. Fig. 3-10 shows the corresponding streamlines computed

from the experimental velocity vectors. For the induced micro flow structures at the outer corner,

there is basically no recirculation for Re = 100 and only some fluctuations in the flow adjacent to

the wall due to the wall roughness are captured by the PIV. At Re = 300, a very small vortex

located at (x = 0.2 mm, y = 0.95 mm) is seen, but its circulatory motion is not fully developed. It

is clear that at Re = 500, the recirculation vortex is fully developed and located at (x = 0.3 mm, y

= 1.07 mm). As the Reynolds number is further increased to 1000 (Fig. 3-10(d)) and then to

1500 (Fig. 3-10(e)), the locations of recirculation vortices stay at the same point and only the size

and strength are increased with the Reynolds number.

For flow structures near the inner corner, the micro flow structures that form due the flow

separation always start right after the sharp edge as the flow separates. Again, there is basically









no separation vortex for Re = 100. The separation vortex is very clear for Re = 300. As the

Reynolds number is further increased, the size and strength of the separation vortex are also

increased accordingly. However, the growth of the vortex seems saturated after Re = 1000 as

there is no significant difference in the size between Re = 1000 and Re = 1500 but the strength

continues to increase as discussed later. For Re = 1000, the inner corner vortex approximately

occupies 20% of the width of the channel in the downstream of the bend.

In summary, micro-structured recirculation vortices are induced when the flow is making

the turn in a serpentine micro-channel. These vortex structures are responsible for the bend

additional pressure drops for the serpentine micro-channel as compared to a straight

micro-channel. The following presents the measured pressure drops and discussions for

serpentine channels.

3.4.2 Circulation Calculation

In order to further substantiate the relatively large bend pressure drops, we calculated the

circulation, r, for every induced vortex from the velocity Hield given in Fig. 3-9. The circulation,

r, that is the strength of the vortex is defined as:


F = Vx V)-dAi (3-4)

The results of the calculated vortex circulation are given in Table 3-2. In general, the outer

vortices are three to six times stronger than the inner vortices. Figure 3-11 shows the total vortex

circulations as a function of the Reynolds number. The total circulation is the sum of the absolute

values of the inner and outer vortices. The similar trends between the total vortex circulation

(Figure 3-1 1) and the bend pressure drop of Dh = 0.209 mm channel (Figure 3-6) serve to

confirm the measured data.










3.4.3 Shear Strain

For further understanding the micro-structures of the flow, the flow shear strain rate

distributions were computed based on the Eq. (3-5) and plotted in Figure 3-12.


1 Su av
S=--+-(35


As we examine Figure 3-12, the shear strain rates generally increase with the Reynolds number

and there is an uneven distribution pattern with highest rates concentrated along the inside wall

and they peak around the sharp edge. Before the vortices appear, the velocity only changes much

around the bend, so we can see bright color around the bend when Re = 100. After the vortices

appear, the velocity also changes a lot from the vortex to the main stream, so we can see the

color change around the vortex structure.

3.5 Summary

A micron-resolution particle image velocimetry system has been built. The minimum

interframing time can be set to 200ns which make the system has the ability to measure the

velocity up to 10m/s. The flow structure in a serpentine micro-channel with miter bends was

conducted experimentally. The following conclusions were obtained:

* The Micro-PIV system is verified by the flow field in the micro-channel with the hydraulic
diameter of 0.209 mm.

* The flow micro structures around the bend of a serpentine micro-channel can be divided into
three categories depending on the flow Reynolds number. When Re<100, there is no induced
flow recirculation and flow separation. When Re>100, vortices and flow separation appear
and further develop. The outer corner vortex develops along the wall of the channel, and the
vortex center moves slightly from the upper stream to the down stream with the increasing of
the Re number. The inner wall vortex due to flow separation develops immediately after the
flow makes the turn. When Re is around 1000, the inner wall vortex approximately occupies
20% of the width of the channel in the downstream side of the bend. When Re>1000-1500,
the shape and size of the outer and inner vortices become almost constant.

* The shear strain rates generally increase with the Reynolds number and there is an uneven
distribution pattern with highest rates concentrated along the inside wall and they peak










around the sharp edge. After the vortices appear, the velocity also changes a lot from the
vortex to the main stream, so we can see the color change around the vortex structure.

Table 3-1. Specification of the Nd:YAG laser (Continuum Minilite II)


Value
532 nm
25 mJ
3-5 nsec
Vert.
<3 mm
<3 mradx
1-15 Hz


Parameters
Wavelength
Energy
Pulse width
Polarization
Beam size
Divergence
Repetition Rate


Table 3-2.
Re
100
300
500
1000
1500


Calculated vortex circulation
Inner Wall Vortex Strength (mm2/S)
0.082
4.10
10.97
28.10
97.99


Outer Wall Vortex Strength (mm2/S)
-0.41
-12.47
-77.48
-203.9
-266.9











Beam
Stop


Stage B


Spherical
Concave
Lens


A Spherical
GORYBX
Lens


Figure 3-1. Top view of the optical layout of the laser beam alignment


1240 ns
A: Camuera
Shutter Trigger


Shutter Opens -' ~


152 ps 920 ns 200ns dead tune

j~~~ CCD Readut Time of Image 1 | CCD Readut Time oflag Image 2

rTmte Image 1I Integration Time Image 2 .


B: Laser A
Flash Lamp

C: Laser A
Q-Switch
D: Laser B
Flash Lamp
E: Laser B
Q-Switch


Inetegratlo


L


|
I
.1


30~s


:30ps


InterfranmigTime at


200 ms


Figure 3-2. Timing diagram for the two lasers and CCD camera



























Figure 3-3. Fluorescent images at straight and serpentine micro-channels : A) A real image of
the straight micro-channel with hydraulic diameter of 0.209 mm and B) the serpentine
micro-channel with hydraulic diameter of 0.172 mm (a 10x objectives used; white
spots are the fluorescent particles).


CCD Chamera


Figure 3-4. Schematic of micro-PIV system



































Figure 3-5. Photo of the optical sub system


Figure 3-6. Photo of the laser beam alignment component



















- -e 1.29 mm/s


200

















50


_______________
ff _t I _t _t r
t_ C C C C C C
r r r r r r r

rrrrrrrrr rrrrrr
'C C'C~C
C C C 'C C 'C
rr--
'C C 'C C C


r
C

_ _C


C

_ _
_ _
tf


~'C ~C~~CC~
--C --r --r
--F --F --F --C --F --F --F
--F --F --F --F --F --F ~- ~- --F --F
++++++++++


I I I I I I I I I I


500


200


300

x (pm)


400


O






50














150






200


0 02 04 OB OB 1 12 1.4 16 18
u (mm/s)


Figure 3-7. Micro-PIV results for low speed flow. A) Velocity vectors (1 12 pairs of images

were ensemble-averaged) B) Comparison of the measurements with the theoretical

profile (Re = 0.3).









Outer Wall Vortex







0.8

E

Inner Wall Vortex







0.2 04 0.6 0.8 12 1 6 1
x [mm]

Figure 3-8. Typical velocity vector in the serpentine micro-channel at Re = 500.
















CC_)CIC_
,r~~c~,~,,l r

I .




I~
rr

,
rri-

Il I I I

I


0:2 0:4
x[mm]


x[mm]


x[mm]


x [m m]


Figure 3-9. Flow structure at the outer wall A) Re = 100 B) Re =300 C) Re = 500 D) Re = 1000

E) Re 1500 and at the inner wall F) Re = 100 G) Re =300 H) Re = 500 I) Re = 1000
J) Re = 1500










0.0



S0.7-





x [mm]

0.8 -- -




E 0.7





x [mm]

0.8



S0.7



I>



0.8



S0.7~-





x [mm]

Figure 3-9. Continued










0.8-



E
E 0.7-




Figurel~ 3-9 Continued













































I I I I I I I I


I I I I I I I I


1.2 C


0.5



0.4-



0.2-


I I I I I I I I


0.2 0.4 0.6 0.8
X~m m)


1 1.2 1.4 1.6 1.


O 0.2 0.4 0.6 0.8
X~m m)


1 1.2 1.4 1.6 1.


Figure 3-10. Streamlines at different Re numbers: A) Re
Re = 1000, and E) Re = 1500


100, B) Re


S300, C) Re


500, D)














I I I I I I I I


I I I I I I I I


1.2 C


I I I I I I I I


O 0.2 0.4 0.6 0.8
X~m m)


1 1.2 1.4 1.6 1.8


I I I I I I I I


0.8 t


0.2 0.4 0.6 0.8
X~m m)


1 1.2 1.4 1.6 1.


Figure 3-10.


Continued





I I I I I I I I


0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.

X~m m)


inued















-I


-I


1.2 C


E
E
r



















Figure 3-10.











E
E
r

r
a,
b
co
x
a,



m


O




Count


100


350


300


250






150


100


50


10 100

Reynolds nurnber, Re


Figure 3-11. Total vortex circulation vs. Reynolds number.


































-10
-20











501

40






40 30

20
101


to10,1










soo |
620


OB\
Y (mm) O 4


Figure 3-12. Distribution patterns of shear strain rates. A) Re = 100, B) Re

D) Re = 1000, E) Re = 1500.


300, C) Re


500,

























20



-40

-B

12


08
Y (mm) O4

02 04 OS aB 1 12 14I Is
r(mm)



E
14 80

40

40


"20

~-40-
60







06
Y (mm) O 4

01 04 04 00I 1 11 14 15




Figure 3-12. Continued








































61


0









CHAPTER 4
ADIABATIC GAS-LIQUID TWO-PHASE FLOW

In this chapter, adiabatic gas-liquid flow patterns and void fractions in micro-channels

were experimentally investigated. Using nitrogen and water, experiments were conducted in

rectangular micro-channels with hydraulic diameters of 0.209 mm, 0.412 mm and 0.622 mm,

respectively. Gas and liquid superficial velocities were varied from 0.06-72.3 m/s and 0.02-7.13

m/s, respectively. The main obj ective is focused on the effects of micro-scale channel sizes on

the flow regime map and void fraction. The instability of flow patterns was observed. Four

groups of flow patterns including bubbly-slug flow, slug-ring flow, dispersed-chum flow and

annular flow were observed in micro-channels of 0.412 mm and, 0.622 mm. In the

micro-channel of 0.209 mm, the bubbly-slug flow became the slug-flow and the dispersed-churn

flow disappeared. The current flow regime maps showed the transition lines shifted to higher gas

superficial velocity due to a dominant surface tension effect as the channel size was reduced. The

regime maps presented by other authors for mini-channels were found not applicable for

micro-channels. Time-averaged void fractions were measured by analyzing 8000 high speed

video images for each flow condition. The void fractions hold a non-linear relationship with the

homogeneous void fraction as oppose to the relatively linear trend for the mini-channels. A new

correlation was developed to predict the non-linear relationship that fits most of the current

experimental data and those of the 0. 1 mm diameter tube reported by Kawahara et al. within

15%. Two-phase frictional pressure drop can be predicted within 10% by Lee and Lee's

model .

4.1 Introduction and Background

The flow patterns of adiabatic liquid-gas two-phase flow in the macro-channel have been

extensively studied in the past (Mandhane et al. 1974, Taitel and Dukler 1976). Since the










buoyancy effect is suppressed by the surface tension, the flow patterns in the mini/micro channel

are different from those observed in the macro-channel (Ghiaasiaan and Abdel-Khalik 2001).

Recently many researchers published research results on the gas-liquid two-phase flow patterns

in micro/mini channels. Wilmarth and Ishii (1994) researched on adiabatic concurrent vertical

and horizontal two-phase air-water flows through narrow rectangular channels with gap widths

of I and 2 mm. Five flow regimes (stratified smooth, plug, slug, dispersed bubbly, wavy annular)

and three transition regions (elongated plug, elongated slug, cap-bubbly) were identified for the

horizontal flow. Mishima and Hibiki (1996) measured the flow regimes, void fraction and

frictional pressure loss for air-water flow in vertical capillary tubes with inner diameters from 1

to 4 mm. Bubbly flow, slug flow, churn flow and annular flow were observed. Churn flow was

never observed in the 1 mm channel. Coleman and Garimella (1999) studied air-water flows in

four round tubes with 1.3 mm, 1.75 mm, 2.6 mm, and 5.5 mm inner diameters. Eight flow

patterns (bubble, dispersed, elongated bubble, slug, stratified, wavy, annular-wavy, and annular)

were observed. Triplett et al. (1999) investigated the air-water two-phase flow patterns in

circular channels with 1.1 and 1.45 mm inner diameters and in semi-triangular channels with

hydraulic diameters of 1.09 and 1.49 mm. The results showed bubbly, churn, slug, slug-annular

and annular patterns can be observed but they poorly agreed with the previous transition models

and correlations for macro-channels. Chen et al. (2002) presented the nitrogen-water two-phase

flow regimes in circular channels with 1.0 and 1.5 mm. Five flow patterns (bubbly, slug,

bubble-train slug, churn, and annular) were found. Kawahara et al. (2002) investigated the

two-phase nitrogen-water flow patterns in a 0.1 mm diameter circular tube. Intermittent and

semi-annular flows were observed while bubbly and churn flows were not observed. Qu et al.

(2004) studied the nitrogen-water two-phase flow in a rectangular micro-channel with a gap of









0.406 mm. The results revealed the dominant flow patterns were slug and annular flows, with the

bubbly flow occurring only occasionally and stratified, and the churn flow was never observed.

Void fraction is also an important issue in heat transfer and flow characteristics for

gas-liquid two-phase flows. Armand et al. (1946) investigated the void fraction for the horizontal

and vertical air-water flow in macro-channels and gave a correlation widely used by others.

Zuber and Findlay (1965) built a model named drift flux model to correlate the void fraction data

in two-phase flow. This model relates the gas velocity with the mixture mean velocity,

distribution parameter Co and the mean drift velocity V,, which can be given by:


/G 0 G L j) + V (4 -1)


Co depends on the pressure, the channel geometry and the flow rate for a given flow pattern. Ali

et al. (1993) found that the mean drift velocity V, can be neglected in narrow channels due to the

inability of the bubbles to rise through the stagnant liquid and reported that the void fraction in

narrow channels with the hydraulic diameter around 1 mm can be approximately given by the

Armand-type correlation with a different distribution parameter. Chung et al. (2004) investigated

the void fraction in a 0.1 mm diameter circular tube and a square micro-channel with a hydraulic

diameter of 0.096 mm and found the void fraction was independent of the channel geometry in

their experiment. Kawahara et al. (2002) experimentally achieved a non-linear relationship

between the measured void fraction and the homogeneous void fraction in a 0.1 mm diameter

tube. According to the above literature review, more experimental data for the flow patterns and

void fraction in the channels of sizes from 1 mm to 0. 1 mm need to be obtained to understand the

flow performance in micro-channels.

To evaluate the frictional pressure drop of two-phase flow, there were a lot of models and

correlations to predict it for macro-channels, mini-channels and micro-channels. Table 4-1 listed










the previous two-phase pressure drop correlations. Triplett et al. (1999) researched on the

two-phase pressure drop for the channels with hydraulic diameter of 1.1 and 1.45 mm. He found

the homogeneous model provided the best agreement with experimental data for bubbly and slug

flow patterns, but all of the widely used correlations significantly over predicted the frictional

pressure drop for annular flow. Kawahara et al. (2002) found Lee and Lee's model present the

good agreement (within +10%) with experimental data for his circular channel of 0. 1 mm

diameter. Zhao and Bi (2001) found the Lockhart-Martinelli correlation well predicted the

two-phase pressure drop for the triangular channels with hydraulic diameters of 0.866, 1.443 and

2.886 mm.

In this chapter, three near-square micro-channels with the hydraulic diameters of 0.209 mm,

0.412 mm and 0.622 mm were fabricated by laser etching to investigate the nitrogen-water two

phase flow patterns, regime maps and time-averaged void fraction. The main obj ectives of this

study are to (1) obtain the flow patterns using a high speed CCD video camera, construct flow

regime maps for three micro-channels with superficial velocities of nitrogen and water ranging

from 0.06 to 72.3 m/s and 0.02 to 7.13 m/s, respectively, and investigate the size effect on the

flow regime maps, (2) compare the new flow maps with the mini-channel flow map based on the

Weber number model, (3) evaluate the time averaged void fraction for each micro-channel and

compare them with previous correlations, and build an empirical correlation for micro-channels

based on current data. Check the predictive ability of the new correlation by using existing

time-averaged void fraction data in the literature, (4) obtain the two-phase frictional pressure

drops and evaluate the present pressure drop models.

Since the maj ority of publications in the literature were dealing with the air-water flows,

the current work is aimed at providing fundamental understanding and design information for









nitrogen-water two-phase flows in micro-channels due to their close relationship with the PEM

fuel cells that are receiving top priority for their central role in the hydrogen economy.

4.2 Experimental Apparatus

Fig. 4-1 shows the schematic of the experimental apparatus and the mixer used to

investigate the adiabatic nitrogen-water two-phase flow in micro-channels. It includes a syringe

infusion pump (Cole-Parmer Instrument), 60ml syringe (McMaster), micro-filter (Swagelok),

nitrogen gas cylinder, regulator (McMaster), flow meters (Omega), valves (Swagelok),

Fiber-Lite MI-150 high intensity illuminator (Dolan-Jenner), micro-channels, high speed CCD

camera (Redlake), and computerized image acquisition system.

The de-ionized water with flow rates ranging from 0.5ml/min to 46ml/min, which can be

set on the panel of the infusion pump, was driven to the micro-channel test section. The 2Cpm

micro-filter can remove any particles or bubbles before the flow entered into the micro-channel.

The nitrogen gas was released from the compressed gas cylinder. After the regulator, the gas

pressure was reduced to 0-30 PSI. The gas flow rate was measured by two volume flow meters

with ranges of 0-50 SCCM and 0-2610 SCCM, respectively. The mixer was fabricated as a

bubble generator. A needle with a 0.2 mm inner diameter was connected to the 1/8 inch gas tube.

It was inserted onto the centerline of the 1/8 inch liquid tube. After going through the 1/8 inch

gas tube and the needle, the gas flow was mixed with the de-ionized water coming from the 1/8

inch liquid tube and directed into the micro-channel. The superglue was used to bond the

micro-channel to the 1/8 inch tube, and it can be easily removed by the superglue remover, so the

micro-channel can be replaced easily to make up different test sections. Two pressure

transducers with a +0.5% FS accuracy were installed at the inlet and outlet of the micro-channel

respectively to measure the upstream and downstream pressure. The data acquisition system









started recording when the flow can be considered as steady state. The test sections were placed

horizontally. All experiments were conducted in room temperature and under atmospheric

pressure at the discharge of the test section. Flow visualization was achieved by the high speed

CCD camera, which can operate at a frame rate up to 8000 fps and a shutter speed of 1/8,000 s.

In this work, the frame rate of 1000 fps and a shutter speed of 1/2,000 s were used. The

resolution of the camera was 240(H) x 210(V) pixels. Two Fiber-Lite illuminators provided the

high intensity light, which was directed onto the test section by two optical fiber light guides. An

adjustable microscopic magnification lens was used to magnify the test section. The view field

was near the outlet of the micro-channel to minimize the entrance effect, and the view field

length was 1.48 mm.

Fig. 4-2 shows the photograph of three size micro-channels and schematic of the

micro-channel used in the experiment. The micro-channel was laser etched in a silicon substrate

and then a Pyrex thin cover glass plate was anodically bonded on the top of the substrate. Two

small connection tubes which can be inserted into the inlet and outlet assembly were connected

with the small reservoirs. A microscope (Olympus BX50), a 10x obj ective lens and a CCD

camera were used to measure the dimensions of the micro-channels.

In order to facilitate a meaningful discussion, the relative dominance of the forces involved

in the two-phase flow is analyzed through six dimensionless groups. These are defined as


follows: Bo= gCL pG)D /q~ Ca = pj, /o ReGS G GjDhg G ReLS L LjDh Lu

GS, PG j Dh ",an d LS, PLJ jjh Here g is gravitational acceleration, p is density,


Dh is hydraulic diameter of the channel, o is surface tension, C1 is viscosity, and j is superficial

velocity. The subscripts "L", "G" mean the variables are based on liquid, gas flow respectively

and "LS", "GS" mean the dimensionless numbers are based on superficial liquid, superficial gas










flow respectively. Table 4-2 lists the ranges of those dimensionless parameters for the three

channels under experimental conditions. For comparison purposes, parallel values for a 10 cm

macro-scale channel are also provided to focus on the scale effects.

With the information given in Table 4-2, we can examine the maj or differences on the

relative importance of various forces involved in a gas-liquid flow between the macro and micro

scales. For the flow rates used in our experiments, both the surface tension and the viscous forces

are at least two to three orders of magnitude smaller than the gravitational and inertia forces for

the macro-scale channel as indicated in Table 4-2. Whereas for the three micro channels in our

experiments, it is very clear that the gravitational and viscous force are dominated by the surface

tension and inertia forces by at least two orders of magnitude. Comparing between the macro and

micro scales, we can conclude that the maj or change in the force balance is the surface tension

which is negligibly small in the macro scale and then becomes dominant in the micro scale while

the inertia force is important in both scales as it is proportional to the momentum of the flow

only. As a result, the following results and discussion are based on the scenario that the

two-phase micro-channel flow is dominated by the balance between surface tension and inertia.

4.3 Results and Discussions

4.3.1 Two-Phase Flow Patterns

The high speed CCD camera can record a continuous video for 8 seconds with a frame rate

of 1000 fps. Since the frame rate was set at 1000 fps, one image was recorded for every 1ms. For

a specific channel size and each flow condition, a total of 8000 images were obtained in one

continuous video. From the recorded images, the dynamic structures of the two-phase flow were

obtained and the instability of the flow pattern was observed: At a certain gas and liquid

superficial velocity, the micro-channel two-phase flow pattern changes with time at a fixed

downstream location. Moving the viewing window from the end of the channel to the middle of









the channel, the same phenomenon was found. A scale bar was thought to be helpful in

estimating the size of flow structures. It was developed by multiplying the pixel size of the

camera by the number of pixels and then dividing it by the magnification factor. For example, in

our experiment the pixel size of the CCD camera was 7.4 microns and the magnification factor

was around 1.1 in this experiment, so the actual 100-micron length was covered in 15 pixels in

the image, and the uncertainty was 2-3 microns. A variety of flow patterns appeared such as

"single-phase liquid", "bubbly flow", "slug flow", "bubble-train slug flow", "liquid ring flow",

"liquid lump flow", etc. Only limited numbers of typical flow pattern images from our

experiment are given in Fig. 4-3. According to the appearance of the transition flow patterns

such as the "liquid ring flow", "liquid lump flow", and "disruption tail of the slug", the entire

flow patterns in the present micro-channels can be categorized into four basic flow patterns

based on the balance between the inertia and surface tension. As indicated by the values of

Webber numbers in Table 4-1, the relative dominance between inertia and surface tension covers

a wide span ranging from where surface tension is three orders of magnitude larger than the

inertia to where it is two orders of magnitude smaller. The four basic flow patterns are explained

below:

1) Bubbly-.1hig flow: This regime is dominated by the surface tension force. It mainly has the

"slug flow", and occasionally "bubbly flow" would show up. Transitional flow patterns of

"liquid ring flow" and "liquid lump flow" do not appear here. It usually appears at a low gas

flow rate. The "slug flows" were separated by a thick liquid bridge. The width of nitrogen gas

slugs is slightly smaller than that of the channel due to the existing smooth and thin liquid film

on the walls. Occasionally, some spherical bubbles, whose diameters are much smaller than the

width of the channel, appear.










2) Slug-Ring flow: This regime is controlled by the balance between the surface tension force

and the inertia force, also called the transition regime. Surface tension force and inertia force are

comparable to each other in this region. It mainly features the "slug flow", "liquid ring flow",

"bubble-train slug flow", and occasionally "bubbly flow". It often appears at intermediate gas

flow rates. The liquid bridge sometimes is thick and forms the "slug flow", while other times it is

quite thin and forms the "bubble-train slug flow", and even at times it disappears half and forms

the "liquid ring flow". The ring-shaped liquid film is smooth and axi-symmetrically distributed

around the channel inner wall. The nose of the slug is flatter than that observed in a bubbly-slug

flow.

3) Dispersed-Churn flow : In this regime, the flow is strongly influenced by the inertia force but

not totally dominated. The main characteristic feature is a mixture of small vapor slugs and

liquid chunks. It has no stable "slug flow". Dispersed-churn flow is also called bubbly/slug,

liquid/slug, and ring/slug by other researchers. It normally appears at the intermediate liquid and

gas flow rates. For example, among the dispersed-churn flows from the recorded images, we can

see the "disruption tail of the slug" flow pattern usually followed by some very small shedding

bubbles.

4) Annular flow: This regime is totally dominated by the inertia force. It mainly consists of the

flow pattern of "gas core with a smooth interface", and occasionally the "liquid lump flow". It

usually appears at a low to intermediate liquid flow rate together with a high gas flow rate. The

water film flows along the channel inner wall while the nitrogen gas core flows through the

center of the channel. The gas-liquid interface is smooth due to the weak interaction between the

gas and liquid at the interface in the micro-channel, which is different from the wavy interface

observed in mini-channels and macro-channels.









Fig. 4-4 shows the instable temporal pressure measurement at the upstream and

downstream for a slug-ring flow. This instability of Pin can be attributed to or cause the density

wave oscillation in the micro-channel, which was also found in parallel channels and believed to

be intrinsic to the test module itself (Qu and Mudawar 2004). The density oscillation could


change the gas inertia force PG G at the interface. That could be the reason why the time

instability of flow patterns observed in the micro-channel.

4.3.2 Flow Regime Maps

Based on the images and pattern distinctions discussed above, we have summarized our

observations using two-phase flow regime maps. Traditionally, the regime map was developed

with the superficial velocities of water and nitrogen, jL and jG, as the vertical and horizontal

coordinates, respectively. Instead of the superficial velocities, we decided to use the respective

gas and liquid Webber numbers as the coordinates for the regime maps. Essentially, the Webber

number is the dimensionless superficial velocity square and physically it represents the ratio of

inertia to surface tension that is the guiding parameter for two-phase flow patters in

micro-channels. Fig. 4-5 shows the regime maps for the three channel sizes. The solid lines are

used to indicate the boundaries between different flow patterns. Figs. 4-5(a) and 4-5(b) provide

the two-phase flow regime maps for the current micro-channels with hydraulic diameters of

0.622 mm and 0.412 mm, respectively. Fig. 4-5(c) shows the flow regime map for the

micro-channel with a hydraulic diameter of 0.209 mm.

In general, for the lager channels (0.622 mm and 0.412 mm), the regime maps are relative

similar as shown in Figs. 4-5(a) and 4-5(b). They all have bubbly-slug flows located in the lower

left corner representing very small Webber numbers that correspond to a total dominance by the

surface tension force. For higher gas velocities that are associated with larger gas Webber









numbers and dominance by the inertia force, the flow pattern becomes he annular flow and it is

not very sensitive to the liquid velocities. Between the bubbly-slug flow and the annular flow, we

found the slug-ring and dispersed-churn flows that corresponds to the relatively balance between

the inertia and the surface tension and neither one is dominant. The slug-ring flow is under

relatively more control by the surface tension while the disperse-churn is controlled more by the

inertia as a larger inertia force offered by the higher liquid flow is needed to break the slug into

dispersed fragments. This is why the disperse-churn flow is located above the slug-ring flow.

While for the smallest channel (0.209 mm), the regime map displays some differences from

those of the larger channels. We observed that the bubbly flow pattern was no longer present and

the slug flow filled its place in the lower left corner, lower WeLS and WeGS (l0WeT}G and jL ). A

plausible explanation is that as the channel size gets smaller the surface tension force holds a

deeper control over the inertia for the same low gas flows that prevents the break up of the bridge

between slugs to form bubbles. Therefore the slug flow resulted. The dispersed-churn flow was

also absent in Fig. 4-5(c), the slug-ring flow took its place. Again, the reason is that the strong

surface tension effect prevented break-down of the slugs and the disruption of the gas-liquid

interface.

From the current experimental data, we also observed the boundary lines have a tendency to

shift slightly to right, namely higher WeGS Or gas superficial velocity, as the hydraulic diameter

was decreased, which was different from what reported by Taitel et al. (1980) that the boundary

line was not affected by tube diameter for circular vertical macro-tubes, or by Mishima and Ishii

(1984) that the boundary line shifted to the left in vertical macro-tubes as the tube diameter was

decreased. This again may be explained by the stronger surface tension effect in micro-channels

that requires a higher inertia force (boundary line moving to the right) to balance in order to









maintain the same flow pattern. Tabatabai and Faghri (2001) reported a new flow map based on

their theoretical study that accounted for surface tension effects in horizontal miniature and

micro tubes. They showed an increasing ratio of gas superficial velocity to liquid superficial

velocity with the decreasing of hydraulic diameter, which indicated a right shit of the transition

boundary lines too.

4.3.3 Comparison with Prior Mini-Channel Flow Map

Akbar et al. (2003) reviewed the flow maps in mini-channels with hydraulic diameter around

1 mm and concluded that there were some similarities between the flow regime transitions in

mini-channels and channels operating under microgravity. They developed a flow map for

circular and near-circular mini-channels based on the Weber number, which can be represented

by the following expressions:

* Surface tension dominated region (including bubbly, plug, and slug flows):

O For Wes < 3.0, WeGS < .11We 315

oFor Wes > 3.0, WeGS <1.0

* Annular flow region:

WeGS >11.0We S4, Wes <3.0

* Dispersed flow region:

Wes > 3.0 WeGS > 1.0

This model can reasonably explain the flow maps for circular and near-circular mini-channels

with hydraulic diameter around 1 mm including the data of Mishima et al. (1996), Triplett et al.

(1999), and Yang & Shieh (2001). However, it only provided a fair prediction to the data of Zhao

and Bi (2001) due to the channel geometry effects. Fig. 4-6 shows the transition lines predicted

by the Weber number model (solid lines) with the current data for the channel with Dh = 0.622










mm (dashed lines). A poor agreement was found. One of the possible reasons might be the

significant sensitivity of gas-liquid flow patterns to the working fluid, channel geometry and

channel size. Another possible reason may be related to some special flow characteristics

associated specifically with micro-channels. The liquid and gas flow remain laminar even at high

flow rates, and a weaker interaction between the liquid and gas at the interface in micro-channels

than in mini-channels. We may conclude that the flow regime criteria developed for

mini-channels should not be applied for micro-channels without further verification.

4.3.4 Time-Averaged Void Fraction

For each gas-liquid flow combination, the time-averaged void fraction can be estimated by

analyzing its 8000 recorded images. The method of analyzing the time-averaged void fraction is

described as follows. 22 data points were selected from the video image files for each channel

size to cover the entire range of the homogeneous void fraction. It is noted that each data point

corresponds to a specific homogeneous void fraction. The homogeneous void fraction is defined

as P = jG G L), which has a range between zero and one. The physical meaning of the

homogeneous void fraction is that the actual void fraction is equal to the homogeneous void

fraction when both phases have the same velocities in a dynamic equilibrium condition. The

actual void fraction would deviate from the homogeneous void fraction for the dynamic

non-equilibrium conditions investigated in the current study where the two phases have

non-equal velocities (slip ratio) in different flow regimes. Each recorded image covers the flow

pattern for a streamline distance of 1.48 mm. The instantaneous void fraction on each image can

be calculated by estimating the ratio of the volume occupied by the gas to that of the whole

region on each image field. The time averaged void fraction was obtained by adding all the

instantaneous void fractions and dividing the sum by the total number of images, the

time-averaged void fraction, a, can be determined and expressed as follows :












a =1 nI =1 J=1 k=1 1 m=,N + (4-2)
N N g

Eq. (4-2) represents a strategy that we divided the images into three maj or groups based on the

number of images for a specific type. For the total recorded images, approximately, 90% of all

the images belong to either pure liquid type or gas core with a smooth interface, and all other

types such as "liquid ring flow", "liquid lump flow", and "bubbly flow" account for only 10%.

As a result, we chose "pure liquid" (zero void fraction), "gas core with a smooth interface" and

"all the rest types combined" as the three groups. Therefore, in Equation (4-2), at,2, ag,,, am,k are

the estimated void fractions for "pure liquid type", "gas core with a smooth interface type", and

"any other type', respectively. N is the total number of the recorded images. Nz, N,, N,, are the

number of the images of "liquid", "gas core with a smooth interface", and "other types",

respectively. According to the error propagation, the uncertainty of the estimated time-averaged

void fraction, da, can be expressed as:



Aa= a;+ a, + a-I (4-3)


where dAm Au, a,, d, are the uncertainties of the void fractions for "liquid", "gas core with a

smooth interface", and "all other flow pattern", respectively. Even though, the void fraction of

"pure liquid" is zero, there is still an uncertainty associate with it because of possible trace

amount of gas in the liquid core, but in general this uncertainty is very small compared to other

types. Based on the above, we estimated that the range of uncertainties for the time averaged

void fractions is from 3.1% to 9.8%.










Fig. 4-7 shows the measured time-averaged void fraction results for the present three

micro-channels. Also shown in Fig. 4-7 is the data given by Kawahara et al. (2002) for a

micro-tube with 0.1 mm in diameter. The dotted line represents the homogeneous void fraction P.

Ali et al. (1993) suggested that the void fraction in narrow channels with a Dh around 1mm can

be correlated with the equation, ct = 0.8 P. When applying this correlation to our results, we

found that for the vast maj ority of our data, it overestimated the void fractions, especially for the

smaller channels. The predictions become worse as the size of the channel is decreased further.

The over-predictions are more than 100% for many data points. The time-averaged void fraction

patterns for the smaller channels showed a non-linear relationship with the homogeneous void

fraction. As explained before, when the channel sizes are smaller, the effects of surface tension

are more prevalent, and allow the liquid film to bridge the gas core more easily, so the flow

pattern is more likely to be bubbly-slug flow, which results in a lower time-averaged void

fraction due to the absence of gas phase.

Based on our own data for the three micro-channel sizes (0.209 mm, 0.412 mm and 0.622

mm) and those of Kawahara et al. (2002) for a 0. 1 mm diameter micro-tube, we have developed

an empirical correlation of the time-averaged void fraction for micro-channels with hydraulic

diameters less than 1 mm. The correlation is expressed in Eq. (4-4) and Eq. (4-5)

05"
a= (4-4)
S1 (1 C)/70 5
0.266
C =(4-5)
1 +13.8 e-6 88Dh

where the unit of Dh is in mm. Fig. 4-8 shows the comparison between the predictions by the

new correlation and the corresponding measured results. Fig. 4-9 is a plot of the up/ad VS P foT

all the data points in Fig. 4-8, where up and ad are the void fraction predicted by the correlation









and that of the measured data, respectively. 57 of our 66 data points fall within 15%. Most of

the outliers came from Kawahara et al's data (17 out of 26 outliers) which may be attributed to

the lack of the total number of sample images (200-300) in their experiment resulting in higher

uncertainties. If the uncertainty range was increased to 35%, only 2 data out of 66 were out of

the range.

4.3.5 Frictional Pressure Drop

Currently most of the two-phase pressure drop models are based on the model of Lockhart-

Martinelli (1949), such as Mishima and Hibiki (1996), Lee and Lee (2001), Qu and Mudawar

(2004). To compare our experimental data with the prediction of those models, the Martinelli

parameter X should be determined experimentally first, which is defined as:


(dP /dz),
X = (4-6)
(dP /dz) G

(dP / dz)L and (dP / dz)G are the frictional pressure drop of single phase liquid and vapor with

the same mass flow rate respectively. Then insert X into the above models to get the two-phase

frictional pressure drop. Fig. 4-10 shows the comparison between the experimental data of the

micro-channel (Dh = 0.412 mm) and the value predicted by those models. From the figure, we

can see Lockhart-Martinelli's model (C=5) obviously underestimate the pressure drop here.

Mishima and Hibiki's model can predict the pressure drop very well. All of the data fall in 10%

of the predicted value. Lee and Lee' s model may also predict well, but it' s worse than Mishima

and Hibiki's model for out experimental data.

4.4 Summary

Nitrogen-water flow patterns in rectangular micro-channels with hydraulic diameters of

0.209 mm, 0.412 mm and 0.622 mm were obtained and analyzed. Based on our experimental









results and comparison with other results in the literature, the following conclusions can be

obtained:

* The phenomenon that micro-channel flow pattern changes with time at a fixed location under
a certain gas and liquid superficial velocity was found, which can be attributed to the density
wave oscillation in the micro-channel. According to the appearance of the transition flow
patterns such as "liquid ring flow", "liquid lump flow" and "disruption tail of the slug", four
flow patterns can be defined for micro-channels with the hydraulic diameters of 0.412 mm
and 0.622 mm: bubbly-slug flow, slug-ring flow, dispersed-churn flow and annular flow. For
the micro-channel with the hydraulic diameters of 0.209 mm, the bubbly-slug flow became
the slug-flow and the dispersed flow disappeared.

* The current flow regime maps show the transition boundary lines shift to high WeGS Or gas
superficial velocity with the decreasing of the hydraulic diameter. It can be explained by the
strong surface tension effect in micro-channels. The micro-channel flow maps were
compared with the mini-channel flow map based on the Weber number model, which showed
poor agreement.

* Time-averaged void fractions of each micro-channel were measured for 22 runs to cover the
whole range of homogeneous void fraction. The data of each run were obtained from the
analysis of 8000 flow pattern images captured at a certain gas and liquid superficial velocity.
With the decreasing of the hydraulic diameter, the time-average void fraction showed a
non-linear relationship with the homogeneous void fraction. A new empirical correlation was
proposed to predict the non-linear relationship, and most of the current experimental data and
Kawaraha' s data fall within 15% of the new correlation. The uncertainty of this
measurement method was analyzed and the uncertainty range was approximately from 3.1%
to 9.8% under the current experimental conditions.

* Lockhart-Martinelli's model (C=5) which was widely used to predict the two-phase frictional
pressure loss in macro-channel obviously underestimate the pressure drop in micro-channel.
Mishima and Hibiki's model formulated from experimental data of small channels can
predict the pressure drop here very well. All of the data fall within 10% of the predicted
value. Lee and Lee' s model can also predict well, but it' s worse than Mishima and Hibiki's
model for out experimental data.









Table 4-1. Generalized two-phase frictional pressure-drop correlations.
Correlation Reference Frictional pressure drop
1 Homogeneous model dP } 2 f G pI P,
(1994) = 1+D x,


Lockhart-Martinelli
(1949)


dP 2 f,G2 (1- x) .
dzJ p,D,


XX
(dP/dz),

20 for turbulent liquid-turbulent vapor
12 for laminar liquid-turbulent vapor
10 for turbulent liquid-laminar vapor
5 for laminar liquid-laminar vapor


Mishima and Hibiki
(1996)


dP
dz


2 f,G (1- x)2
pD,


Lee and Lee (2001)


dP 2 f,G (1- x)2

a= 1+d --+X


C = 6. 185x102 Re76
for laminar liquid-turbulent vapor




=1-+
XX
C = 2 11- e-319D' 0.00418G + 0.0613)


Qu and Mudawar (2004)


(+C 12


C =211- e-319D,











Table 4-2. Non-dimensional parameters for a macro-channel and micro-channels
Bo Ca Re We
(Ratio of (Ratio of viscous (Ratio of inertia force to viscous (Ratio of inertia force to surface
gravitational force force to surface force) tension force)
to surface tension tension force) ReLS ReGS WeLS WeGS
force)


1354.3
0.0117
0.0230
0.0525


10cm Channel
Channel 1
Channel 2
Channel 3


0.00047-0.12
0.00023-0.08
0.00035-0.04
0.00015-0.02


4665-1166276
4.64-1670
14.1-1602
9.36-1436


6320-63200
7-1631
7-1838
7-2270


2.21-138333
0.001-135
0.005-63
0.0014-34


1.6-158
0.0005-32
0.0003-28
0.0003-33












IIluminator


Fiber optic


Syringe pumip



Flow meter


II~



Computer
Flow


Figure 4-1. Schematic of the flow visualization apparatus and the mixer.

















81


























































Figure 4-2. Photoes of the experimental apparatus


I ~f~p'i=r~~` "IF I o~v.h~iters
t~~ulator~~iarP~i~






















Connection tube


Figure 4-2. Photograph of micro-channels and schematic of the micro-channel.



















Figure 4-3. Typical flow patterns in the micro-channel: A) Bubbly-Slug flow B) Slug-Ring
flow C) Dispersed-Churn flow D) Annular flow.










































































C



. I I~ I I I I I I I I I


I- I- I -I I I I I I I I I I I I


I- I I -I I I I I I I I I I lI l


L.J

I I- I -I I I- I I- I- I I. I. I. I. I


L.J

I. I. I I I. I I. I. I I. I. I. I I I.


_ I
Lu

I I I I I I I I -


Y


W


D


:`6
LY : PL~I1


Figure 4-3. Continued



























15.5-




15.0-




14.5 "ll "lI
O 20 40 60 80 100

t (s)


Figure 4-4. Temporal records of inlet and outlet pressures (Slug-Ring flow, jL = 0.215m/s, jG
1.2m/s)


100


Dispersed-Churn florw









Slug_Ring flow /




o~~~ oo + 4 *
0 co o & 44/ ***
o co o &*/ ** *
Bubbly-Slng flow /Arnnlarflorw
oo~~~ oo o o + *

-1E-3 0.0-1 0.-1 1 10

..E'
cc


0 .1 -




0.0-1-




1 E-3
1E-4


Figure 4-5. Flow regime maps for three micro-channels: A) Dh = 0.622 mm B) Dh = 0.412 mm
C) Dh = 0.209 mm














































































10 100


Figure 4-5. Continued


1 111 111 II I I 111


Dispersed-Churn flow



A~ &c & AA & W a*


+ AA ++ & A




Slig-Ring florw/
o o a +

o o o B,4 && *
o o o oX & ~ L AA *

o o o o o w AA *
Bubbly-Slug flow Annal lar flowv


10-




1










0.01


1 E-3
1E-4


1E-3 0.01


1 10


We
Gs


100




10 -















0.01 .




1E-3 -


& & & A A A


& 4


+ +++ 4 + A
Slug~_Ring Flow


4 44




o o &

o o


+ 4


oo o


AA AA~ AA + & &

& 000 AA AA&







o AA AA A 9 *

0 0~+ 41 As A *
o oo &~ **+ *
Flow Annular Flow
o o coo ~* *


0.1

We
Os












I 1 11111111 1 1 1111111 1 1 1111111 1 111111


10










.1


o



-- 0.01


Predicted trans ition Ilne
to dispersed flove

Exp erim ental trans ition line
to dispersed-churn flote.
-..


ii
ExperimrnntalItra nsition line
to annu lar f lov.


bP .Pred it ted trans it ion line


;.d~ ,to annularfle ...


Experimental transition Predicted transition
line to slug-ring flo=A line to s lu g-an nular floan.


1 *****I 1 11 = *****I ====1 1 *****I1
0.1 1 10 100 1000

Su perfcial gas velcits, jG~r(FIS,


Figure 4-6. Flow map comparison between micro-channel and mini-channel predicted by the
Weber number model.


flow,c0.= B
p
=0.622mm
=0.41 2mm
=0.209mm 4
. d = .1mm o.


-----Homogeneous
- Ali et al. cO.=.B~
O Experiment, D
n Experiment, D
Experiment, D
+ Kawahara et al


*t


,/,o

a
n
,n a
n
a 4 'tt B~ B
~~ tft *


t, "
4


4


0.2 0.4 0.6

Homogen eous void fraction p.


0


Figure 4-7. Measured time-averaged void fraction results vs two previous correlations
































































n a -9 4
4
b~ O d ~d O~n(P 0~8

a
..~_.~..~._~..~~._~..~~.~~..~_.~~..~_.~~
B $


1.0


Empirical co rrelation, C=0.22
----- Empirical co rrelation, C=0.1 4
0.8 --- ---- Empirical co rrelation, C=0.06 ,
Kawiraha ra's correlation, C=0.03
0 Experiment, D~=0.622mm
a Experiment, D=0.412mm 6A
0. -B a Experiment, D=0.209mm o
4 Kawirahara et al. D=0.1 mm +











0. 0 0.2 0.4 0.6 0. 1.






2.5






+ D=0.622mm
a D =0.41 2mm

2.0 D =0.209mm
4 D =0.1mm, from Kawrahara et al.
f115% E stimatio n Line
n ~~--- --- +35% E stimatio n Line
1.5-


0.0 0.2 0.4 0.6 0.8 1 .01

Hornogeneous void fraction, p


Figure 4-9. Ratio of predicted and experimental time-averaged void fraction vs. homogeneous
void fraction p


10 0































0 2 4 6 8 10 12 14 16

(AP/AL)T (experimental) [MPalm]


0 2 4 6 810 12 14 16

(AP/AL)T (calculated) [MPalm]

Figure 4-10. Comparison between the experimental data and the models (Dh = 0.412 mm) A)
Lockhart-Martinelli's model (C = 5) B) Lee and Lee's model C) Mishima and
Hibiki's model




89












16


1 4 +1 0%


12-


10-








4-



C va lue g ve n by M ishirna and H ibik i


0 2 4 6 8 10 12 14 16

(AP/AL)T (calculated) [MPalm]


Figure 4-10. Continued









CHAPTER 5
MICRO-BUBBLE DISPENSER

Bubble generation in a simple co-flowing micro-channel with a cross-section area of

1.69x0.07 mm2 was experimentally and numerically investigated. Air and water were used as the

gas and liquid, respectively. Mixtures of water-glycerol and water-Tween 20 were also used to

obtain the effects of viscosity and surface tension. The experimental data shows that the break-up

process is periodic under certain operating conditions. The break-up dynamics are also examined

using three dimensional incompressible two-phase flow numerical simulation based on the

volume of fluid (VOF) method. The simulation successfully predicts the flow behavior and

provides a more detailed examination of the bubble shape. The physics can be further explained

by the detailed micro-PIV measurements which show that the bubble is formed due to the

velocity component perpendicular to the gas flow created by the sudden change of the liquid

velocity distribution around the barrier. The bubble length L is dependent on the liquid flow rate

Qz and gas flow rate Q and the ratio ofL to the channel width w is a function of the ratio of gas

and liquid flow rates Qg Qz which is similar to that previously used in the T-junction case. The

bubble frequency fis found to be related to w, channel depth h, and Qzeg (0g 1904). This

formulation shows a good agreement with the experimental data at the low frequency region.

Different bubble shapes can be obtained at different liquid viscosities and surface tensions. The

ratio L w can still be predicted by a modified equation which uses the real bubble width wb Of an

equivalent bubble length Le.

5.1 Introduction and Background

Single phase and multiphase flows in micro-geometries have been investigated by many

researchers in recent years (Brutin and Tadrist 2003; Xiong and Chung, 2007a & 2007b).

Microfluidic devices can be applied in many scientific and industrial developments such as









on-chip separation (Fu et al. 1999), chemical reaction (Song et al. 2003) and biochemical

synthesis (Zheng et al. 2004). These devices require the control of small volumes of fluids, and

the understanding of multiphase flows, especially with a special interest in formation of

gas-liquid dispersions. Gas-liquid dispersion is common in macroscopic processes and products

of the chemical, health-care, and food industries. Not surprisingly, many studies of

emulsification and droplet behavior have been performed in macroscopic, unbounded shear, and

extensional flows (Stone et al. 2004). Recent investigations focused on generating and

manipulating emulsions with microfluidic devices are motivated by the potential to use

controlled flows and structures on the scale of the droplets to tailor the properties of the

emulsions. In particular, it' s of interest to control the droplet size and the distribution of sizes.

The microchannel geometry takes on added significance because it can influence the relative rate

of rotation to extension in the flow, which is fundamental to break-up processes. Currently

several techniques exist for the generation of bubbles (Ganan-Calvo and Gordillo 2001;

Garstecki et al. 2004; Gordillo et al. 2004; Guillot and Colin 2005; Xu et al. 2006; Haverkamp et

al. 2006). First is the T-junction. In the T-junction case, the continuous flow is in one arm and

sheared off by a dispersion flow in the perpendicular arm. The break-up of gas-liquid threads is

dominated by the pressure drop across the bubble as it forms, and the size of the bubbles is

determined solely by the ratio of the volumetric flow rates of the two fluids. A scaling law for

the size of the discrete fluid segments can be written as (Garstecki et al. 2006):


L / w =1+a (5 -1)


where L is the length of the bubble slug, w is the width of the channel, Qg and Qz are the gas and

liquid flow rates respectively, and a is a constant of order one, whose particular value depends









on the geometry of the T-junction. Second is the flow-focusing device. The first type of the

flow-focusing device arranges two channels in a concentric manner upstream of a small orifice to

create a strong extensional flow (Stone et al. 2004). The bubble size is effectively set by the size

of the orifice designed into the micro-channels under an operating condition while it can also

produce threads that break into drops substantially smaller than the orifice in other cases. The

second type uses a water nozzle and does not have an orifice. The bubble is formed in a

co-flowing water j et discharging into a stagnant air atmosphere (Sevilla et al. 2005). Recently

Cubaud et al. (2005) used a four-crossed square channel to generate the bubble. The results

showed the breakup occurs at the intersection and the bubble size and distribution can be

expressed by the same equation as Eq. (5-1) with a-1. The empirical expression can well predict

the bubble length when 0.1<(Qg+Qz)/e<1. For (Qg+Qz)/el<0.04, the flow becomes annular. The

control of drop breakup in microdevices such as those mentioned above is influenced

significantly by surfactants and wetting characteristics. For example, the continuous phase

should be the phase that most strongly wets the boundaries. Contact angles and wetting

properties depend on the type and concentration of surfactant, and such surfactant effects on drop

formation in a T-junction have been investigated experimentally (Dreyfus et al. 2003), but have

yet to be analyzed in detail; In addition, because shear rates can be large, new interfacial area is

created rapidly. Thus, the kinetics, and possibly theology, of surfactants may also play

significant roles in the emulsion formation process.

In this paper, we describe a co-flowing device which is easy to be scaled up or multiplexed

due to the simple structure. The obj ectives of this work are to 1) obtain the physics of the bubble

break-up process, 2) discuss the flow parameters affecting the bubble length and get a









formulation of the bubble length, 3) analyze the bubble generation frequency, and 4) evaluate the

effect of fluid viscosities and surface tension on bubble formation.

5.2 Experimental Setup

5.2.1 Dispenser Fabrication

The 3-D schematic of the co-flowing micro-channel is shown in Fig. 5-1(a). The

micro-channel was made of glass and silicon fabricated in a clean room environment. The

fabrication steps include a selective deep reactive ion etching of a double-sided polished silicon

wafer. The inside barrier (splitter plate) can be made by first covering a photo-resist layer and

then creating patterns with photolithography, leaving the barrier with a desired width and the gas

and liquid channel exposed. Pyrex thin cover glass plate was anodic bonded on the top of the

etched silicon wafer. Three larger holes are etched through the bottom of the wafer and glued

with 1/16" soft tubes. In Fig. 5-1(b), w is the width of the main channel, w, and wl are the width

of the gas and liquid channel respectively, d is width of the barrier, and h is the depth of the

micro-channel. A microscope (Olympus BX50) and a CCD camera with a pixel size 6.45 Clm

were used to measure the dimensions of the micro-channel. The geometries are measured as: w =

1.691 mm, w, = wl = 0.545 mm, d 0.601 mm, and h 0.07 mm. The depth of the micro-channel

was measured by the Veeco Wyko NT 1000 optical profiler. Figure 5-2 shows the depth and 3-D

image measured by the profiler.

5.2.2 Apparatus

Fig. 5-3 shows the schematic of the experimental flow visualization apparatus used to

investigate the bubble dispersion in the co-flowing micro-channel. It includes two syringe

infusion pumps (Cole-Parmer Instrument), 60ml and 3ml syringes (McMaster), micro-filter

(Swagelok), Fiber-Lite MI-150 high intensity illuminator (Dolan-Jenner), micro-channels, and









high speed CCD camera (Redlake). The liquid fluid at flow rates ranging from 3ml/h to 63ml/h,

which can be set on the panel of the infusion pump with an accuracy of +0.5%, was driven to the

micro-channel test section. The 2 Cpm micro-filter can remove any particles or bubbles which

may block the micro-channel before the flow enters into the test section. The gas flow at flow

rates ranging from 0.21ml/h to 126ml/h was driven to the channel from the other syringe pump.

The test sections were placed horizontally. All experiments were conducted at room temperature,

20oC, and under atmospheric pressure at the discharge of the test section. Flow visualization was

started after some equilibration time when changing the flow parameters. It was achieved by

using a high speed CCD camera, which can operate at a frame rate up to 8000 fps and a shutter

speed of 1/8,000 s. In this work, the frame rate of 500 fps was used. The resolution of the camera

was 480(H) x 420(V) pixels. Two Fiber-Lite illuminators provided the high intensity light,

which was directed onto the test section by two optical fiber light guides. An adjustable

microscopic magnification lens was used to magnify the test section.

In this experiment, the air was used as the gas fluid. Water (viscosity Cl=0.92 mPa-s) and

three aqueous solutions of glycerol, 50% (w/w) glycerol (Cl=7.3 1 mPa-s), 30% (w/w) glycerol

(Cl=2.68 mPa-s), and 10% (w/w) glycerol (Cl=1.19 mPa-s) were used as the liquid fluid. The

viscosity of water-glycerol mixture was measured at room temperature, 20oC, by means of a

rotary viscosimeter. To change the gas-liquid interfacial tension and evaluate its effect to bubble

generation, 2% (w/w) Tween-20 surfactant is added into the water and mixed for approximately

40 minutes at room temperature. The dilute solution of Tween-20, 2% (w/w), is larger than the

critical micellar concentration (CMC) in water, 0.007% (0.059mM). The surface tension

measured by a digital tensiometer changes from around 72mN/m (water + air) to 37mN/m

(water/Tween-20 + air). It has to be pointed out that small change in temperature [~O(10)K] and










composition can result in 5% variation around the measured values. Image analysis software

ImagJ was used to analyze the image frames to determine the bubble size.

To further understand the break-up physics, a micron-resolution particle image velocimetry

system (micro-PIV), shown in Fig. 5-4, was used where fluorescent particles (Duke Scientific)

were seeded into the de-ionized water flow. Two Nd:YAG lasers (Continuum) were directed to

the same optical path by optical lenses (Edmund) and expanded by a beam expander made up of

a concave and a convex lens. The 0.69 Clm particles absorb green light (~542nm) and emit red

light (~612nm). The emitted light is imaged through a 10x obj ectives lens (NA=0.3) and passed

to the fluorescent filter cube (Olympus), where the green light from the background reflection is

filtered out and the red fluorescence from the sub-micron particles is passed to the 0.5x lens

(Olympus) and recorded on the CCD camera (Cooke). The concentration of the fluorescent

particles solution was prepared to ensure at least 5-10 seed particles in each interrogation volume.

In this work, this time delay is set to be 100 Cls, so the particles move approximately 1/8th Of an

interrogation window between pulses. The interrogation windows measure 64 camera pixels

square, thus the particles moves approximately 8 pixels between laser pulses. Assume that the

measured velocity is accurate to within 1/5th of a pixel. It results in an experimental uncertainty

of less than +2.5% (Prasad et al 1992).

5.3 Numerical Simulation

The numerical simulation presented here is used to examine the bubble dynamics in the

break-up process. Since the simulation includes two fluids and time dependent bubble motion,

the Volume of Fluid (VOF) method is applied. The main purpose of the VOF method is to track

the interface between two phases. That is accomplished by solving the continuity equation for









volume fraction of phases at the interface. Suppose there are n phases, and for the ith phase, the

continuity equation at interface is in the form of:



St(a, p,) + V (apF,) (Yiz/l -i #2) (5-2)


a, is the volume fraction of the ith fluid in the cell, p, is density of ith fluid, 9, is the velocity

vector of the ith fluid, n is the total number of phases, ri2,, is mass transfer from phase j to phase

i. For every non-primary phase, Eq. (5-2) will be solved. For the primary phase, its volume

fraction is calculated by:


~a,= 1 (5 -3)


In this simulation, the primary phase is set to be water and air is the secondary phase. The

Navier-Stokes equations are discretized on a standard marker and cell (MAC) grid with

velocities on cell walls and the rest of the properties at the cell centers. A QUICK discretization

scheme is used for the convective terms and a second order discretization scheme is used for the

viscous terms. The simulation mesh is shown in Fig. 5-5. The total number of cells is about

220000. The width and depth of the simulation region are the same with the device used in the

experiment, which are 1.691 mm and 0.07 mm, respectively. In the length direction, only a

portion of the micro-channel is simulated in order to reduce the computational time. The lengths

of air and water inlets are set to be 1 mm and the total simulation region is 10 mm long. This

computation region is where an air bubble is generated and breaks up. Thus it can capture the

main physical phenomena.









5.4 Results and Discussions


5.4.1 Bubble Break-Up

The bubble generation process can be observed from a video recorded by the high speed

camera. Fig. 5-6 shows the time evolution of a periodic break-up procedure and the

corresponding bubble shape prediction by the simulation. In the simulation results, blue denotes

pure liquid with void fraction of zero and red denotes pure gas with void fraction of one.

During a typical period, there are two steps in the process. Firstly, after the pinch-off of a

bubble, the gas ligament expands vertically downward and horizontally until a neck appears.

Since the top interface is bounded by the channel, the ligament only develops downward

vertically. This period to from the pinch-off to the neck appearing is called the gas ligament

expansion. After the ligament expansion, the neck propagates downstream and its diameter

decreases until it finally breaks, thereby forming a new leaving bubble. The newly formed

bubble is immediately bounded as a gas slug due to the high surface tension force in the small

channel. This period to from the neck appearing to the formation of the new bubble is named the

gas ligament collapse. From the last image, we can see the next periodic break-up sequence

begins. From the Young-Laplace equation, the Laplace pressure jump across the interface equals

to o(1/ra+1/rr) where ra and rr are the axial and radial radii of curvature, respectively. Both of

them are proportional to the corresponding wetting angles which are varying with time, but they

are bounded by the width w and height h of the channel, respectively. Since w >h in our channel

and rr is minimum at the moment of break-up, the maximum Laplace pressure jump almost

equals to o/remin. If the total pressure difference between gas and liquid exceeds the maximum

Laplace pressure jump, bubble break-up would take place. Otherwise no break-up exists.










The experiment data show that the periodic break-up only exists under certain operating

conditions. There are two typical unsteady break-up processes in the experiment, which are

shown in Fig. 5-7. The first one, shown in Fig. 5-7a), is the case where the liquid flow rate is so

low that the neck can not be broken before the gas ligament flows out the channel. The second

one, shown in Fig. 5-7b) and 5-7c), is the case where the ratio of gas and liquid flow rates is so

high that the neck is stretched to a very thin gas ligament no matter what the flow rate is,

intermediate or high.

Fig. 5-8 shows the instantaneous micro-PIV measurements in one period around the barrier.

From Fig. 5-8, we can see that when the liquid enters into the main channel from the liquid

sub-channel, it pushes upward due to its larger momentum. As a result, velocity components

perpendicular to the gas ligament exist around the barrier which press the bubble interface and

form the neck. After the break-up, the high liquid velocity on the top of the bubble pushes it to

the bottom wall and forms a gas slug (Fig. 5-8e), then a new periodic cycle begins.

5.4.2 Bubble Distribution and Bubble Size

Over a wide range of gas and liquid flow rates, the bubbles are generated uniformly. Fig.

5-9 shows the uniform bubble distribution near the exit of the channel at different gas and liquid

flow rate ratios. Assume that D denotes the distance between the two consecutive bubbles. The

bubble length L increases while D decreases with the flow rate ratio.

Changing the gas and liquid flow rates can achieve different bubble lengths. Fig. 5-10

shows the dependence of bubble length L on the gas and liquid flow rates. From Fig. 5-10a) it

was found at a fixed liquid flow rate, the bubble length increases with the gas flow rate. That' s

because with a higher flow rate the gas has a larger force to push the liquid and resist the liquid

pressure at the neck, so both of the expansion and collapse time to and to increase which leads to

a longer bubble. While from Fig. 5-10b) we can see at a fixed gas flow rate, L decreases with the









liquid flow rate. The same physics can be applied here. The increasing liquid momentum cuts the

neck quickly and shortens the time of both stages which results in a bubble with a short length.

Fig. 5-11 shows the data of L/w at the gas-liquid flow rate ratio ranging from 0.01 2 with

one gas flow rate 5ml/h and three different liquid flow rates chosen as 21ml/h, 42ml/h, and

63ml/h respectively. It was found that under current experimental conditions, except for the high

gas to liquid ratio data shown as the hollow triangles in the figure where the gas flow rate was

kept constant at Qg = 5ml/h, the rest of the data can be correlated successfully by Eq. (5-1) with

oc = 1, which is based on fitting with the experimental data in a T-channel which is shown as the

solid line in Fig. 5-11 and expressed as:


L /w = + (5-4)


The reason why the hollow triangle data deviate from Eq. (5-4) is given as follows: From Fig.

5-8, we know that the bubble break-up physics is similar to that in a T-junction as the bubble

break-up requires a vertical liquid velocity component to pinch off the neck. Oak et al. (2004)

demonstrated that in the co-flowing micro-channel, when the liquid flow rate is increased,

around the barrier there is a correspondingly higher vertical component that is used to form the

bubble. So when the liquid flow rate is larger than the critical value, the flow dynamics is almost

identical to the T-junction case. When the liquid flow rate is less than the critical value, only a

portion of the liquid velocity is used in the bubble formation, which lowers the effectiveness of

QL, As a result, the L/W is increased from that predicted by Eq. (5-4).

5.4.3 Bubble Frequency

For the macro channel, the bubble velocity is related with the mixture mean velocity

U,+ U1 and the mean drift velocity Ugz, which can be given by (Zuber and Findlay 1965):









U= Co(UG+U1)+Ug; (5-5)

Co is the distribution parameter. The mean drift velocity Ug; can be neglected in micro-channels

due to the inability of the bubbles to rise through the stagnant liquid (Ali et al. 1993) and Cubaud

et al. (2005) found Co 1 in micro-channels. Hence


U = (5-6)
w-h

Assume T is the total time of formation of one bubble, then

D = UiT = Uilte + tc) (5-7)

Assume the left and right side of the bubble is nearly spherical and the small volume of the

film thickness (~1%-3% of the total bubble volume from the image) can be neglected, then the

gas volume in a bubble is approximately estimated to be ((L-w) -w + -w2/4) -h. According to the

mass conversation, the relationship between L and D can be written as


(DL~+ 2D-L+ 1-
(5-8)

4 4

Combine Eqs. (5-4) (5-8), and the bubble frequency can be calculated as:


1 1 e; 0
frIe (5-9)
T te +t raa


Fig. 5-12 shows the experimental bubble frequencies and the theoretical one expressed by Eq.

(5-9). The experimental values are calculated by checking the video and getting the time of

bubble formation in one period. From Fig. 5-12, we can see the experimental data agree well

with the predicted one at the low frequency region. But there is an underestimation at the high









frequency region since in this region the gas flow rate is high and the bubble shape at the

interface shows an elliptical shape. When Eq. (5-8) is applied, the gas volume is underestimated

which results in the underestimation of frequency.

5.4.4 Effect of Viscosity and Surface Tension

Mixtures of water-glycerol and water-Tween 20 were used to obtain the effects of viscosity

and surface tension on the bubble generation respectively. The recorded data shows that the

bubble formation still can be steady and periodic as the pure water under the same operating

conditions. However, we have found some changes on the bubble shapes at different viscosities

and surface tensions. Fig. 5-13 shows the bubble shapes with different viscosities and surface

tensions at QL = 21Iml/h and QL = 42ml/h. With the increasing of the viscosity, the fi1m thickness

is obviously increased. A typical example is that the bubble shape changes from a slug to an

approximately spherical bubble at the lower Q/Qz. At this time, we can not use the channel

width w to be the bubble width wb. Hence a modified equation can be obtained by using wb to

replace w in Eq. (5-4). Fig. 5-14 shows the measured L/i at different ratios of gas to liquid flow

rate. The experimental data shows a good agreement with the ones predicted by the modified

equation. If w was still used here, the bubble length would be overestimated by around 6%,

18.7%, and 31.2% respectively. From Fig. 5-13, we also see the bubble changes to a tadpole-like

shape due to the decrease of surface tension. The tail of the bubble decreases with gas and liquid

flow rates. The reason may be at the interface that the increasing inertia forces push and shorten

the tail. To compare the bubble length with the former results, we define an equivalent bubble

length Le for the tadpole-like bubbles, which can be approximately calculated by:


Ab Pixels covered by the bubble area
L, (5-10)
ew Pixels covered by the channel width









where Ab is the bubble area obtained from the flow image. It is the area enclosed by the bubble

interface. This interface can be detected by an image processing function in the commercial

software ImageJ, Edge Detection Function, which uses the gradient of the pixel values around

the interface to detect it. Fig. 5-15 shows the Le/w at different surface tensions. The data also

have a good agreement with the predict ones. The conclusion can be made that under current

operating conditions, the bubble length can still be predicted by a modified equation which uses

the real bubble width wb or an equivalent bubble length Le. Fluid viscosity and surface tension

have a maj or effect on the bubble shape.

5.4 Summary

In this chapter, we experimentally and numerically investigated the formation of bubbles in

a simple co-flowing micro-channel, which has a compact size to be easily scaled up or

multiplexed and can generate micro-bubbles roughly from 0.1CL to 0.6C1L under current

operating conditions. The break-up process, bubble length, bubble frequency, and effects of

viscosity and surface tension were comprehensively studied. The following conclusions can be

made:

* Bubble break-up is obtained by the velocity distribution change around the barrier. It is
periodic under certain operating conditions, and it becomes unsteady and nonperiodic when
Qzis less than some critical values or Qg/Qz is too large. The process has two steps: gas
ligament expansion and collapse.

* The bubble length L is dependent on Qg and Ql, and has a quantitative relationship with
channel width w and Q/Ql, which is the same as that used for the T-junction since the
break-up process becomes similar with that of T-junction under the operating conditions.

* At the low frequency region, bubble generation frequency is a function of channel width w,
channel depth h and Qze~g/(Qg 144). This functional relationship provides a very good
prediction at the low frequency region.

* The liquid viscosity affects the film thickness while the surface tension changes the bubble
shape. The dimensionless bubble length L/w can still be predicted by a modified equation
which uses the real bubble width wb or an equivalent bubble length Le.















Gas



Liquid


Figure 5-1. Schematic of the co-flowing micro-channel: A) 3-D and B) 2-D


X:1.264 mm


Figure 5-2. 3-D image and depth measurement by the optical profiler














Liquid


Fiber optic



Microlchannel


SHigh SpeedC amr


Syringe pumlp


Comilp ute r


Figure 5-3.


Schematic of the experimental flow visualization apparatus


CCD Camnem


Syringe pumlp


Figure 5-4.


Schematic of micro-PIV measurement for micro-bubble dispenser


II~uinatoric~

































t = Os


Air inlet


0.07mm (10 gr ds)




Waiter inlet

Figure 5-5. Schematic of 3D CFD mesh


t = Os


t = 0.04s t = 0.04s




t = 0.15s t = 0.15s




t = 0.20s t = 0.20s




t 023 =0.3


t = 0.26s t = 0.26s




Figure 5-6. Time evolution of the periodic bubble generation process (Qg = 6.3ml/h, Qz
21ml/h, Air+Water) and the prediction by CFD simulation












A B C



n;11 Rr ,


Figure 5-7. Unsteady break-up process at different flow rates: A) Q g 2.4ml/h, Q; = 3ml/h B)
Qg= 105ml/h, Q, 42ml/h and C) Q, 37.5ml/h, Q, 15ml/h

A

f-'- -+--



r ,- -, -+ -, -


~rr~r

PP~~~~~*~~~~~~~-,,~~~,,,,,,,
f/*r

afPP~~~,,,,,,,,,,,,,,,,,,,,,,,
-r,
~~~~~~l~~~~~~~-l~t~~~~







-t ~-~ c


"'"


"I""


Figure 5-8. Instantaneous micro-PIV measurements around the barrier (Q, = 21ml/h, Qg
6.3 ml/h)





107

























_f___f

f-i-fff-t~








~rnn~~~~~~~~~



~~~~~~~,,,,, ,

~~n,,,,,,,,

;.--r.---.-- .-.r~~,,,,,,,______ _

-~ ~ ir Cj- ~~ ~ ~ ~ -) ~ f f f f f

-------~t -~ -- -- --~~ ~ ~ -, -f ~ ~ ~ t f ~ f f f

~~~~~~~~~~ff~f~f












--r ~~-- t ~ ~~+ I + + -- ~ + + t f --~ --? --t ~ + + +

+ + -- ~ t + t ~~ I C -- + r + + + + --r + + + +

--+ ~- fffff^-fl I fff-r----fff--l'~' F~


+ -e~


11,


~rt

f--'nn





n













f~rrf~~~r,,~,,,,,,~



P~~~~~r,,,,,
7












~ ~~~ ~~,,~ ,, ~ ,,,,,~, _t t~ ~

E .. ~ ~~ ~~ _e -+ -+ n n ~~~ ~ ,,,~,,, _t -- --r ~-f~~~~--e --e --r ~~

t,,~tt~~~~ ,,,~~

t --*~--- t~ t--e




FigureS-8. Continued



























r'r'
~l~~~rrr~
~f~r~rr,




r~~rrr







~~* ~F ~




3-~-


1

n~~n~~~~P~~


~~,~r~~~ff
~nrr~l~~~~f~




IrrAAAr~~~


III 1 ~1


-*-*~


7+"-'~~*~f~





~ -t ~t ~ ~~ ~ -, ~t --* -t ~ -t --t~--* ~ ~~


I


_n___l


-f-----


-+---r


~-*-+


- f l _


~f-f-~-ff-f
f-f~-~ff~~~ffff


e.*a


Figure 5-8. Continued

































a, = 1 ml/h, Air+Water =




I





I5


Figure 5-9. Bubble distribution along the channel at different flow rates: A) Qge Qz 0.01 (Qz
21ml/h, Qg= 0.21ml/h) B) Qge Qz 0.1 (Qz 21ml/h, Qg= 2.1ml/h) C) Qge Qz 0.5 (Ql
S21ml/h, Qg 10.5ml/h) D) Qge Qz 1 (Qz = 21ml/h, Qg = 21ml/h)


Og (ml/h)

Figure 5-10. Dependence of the bubble length L on the A) gas flow rate (Qz = 18ml/h) and B)
liquid flow rate (Qg = 5ml/h)


5
,.......













5.5


5.0 Qn = 5 ml/h, Air+Water


4.5-


4.0-


E 3.5-


3.0-


2.5-


2.0 -


1.5lllII
0 10 20 30 40 50

O, (ml/h)


Figure 5-10. Continued




4 -1 Q = 21 ml/h, Air+Water

O, = 42 ml/h, Air+Water
A a0 = 63 ml/h, Air+Water/
3-n
n Q = 5 ml/h, Air+Water
-L/w=1+Q, 1














0.01 0.1 1




Figure 5-11. Dimensionless ratio (L w) with the ratio of gas and liquid flow rates





111
































U. I ', I I I
0.1 1 10

OO 1(Q +Q,1/4)


Bubble frequency with different liquid and gas flow rates (Air +water)


I III Il I 11 1 I 1 I 1111 I 1 I I
0.01 0.1 1

Q 10


SExp erimentalI data
- Eq. (7)


Figure 5-12.


5 -


4 _

















1-


o Air +Water-Glycerol (10% ~dw)
oAir +Water-Glycerol (30% ~dw)
n Air +Water-Glycerol (50% ~dw)
-L/w =1+Q 10
b gl


Figure 5-14. Dimensionless ratio (L/i .) with the ratio of gas and liquid flow rates






















I _I __ __


'-Y





Ci~- 7


~iff~


~


I _


1rFla~


__


I ~n


QL g





0.1


Air + Water
o 72mN/m, C
S0.92 mPa-s


Air +
Water-Glycerol
(30%)
a = 72mN/m, C
= 2.68 mPa-s


Air +
Water-Tween20
a = 37mN/m, CL
= 0.92 mPa-s


0.5


QL g





0.1


0.5


Air + Water
o 72mN/m, C
S0.92 mPa-s


Air +
Water-Glycerol
(10%)
a = 72mN/m, C
= 1.19 mPa-s


Air +
Water-Glycerol
(30%)
a = 72mN/m, C
= 2.68 mPa-s


Air +
Water-Glycerol
(50%)
a = 72mN/m, C
= 7.31 mPa-s


Air +
Water-Tween20
a = 37mN/m, CL
= 0.92 mPa-s


Figure 5-13. Bubble shapes at different viscosities and surface tensions: A) Qz = 21ml/h B) Qz
= 42ml/h


Air +
Water-Glycerol
(10%)
a = 72mN/m, C
1 1. mPa-s


Air +
Water-Glycerol
(50%)
a = 72mN/m, C
= 7.31 mPa-s


~~lir"


-~.Z













41 aQ,=21 rnl/h,Air+Water-Tween 20
n Q. = 42 rnl/h, Air+Water-Tween 20
3+ O =l B3 rnl/h, Alr+Water-Tween 20 ,
-L /w=1+Q, /














0.01 0.1 1




Figure 5-15. Dimensionless ratio (Le w) with the ratio of gas and liquid flow rates









CHAPTER 6
CONCLUSIONS AND RECO1V1VENDATIONS

In this research, many features of the single- and two-phase pressure-driven flows in

micro-channels were experimentally and numerically investigated. Maj or accomplishments and

recommendations for future research are provided in the following.

6.1 Accomplishments and Findings

1. For straight micro-channels, the experimental Poiseuille numbers show agreement with
standard laminar incompressible flow predictions when the Re is less than a value around
1500. The discrepancy observed by the former researchers is the result of unaccounted bias
in experiment setups, such as not accounting for increased pressure drop in the entrance
region or unreliable inlet and outlet losses.

2. The flow micro structures around the bend of a serpentine micro-channel can be divided into
three categories depending on the flow Reynolds number. When Re<100, there is no induced
flow recirculation and flow separation. When Re>100, vortices and flow separation appear
and further develop. The outer corner vortex develops along the wall of the channel, and the
vortex center moves slightly from the upper stream to the down stream with the increasing of
the Re number. The inner wall vortex due to flow separation develops immediately after the
flow makes the turn. When Re>1000-1500, the shape and size of the outer and inner vortices
become almost constant.

3. In serpentine micro-channels, the additional pressure drop due to miter bends can be divided
into two groups. The first group is for Re<100 where there is no eddies and the additional
pressure drop is very small for all of the channels. The other group is for flows with the
Reynolds numbers exceeding the threshold values that are in the range of 100-300. When the
Reynolds is higher than the threshold value, we found the flow separation and formation of
vortices that appear on the inner and outer wall around the miter bend. These vortices
increase in strength with increasing Re number that causes the bend pressure drop to increase
sharply with the Re number. The experimental results also show the bend pressure drop
increases with decreasing hydraulic diameters. Bend loss coefficient Kb is a function of the
Re number only when Re<100, a function of the Re number and channel size when Re>100,
and almost keeps constant and changes in the range of +10% when Re is larger than some
value in 1000-1500. The trend of the experimental pressure drop is consistent with the flow
structure change.

4. The phenomenon that micro-channel flow pattern changes with time at a fixed location under
a certain gas and liquid superficial velocity was found, which can be attributed to the density
wave oscillation in the micro-channel. According to the appearance of the transition flow
patterns such as "liquid ring flow", "liquid lump flow" and "disruption tail of the slug", four
flow patterns can be defined for micro-channels with the hydraulic diameters of 0.412 mm
and 0.622 mm: bubbly-slug flow, slug-ring flow, dispersed-churn flow and annular flow. For
the micro-channel with the hydraulic diameters of 0.209 mm, the bubbly-slug flow became









the slug-flow and the dispersed flow disappeared. The current flow regime maps show the
transition boundary lines shift to high WeGS Or gas superficial velocity with the decreasing of
the hydraulic diameter. It can be explained by the strong surface tension effect in
micro-channels. The micro-channel flow maps were compared with the mini-channel flow
map based on the Weber number model, which showed poor agreement.

5. Time-averaged void fractions of each micro-channel were measured for 22 runs to cover the
whole range of homogeneous void fraction. The data of each run were obtained from the
analysis of 8000 flow pattern images captured at a certain gas and liquid superficial velocity.
With the decreasing of the hydraulic diameter, the time-average void fraction showed a
non-linear relationship with the homogeneous void fraction. A new empirical correlation was
proposed to predict the non-linear relationship, and most of the current experimental data and
Kawaraha' s (2002) data fall within 15% of the new correlation. The uncertainty of this
measurement method was analyzed and the uncertainty range was approximately from 3.1%
to 9.8% under the current experimental conditions. The results of this study provide basic
information of the effects of length scale reduction on nitrogen-water two-phase flow
characteristics in micro-scale channels that would be useful for the design of gas-liquid
transport and their separation encountered in low-temperature fuel cells.

6. In a micro-bubble dispenser with co-flowing structure, bubble break-up is obtained by the
pressure drop resulting from the sudden velocity distribution change around the barrier. It is
periodic under certain operating conditions, and it becomes unsteady and nonperiodic when
Qi is less than some critical values or Qg/Q1 is too large. The process has two steps: gas
ligament expansion and collapse.

7. The bubble length L is dependent on Q, and Q1, and has a quantitative relationship with
channel width w and Q,/Q1, which is the same as that used for the T-junction since the
break-up process becomes similar with that of T-junction under the operating conditions. At
the low frequency region, bubble generation frequency is a function of channel width w,
channel depth h and Q1Q,/(Q,+Q1-x/4). This functional relationship provides a good
prediction at the low frequency region. The liquid viscosity affects the film thickness while
the surface tension changes the bubble shape. The dimensionless bubble length L/w can still
be predicted by a modified equation which uses the real bubble width wb or an equivalent
bubble length Le.

6.2 Future Research

Future research to further understand the micro-scale pressure-driven flow can be

performed both experimentally and numerically.

6.2.1 Experimental Study

1. Segmented bubble transport in serpentine micro-channels to compare with gas-liquid
two-phase flow motion and transport in straight micro-channels.

2. Rapid micro-T-junction mixer.











3. Droplet transport in micro-T-junction and serpentine micro-channels.

6.2.2 Numerical Study

1. A general micro-scale two-phase flow model incorporate the inertia force, viscous force,
surface tension force to predict the flow patterns, void fraction and frictional pressure drop.

2. A new model to predict the enhanced mixing induced by the segmented micro-bubble/droplet









APPENDIX
TIMINTG PROGRAM FOR MICRO-PARTICLE IMAGE VELOCIMETRY

The timing controller LC880 needs to be programmed to synchronize the laser and CCD
camera. The following channels refer to:

Channel A: Reference clock
Channel B: Control the CCD Camera
Channel C: Control the Flashlamp of laser 1
Channel D: Control the Q-Switch of laser 1
Channel E: Control the Flashlamp of laser 2
Channel F: Control the Q-Switch of laser 2

Overall LC880 settings: Programming preset A, Using 40 MHz internal clock.
Channel A:
Free-running clock: High duration: 1.000000 ms; low duration: 1.000000 ms.
Channel B:
Delayed pulse: Delay after trigger 50.000000 ns then pulse output 1.000000 ms. Invert
output (pulse from high to low).
Triggering options: Trigger on rising edge. Skip 100 triggers before triggering.
Trigger Input Logic:
inB = outA;
Channel C:
Delayed pulse: Delay after trigger 0.853800 ms then pulse output 15.000000 us.
Triggering options: Trigger on rising edge. Unlimited retriggering.
Trigger Input Logic:
inC = not outB;
Channel D:
Delayed pulse: Delay after trigger 152.000000 us then pulse output 15.000000 us.
Triggering options: Trigger on rising edge. Unlimited retriggering.
Trigger Input Logic:
inD = outC;
Channel E:
Delayed pulse: Delay after trigger 0.856300 ms then pulse output 15.000000 us.
Triggering options: Trigger on rising edge. Unlimited retriggering.
Trigger Input Logic:
inE = not outB;
Channel F:
Delayed pulse: Delay after trigger 152.000000 us then pulse output 15.000000 us.
Triggering options: Trigger on rising edge. Unlimited retriggering.
Trigger Input Logic:
inF = outE;










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BIOGRAPHICAL SKETCH

Renqiang Xiong was born in 1978, in China. He grew up predominantly in Jingdezhen city,

Jiangxi Province, China, and received his Bachelor of Science in energy engineering and Master

of Science in optical engineering from Zhejiang University in June 1999 and May 2002,

respectively. Renqiang moved to the Sunshine state in Spring 2003 and enrolled in the

Department of Mechanical and Aerospace Engineering at the University of Florida where he

received a Master of Science in mechanical engineering with minor in statistics in August 2005.

He then continued to pursue his PhD degree and worked as a research assistant on a part-time

basis with Dr. Jacob N Chung. In the meantime, he is also pursuing a Master of Science in

electrical and computer engineering. His research interests include microfluidics, micro-PIV,

MEMS, and cryogenics.





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SINGLEAND TWO-PHASE PRESSURE-DRIVEN FLOW TRANSPORT DYNAMICS IN MICRO-CHANNELS By RENQIANG XIONG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 1

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2007 Renqiang Xiong 2

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ACKNOWLEDGMENTS I would like to express my si ncere appreciation to my advisor, Dr. Jacob N Chung, for his invaluable patience, support a nd encouragement. Without his direction and support, this work would not go further. Many thanks go to Dr. Steve Wereley from Purdue University and Dr. Lichuan Gui from University of Mississippi for helping me to build the Micro-PIV system and tutorials in this research. Drs. S.A. Sherif, Corin Segal, William E. L ear, Jr, and Jason E. Butler were extremely helpful in several aspects of this research while serving on my supervisory committee. Their suggestions and encouragement have shaped this work considerably. My fellow graduate students, Kun Yuan, Yunwhan Na, Yan Ji and Mo Bai, have graciously given their time and experience. Fina lly, I would like to th ank my parents and my elder brothers family for the most needed encouragement to finish my studies. Special thanks are given to my wife, Xiaoxing Feng, for years of support. Without her sacrifice, it would have been impossible for me to complete this work. 3

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TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................3 LIST OF TABLES................................................................................................................. ..........6 LIST OF FIGURES.........................................................................................................................7 NOMENCLATURE........................................................................................................................9 ABSTRACT...................................................................................................................................12 CHAPTER 1 INTRODUCTION................................................................................................................. .14 1.1 Research Background.......................................................................................................14 1.2 Research Objectives..........................................................................................................16 1.3 Research Overview...........................................................................................................16 2 ENTRANCE FLOW AND BEND EFFECT..........................................................................18 2.1 Introduction and Background...........................................................................................19 2.2 Experimental Setup...........................................................................................................22 2.2.1 Micro-Channels Fabrication...................................................................................22 2.2.2 Apparatus................................................................................................................23 2.3 Data Reduction and Analysis............................................................................................24 2.4 Results and Discussion..................................................................................................... 28 2.4.1 Friction Factor........................................................................................................28 2.4.2 Bend Loss Coefficient............................................................................................28 2.5 Summary...........................................................................................................................30 3 FLOW STRUCTURES AROUND A BEND.........................................................................36 3.1 Introduction and Background...........................................................................................36 3.2 Micro-PIV System............................................................................................................39 3.2.1 Laser Beam Alignment...........................................................................................39 3.2.2 Timing Scheme.......................................................................................................40 3.2.3 Fluorescent Particles Image....................................................................................42 3.2.4 Measurement Depth................................................................................................43 3.3 System Validation.......................................................................................................... ...44 3.4 Results and Discussion..................................................................................................... 45 3.4.1 Flow Structures Around The Miter Bend...............................................................45 3.4.2 Circulation Calculation...........................................................................................46 3.4.3 Shear Strain............................................................................................................4 7 3.5 Summary...........................................................................................................................47 4

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4 ADIABATIC GAS-LIQUID TWO-PHASE FLOW..............................................................62 4.1 Introduction and Background...........................................................................................62 4.2 Experimental Apparatus...................................................................................................66 4.3 Results and Discussion..................................................................................................... 68 4.3.1 Two-Phase Flow Patterns.......................................................................................68 4.3.2 Flow Regime Maps.................................................................................................71 4.3.3 Comparison With Prior Mini-Channel Flow Map..................................................73 4.3.4 Time-Averaged Void Fraction...............................................................................74 4.3.5 Frictional Pressure Drop.........................................................................................77 4.4 Summary...........................................................................................................................77 5 MICRO-BUBBLE DISPENSER............................................................................................91 5.1 Introduction and Background...........................................................................................91 5.2 Experimental Setup...........................................................................................................94 5.2.1 Dispenser Fabrication.............................................................................................94 5.2.2 Apparatus................................................................................................................94 5.3 Numerical Simulation....................................................................................................... 96 5.4 Results and Discussion..................................................................................................... 98 5.4.1 Bubble Break-Up....................................................................................................98 5.4.2 Bubble Distribution and Bubble Size.....................................................................99 5.4.3 Bubble Frequency.................................................................................................100 5.4.4 Effect of Viscosity and Surface Tension..............................................................102 5.4 Summary.........................................................................................................................103 6 CONCLUSIONS AND RECOMMENDATIONS...............................................................115 6.1 Accomplishments and Findings......................................................................................115 6.2 Future Research..............................................................................................................116 6.2.1 Experimental Study..............................................................................................116 6.2.2 Numerical Study...................................................................................................117 APPENDIX TIMING PROGRAM FOR MI CRO-PARTICLE IMAGE VELOCIMETRY...118 LIST OF REFERENCES.............................................................................................................119 BIOGRAPHICAL SKETCH.......................................................................................................125 5

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LIST OF TABLES Table page 2-1 Dimensions of three groups of micro-channels.................................................................31 2-2 Comparison of current pipe length s with those of entrance regions..................................31 3-1 Specification of the Nd:YAG la ser (Continuum Minilite II).............................................48 3-2 Calculated vortex circulation.............................................................................................48 4-1 Generalized two-phase fricti onal pressure-drop correlations............................................79 4-2 Non-dimensional parameters for a macro-channel and micro-channels............................80 6

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LIST OF FIGURES Figure page 2-1 Three groups of fabricated micro-channels.......................................................................32 2-2 Experimental pressure drop measurement apparatus.........................................................33 2-3 Pressure drop defect K(x+) vs x+........................................................................................33 2-4 Experimental pressure gradients without removing the entrance effect (Pl-Psh)/( LlLsh) vs Re number.......................................................................................34 2-5 Experimental friction factor vs. Re number in straight micro-channels............................34 2-6 Bend additional pressure drops vs. Re number in serpentine micro-channels..................35 2-7 Bend loss coefficients vs Re numb er in serpentine micro-channels..................................35 3-1 Top view of the optical layout of the laser beam alignment..............................................49 3-2 Timing diagram for the two lasers and CCD camera........................................................49 3-3 Fluorescent images at straight and serpentine micro-channels..........................................50 3-4 Schematic of micro-PIV system........................................................................................50 3-5 Photo of the optical subsystem..........................................................................................51 3-6 Photo of the laser b eam alignmen t component..................................................................51 3-7 Micro-PIV results for low speed flow...............................................................................52 3-8 Typical velocity vector in the serpentine micro-channel at Re = 500................................53 3-9 Flow structure at the outer wall and at the inner wall........................................................54 3-10 Streamlines at di fferent Re numbers..................................................................................57 3-11 Total vortex circulat ion vs. Reynolds number...................................................................59 3-12 Distribution patterns of shear strain rates..........................................................................60 4-1 Schematic of the flow visual ization apparatus and the mixer............................................81 4-2 Photograph of micro-channels a nd schematic of the micro-channel.................................83 4-3 Typical flow patterns in the micro-channel.......................................................................83 7

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4-5 Flow regime maps fo r three micro-channels.....................................................................85 4-6 Flow map comparison between micro-ch annel and mini-channe l predicted by the Weber number model.........................................................................................................87 4-7 Measured time-averaged void fraction results vs two previous correlations.....................87 4-8 Comparison between the new co rrelation and experimental data.....................................88 4-9 Ratio of predicted and experimental time-averaged void fraction vs. homogeneous void fraction ....................................................................................................................88 4-10 Comparison between the experimental data and the models ( Dh = 0.412mm)..................89 5-1 Schematic of the co-flowing micro-channel....................................................................104 5-2 3-D image and depth measurement by the optical profiler..............................................104 5-3 Schematic of the experimental flow visualization apparatus...........................................105 5-4 Schematic of micro-PIV measur ement for micro-bubble dispenser................................105 5-5 Schematic of 3D CFD mesh............................................................................................106 5-6 Time evolution of the periodic bubble generation process ( Qg = 6.3ml/h, Ql = 21ml/h, Air+Water) and the prediction by CFD simulation.........................................................106 5-7 Unsteady break-up process at different flow rates...........................................................107 5-8 Instantaneous micro-PIV m easurements around the barrier ( Ql = 21ml/h, Qg = 6.3ml/h)....................................................................................................................... .....107 5-9 Bubble distribution along the ch annel at different flow rates..........................................110 5-10 Dependence of the bubble length L on the gas flow rate ( Ql = 18ml/h) and liquid flow rate ( Qg = 5ml/h)......................................................................................................110 5-11 Dimensionless ratio ( L/w ) with the ratio of gas and liquid flow rates.............................111 5-12 Bubble frequency with different liqui d and gas flow rates (Air +water).........................112 5-13 Bubble shapes at different vi scosities and surface tensions.............................................113 5-14 Dimensionless ratio ( L/wb) with the ratio of gas and liquid flow rates............................112 5-15 Dimensionless ratio ( Le/w ) with the ratio of gas and liquid flow rates............................114 8

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NOMENCLATURE A Area [m2] Ai Area of interrogation window [ m2] B Coefficient in Eq. 2-6 Bo Bond number C Coefficient in Eq. 4-4 Cv Volumetric concentration [ m-3] C0 Coefficient in Eq. 4-1 Ca Capillary number dP/dz Pressure gradient [Pa/m] D Diameter [mm] f Fraction factor fre Frequency [1/s] g Gravity acceleration [m/s2] j Superficial velocity [m/s] K Pressure drop defect Kb Bend loss coefficient L Length [mm] Ld Entrance length [m] m Mass transfer rate [g] n Refraction index N Total number NA Numerical aperature 9

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P Pressure [Pa] Q Flow rate [ml/min] Re Reynolds number S Depth of micro-channels [mm] T Time [s] u Local velocity at x direction [m/s] U Mean velocity [m/s] Vgj Mean drift velocity [m/s] W/w Width [mm] We Weber number X Martinelli parameter x The coordinate along the length x+ Dimensionless entrance length y The coordinate along the width Zm Measurement depth [ m] Greek letters Variable difference Aspect ratio Homogeneous void fraction Circulation [mm2/s] Differential value Wavelength of light in a vacuum [ m] Viscosity [kg/m s] 10

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Light collection angle Density [kg/m3] Surface tension [N/s] Subscripts b 90 bend c Cross-section dev Developing and developed flow exp Experimental result fd Fully developed G/g Gas GS Superficial gas h Hydraulic diameter i Particle image io Inlet and outlet L/l Liquid LS Superficial liquid l Long straight micro-channel m Other type of flow patterns p Fluorescent particles s Serpentine micro-channel sh Short straight micro-channel 11

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Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SINGLEAND TWO-PHASE PRESSURE-DRIVEN FLOW TRANSPORT DYNAMICS IN MICRO-CHANNELS By Renqiang Xiong August 2007 Chair: Jacob N Chung Major: Mechanical Engineering The pressure-driven flow in a micro-channel is an important component of the micro-scale fluid dynamics and widely applied in many fields such as cooling of IC chips, micro-fuel cell fluid transport, and lab-on-a-c hip. To enrich the current funda mental knowledge of micro-scale fluid dynamics, some experimental and nu merical investigations were performed. The pressure drops of liquid flow in straight and serpentine micro-channels with hydraulic diameters of 0.209 mm, 0.412 mm, and 0.622 mm were evaluated. To segregate the bends and entrance effects individually from the total pressure drop, for each size, three types of micro-channels: straight short, straight long, and long serpentine, were fabricated. An in-house micron-resolution particle image velocimetry system (micro-PIV) was built at the University of Florida and used to obtain the deta iled velocity vector field in micro-scale channels. The friction factor result shows that the conve ntional theory is still valid under the current channel size. The additional pressure drop is consistent with th e flow structure around the bend measured by the micro-PIV. Adiabatic nitrogen-water flow patterns and void fractions in straight micro-channels were experimentally investigated. Gas and liquid superfi cial velocities were varied from 0.06-72.3 m/s and 0.02-7.13 m/s, respectively. The instability of flow patterns was observed. Four groups of 12

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flow patterns including bubbly-slug flow, slug-ring flow, dispersedchurn flow and annular flow were observed in micro-channels of 0.412 mm and, 0.622 mm while in the micro-channel of 0.209 mm, the bubbly-slug flow became the slug-flow and the dispersed-churn flow disappeared. The current flow regime maps showed that the tr ansition lines shifted to a higher gas superficial velocity due to a dominant su rface tension effect as the ch annel size was reduced. The void fractions hold a non-linear relationship with the homogeneous void fraction as oppose to the relatively linear trend for the mini-channels. A new correlation was deve loped to predict the non-linear relationship that fits most of the current experimental data within %. Bubble generation in a simple co-flowing micro-channel w ith a cross-section area of 1.69 0.07 mm2 was also investigated. Mixtures of wa ter-glycerol and water-Tween 20 were also used to obtain the effects of viscosity and surface tension. The break-up dynamics can be predicted using a three dimensional incompressible two-phase flow numerical model based on the volume of fluid (VOF) method. The bubble lengt h L is dependent on the liquid flow rate Ql and gas flow rate Qg. Further more the ratio of L to the ch annel width w is a function of the ratio of gas and liquid flow rates Qg/Ql which is similar to that previously used in the T-junction case. The bubble frequency is found to be re lated to w, channel depth h, and QlQg/(Qg+Ql /4), and shows a good agreement with the experimental data at the low fre quency region. Different bubble shapes can be obtained at different liquid viscosities and surface tensions. The ratio L/w can still be predicted by a modified equa tion which uses the real bubble width wb or an equivalent bubble length Le. 13

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CHAPTER 1 INTRODUCTION Micro-scale fluid dynamics usually refers to the dynamics of fl uid flow in the devices with length scales less than one millimeter. Studies of such fluid-related phenomena have long been an important part of the fluid mechanical compon ent (Batchelor 1977). Due to the availability of MEMS fabrication methods (Ho and Tai 1998; Stone & Kim 2001), methods for fabricating individual and integrated flow configurations with length scales on the order of tens and hundreds of microns and smaller, micro-scale fl uid dynamics research has received enormous recent attention and been widely applied in many fields such as biotechnology (Beebe et al. 2002), cooling of IC chips (Zhang et al. 2002), micr o-fuel cell (Heinzel et al. 2002) and lab on a chip (Erickson and Li 2004). In ma ny applications, a valuable feat ure of microflows is that the dynamics in a single channel can be repli cated in many channels, so understanding the fundamental knowledge of fluid motion and associat ed transport processes in micro-channels is quite important for the micro-scal e fluid transport system design. In this study, we experimentally and numeri cally investigated many flow features of pressure-driven singleand two-phase flow in mi cro-channels to enrich the current fundamental knowledge of micro-scale fluid dynamics. 1.1 Research Background Micro-scale flows can be manipul ated using many kinds of external fields such as pressure, electric, magnetic, capillary, etc. Pressure-drive n flow is an indispensable component in micro-scale fluid dynamics research It is widely used in microheat exchanger (Brandner et al. 2000), and the pressure drop is a critical parameter to design the micro-pumps. For single phase liquid flow in straight microchannels, many scientists have published numerous papers on the relationship between the friction fa ctor and Re number in the past fifteen years. Some of them 14

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found for a liquid flow an increase of the fric tion factor with the Re number including Wu and Little (1983), Peng and Peterson (1996), Mala and Li (1999), Qu et al. (2000), and Li et al. (2003). They attributed it to surface roughness eff ect or the early transition to turbulent flow (Re=300-500) in straight micro-channels. However, recent studies showed general agreement with theoretical macro-scale predictions for friction factors in cluding Judy et al (2002), Wu and Cheng (2003), Hetsroni et al. (2005) and Kohl et al. (2005). They attributed the deviation from the theoretical prediction in the previous liter atures to the size measurement uncertainties and neglect of the entrance effects. Hence, the relati onship is not clear yet. The studies for liquid flow in serpentine micro-channels just started (L ee et al. 2001; Maharudra yya et al. 2004). It is of concern in the field of micro-fuel cell. Most measurements of microflows have been performed with optical microscopes. An adaptation of particle image velocimetry known as micro-PIV can yield a spatial resolution of the flow field of approximately one micron (San tiago et al. 1998). Due to the high expense of purchasing such a commercial system, around $500,000, building an in-house micro-PIV system became timely to speed up the progress of micr o-scale fluid dynamics research at the University of Florida. Two-phase flow in micro-channels is also a major research subject in micro-scale fluid dynamics. Recent researches show that the surfa ce tension becomes dominant when the channel size decreases which may result in a big change in the flow pattern and flow map, even the void fraction (Kawahara et al. 2002). A study of the size effect on those flow features need to be performed to provide a clear image of the micro-scale two-phase flow. Micro-bubble dispenser is one of the fundamental elements in a lab-on-a-chip system. It can be integrated with other microfluidic components including valves, pumps, actuators, 15

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switches, sensors, mixers, filters, separators, heat ers, etc. to succeed with chemical synthesis, analysis, and reactions using only very small fluids volumes (Stone et al. 2004). Recent studies have reported several bubble dispensers but wi th complex structures (Ganan-Calvo and Gordillo 2001; Garstecki et al. 2004). New dispensers with si mple structures that ar e easy to be scaled up or multiplexed need to be designed and tested. 1.2 Research Objectives This research is performed to provide f undamental understanding for the following flow features in micro-scale: Friction factor, entrance effect and bend eff ect for a liquid flow in micro-channels. Flow structure around the bend and its corres pondence to the additional pressure drop. Flow patterns, time-averaging void fraction and two-phase frictional pressure drop for gas-liquid two-phase flow in micro-channels Micro-bubble dispenser with a simple stru cture to generate uniform micro-bubbles. To reach the above objectives, several micro-channels and bubble dispensers need to be fabricated and a micron-resolution particle image ve locimetry system needs to be built to obtain the flow structure in micro-scale. 1.3 Research Overview Chapter 2 presents the flow characteristics of liquid flow in straight and serpentine micro-channels including the friction factor a nd bend loss coefficient. The entrance effect and bend effect are discussed. This chapter can al so refer to Xiong R. and Chung J.N., Flow characteristics of water in straight and se rpentine micro-channels with miter bends, Experimental Thermal and Fluid Science Vol 31(7), pp. 805-812, 2007. Chapter 3 describes an in-hous e micron-resolution particle image velocimetry system (Micro-PIV) used to measure the velocity profile in microscale and discusses the flow structure 16

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around the bend in a serpentine micro-channel. This work has been submitted as Xiong R. and Chung J.N., Effects of miter bend on pressure drop a nd flow structure in microfluidic channels, International Journal of Heat and Mass Transfer 2007. Chapter 4 presents an experimental study of two-phase flow features in straight micro-channels including flow patterns, flow map, time-averaged void fraction and two-phase frictional pressure drop. This chapter can also refer to Xiong R. and Chung J.N., An experimental study of the size effect on adiaba tic gas-liquid two-phase flow patterns and void fraction in micro-channels, Physics of Fluids Vol. 19(3), 033301, 2007. Chapter 5 describes a simple co-flowing micro-bubble dispense r which can be used in a lab-on-a-chip system. A VOF model is used to predict the bubble motion. Bubble size, bubble distribution, bubble frequency, a nd effects of viscosity and surface tension have been investigated in details. This chapter can also refer to Xiong R. and Chung J.N., Formation of bubbles in a simple co-flowing micro-channel, Journal of Micromechanics and Microengineering Vol. 17(5), pp. 1002-1011, 2007. Chapter 6 concludes the research with a summary of the overa ll work and suggests future work. 17

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CHAPTER 2 ENTRANCE FLOW AND BEND EFFECT Flow characteristics of pressure-driven de-ioniz ed water were investigated in straight and serpentine micro-channels with miter bends. The micro-channels had rectangular cross-sections with hydraulic diameters of 0.209 mm, 0.412 mm and 0.622 mm. To evaluate bend loss coefficient in the serpentine micro-channel a nd micro-scale size effect on it, the additional pressure drop due to the miter bend must be obtained. This additional pressure drop can be achieved by subtracting the frictiona l pressure drop in the straight micro-channel from the total pressure drop in the serpentine micro-channel. Since currently there st ill has a debate on the relationship between the friction factor and Re number in the straight micro-channel, the frictional pressure drop had to be obtained expe rimentally here. Three groups of micro-channels were fabricated to remove the inlet and outlet lo sses. The experimental results show that after considering the measurement uncertainties the experimental Poiseuille number can be well predicted by the conventional laminar incompressi ble flow theory when Re number is less than some value around 1500, the discrepancy observed by th e former researchers can be attributed to not accounting for the additional pressure drop in the entrance region. The onset of transition to turbulence might be at 1500-1700. For serpentine micro-channels, the additional pressure drop can be divided into two regions. One is Re<100. Its very small since no circulation exists. The other one is Re larger than some value in 100200. At this time the circulation appears and develops at the inner and outer wall of the bend. The additional pressure drop increases sharply with Re number. The bend loss coefficient was obs erved to decrease and tend to be a constant with decreasing Re number. Its found to be larger than the pr edicted value for macro-channel turbulent flow and related with the channel size when flow separation appears, namely Re>100-200. 18

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2.1 Introduction and Background In recent years, the proliferation of MEMS and micro-fluidic device s has resulted in the use of micro-channels in many applications in cluding propulsion and power generation of micro air vehicles, micro-scaled cooling systems of elect ronic devices, micro satellites, etc. Because of the wide range of uses for micro-channels, it is im portant to be able to well predict their behavior which requires a good knowledge of flow char acteristics in stra ight and serpentine micro-channels (Ho and Tai 1998). Flow characteristics in circular and non-circular macro-ducts with curved bends have been extensively studied (Humphrey et al. 1981; Berger et al. 1983; Brad shaw et al. 1987) in the past years. However, there were limited literature s on single phase flow characteristics in the channels with miter bends in the past. Streeter (1961) reported the bend loss coefficient for miter bend was taken to be around 1.1 for engineering a pplications, which was usually for turbulent flow. Yamashita et al. (1984, 1986) and Kushida et al. (1985) studied threedimensional flow and heat transfer in miter-bend experimentally and numerically. They found a decreasing trend of the bend loss coefficient with Re number in laminar and turbulent flow region and analyzed the effects of Re number and asp ect ratio on the flow structures Though significant attention has been paid to the flow in macro-systems w ith bends, research on flow characteristics in micro-systems with bends has recently been started. In most practic al applications the micro-channels are not straight due to requi red turns and sometimes it is complicated and expensive to keep the micro-ch annel straight. To minimize the pressure losses in the flow through the micro-channels for optimum de sign, flow characteri stics in serpentine micro-channels with miter bends must be also well understood. Lee et al (2001) researched on the gas flow in micro-channels having the dimensions 20 1 5810 m3 with bends of miter, 19

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curved and double-turn. They found the flow ra te through the channel with the miter bend was the lowest at a certain inlet pr essure and the largest drop was found in the miter bend with the lowest flow rate. They also found the secondary flow could develop in micro-channels, contrary to expectations. Maharudrayya et al. (2004) studied the pressure losses and flow structures of laminar flow through serpentine channels with miter bends by a CFD code but they didnt consider the micro-scale effect. After literature re view, it can be seen that the experimental work of liquid flow in serpentine micro-channels with miter bends and the micro-scale size effect on flow characteristics have ne ver been reported before. As we know, the additional pressure loss due to the miter bend in serpentine channels was usually related with the flow separation and reattachment around the bend. To evaluate the bend loss coefficient, the additional pressure drop must be achieved. It can be calculated by subtracting the frictional pressure drop of straight micro-channe ls from the total serpentine micro-channel pressure drop. Hence, the issu e of frictional pressure drop in straight micro-channels was involved in this work too. For recent 15 years, many scientists have published numerous papers on the flow characteristics in straight microchannels. Some of them found flow characteristics in the straight micro-channel were quite different with those pr edicted by the conventiona l laminar flow theory. One of the important flow performances was the relationship between the friction factor and Re number. For liquid flow in straight micro-channels, an increase of friction factor with Re number under certain conditions was found by the scientists including Wu and Little (1983), Peng and Peterson (1996), Mala and Li ( 1999), Papautsky et al. (1999), Qu et al. (2000), Pfund et al. (2000), and Li et al. (2003). Wu and Littles (1 983) friction factor measurements appear to correlate with surface roughness, as the results agreed well with theory for smooth channels, but 20

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the agreement decreased as the roughness increased. In an effort to understand the influence of geometrical parameters (specifi cally, hydraulic diameter and asp ect ratio) on flow resistance, Peng et al. (1994) considered wate r flows in rectangular machined steel grooves enclosed with a fiberglass cover. A large range of Re were obtained (50 to 40 00), and a geometrical dependence was observed. For the most part, the friction factor increased with increasing H/W and also with increasing Dh (holding H/W constant). Nonlinear trends between pressure drop and flow rate were observed for Re as low as 300 by Mala and Li (1999), specially for water flowing through a 0.13mm diameter stainless steel mi cro-tube. At small Re number (Re<100) the measured friction factors were consistently higher in stainless steel and fused sili ca micro-tubes. Measured flow friction for trapezoidal channels was 8 to 38% hi gher than macroscale predictions for the range of parameters studied by Qu et al. (2000), and a dependence on Dh and Re was also observed. However, there were some other scientists findi ng general agreement with theoretical macroscale prediction for friction factor in cluding Flockhart and Dhariwal (1998), Jiang et al. (1995), Sharp et al. (2000) and Wilding et al. (1994), Xu et al. (2000), Judy et al. (2002), Wu and Cheng (2003), Hetsroni et al. (2005), and Kohl et al. (2005). Jiang et al. (1995) got a linear relationship between flow rate and pressure drop in micro-channels with various cross-sectional shapes. In the circular case, the friction factor matche d theoretical predictions within 10%-20%. Wilding et al. (1994) found the result for water flowing in silicon micro-machined channels agreed well with theory for at least the lower Re number (Re around 17 to 126) tested. Flockhart and Dhariwal (1998) found a good agreement between the numerical calcula tions for flow in trapezoidal channels and the experimental results for Re <600. Sharp et al. (2000) found the microscale measurements of the friction factor generally agree with th e macroscale laminar theory to within % experimental error over all Re numbers up to transition (around 50
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through circular fused silica micro-channels with hydraulic diameter 0.075 to 0.242 mm. This group attributed the deviation from the theoretical prediction in the previ ous literatures to the size and measurement uncertainties. Hence, the re lationship between the fr iction factor and Re number in straight micro-channe ls is not clear yet. The frictio nal pressure drop in straight micro-channels cant be calculated by a unive rsal formulation and need to be achieved experimentally here. In our research, three groups of micro-channels were fabr icated. Each group has three micro-channels with the same size: straight long, straight short and single serpentine with miter bends. The straight long and strai ght short micro-channels were used to achieve the reliable frictional pressure drop in straight micro-channe ls, and the serpentine micro-channels were used to get the additional pressure drop due to the m iter bend. The main objective of this study is to achieve this additional pressure drop and bend loss coefficient to evaluate flow characteristics in serpentine micro-channels, and compare it with the bend loss coefficient in macro-channels. The Poiseuille number for straight micro-channels ca n also be achieved experimentally and compared with the previous conclusions. 2.2 Experimental Setup 2.2.1 Micro-Channels Fabrication Fig. 2-1 a) to d) shows the photographs of straight and serpentin e micro-channels and schematic of the straight micro-channel used in this work. The micro-channel was laser etched in a silicon plate and then a Pyrex thin cover glass plate was anod ically bonded on the top of the plate. The micro-channel plates have two dimensions of 30 12 2 mm3 (straight long and serpentine) and 11 12 2 mm3 (straight short). Two small connec tion tubes which can be inserted into the inlet and outlet assembly were connect ed with the small reservoirs. Each of the 22

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serpentine micro-channels had fi ve straight micro-channels with the same size and eight miter bends. A microscope (Olympus BX50), a 10 objective lens and a CCD camera with pixel size 6.45 m were used to measure the dimensions of th e micro-channels recta ngular cross-sections, which were listed in Table 2-1. 2.2.2 Apparatus Fig. 2-2 shows schematic and 3-D assembly drawing of the experimental apparatus used to investigate the pressure-driven de -ionized water flow in straight and serpentine micro-channels. It includes a syringe infusion pump (Cole-Parmer Instrument), 60ml syringe (Mcmaster), micro-filter (Swagelok), pressure transducers (K avlico), straight and serpentine micro-channel test sections and computerized data acquisition system. The de-ion ized water at the flow rate from 0.1ml/min to 70ml/min, which can be set on the panel of the infusion pump with an accuracy of 0.5%, was driven to the microchannel test section. The 2 m micro-filter can remove any particles or bubbles which may block th e micro-channel before the flow enters into the test section. Owing to the unava ilability of appropriate internal pressure sensors which would allow in situ measurements, two pressure transducers with 0.5% FS accuracy were installed at the inlet and outlet of the micro-channel to m easure the upstream and downstream pressure and then sent to the data acquisition system. To get the accurate pressure at the upstream, two pressure transducers with different measur ement range were use d. The one with large measurement range (0-150PSI) was used for smalle r micro-channels/larger flow rates, and the other one with small range (0-15PSI) were used for larger micro-channels/smaller flow rates. The data started recording when the pressures di dnt change heavily for some time, which can be considered as steady state. The digital pressure output signals (0.5V-4.5V ) were collected by an A/D data acquisition board (Measurement Co mputing PCI-DAS6034). This board has 16 single 23

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ended or 8 differential channels, 16 bits reso lution and the maximum sampling rate can be 200 KS/s. For the signal range of V, the absolute accuracy is .9 LSB. A Labview program can read the signals from the board, s how the pressure data in real tim e and save them to a data file. The test sections were placed horizontally, a nd all experiments were conducted at room temperature. Since the pressure measurements we re made between the inlet and outlet, which is beyond the actual length of the micro-channel, th ere should be contraction and expansion losses in pressure drop from the inlet to micro-channel and micro-channel to the outlet. In our work, the pressure drops for the short a nd long straight micro-channels were measured separately. The short micro-channel has the entr ance effect while the long microchannel has the entrance effect and the friction effect, so the difference of thes e two pressure drops can be considered as the pressure drop due to the stra ight friction factor. Besides th ese two effects, the serpentine micro-channel has one more effect, bend effect. Th is effect is introduced by the flow separation around the corner and will be evaluate d individually at the late section. 2.3 Data Reduction and Analysis For a laminar flow in a macro-scale rectangular channel, the length of the developing flow in the entrance region can be estimated by th e following equation given by Shah and London (1978): h dD L Re04.007.006.02 (2-1) Table 2-2 shows the minimum and maximum Ld/Dh for the flow rate range in our experiment and the L/Dh for the current short and long channels It is clear that for a substantial number of cases, the flows are not fully developed under the current experimental conditions. The follow addresses the estimation of the friction factor for both entrance and fully developed flows. 24

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For a fully developed laminar flow in a macr o-scale rectangular channel with an aspect ratio Shah and London (1978) used a power series for the friction factor and fitted the coefficients using their experimental data as below: 234(Re)96(11.35531.94671.70120.95640.2537)fdf5 (2-2) This empirical equation can approximate the twodimensional theoretical exact solution (Nguyen and Wereley 2006) for the fully developed friction factor with an error le ss than 0.05%. For the current micro-channels, the aspect ratio range is from 0.9 to 0.97, so the corresponding theoretical Poiseuille numbers (fRe)fd for the fully developed flow are around 57. However, the current micro-channels may not be long enough fo r the flow to become fully developed under laminar flow conditions. Actually in many practic al applications, flows generally can not reach the fully developed state in microchannels as they are relatively short due to space limitations in micro-systems. For a developing flow, its pressure drop is highe r than the fully developed flow. As a result, the pressure drop from the inlet of the channel to a downstream location x in the entrance region is the sum of the fully developed pressure dr op and the pressure drop defect given by the equation below (Kakac et al. 1987): 2Re 2dev fdU PfxKx (2-3) hD x x Re (2-4) where K(x+) is the pressure drop defect given by: ReReapp fdKxffx (2-5) 25

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2 5.0 5.01 44.34Re4 44.3 4Re xB x fxK x ffd app (2-6) where fapp is the apparent friction factor and Eq. (2-6 ) is given in Kalkac et al. (1987). According to White (1991), the constant B in Eq. (2.6) is equal to 2.93 10-4. As plotted in Figure 2-3, the pressure drop defect K(x+) for the current micro-channels begins at the value of 0 for x+ = 0 and increases asymptotically to the fully developed constant value K( ) which has a dependence upon the channel aspect ratio for rectangular ch annels as suggested by Shah and London (1978). 5 4 3 29959.29089.85921.93089.32197.16796.0 K (2-7) Eq. (2-7) determines the fully developed K( ) for a rectangular channel with an uncertainty of 0.04%. So the pressure drop for the straight short, s hP and straight long channel, can be expressed as: lP sh dev io shLxPPP (2-8) l dev io lLxPPP (2-9) where Pio is the inlet and outlet assembly losses due to changes in tubing diameter, tees and elbows as indicated in Figure 2-1( e). Straight short and straight long micro-channels have the same channel size but different channel length. Since the inlet and outlet pressure losses are proportional to U2, the inlet and outlet losses are the same for both lengths of the channels under a given Re number because that both have two ends placed in the same inlet and outlet assembly. Psh and Pl are the measured pressure drops for the straight short and straight long ch annels, respectively. Hence, the experimental friction factor that takes the entrance effect into consideration is estimated by the following equation: 26

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shl h sh l shlLL D LKLK U PP f 2/2 exp (2-10) For the serpentine micro-channels, the meas ure pressure drop can be expressed as: b s dev io sPNLxPPP (2-11) where Ps is the measured pressure drop for the serpentine channel and Pb is the additional pressure drop due to the miter bend. N is the number of miter bends. So Pb and the bend loss coefficient, can be written as: bK 2 2/ 2/2 2 2U N LKLK LL LL LKLK U PP U PP Pl s shl ls sh l sh l ls b (2-12) N LKLK LL LL LKLK U PP U PP Kl s shl ls sh l shl ls b 2/ 2/2 2 (2-13) According to the error propagation analysis, th e uncertainty of the fr iction factor and bend loss coefficient can be expressed as: 2/1 2 2 2 2/ )/( 2 Re Re)( LP LP Q Q A A D D f fh h (2-14) 2/1 2 2 2)( 22 b b b bP P Q Q A A K K (2-15) The uncertainty range of the fr iction factor and bend loss coeffi cient can be calculated to be 10.2 15.1% and 12.3%16.1%. 27

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2.4 Results and Discussion 2.4.1 Friction Factor Fig. 2-4 shows the comparison between the experimental pressure gradients without removing the entrance effect, ( PlPsh)/(Ll-Lsh), and theoretical results for the current micro-channels. The dot lines represent the pressu re gradients predicted by the 2-D conventional laminar incompressible flow theory, which shows a linear relationship with Re number theoretically. However, as the Re number incr eases, the measured pressure gradients shows a non-linear relationship with Re num ber. Some former researcher s attribute it to the early transition to turbulence at Re=700. However, from Fig. 2-5, we can conclude it doesnt result from the early transition to tu rbulence but may from not accounting for additional pressure drop in the entrance region of the channel. Fig. 2-5 shows the comparison between the experimental friction f actor calculated by Eq. (2-10) and theoretical results predicted by Eq. (2-2). The solid line represents the predicted friction factor for fully developed flow, and the vertical bars denote the measurement uncertainty. From Fig. 2-5, we can see afte r the experimental uncertainties are considered, the experimental results show agreement with standard laminar incompressible flow predictions when Re<1500. Its believed that the consistent offset observe d by the previous researchers is the result of unaccounted for bias in experime ntal setups. When Re equals to 1500-1700, fRe begins to deviate from the theoretical value which may suggest the transition to turbulence. 2.4.2 Bend Loss Coefficient For laminar flow, the additional pressure drop is related with the flow separation which need energy to be maintained and results in an additional pressure drop not associated with frictional losses. As we know, in micro-channels, the flow usually keeps in laminar flow region, so the flow pattern along the miter bend aff ects the additional pressure drop pretty much. 28

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Maharudrayya et al. (2004) used CFD simulati on and obtained the flow pattern along a miter bend at different Re numbers. When Re = 100, there are no eddies aroun d the inner and outer wall. While Re = 210, significant re circulation at the inner and outer wall appears. The size and intensity of both vortices increase with increasing Re number. Figure 2-6 shows the experimental additional pr essure drop under different Re numbers. It can be divided into two regions. One is Re<100. There is no eddi es and the additional pressure drop is very small for all of the channels. The other one is the circulat ion appears on the inner and outer wall and develops with increasing Re nu mber. The critical Re number is in the range 100-200. At this time the additional pressure drop increases sharply. Th e experimental results also show the additional pressure drop increases with decreasing hydraulic diameters. From Fig. 2-6, the additional pressure dr op of the micro-channel with hy draulic diameter 0.209 mm is around 0.5atm when Re number reaches around 850, which is approximately equal to the frictional pressure drop of the same size strai ght micro-channel with 23.7 mm length, 101% of the current total length. Hence, the additional pressure drop due to the miter bend is also a big source of the micro-channel pressure drop, especially for small size and short length micro-channels. Since the pressure drop for channel 1 is pre tty high, Re number can only reach around 850 and the upstream pressure will exceed the measur ement range of the transducer. Here the bend loss coefficients are calculated by using Eq. (2-1 3) and compared at Re number from 47-2268, which is shown in Fig. 2-7. The solid line repres ents the bend loss coefficient of the miter bend, 1,1, reported by Streeter (1961). From Fig. 2-7, we can see bend loss coefficients of the micro-channels are all larger than 1.1. It is a similar conclusion with that of Yamashita et al. (1984), the bend loss coefficient in laminar flow region is larger th an that in turbulent region. 29

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The second characteristic is it s dependent of Re number a nd decreases with increasing Re number, which is also different with turbulent fl ow. For macro-channel tur bulent flow at larger Re number, Kb almost wont change with Re number. Wh en Re is larger than some value in 1300-1500, Kb almost keeps constant and changes in the range of 10%. The last characteristic is the size effect on Kb. Its larger for smaller channel when there is flow separation, namely Re>100-200. After considering the measurement uncertainty, these two curves still have difference. The quantitative relationship need s more experiments and simulation to be determined. 2.5 Summary The investigation of a pressu re-driven water flow in stra ight micro-channels and in serpentine micro-channels with miter bends wa s conducted experimentally A short straight and a long straight micro-channel with the same channel size were fabricated and used to isolate the inlet and outlet assembly extra pressure losses. The following conclusions were obtained: The experimental friction factors show good agreement with the classical laminar incompressible flow predictions after considering the measurement uncertainties when the Re is less than 1500. When the Re is larger than 1500, the onset of transi tion to turbulence may take place. For laminar flows in micro-cha nnels, the frictional pressure drops in the developing entrance region can s till be predicted by the classical macro-scale equations for developing flows. In general, the frictional pres sure drop in a micro-channel can be estimated by macro-scale theories and correlations. In serpentine micro-channels, the additional pressure drop due to miter bends can be divided into two groups. The first gr oup is for Re<100 where there is no eddies and the additional pressure drop is very small for all of the channels. The other group is for flows with the Reynolds numbers exceeding the th reshold values that are in the range of 100-300. When the Reynolds is higher than the threshold value, we found the flow separation and formation of vortices that appear on the inner and outer wall around the miter bend. These vortices increase in strength with increasing Re numbe r that causes the bend pressure drop to increase sharply with the Re number. The experimental results also show the bend pressure drop increases with decreasing hydraulic diameters. Bend loss coefficient Kb is a function of the Re number only when Re<100, a function of th e Re number and channel size when Re>100, and almost keeps constant and changes in the range of 10% when Re is larger than some 30

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value in 1000-1500. The trend of the experimental pressure drop is consistent with the flow structure change. The flow structures around the serpentine microchannel can also be achieved by a relatively new laser diagnostic technique micron-resoluti on particle image velocimetry (Micro-PIV), which is present in Chapter 5 in details. Table 2-1. Dimensions of th ree groups of micro-channels Total length of the micro-channels L 0.3mm Channel group No. Width W2 m Depth S m Hydraulic Diameter Dh (mm) Long Channel Ll (mm) Short Channel Lsh (mm) Serpentine Channel Ls (mm) Channel 1 213 206 0.2094 23.6 4.1 118 Channel 2 419 406 0.4124 23.5 4 117.5 Channel 3 630 615 0.6224 23.8 4.2 119 Table 2-2. Comparison of current pipe lengths with those of entrance regions. L/Dh (Straight short) L/Dh (Straight long) Re Ld/Dh Channel 1 Channel 2 Channel 3 Channel 1 Channel 2 Channel 3 47 4.23 2268 204.12 19.58 9.70 6.74 112.7 56.98 38.24 31

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A B C D E Figure 2-1. Three groups of fabricated mi cro-channels: A) Photograph of a group of micro-channels (Dh = 0.209 mm) B) Dh = 0.412 mm C) Dh = 0.622 mm D) Schematic of the straight micro-channel E) Sche matic showing inlet and outlet elbows. 32

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Figure 2-2. Experimental pre ssure drop measurement apparatus Figure 2-3. Pressure drop defect K(x+) vs x+. 33

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Figure 2-4. Experimental pressure gradients without removing the entrance effect (Pl-Psh)/( Ll-Lsh) vs Re number. Figure 2-5. Experimental friction factor vs Re number in straight micro-channels 34

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Figure 2-6. Bend additional pressure drops vs Re number in serpentine micro-channels Figure 2-7. Bend loss coefficients vs Re number in serpentine micro-channels 35

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CHAPTER 3 FLOW STRUCTURES AROUND A BEND From chapter 3, we know the bend additional pre ssure drop is related to the flow structure around the bend, here a micron-resolution particle image velocimetry (micro-PIV) system was built and used to obtain the detailed velocity vect or field in a serpentine micro-channel. The micro-PIV system was verified fi rst by the velocity pr ofile in a straight micro-channel of 0.209 mm. It was found that the vortices around the outer and inner walls of the bend do not form when Re<100. Those vortices appear and continue to develop with th e Re number when Re>100, and the shape and size of the vortices almost remain constant when Re is larger than a value in 1000-1500. The results are compatible with those in chapter 3. 3.1 Introduction and Background In curved channels, the centrifugal force driv es the more rapid fluid toward the concave part of the curved channel while the fluid in the convex part is slowing down causing a secondary flow at a right angle to the main flow The magnitude of the secondary flow increases with a decreasing bend radius and increasing fluid velocity. As exp ected, the curved channel will cause a much higher friction loss than that of the corresponding straight tube for both laminar flow and turbulent flow. In prev ious works, the researchers used computational method or color dye to visualize the flow structure. Here a re latively new experimental technique, microscopic particle image velocimetry (micro-PIV) was used to measure the velocity field. The micron-resolution Particle Image Velocimetry ( PIV) system was first developed by Santiago et al. (1998) to investigate micros cale fluid flow. He used an ep i-fluorescent microscope with a continuous Hg-arc lamp, and a Princeton Instrument s intensified CCD camera to record the flow around a nominally 30 m diameter cylinder in a Hele-Shaw flow cell. A bulk velocity of 50 m/s was measured with a spatial resolution of 6.9 m.9 m1.5 m, based upon the size of the first 36

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correlation window and the depth-of -field of the microscope. Late r, the system was modified by Meinhart et al. (1999) to measure higher speed flow using th e pulsed laser. It is becoming one of the most versatile experimental t ools in microfluidic research. Though PIV has evolved from conventional PIV, there are several im portant factors which differentiate PIV from conventional PIV. One hardware difference is the method of illumination in PIV, i.e. volume illumination. The conventional PIV used a light sheet to illuminate a single plane of the flow with the thickness less than the depth of field of the image recording system. Volume illumination is an alternative approach, whereby the test section is illumina ted by a volume of light. This illumination model may be necessary for obtaining two-dimensional measurements when optical access is limited to only one direction or in micr o-scale geometries in which alignment of the light sheet is difficult. It is advantageous when one is intere sted in measuring flows through micro electromechanical systems for which optical access is limited to one direction and the length scale is of the order of micrometers (M einhart et al. 2000a). The small length scales associated with microfluidic devices require th at the thickness of the measurement plane should be only a few micrometers. Sin ce it is difficult to form a li ght sheet that is only a few micrometers thick and virtually impossible to alig n such a light sheet w ith the optical plane, volume illumination is the only feasible illumina tion method for most micro-PIV applications. One shortcoming for volume illumination is it causes significant background noise and limits the particle concentration by reduci ng the signal to noise ratio (Gui et al. 20 02; Meinhart et al. 2000b). Image processing and advanced interrogation al gorithms can be used to enhance image quality and to increase the signal-to-noise ratio The images taken in micro-PIV are usually in 37

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worse condition, i.e. lower signalto-noise ratio, than those in th e conventional PIV. Errors in PIV measurements can be reduced by improvi ng the experimental c onditions and by using advanced interrogation algorithms such as the average correlation method. Ensemble average correlation method is a time-averaged PIV algor ithm developed by Meinhart et al. (2000b) to improve the signal to noise ratio, especially in case of the volume illumination. This algorithm can only be applied to steady or periodic flow fields. Since most typical microfluidic devices are working in steady flow conditions, the time averaged velocity field is sufficient to resolve the micro-scale flow. The central difference image co rrection algorithm (Wereley and Gui 2003) is a very effective and accurate method, especially for making measurements in regions of high velocity gradient. This method is a combination of the central differe nce interrogation algorithm developed by Wereley and Meinhart (2001) the continuous window shifting technique developed by Gui and Wereley (2002) and the modified image correction algorithm originally introduced by Huang et al. (1993). This central difference image corr ection method shows the significant reduction in the evaluatio n error, i.e. the bias and random errors, when compared to other more traditional methods. Another important difference is the size of seed particles. Since a seed particle should be small enough compared to the dimension of the microfluidic device not to disturb the flow pattern, relatively small seed particles are required in PIV. However, when the particle diameter is much smaller than the wavele ngth of the illumination light, scattering from the particles is too weak to image them using elastic scattering, i.e. the frequency of the scattered light is the same as that of the incident light. An inelastic scatte ring technique such as fluorescence can be used to increase the signal-to-noise rati o by filtering the background light. 38

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Brownian motion is another f actor to be considered in PIV since Brownian motion becomes significant when the particle or the flow velocity is very small, and eventually causes errors in the velocity measurement and increa ses the uncertainty in the particle location. Brownian motion has two major effects on PIV measurements. One effect decreases the accuracy in estimating the partic le displacement between the two light pulses, i.e. the time interval. Brownian motion also can cause errors in estimating the particle location during the illumination exposure. The latter problem can be solved readily by using pulsed lasers which reduce the exposure time so signi ficantly (to 5 ns) that Browni an motion has no effect (Nguyen and Wereley 2002). The former error can be re duced by increasing the time interval. Though long time interval values generally have been a voided in PIV evaluation because of the larger evaluation error associated with the longer time interval, th is problem can be minimized with advanced interrogation algorithms such as th e central difference in terrogation. Also the Brownian motion error is furt her reduced by a factor of iN / 1 when Ni particle images are averaged in a single interrogation spot. In this chapter, the main objective is to 1) build an in-house micro-PIV system and 2) achieve the flow structures unde r different Re numbers to expl ain the pressure drop data in chapter 3. 3.2 Micro-PIV System 3.2.1 Laser Beam Alignment Two Nd:YAG laser machines(Continuum Minilite II) were used to create the illumination source. Some useful information of the laser is listed in Table 3-1. To make the two lasers illuminate approximately the same region, a laser beam alignment component is constructed to combine these two lasers in the same optical ax is. Fig. 3-1 shows the top view of the optical 39

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layout of the laser beam alignment component. A half waveplate (Newport) changes the vertical polarization of laser B to be horizontal polarization while laser A still keeps the vertical polarization. The beam merger, a dielectric polarizer (Newport), reflects the laser with vertical polarization, namely laser A and transmits the laser with horizontal polarization, namely laser B. A beam stop absorbs the light that transmits the beam merger. A linear and rotation stage A with high precision was fixed beneath the beam merg er and another linear high precision positioning stage B was fixed beneath the laser B output. Rotate stage A to change the incline angle of laser A and make the intensity of the reflection beam maximum. After that, adjust stage B to make laser B merge into the optical axis of laser A. A beam expander includi ng two spherical concave and convex lenses (Newport) expands the size of the laser beam af ter the beam merger. Adjusting the distance between these two lenses can change the expanded laser beam size. The reason why the spherical lenses were used here is to create volume illumination for micro-PIV measurement. 3.2.2 Timing Scheme Since the laser beams are pulsed and the pulse width is so short, 35 nsec from Table 3-1, the CCD camera shutter is required to keep ope n to make the frame exposed during the pulse width. And one frame is required to be exposed once. Hence a timing scheme is required to externally control the two lasers and CCD camera. To externally control the laser, turn th e real panel FLASHLAMP and Q-SWITCH switch of the laser machine Minilite II from INT to EXT. It will disable the internally generated signals which respectively fire the flash lamp and open the Q-switch. At the same time, these switches let the Minilite II accept TTL si gnals into the FLASH LAMP TRIG IN and Q-SWITCH TRIG IN BNC ports to trigger flash lamp firing and Q-sw itch opening. The Q-switch delay can adjust the output pulse energy. For Minili te II, the delay of about 152 s yields highest energy laser pulse. 40

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The time delay between the two lasers firing the flash lamp is quite important and should be chose carefully since it sets the interframing time. A specialized CCD camera (Cooke Sensicam QE), 1376 x 1040 pixels, was used to record the flow field. It uses thermo-e lectrical cooling to cool down to -12C, which lowers the readout noise low to 4 e-rms so the weak fluorescent sign al can be measured. The interframing time low to 500 ns make it enough to measure the fl ow with high Reynolds number up to 2000. To externally control the CCD came ra, set the operation mode to doubl e shutter in the software and use a coaxial cable to connect the TRIG IN BNC por ts with the timing controller. The double exposure is controlled via an external TTL trigger signal from the controller. A timing controller (Labsmith LC 880) was used to realiz e the timing scheme. It has 8 input and 8 output channels. It is also able to send a triggerpulse delay from 50ns to 1370s and trigger-pulse duration from 7.7ms to 1370s with the resolution of 10 ns. A RS232 interface connects the controller with the computer to make remote control. Connect the two lasers (4 output ports) and the CCD camera (1 output ports ) with the controller, and TTL trigger signals can be sent to them via some coaxial cables. Fi g. 3-2 shows the timing di agram for the two lasers and CCD camera. How to program LC 880 to reali ze this time scheme refers to the Appendix. When the shutter trigger signal falls, the s hutter opens after a very short period. The integration time for image one will be finished some time after the trigger signal rises again and the integration time for image two starts. What we need control is to send two laser pulses by setting a proper time delay from the trigger signal to make one pulse be in the integration time of image one and the other pulse in the integration time of image tw o, so in each integration time the image will be exposed once, which is called double frames double shutter. The interfaming time can be shortened by sending the first pulse at the end of the image ones integration time 41

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and the second pulse at the beginning of the imag e twos integration time. After testing the CCD camera, we find the minimum interframing time for our CCD camera can reach 300ns which is enough short for our experiment. Another important issue is the rising dur ation of the trigger signal must be long enough for the CCD to read out the two images. 3.2.3 Fluorescent Particles Image To visualize the flow field in the micr o-channel, fluorescent particles, polymer micro-spheres (Duke Scientific R500), are seeded in the flow. These micro-spheres have a measured mean diameter of 0.49 m and approximate a number of 1.511 per mL. They also have the excitation maxima of 542 nm and the emission maxima of 612 nm with 70 nm stokes shift. A filter cube (Olympus U-MWIG), assembled in the microscope (Olympus BX50), reflects the light with wavelengths between 520 and 550 nm, exciting TMRM (maximum excitation at 548 nm), and transmits fluorescence through a highpass filter (565 nm). The process of taking fluorescent particles image was th at the expanded laser beam was delivered into the microscope, where the filter cube directs the beams to the ob jective lens. The objective lens relays the light onto the micro-channel, where it illuminates the en tire flow volume. Fluorescent particles in the cone of illumination absorb the illumination light, =532nm, and emit a distribution of red light, =612nm. The emitted red light can go through the filter cube and is recorded onto the CCD camera while the reflected green light from the background is filtered out by the filter cube. According to the timing scheme, the CCD camera shutter was opening when the lasers came. Hence two consecutive fluorescent particles images were recorded. Fig. 3-3 (a) and (b) show the real images and schematics of a straight mi cro-channel with the hydr aulic diameter of 209 m and a serpentine micro-channel havi ng a rectangular cross-section 650 m 100 m with hydraulic diameter of 0.173 mm. 42

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3.2.4 Measurement Depth Fig. 3-4 shows the schematic of micro-PIV used to investigate the pressure-driven de-ionized water flow in serpen tine micro-channels. Fig. 3-5 a nd Fig. 3-6 show the photo of the system and the laser beam alignment component. Firstly the fluorescent particles were seeded into the de-ionized water flow. Two Nd:YAG lasers were directed to the same optical path by optical lenses and expanded by a beam expande r made up of a concave and a convex lens. The 0.69 m particles absorb green light ( 542nm) and emit red light ( 612nm). The emitted light is imaged through a 10 objectives lens (NA=0.3) and passed to the fluorescent filter cube, where the green light from background reflection is filtered out a nd the red fluorescence from the sub-micron particles is passed to the 0.5 lens and recorded on the CCD camera. With the micro-PIV technique, the dept h of field is described by Meinhart et al. (2000a) as: p p mD D NA n z tan 16.2 32 (3-1) where n is the index of refraction of the immers ion medium between the microfluidic device and the objective lens, is the wavelength of light in a vacuum, NA is the numerical aperture of the objective lens, Dp is the diameter of the PIV particle and is the small light collection angle. In our case, n was 1, was 612 nm, NA was 0.3, d was 0.69 m and tan was 0.31. Therefore, the depth of field was calculated to be 26.06 m. The concentration of the fluorescent particles solution was prepared to ensure at least 5-10 se ed particles in each interrogation volume. The necessary minimum seed density was estim ated using the equa tion (Li et al. 2006): )2(mivpzACN (3-2) where Np is the desired minimum number of pa rticles in each inte rrogation volume; Cv is the volumetric concentration of the fluorescent particle solution; Ai is the area of each interrogation 43

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window. The interrogation windows in current experiments measure 42 m square. Adjacent interrogation windows were ove rlapped by 50%, yielding a spatial resolution of 21 m. To achieve this spatial resolution required a volumetric particle c oncentration of approximately 0.0082%. This volume fraction of seed particles is small enough to neglect any two-phase effects, and the working fluid can be considered a single-pha se fluid. In this work, this time delay is set to be 1-15 s for the micro-channel flow at different Re numbers, so the particles move approximately 1/4th of an interrogation wi ndow between pulses. The interrogation windows measure 32 camera pixels square, thus the partic les moves approximately 8 pixels between laser pulses. Assume that the measured velocity is accura te to within 1/5th of a pixel. It results in an experimental uncertainty of less than 2.5% (Prasad et al. 1992). 3.3 System Validation To validate the micro-PIV system, the veloc ity field is initially obtained at room temperature in the straight mi cro-channel of 0.209 mm at lo w Re numbers. The time delay between consecutive frames is 5m s. An interrogation window of 32 32 pixels and a grid size of 16 16 pixels are used. The analytical solution for the velocity profile at the PIV measurement depth can be formulated as: 0 3 3 2 2 22 )2( 12cos 2 12cosh 2 12cosh 12 12 2 )(k m kW Wy k W S k W z k k W y W y dx dPW yu (3-3) where dp/dx is the pressure gradient, W and S are the width a nd depth of the micro-channel respectively. Figure 3-7(a)-(b) shows the results of PIV analysis for the square micro-channel of 0.209 mm and comparison with the theoretical pr ofile computed from Eq. (3-3). The average discrepancy between our PIV measurements and th e predicted velocities is averagely about 4% 44

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for the center line 70 m while about 10% for the measurements closet to the wall due to the near-wall effect. 3.4 Results and Discussions 3.4.1 Flow Structures Around The Miter Bend Figure 3-8 shows a typical image and velocity vector field genera ted by the micro-PIV system. The focus of the flow field in Fig. 3-8 is the effects of the 90 de gree turning on the flow micro-structures around the miter bend in the serp entine micro-channel at Re = 500. We note that the main stream velocity increases while the flow is rounding the corner. It is also apparent that micro-structures of flow recirculation have fo rmed around the outer corner and immediately after the inner corner (flow separati on). A detailed visualization an d discussion on the onset and development of induced vortices around the outer and inner corners with the Re number are given below. Fig. 3-9(a-e) shows the enlarged velo city fields at the oute r corner for the Reynolds numbers ranging from 100 to 1500. Fig. 3-9(f-j) shows the enlarged velocity fields at the inner corner for the same Reynolds numbers. Fig. 310 shows the corresponding streamlines computed from the experimental velocity vectors. For the in duced micro flow structures at the outer corner, there is basically no recirculati on for Re = 100 and only some fluctuations in the flow adjacent to the wall due to the wall roughness are captured by the PIV. At Re = 300, a very small vortex located at (x = 0.2 mm, y = 0.95 mm) is seen, but its circulatory motion is not fully developed. It is clear that at Re = 500, the re circulation vortex is fully devel oped and located at (x = 0.3 mm, y = 1.07 mm). As the Reynolds number is further increased to 1000 (Fig. 3-10(d)) and then to 1500 (Fig. 3-10(e)), the locations of recirculation vortices stay at the same point and only the size and strength are in creased with the Reynolds number. For flow structures near the inner corner, the micro flow structures that form due the flow separation always start right after the sharp edge as the flow separa tes. Again, there is basically 45

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no separation vortex for Re = 100. The separation vortex is very clear for Re = 300. As the Reynolds number is further increased, the size a nd strength of the sepa ration vortex are also increased accordingly. However, the growth of the vortex seems saturated after Re = 1000 as there is no significant differen ce in the size between Re = 1000 and Re = 1500 but the strength continues to increase as discussed later. For Re = 1000, the inner corner vortex approximately occupies 20% of the width of the cha nnel in the downstream of the bend. In summary, micro-structured recirculation vortices are induc ed when the flow is making the turn in a serpentine micro-channel. These vortex structures are responsible for the bend additional pressure drops for the serpentine micro-channel as compared to a straight micro-channel. The following presents the m easured pressure drops and discussions for serpentine channels. 3.4.2 Circulation Calculation In order to further substantia te the relatively large bend pr essure drops, we calculated the circulation, for every induced vortex from the velocity field given in Fig. 3-9. The circulation, that is the strength of the vortex is defined as: AdV (3-4) The results of the calculated vorte x circulation are give n in Table 3-2. In general, the outer vortices are three to six times st ronger than the inner vortices. Figure 3-11 s hows the total vortex circulations as a function of the Reynolds number. The total circula tion is the sum of the absolute values of the inner and outer vortices. The sim ilar trends between the total vortex circulation (Figure 3-11) and the be nd pressure drop of Dh = 0.209 mm channel (Figure 3-6) serve to confirm the measured data. 46

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3.4.3 Shear Strain For further understanding the mi cro-structures of the flow, the flow shear strain rate distributions were computed based on th e Eq. (3-5) and plotted in Figure 3-12. x v y uxy2 1 (3-5) As we examine Figure 3-12, the shear strain ra tes generally increase with the Reynolds number and there is an uneven distributi on pattern with highest rates concentrated along the inside wall and they peak around the sharp edge. Before the vo rtices appear, the velo city only changes much around the bend, so we can see bright color ar ound the bend when Re = 100. After the vortices appear, the velocity also change s a lot from the vortex to the ma in stream, so we can see the color change around the vortex structure. 3.5 Summary A micron-resolution particle image velocime try system has been built. The minimum interframing time can be set to 200ns which make the system has the ab ility to measure the velocity up to 10m/s. The flow structure in a serpentine micro-channel with miter bends was conducted experimentally. The follo wing conclusions were obtained: The Micro-PIV system is verified by the flow field in the micro-channel with the hydraulic diameter of 0.209 mm. The flow micro structures around the bend of a se rpentine micro-channel can be divided into three categories depending on the flow Reynolds number. When Re<100, there is no induced flow recirculation and flow se paration. When Re>100, vortice s and flow separation appear and further develop. The outer corner vortex develops along th e wall of the channel, and the vortex center moves slightly from the upper stream to the down stream with the increasing of the Re number. The inner wall vortex due to fl ow separation develops immediately after the flow makes the turn. When Re is around 1000, the inner wall vortex approximately occupies 20% of the width of the channel in the dow nstream side of the bend. When Re>1000-1500, the shape and size of the outer and in ner vortices become almost constant. The shear strain rates generally increase w ith the Reynolds number a nd there is an uneven distribution pattern with highest rates concentrated along the inside wall and they peak 47

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around the sharp edge. After the vo rtices appear, the velocity also changes a lot from the vortex to the main stream, so we can see the color change around the vortex structure. Table 3-1. Specification of the Nd :YAG laser (Continuum Minilite II) Parameters Value Wavelength 532 nm Energy 25 mJ Pulse width 3-5 nsec Polarization Vert. Beam size <3 mm Divergence <3 mradx Repetition Rate 1-15 Hz Table 3-2. Calculated vortex circulation Re Inner Wall Vortex Strength (mm2/s) Outer Wall Vortex Strength (mm2/s) 100 0.082 -0.41 300 4.10 -12.47 500 10.97 -77.48 1000 28.10 -203.9 1500 97.99 -266.9 48

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Figure 3-1. Top view of the optical layout of the laser beam alignment Figure 3-2. Timing diagram for the two lasers and CCD camera 49

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A B Figure 3-3. Fluorescent images at straight and serpentine microchannels : A) A real image of the straight micro-channel w ith hydraulic diameter of 0. 209 mm and B) the serpentine micro-channel with hydraulic diameter of 0.172 mm (a 10 objectives used; white spots are the fluorescent particles). Figure 3-4. Schematic of micro-PIV system 50

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Figure 3-5. Photo of the optical subsystem Figure 3-6. Photo of the laser beam alignment component 51

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A B Figure 3-7. Micro-PIV results for low speed flow. A) Velocity vectors (112 pairs of images were ensemble-averaged) B) Comparison of the measurements with the theoretical profile ( Re = 0.3). 52

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Figure 3-8. Typical velocity vector in the serpentine micro-channel at Re = 500. 53

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A B C D E Figure 3-9. Flow structur e at the outer wall A) Re = 100 B) Re =300 C) Re = 500 D) Re = 1000 E) Re = 1500 and at the inner wall F) Re = 100 G) Re =300 H) Re = 500 I) Re = 1000 J) Re = 1500 54

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F G H I Figure 3-9. Continued 55

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J Figure 3-9. Continued 56

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A B Figure 3-10. Streamlines at different Re numbers: A) Re = 100, B) Re = 300, C) Re = 500, D) Re = 1000, and E) Re = 1500 57

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C D Figure 3-10. Continued 58

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E Figure 3-10. Continued Figure 3-11. Total vortex circulation vs. Reynolds number. 59

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A B C Figure 3-12. Distribution pattern s of shear strain rates. A) Re = 100, B) Re = 300, C) Re = 500, D) Re = 1000, E) Re = 1500. 60

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D E Figure 3-12. Continued 61

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CHAPTER 4 ADIABATIC GAS-LIQUID TWO-PHASE FLOW In this chapter, adiabatic gas-liquid flow patterns and void fractions in micro-channels were experimentally investigated. Using nitrogen and water, experiments were conducted in rectangular micro-channels with hydraulic diameters of 0.209 mm 0.412 mm and 0.622 mm, respectively. Gas and liquid superficial velocities were varied from 0.06-72.3 m/s and 0.02-7.13 m/s, respectively. The main objective is focuse d on the effects of micro-scale channel sizes on the flow regime map and void fraction. The inst ability of flow patterns was observed. Four groups of flow patterns includi ng bubbly-slug flow, slug-ring fl ow, dispersed-churn flow and annular flow were observed in micro-cha nnels of 0.412 mm and, 0.622 mm. In the micro-channel of 0.209 mm, the bubbly-slug flow became the slug-flow a nd the dispersed-churn flow disappeared. The current flow regime maps showed the transi tion lines shifted to higher gas superficial velocity due to a dominant surface tension effect as the channel size was reduced. The regime maps presented by other authors for mini-channels we re found not applicable for micro-channels. Time-averaged void fractions were measured by analyzing 8000 high speed video images for each flow condition. The void fr actions hold a non-linear relationship with the homogeneous void fraction as oppose to the relati vely linear trend for the mini-channels. A new correlation was developed to predict the non-linear relationship that fits most of the current experimental data and those of the 0.1 mm diameter tube report ed by Kawahara et al. within %. Two-phase frictional pres sure drop can be predicted wi thin % by Lee and Lees model. 4.1 Introduction and Background The flow patterns of adiabatic liquid-gas two-phase flow in the macro-channel have been extensively studied in the past (Mandhane et al. 1974, Taite l and Dukler 1976). Since the 62

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buoyancy effect is suppressed by the surface tension, the flow patterns in the mini/micro channel are different from those observed in the macr o-channel (Ghiaasiaan and Abdel-Khalik 2001). Recently many researchers published research resu lts on the gas-liquid two-phase flow patterns in micro/mini channels. Wilmarth and Ishii (1994 ) researched on adiabatic concurrent vertical and horizontal two-phase air-water flows through narrow rectangular channels with gap widths of 1 and 2 mm. Five flow regimes (stratified smooth, plug, slug, disp ersed bubbly, wavy annular) and three transition regions (el ongated plug, elongated slug, capbubbly) were identified for the horizontal flow. Mishima and Hibiki (1996) m easured the flow regimes, void fraction and frictional pressure loss for air-water flow in vert ical capillary tubes with inner diameters from 1 to 4 mm. Bubbly flow, slug flow, churn flow and annular flow were observed. Churn flow was never observed in the 1 mm channel. Coleman a nd Garimella (1999) studied air-water flows in four round tubes with 1.3 mm, 1.75 mm, 2.6 mm, and 5.5 mm i nner diameters. Eight flow patterns (bubble, dispersed, el ongated bubble, slug, stratified, wa vy, annular-wavy, and annular) were observed. Triplett et al. (1999) investigated the air-water two-phase flow patterns in circular channels with 1.1 a nd 1.45 mm inner diameters and in semi-triangular channels with hydraulic diameters of 1.09 and 1.49 mm. The resu lts showed bubbly, chur n, slug, slug-annular and annular patterns can be observe d but they poorly agreed with th e previous transition models and correlations for macro-channels. Chen et al. (2002) presented the nitrogen-water two-phase flow regimes in circular channels with 1.0 and 1.5 mm. Five flow patterns (bubbly, slug, bubble-train slug, churn, and a nnular) were found. Kawahara et al. (2002) investigated the two-phase nitrogen-water flow patterns in a 0.1 mm diameter circular tube. Intermittent and semi-annular flows were observed while bubbly and churn flows were not observed. Qu et al. (2004) studied the nitrogen-water two-phase flow in a rectangular micro-channel with a gap of 63

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0.406 mm. The results revealed the dominant flow patterns were sl ug and annular flows, with the bubbly flow occurring only occasionally and stratified, and the churn flow was never observed. Void fraction is also an important issue in heat transfer and flow characteristics for gas-liquid two-phase flows. Armand et al. (1946) investigated th e void fraction for the horizontal and vertical air-water flow in macro-channels and gave a correlation widely used by others. Zuber and Findlay (1965) built a model named drif t flux model to correlate the void fraction data in two-phase flow. This model relates the gas velocity with the mixture mean velocity, distribution parameter C0 and the mean drift velocity Vgj, which can be given by: gjLG GVjjC j 0 (4-1) C0 depends on the pressure, the channel geometry a nd the flow rate for a given flow pattern. Ali et al. (1993) found that th e mean drift velocity Vgj can be neglected in narrow channels due to the inability of the bubbles to rise through the stagnant liquid and reported that the void fraction in narrow channels with the hydraulic diameter ar ound 1 mm can be approximately given by the Armand-type correlation with a di fferent distribution parameter. Chung et al. (2004) investigated the void fraction in a 0.1 mm diamet er circular tube and a square micro-channel with a hydraulic diameter of 0.096 mm and found the void fraction was independent of the channel geometry in their experiment. Kawahara et al. (2002) expe rimentally achieved a non-linear relationship between the measured void fraction and the hom ogeneous void fraction in a 0.1 mm diameter tube. According to the above lite rature review, more experimental data for the flow patterns and void fraction in the channe ls of sizes from 1 mm to 0.1 mm need to be obtained to understand the flow performance in micro-channels. To evaluate the frictional pre ssure drop of two-phase flow, th ere were a lot of models and correlations to predict it for macro-channels, mini -channels and micro-cha nnels. Table 4-1 listed 64

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the previous two-phase pressure drop correlations. Triplett et al. (1999) researched on the two-phase pressure drop for the channels with hydraulic diamet er of 1.1 and 1.45 mm. He found the homogeneous model provided the best agreement with experimental data for bubbly and slug flow patterns, but all of the wi dely used correlations significantly over predicted the frictional pressure drop for annular flow Kawahara et al. (2002) found L ee and Lees model present the good agreement (within %) with experimental data for his circular channel of 0.1 mm diameter. Zhao and Bi (2001) found the Lockha rt-Martinelli correlation well predicted the two-phase pressure drop for the triangular channels with hydraulic diamet ers of 0.866, 1.443 and 2.886 mm. In this chapter, three near-squa re micro-channels with the hyd raulic diameters of 0.209 mm, 0.412 mm and 0.622 mm were fabri cated by laser etching to inve stigate the nitrogen-water two phase flow patterns, regime maps and time-averag ed void fraction. The main objectives of this study are to (1) obtain the flow patterns using a high speed CCD video camera, construct flow regime maps for three micro-channels with supe rficial velocities of ni trogen and water ranging from 0.06 to 72.3 m/s and 0.02 to 7.13 m/s, resp ectively, and investigate the size effect on the flow regime maps, (2) compare the new flow ma ps with the mini-channel flow map based on the Weber number model, (3) evaluate the time aver aged void fraction for each micro-channel and compare them with previous co rrelations, and build an empirical correlation for micro-channels based on current data. Check the predictive ab ility of the new correlation by using existing time-averaged void fraction data in the literatu re, (4) obtain the two-phase frictional pressure drops and evaluate the present pressure drop models. Since the majority of publications in the litera ture were dealing with the air-water flows, the current work is aimed at providing funda mental understanding and design information for 65

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nitrogen-water two-phase flows in micro-channels due to th eir close relations hip with the PEM fuel cells that are receiving top priority for their centra l role in the hydrogen economy. 4.2 Experimental Apparatus Fig. 4-1 shows the schematic of the experimental apparatus and the mixer used to investigate the adiabatic nitrogen -water two-phase flow in microchannels. It in cludes a syringe infusion pump (Cole-Parmer Instru ment), 60ml syringe (McMaste r), micro-filter (Swagelok), nitrogen gas cylinder, regulat or (McMaster), flow meters (Omega), valves (Swagelok), Fiber-Lite MI-150 high intensity illuminator (Dolan-Jenner), micro-channels, high speed CCD camera (Redlake), and computerized image acquisition system. The de-ionized water with fl ow rates ranging from 0.5ml/min to 46ml/min, which can be set on the panel of the infusion pump, was driven to the micro-channel test section. The 2 m micro-filter can remove any particles or bubbles be fore the flow entered into the micro-channel. The nitrogen gas was released from the compre ssed gas cylinder. After the regulator, the gas pressure was reduced to 0-30 PSI The gas flow rate was measured by two volume flow meters with ranges of 0-50 SCCM and 0-2610 SCCM, respectively. The mixer was fabricated as a bubble generator. A needle with a 0.2 mm inner diameter was connected to the 1/8 inch gas tube. It was inserted onto the center line of the 1/8 inch liquid tube. After going through the 1/8 inch gas tube and the needle, the gas flow was mixe d with the de-ionized wa ter coming from the 1/8 inch liquid tube and directed into the micr o-channel. The superglue was used to bond the micro-channel to the 1/8 inch tube, and it can be easily removed by the supe rglue remover, so the micro-channel can be replaced easily to make up different test sections. Two pressure transducers with a 0.5% FS accuracy were installed at the inlet and outlet of the micro-channel respectively to measure the upstream and downs tream pressure. The data acquisition system 66

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started recording when the flow can be considered as steady state. The test sections were placed horizontally. All experiments were conducted in room temper ature and under atmospheric pressure at the discharge of the test section. Flow visualization was achieved by the high speed CCD camera, which can operate at a frame rate up to 8000 fps and a shutter speed of 1/8,000 s. In this work, the frame rate of 1000 fps and a shutter speed of 1/2,000 s were used. The resolution of the camera was 240(H) 210(V) pixels. Two Fiber-Lite illuminators provided the high intensity light, which was dire cted onto the test section by tw o optical fiber light guides. An adjustable microscopic magnification lens was used to magnify the test section. The view field was near the outlet of the micro-channel to mi nimize the entrance effect, and the view field length was 1.48 mm. Fig. 4-2 shows the photograph of three size micro-channels and schematic of the micro-channel used in the experiment. The microchannel was laser etched in a silicon substrate and then a Pyrex thin cover glass plate was a nodically bonded on the top of the substrate. Two small connection tubes which can be inserted into the inlet and outlet assembly were connected with the small reservoirs. A microscope (Olympus BX50), a 10 objective lens and a CCD camera were used to measure the dimensions of the micro-channels. In order to facilitate a meani ngful discussion, the relative do minance of the forces involved in the two-phase flow is an alyzed through six dimensionle ss groups. These are defined as follows: /2 hGLDgBo /LLjCa GhGG GSDj Re LhLL LSDj Re hGG GSDjWe2, and hLL LSDjWe2. Here g is gravitational acceleration, is density, Dh is hydraulic diameter of the channel, is surface tension, is viscosity, and j is superficial velocity. The subscripts L, G mean the variables are based on liquid, gas flow respectively and LS, GS mean the dimensionless numbers are based on superficial liquid, superficial gas 67

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flow respectively. Table 4-2 lis ts the ranges of those dimensi onless parameters for the three channels under experimental conditions. For comparison purposes, parallel values for a 10 cm macro-scale channel are also provided to focus on the scale effects. With the information given in Table 4-2, we can examine the major differences on the relative importance of various fo rces involved in a ga s-liquid flow between the macro and micro scales. For the flow rates used in our experiments, both the surface tension and the viscous forces are at least two to three orders of magnitude sma ller than the gravitationa l and inertia forces for the macro-scale channel as indicated in Table 42. Whereas for the three micro channels in our experiments, it is very clear that the gravitat ional and viscous force are dominated by the surface tension and inertia forces by at least two orders of magnitude. Comparing between the macro and micro scales, we can conclude that the major cha nge in the force balance is the surface tension which is negligibly small in the macro scale a nd then becomes dominant in the micro scale while the inertia force is important in both scales as it is proportional to the momentum of the flow only. As a result, the following results and discussion are based on the scenario that the two-phase micro-channel flow is dominated by th e balance between surfa ce tension and inertia. 4.3 Results and Discussions 4.3.1 Two-Phase Flow Patterns The high speed CCD camera can record a contin uous video for 8 seconds with a frame rate of 1000 fps. Since the frame rate was set at 1000 fp s, one image was recorded for every 1ms. For a specific channel size and each flow condition, a total of 8000 images were obtained in one continuous video. From the recorded images, the dynamic structures of the two-phase flow were obtained and the instability of the flow patte rn was observed: At a certain gas and liquid superficial velocity, the micro-channel two-phase flow pattern changes with time at a fixed downstream location. Moving the viewing window fr om the end of the channel to the middle of 68

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the channel, the same phenomenon was found. A scale bar was thought to be helpful in estimating the size of flow structures. It wa s developed by multiplying the pixel size of the camera by the number of pixels and then dividing it by the magnification factor. For example, in our experiment the pixel size of the CCD camera was 7.4 microns and the magnification factor was around 1.1 in this experiment, so the actual 100-micron length was covered in 15 pixels in the image, and the uncertainty was 2-3 microns. A variety of flow patterns appeared such as single-phase liquid, bubbly flow slug flow, bubble-train sl ug flow, liquid ring flow, liquid lump flow, etc. Only limited number s of typical flow pattern images from our experiment are given in Fig. 43. According to the appearance of the transition flow patterns such as the liquid ring flow, liquid lump flow, and disrup tion tail of the slug, the entire flow patterns in the present micro-channels can be categorized into four basic flow patterns based on the balance between the inertia and su rface tension. As indicated by the values of Webber numbers in Table 4-1, the relative domin ance between inertia and surface tension covers a wide span ranging from where surface tension is three orders of magnitude larger than the inertia to where it is two orders of magnitude sm aller. The four basic fl ow patterns are explained below: 1) Bubbly-Slug flow : This regime is dominated by the surf ace tension force. It mainly has the slug flow, and occasionally bubbly flow wo uld show up. Transiti onal flow patterns of liquid ring flow and liquid lu mp flow do not appear here. It usually appears at a low gas flow rate. The slug flows were separated by a thick liquid bridge. Th e width of nitrogen gas slugs is slightly smaller than that of the cha nnel due to the existing smooth and thin liquid film on the walls. Occasionally, some spherical bubbles, whose diameter s are much smaller than the width of the channel, appear. 69

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2) Slug-Ring flow : This regime is controlled by the balance between the surface tension force and the inertia force, also calle d the transition regime. Surface te nsion force and inertia force are comparable to each other in this region. It mainly features the slug flow, liquid ring flow, bubble-train slug flow, and occasionally bubbly flow. It often appears at intermediate gas flow rates. The liquid bridge sometimes is thick and forms the slug flow, while other times it is quite thin and forms the bubble-tr ain slug flow, and even at tim es it disappears half and forms the liquid ring flow. The ringshaped liquid film is smooth a nd axi-symmetrically distributed around the channel inner wall. The nose of the slug is flatter than that ob served in a bubbly-slug flow. 3) Dispersed-Churn flow : In this regime, the flow is strongly influenced by the inertia force but not totally dominated. The main characteristic feature is a mixture of small vapor slugs and liquid chunks. It has no stable slug flow. Dispersed-churn flow is also called bubbly/slug, liquid/slug, and ring/slug by other researchers. It normally app ears at the intermediate liquid and gas flow rates. For example, among the disperse d-churn flows from the recorded images, we can see the disruption tail of the slug flow pattern usually followed by some very small shedding bubbles. 4) Annular flow : This regime is totally dominated by the inertia force. It mainly consists of the flow pattern of gas co re with a smooth interf ace, and occasionally the l iquid lump flow. It usually appears at a low to intermediate liquid flow rate together with a high gas flow rate. The water film flows along the channe l inner wall while the nitrogen gas core flows through the center of the channel. The gas-li quid interface is smooth due to th e weak interaction between the gas and liquid at the interface in the micro-channel, which is different from the wavy interface observed in mini-channels and macro-channels. 70

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Fig. 4-4 shows the instable temporal pressure measurement at the upstream and downstream for a slug-ring flow This instability of Pin can be attributed to or cause the density wave oscillation in the micro-channel, which was also found in pa rallel channels and believed to be intrinsic to the test module itself (Qu and Mudawar 2004). The dens ity oscillation could change the gas inertia force at the interface. That coul d be the reason why the time instability of flow patterns obs erved in the micro-channel. 2 GGj4.3.2 Flow Regime Maps Based on the images and pattern distinctions discu ssed above, we have summarized our observations using two-phase flow regime maps. Traditionally, the regime map was developed with the superficial velocities of water and nitrogen, jL and jG, as the vertical and horizontal coordinates, respectively. Instead of the superficial velocities, we decided to use the respective gas and liquid Webber numbers as the coordinate s for the regime maps. Essentially, the Webber number is the dimensionless superficial velocity s quare and physically it represents the ratio of inertia to surface tension that is the guiding parameter fo r two-phase flow patters in micro-channels. Fig. 4-5 shows the regime maps for the three channel size s. The solid lines are used to indicate the boundaries between different flow patterns. Figs. 4-5( a) and 4-5(b) provide the two-phase flow regime maps for the current micro-channels with hydraulic diameters of 0.622 mm and 0.412 mm, respectively. Fig. 45(c) shows the flow regime map for the micro-channel with a hydrau lic diameter of 0.209 mm. In general, for the lager channels (0.622 mm and 0.412 mm), the regime maps are relative similar as shown in Figs. 4-5(a) and 4-5(b). They all have bubbly-slug flows located in the lower left corner representing very small Webber num bers that correspond to a total dominance by the surface tension force. For higher gas velocities that are associ ated with larger gas Webber 71

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numbers and dominance by the inertia force, the flow pattern beco mes he annular flow and it is not very sensitive to the liquid velocities. Betw een the bubbly-slug flow and the annular flow, we found the slug-ring and dispersed-ch urn flows that corresponds to the relatively balance between the inertia and the surface tens ion and neither one is dominant. The slug-ring flow is under relatively more control by the surface tension wh ile the disperse-churn is controlled more by the inertia as a larger inertia force offered by the high er liquid flow is needed to break the slug into dispersed fragments. This is why the disperse-c hurn flow is located above the slug-ring flow. While for the smallest channel (0.209 mm), th e regime map displays some differences from those of the larger channels. We observed that the bubbly flow pattern was no longer present and the slug flow filled its place in the lower left corner, lower WeLS and WeGS (lower jG and jL ). A plausible explanation is that as the channel si ze gets smaller the surface tension force holds a deeper control over the inertia for the same low ga s flows that prevents th e break up of the bridge between slugs to form bubbles. Therefore the slug flow resulted. The di spersed-churn flow was also absent in Fig. 4-5(c), the slug-ring flow took its place. Again, the reason is that the strong surface tension effect prevented break-down of the slugs and th e disruption of the gas-liquid interface. From the current experimental data, we also observed the boundary lines have a tendency to shift slightly to right, namely higher WeGS or gas superficial velocity, as the hydraulic diameter was decreased, which was different from what reported by Taitel et al. (1980) that the boundary line was not affected by tube diam eter for circular vertical macr o-tubes, or by Mishima and Ishii (1984) that the boundary line shifted to the left in vertical macrotubes as the tube diameter was decreased. This again may be explained by the st ronger surface tension eff ect in micro-channels that requires a higher inertia for ce (boundary line moving to the ri ght) to balance in order to 72

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maintain the same flow pattern Tabatabai and Faghri (2001) re ported a new flow map based on their theoretical study that accounted for surface tension effects in horizontal miniature and micro tubes. They showed an increasing ratio of gas superficial velocity to liquid superficial velocity with the decreasing of hydraulic diameter which indicated a right shit of the transition boundary lines too. 4.3.3 Comparison with Prior Mini-Channel Flow Map Akbar et al. (2003) reviewed th e flow maps in mini-channels with hydraulic diameter around 1 mm and concluded that there were some simila rities between the flow regime transitions in mini-channels and channels operating under mi crogravity. They developed a flow map for circular and near-circular mini -channels based on the Weber number, which can be represented by the following expressions: Surface tension dominated region (incl uding bubbly, plug, and slug flows): For 0 .3 LS, 315 We.011.0L GSWe We For 0 .3 LS, 0 .1 We GSWe Annular flow region: 14.00.11LS GSWe We 0 .3 LSWe Dispersed flow region: 0.3 LSWe 0 .1 GSWe This model can reasonably explain the flow maps for circular and near-circular mini-channels with hydraulic diameter around 1 mm including the data of Mishima et al. (1996), Triplett et al. (1999), and Yang & Shieh (2001). However, it only pr ovided a fair prediction to the data of Zhao and Bi (2001) due to the channe l geometry effects. Fig. 4-6 s hows the transition lines predicted by the Weber number model (solid lines) with the current da ta for the channel with Dh = 0.622 73

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mm (dashed lines). A poor agreement was found. One of the possible reasons might be the significant sensitivity of gas-li quid flow patterns to the worki ng fluid, channel geometry and channel size. Another possible r eason may be related to some special flow characteristics associated specifically with micro-channels. The liq uid and gas flow remain laminar even at high flow rates, and a weaker interaction between the liquid and gas at the inte rface in micro-channels than in mini-channels. We may conclude that the flow regime criteria developed for mini-channels should not be applied for micr o-channels without further verification. 4.3.4 Time-Averaged Void Fraction For each gas-liquid flow combination, the time -averaged void fraction can be estimated by analyzing its 8000 recorded images The method of analyzing the ti me-averaged void fraction is described as follows. 22 data point s were selected from the video image files for each channel size to cover the entire range of the homogeneous void fraction. It is noted that each data point corresponds to a specific homoge neous void fraction. The homoge neous void fraction is defined as = jG/( jG+ jL) which has a range between zero a nd one. The physical meaning of the homogeneous void fraction is th at the actual void fraction is equal to the homogeneous void fraction when both phases have the same velocities in a dynamic equilibrium condition. The actual void fraction would deviate from th e homogeneous void fraction for the dynamic non-equilibrium conditions investigated in the current study where the two phases have non-equal velocities (slip ratio) in different flow regimes. Each recorded image covers the flow pattern for a streamline distance of 1.48 mm. Th e instantaneous void fraction on each image can be calculated by estimating the ra tio of the volume occupied by the gas to that of the whole region on each image field. The time averaged void fraction was obtained by adding all the instantaneous void fractions and dividing th e sum by the total number of images, the time-averaged void fraction, can be determined and expressed as follows : 74

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,,, 111 1,g lmN NN N ligjmk n ijk n lgNNNN NN m (4-2) Eq. (4-2) represents a strategy th at we divided the images into three major groups based on the number of images for a specific type. For the total recorded images, approximately, 90% of all the images belong to either pure liquid type or gas core with a smooth interface, and all other types such as liquid ring flow, liquid lu mp flow, and bubbly flow account for only 10%. As a result, we chose pure liquid (zero void fraction), gas core with a smooth interface and all the rest types combined as the thr ee groups. Therefore, in Equation (4-2), l,i, g,j, m,k are the estimated void fractions for pure liquid type, gas core with a smooth interface type, and any other type, respectively. N is the total number of the recorded images. Nl, Ng, Nm are the number of the images of liquid, gas core with a smooth interface, and other types, respectively. According to the error propagation, the uncertainty of the estimated time-averaged void fraction, can be expressed as: 2 22 g l lgN N NNN m mN (4-3) where l, g, m are the uncertainties of the void fract ions for liquid, gas core with a smooth interface, and all other flow pattern, respectively. Even though, the void fraction of pure liquid is zero, there is still an uncerta inty associate with it b ecause of possible trace amount of gas in the liquid core, bu t in general this uncertainty is very small compared to other types. Based on the above, we estimated that th e range of uncertainties for the time averaged void fractions is from 3.1% to 9.8%. 75

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Fig. 4-7 shows the measured time-averaged void fraction results for the present three micro-channels. Also shown in Fig. 4-7 is th e data given by Kawahara et al. (2002) for a micro-tube with 0.1 mm in diameter. The do tted line represents the homogeneous void fraction Ali et al. (1993) suggested that the vo id fraction in narrow channels with a Dh around 1mm can be correlated with the equation, = 0.8 When applying this corre lation to our results, we found that for the vast majority of our data, it ov erestimated the void fractions, especially for the smaller channels. The predictions become worse as the size of the channel is decreased further. The over-predictions are more than 100% for ma ny data points. The time-averaged void fraction patterns for the smaller channels showed a nonlinear relationship w ith the homogeneous void fraction. As explained be fore, when the channel sizes are sma ller, the effects of surface tension are more prevalent, and allow the liquid film to bridge the gas core mo re easily, so the flow pattern is more likely to be bubbly-slug flow, which results in a lower time-averaged void fraction due to the absence of gas phase. Based on our own data for the three microchannel sizes (0.209 mm, 0.412 mm and 0.622 mm) and those of Kawahara et al. (2002) for a 0.1 mm diameter micro-tube, we have developed an empirical correlation of the time-averaged void fraction for micro-channels with hydraulic diameters less than 1 mm. The correlation is expressed in Eq. (4-4) and Eq. (4-5) 0.5 0.51(1)pC C (4-4) hDe C88.68.131 266.0 (4-5) where the unit of Dh is in mm. Fig. 4-8 shows the comp arison between the predictions by the new correlation and the corresponding measured results. Fig. 4-9 is a plot of the p/ d vs for all the data points in Fig. 4-8, where p and d are the void fraction predicted by the correlation 76

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and that of the measured data, respectively. 57 of our 66 data points fall within %. Most of the outliers came from Kawahara et als data (17 out of 26 outlier s) which may be attributed to the lack of the total num ber of sample images (200-300) in th eir experiment resulting in higher uncertainties. If the uncertainty range was increa sed to %, only 2 data out of 66 were out of the range. 4.3.5 Frictional Pressure Drop Currently most of the two-phase pressure drop models are based on the model of LockhartMartinelli (1949), such as Mishima and Hibiki (1996), Lee and Lee ( 2001), Qu and Mudawar (2004). To compare our experiment al data with the prediction of those models, the Martinelli parameter X should be determined experimentally first, which is defined as: G LdzdP dzdP X )/( )/( (4-6) LdzdP )/( and are the frictional pressure drop of single phase liqui d and vapor with the same mass flow rate respectively. Then insert X into the above models to get the two-phase frictional pressure drop. Fig. 4-10 shows the co mparison between the experimental data of the micro-channel (Dh = 0.412 mm) and the value predicted by those models. From the figure, we can see Lockhart-Martinellis model (C=5) obviously underestimate the pressure drop here. Mishima and Hibikis model can predict the pressur e drop very well. All of the data fall in % of the predicted value. Lee and Lees model may also predict well, but its worse than Mishima and Hibikis model for out experimental data. GdzdP )/ (4.4 Summary Nitrogen-water flow patterns in rectangular micro-channels with hydraulic diameters of 0.209 mm, 0.412 mm and 0.622 mm were obtained and analyzed. Based on our experimental 77

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results and comparison with other results in th e literature, the followi ng conclusions can be obtained: The phenomenon that micro-channe l flow pattern changes with time at a fixed location under a certain gas and liquid superficial velocity was found, which can be attributed to the density wave oscillation in the micro-channel. According to the appearance of the transition flow patterns such as liquid ring flow liquid lump flow and disr uption tail of the slug, four flow patterns can be defined fo r micro-channels with the hydraulic diam eters of 0.412 mm and 0.622 mm: bubbly-slug flow, sl ug-ring flow, dispersed-churn flow and annular flow. For the micro-channel with the hydraulic diamet ers of 0.209 mm, the bubbly-slug flow became the slug-flow and the dispersed flow disappeared. The current flow regime maps show the transition boundary lines shift to high WeGS or gas superficial velocity with the decreasing of the hydraulic diamet er. It can be explained by the strong surface tension effect in micro-cha nnels. The micro-channel flow maps were compared with the mini-channel flow map ba sed on the Weber number model, which showed poor agreement. Time-averaged void fractions of each micro-cha nnel were measured for 22 runs to cover the whole range of homogeneous void fraction. Th e data of each run were obtained from the analysis of 8000 flow pattern images captured at a certain gas and liqui d superficial velocity. With the decreasing of the hydraulic diamet er, the time-average void fraction showed a non-linear relationship with the homogeneous void fraction. A new empirical correlation was proposed to predict the n on-linear relationship, an d most of the current experimental data and Kawarahas data fall within % of the new correlation. The uncertainty of this measurement method was analyzed and the uncer tainty range was approximately from 3.1% to 9.8% under the curren t experimental conditions. Lockhart-Martinellis model (C=5 ) which was widely used to pr edict the two-phase frictional pressure loss in macro-channel obviously underes timate the pressure drop in micro-channel. Mishima and Hibikis model formulated from experimental data of small channels can predict the pressure drop here very well. All of the data fall within % of the predicted value. Lee and Lees model can also predict we ll, but its worse than Mishima and Hibikis model for out experimental data. 78

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79 Table 4-1. Generalized two-phase frictional pres sure-drop correlations. Correlation Reference Frictional pressure drop 1 Hom ogeneous model (1994) v vl hl tpx D Gf dz dP 1 22 2 Lockhart-M artinelli (1949) v l l l hl ldzdP dzdP X X X C D xGf dz dP )/( )/( 1 1 )1(22 2 2 2 2 C = 20 for turbulent liq uid-turbulent vapor C = 12 for laminar liquid-turbulent vapor C = 10 for turbulent liquid-laminar vapor C = 5 for laminar liquid-laminar vapor 3 Mishima and Hibiki (1996) 2 hD l l hl leC X X C D xGf dz dP319 2 2 2 2121 1 1 )1(2 4 Lee and Lee (2001) 726.02 2 2 2 2 2Re10185.6 1 1 )1(2Lo l l hl lC X X C D xGf dz dP for laminar liquid-turbulent vapor 5 Qu and Mudawar (2004) 0613.000418.0121 1 1 )1(2319 2 2 2 2 2 G eC X X C D xGf dz dPhD l l hl l

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Table 4-2. Non-dimensional parameters for a macro-channel and micro-channels Re (Ratio of inertia force to viscous force) We (Ratio of inerti a force to surface tension force) Bo (Ratio of gravitational force to surface tension force) Ca (Ratio of viscous force to surface tension force) ReLS ReGS WeLS WeGS 10cm Channel 1354.3 0.00047-0.12 4665-1166276 6320-63200 2.21-138333 1.6-158 Channel 1 0.0117 0.00023-0.08 4.64-1670 7-1631 0.001-135 0.0005-32 Channel 2 0.0230 0.00035-0.04 14.1-1602 7-1838 0.005-63 0.0003-28 Channel 3 0.0525 0.00015-0.02 9.36-1436 7-2270 0.0014-34 0.0003-33 80

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Figure 4-1. Schematic of the flow vi sualization apparatus and the mixer. 81

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Figure 4-2. Photoes of th e experimental apparatus 82

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Figure 4-2. Photograph of micro-channels and schematic of the micro-channel. A Figure 4-3. Typical flow patterns in the mi cro-channel: A) BubblySlug flow B) Slug-Ring flow C) Dispersed-Churn flow D) Annular flow. 83

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B C D Figure 4-3. Continued 84

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Figure 4-4. Temporal records of inle t and outlet pressures (Slug-Ring flow, jL = 0.215m/s, jG = 1.2m/s) A Figure 4-5. Flow regime maps for three micro-channels: A) Dh = 0.622 mm B) Dh = 0.412 mm C) Dh = 0.209 mm 85

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B C Figure 4-5. Continued 86

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Figure 4-6. Flow map comparison between mi cro-channel and mini-c hannel predicted by the Weber number model. Figure 4-7. Measured time-a veraged void fraction results vs two previous correlations 87

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Figure 4-8. Comparison between the new correlation and experimental data Figure 4-9. Ratio of predicted and experimental time-averaged void fraction vs. homogeneous void fraction 88

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A B Figure 4-10. Comparison between the e xperimental data and the models ( Dh = 0.412 mm) A) Lockhart-Martinellis model ( C = 5) B) Lee and Lees model C) Mishima and Hibikis model 89

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C Figure 4-10. Continued 90

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CHAPTER 5 MICRO-BUBBLE DISPENSER Bubble generation in a simple co-flowing micro-channel w ith a cross-section area of 1.69 0.07 mm2 was experimentally and numerically invest igated. Air and water were used as the gas and liquid, respectively. Mixtures of water-g lycerol and water-Tween 20 were also used to obtain the effects of viscosity and surface tension. The experimental data shows that the break-up process is periodic under certain operating conditions. The breakup dynamics are also examined using three dimensional incompressible two-pha se flow numerical si mulation based on the volume of fluid (VOF) method. The simulation successfully pred icts the flow behavior and provides a more detailed examination of the bubbl e shape. The physics can be further explained by the detailed micro-PIV measurements which show that the bubble is formed due to the velocity component perpendicular to the gas fl ow created by the sudde n change of the liquid velocity distribution around th e barrier. The bubble length L is dependent on the liquid flow rate Ql and gas flow rate Qg, and the ratio of L to the channel width w is a function of the ratio of gas and liquid flow rates Qg/Ql which is similar to that previously used in the T-junction case. The bubble frequency f is found to be related to w channel depth h and QlQg/(Qg+Ql/4) This formulation shows a good agreement with the experimental data at the low frequency region. Different bubble shapes can be obt ained at different liquid viscos ities and surface tensions. The ratio L/w can still be predicted by a modified equation which uses the real bubble width wb or an equivalent bubble length Le. 5.1 Introduction and Background Single phase and multiphase flow s in micro-geometries have been investigated by many researchers in recent years (Brutin and Tadrist 2003; Xiong and Chung, 2007a & 2007b). Microfluidic devices can be a pplied in many scientific and in dustrial developments such as 91

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on-chip separation (Fu et al. 1999), chemical reaction (Song et al. 2003) and biochemical synthesis (Zheng et al. 2004). Thes e devices require the control of small volumes of fluids, and the understanding of multiphase flows, especially with a special intere st in formation of gas-liquid dispersions. Gas-liqui d dispersion is common in macr oscopic processes and products of the chemical, health-care, and food i ndustries. Not surprisi ngly, many studies of emulsification and droplet beha vior have been performed in macroscopic, unbounded shear, and extensional flows (Stone et al. 2004). Recent investigati ons focused on generating and manipulating emulsions with microfluidic devices are motivated by the potential to use controlled flows and structures on the scale of the droplets to tailor the properties of the emulsions. In particular, its of interest to control the droplet size and the distribution of sizes. The microchannel geometry takes on added signifi cance because it can influence the relative rate of rotation to extension in the flow, which is fundamental to break-up processes. Currently several techniques exist for the generation of bubbles (Ganan-Calvo and Gordillo 2001; Garstecki et al. 2004; Gordillo et al. 2004; Guillot and Colin 2005; Xu et al. 2006; Haverkamp et al. 2006). First is the T-junction. In the T-junctio n case, the continuous fl ow is in one arm and sheared off by a dispersion flow in the perpendicu lar arm. The break-up of gas-liquid threads is dominated by the pressure drop across the bubbl e as it forms, and the size of the bubbles is determined solely by the ratio of the volumetric flow rates of the two fl uids. A scaling law for the size of the discrete fluid segments can be written as (Garstecki et al. 2006): l gQ Q wL 1 / (5-1) where L is the length of the bubble slug, w is the width of the channel, Qg and Ql are the gas and liquid flow rates respectively, and is a constant of order one, whose particular value depends 92

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on the geometry of the T-junction. Second is th e flow-focusing device. The first type of the flow-focusing device arranges two ch annels in a concentric manner upstream of a small orifice to create a strong extensional flow (Stone et al. 2004). The bubble si ze is effectively set by the size of the orifice designed into the micro-channels under an operati ng condition while it can also produce threads that break into dr ops substantially smaller than the orifice in other cases. The second type uses a water nozzl e and does not have an orifice. The bubble is formed in a co-flowing water jet discharging into a stagnant air atmosphere (Sevilla et al. 2005). Recently Cubaud et al. (2005) used a four-crossed square channel to generate the bubble. The results showed the breakup occurs at the intersection and the bubble size and distribution can be expressed by the same equation as Eq. (5-1) with =1. The empirical expression can well predict the bubble length when 0.1<( Qg+ Ql)/ Ql<1. For ( Qg+ Ql)/Ql<0.04, the flow becomes annular. The control of drop breakup in microdevices such as those mentioned above is influenced significantly by surfactants and wetting characteristics. For example, the continuous phase should be the phase that most strongly wets the boundaries Contact angles and wetting properties depend on the type and concentration of surfactant, and such surfactant effects on drop formation in a T-junction have b een investigated experimentally (Dreyfus et al. 2003), but have yet to be analyzed in detail; In addition, because shear rates can be large, new interfacial area is created rapidly. Thus, the kinetics, and possi bly rheology, of surfact ants may also play significant roles in the emul sion formation process. In this paper, we describe a co-flowing devi ce which is easy to be scaled up or multiplexed due to the simple structure. The objectives of th is work are to 1) obtain the physics of the bubble break-up process, 2) discuss the flow parameters affecting the bubble length and get a 93

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formulation of the bubble length, 3) analyze the bubble generation fr equency, and 4) evaluate the effect of fluid viscosities and surface tension on bubble formation. 5.2 Experimental Setup 5.2.1 Dispenser Fabrication The 3-D schematic of the co-flowing micro-channel is shown in Fig. 5-1(a). The micro-channel was made of glass and silicon fa bricated in a clean room environment. The fabrication steps include a sele ctive deep reac tive ion etching of a doubl e-sided polished silicon wafer. The inside barrier (splitter plate) can be made by first covering a photo-resist layer and then creating patterns with photolit hography, leaving the barrier wi th a desired width and the gas and liquid channel exposed. Pyrex thin cover glass plate was anodic bonded on the top of the etched silicon wafer. Three larger holes are etched through the bottom of the wafer and glued with 1/16 soft tube s. In Fig. 5-1(b), w is the width of the main channel, wg and wl are the width of the gas and liquid channel respectively, d is width of the barrier, and h is the depth of the micro-channel. A microscope (Olympus BX50) and a CCD camera with a pixel size 6.45 m were used to measure the dimensions of the micro-channel. The geometries are measured as: w 1.691 mm, wg = wl 0.545 mm, d 0.601 mm, and h 0.07 mm. The depth of the micro-channel was measured by the Veeco Wyko NT1000 optical pr ofiler. Figure 5-2 shows the depth and 3-D image measured by the profiler. 5.2.2 Apparatus Fig. 5-3 shows the schematic of the experimental flow visualizati on apparatus used to investigate the bubble dispersion in the co-flowi ng micro-channel. It includes two syringe infusion pumps (Cole-Parmer Instrument), 60ml and 3ml syringes (McMaster), micro-filter (Swagelok), Fiber-Lite MI-150 high intensity illuminator (Dolan -Jenner), micro-channels, and 94

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high speed CCD camera (Redlake). The liquid fluid at flow rates ranging from 3ml/h to 63ml/h, which can be set on the panel of th e infusion pump with an accuracy of 0.5%, was driven to the micro-channel test section. The 2 m micro-filter can remove a ny particles or bubbles which may block the micro-channel before the flow enters into the test section. The gas flow at flow rates ranging from 0.21ml/h to 126ml/h was driven to the channel from the other syringe pump. The test sections were placed horizontally. All experiments were conducted at room temperature, 20oC, and under atmospheric pressure at the discharg e of the test section. Flow visualization was started after some equilibration time when changing the flow parameters. It was achieved by using a high speed CCD camera, which can operate at a frame ra te up to 8000 fps and a shutter speed of 1/8,000 s. In this work, the frame rate of 500 fps was used. The resolution of the camera was 480(H) 420(V) pixels. Two Fiber-Lite illuminato rs provided the high intensity light, which was directed onto the test section by tw o optical fiber light gui des. An adjustable microscopic magnification lens was used to magnify the test section. In this experiment, the air was used as the gas fluid. Water (viscosity =0.92 mPa s) and three aqueous solutions of gl ycerol, 50% (w/w) glycerol ( =7.31 mPa s), 30% (w/w) glycerol ( =2.68 mPa s), and 10% (w/w ) glycerol ( =1.19 mPa s) were used as the liquid fluid. The viscosity of water-glycerol mixture wa s measured at room temperature, 20oC, by means of a rotary viscosimeter. To change the gas-liquid interfacial tension and evaluate its effect to bubble generation, 2% (w/w) Tween-20 surfactant is added into the wate r and mixed for approximately 40 minutes at room temperature. The dilute soluti on of Tween-20, 2% (w/w), is larger than the critical micellar concentrati on (CMC) in water, 0.007% (0 .059mM). The surface tension measured by a digital tensiometer changes from around 72mN/m (water + air) to 37mN/m (water/Tween-20 + air). It has to be pointed out that small change in temperature [ O (10)K] and 95

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composition can result in 5% va riation around the measured values. Image analysis software ImagJ was used to analyze the image frames to determine the bubble size. To further understand the break -up physics, a micron-resoluti on particle image velocimetry system (micro-PIV), shown in Fig. 5-4, was us ed where fluorescent particles (Duke Scientific) were seeded into the de-ionized water flow. Tw o Nd:YAG lasers (Continuum) were directed to the same optical path by optical lenses (Edm und) and expanded by a beam expander made up of a concave and a convex lens. The 0.69 m particles absorb green light ( 542nm) and emit red light ( 612nm). The emitted light is imaged through a 10 objectives lens (NA=0.3) and passed to the fluorescent filter cube (Olympus), where the green light from th e background reflection is filtered out and the red fluorescence from the sub-micron particles is passed to the 0.5 lens (Olympus) and recorded on th e CCD camera (Cooke). The con centration of the fluorescent particles solution was prepared to ensure at least 5-10 seed partic les in each interrogation volume. In this work, this time delay is set to be 100 s, so the particles move approximately 1/8th of an interrogation window betw een pulses. The interrogation wi ndows measure 64 camera pixels square, thus the particles moves approximately 8 pixels between laser pulses. Assume that the measured velocity is accurate to within 1/5th of a pixel. It results in an experimental uncertainty of less than 2.5% (Prasad et al 1992). 5.3 Numerical Simulation The numerical simulation presented here is used to examine the bubble dynamics in the break-up process. Since the simulation includes two fluids and time dependent bubble motion, the Volume of Fluid (VOF) method is applied. The main purpose of the VOF method is to track the interface between two phases. That is acco mplished by solving the continuity equation for 96

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volume fraction of phases at the interface. Suppose there are n phases, and for the i th phase, the continuity equation at inte rface is in the form of: 1()()(n iiiii jiij jvm t ) m (5-2) i is the volume fraction of the i th fluid in the cell, i is density of i th fluid, is the velocity vector of the i th fluid, n is the total number of phases, iv j im is mass transfer from phase j to phase i For every non-primary phase, Eq. (5-2) will be solved. For the primary phase, its volume fraction is calculated by: 11n j j (5-3) In this simulation, the primary phase is set to be water and air is the secondary phase. The Navier-Stokes equations are discretized on a standard marker and cell (MAC) grid with velocities on cell walls and the rest of the properties at the cell centers. A QUICK discretization scheme is used for the convective terms and a s econd order discretization scheme is used for the viscous terms. The simulation mesh is shown in Fig. 5-5. The total number of cells is about 220000. The width and depth of the simulation regi on are the same with the device used in the experiment, which are 1.691 mm and 0.07 mm, resp ectively. In the length direction, only a portion of the micro-channel is simulated in orde r to reduce the computational time. The lengths of air and water inlets are set to be 1 mm and the total simulation region is 10 mm long. This computation region is where an air bubble is generated and break s up. Thus it can capture the main physical phenomena. 97

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5.4 Results and Discussions 5.4.1 Bubble Break-Up The bubble generation process can be observed from a video recorded by the high speed camera. Fig. 5-6 shows the time evolution of a periodic break-up procedure and the corresponding bubble shape prediction by the simulation. In the simulation results, blue denotes pure liquid with void fraction of zero and re d denotes pure gas with void fraction of one. During a typical period, there are two steps in the process. Firstly, af ter the pinch-off of a bubble, the gas ligament expands vertically downward and horizontally until a neck appears. Since the top interface is bounded by the cha nnel, the ligament onl y develops downward vertically. This period te from the pinch-off to the neck a ppearing is called the gas ligament expansion. After the ligament expansion, th e neck propagates downstream and its diameter decreases until it finally breaks, thereby form ing a new leaving bubble. The newly formed bubble is immediately bounded as a gas slug due to the high surface tension force in the small channel. This period tc from the neck appearing to the fo rmation of the new bubble is named the gas ligament collapse. From the last image, we can see the next periodic break-up sequence begins. From the Young-Laplace e quation, the Laplace pressure ju mp across the interface equals to (1/ra+1/rr) where ra and rr are the axial and radial radii of curvature, respectively. Both of them are proportional to the corr esponding wetting angles which ar e varying with time, but they are bounded by the width w and height h of the channel, respectively. Since w>>h in our channel and rr is minimum at the moment of break-up, the maximum Laplace pressure jump almost equals to /rrmin. If the total pressure difference be tween gas and liquid exceeds the maximum Laplace pressure jump, bubble break-up would take place. Otherwis e no break-up exists. 98

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The experiment data show that the period ic break-up only exists under certain operating conditions. There are two typical unsteady break -up processes in the experiment, which are shown in Fig. 5-7. The first one, shown in Fig. 57a), is the case where the liquid flow rate is so low that the neck can not be broken before th e gas ligament flows out the channel. The second one, shown in Fig. 5-7b) and 5-7c), is the case where the ratio of gas and liquid flow rates is so high that the neck is stretched to a very thin gas ligament no matter what the flow rate is, intermediate or high. Fig. 5-8 shows the instantaneous micro-PIV me asurements in one period around the barrier. From Fig. 5-8, we can see that when the liqui d enters into the main channel from the liquid sub-channel, it pushes upward due to its larger momentum. As a result, velocity components perpendicular to the gas ligament exist around the barrier which press the bubble interface and form the neck. After the breakup, the high liquid velocity on th e top of the bubble pushes it to the bottom wall and forms a gas slug (Fig. 58e), then a new periodic cycle begins. 5.4.2 Bubble Distribution and Bubble Size Over a wide range of gas and liquid flow ra tes, the bubbles are generated uniformly. Fig. 5-9 shows the uniform bubble distribution near the exit of the cha nnel at different gas and liquid flow rate ratios. Assume that D denotes the distance between the two consecutive bubbles. The bubble length L increases while D decreases with the flow rate ratio. Changing the gas and liquid flow rates can achieve different bubbl e lengths. Fig. 5-10 shows the dependence of bubble length L on the gas and liquid flow rates. From Fig. 5-10a) it was found at a fixed liquid flow rate, the bubble length increases with the gas flow rate. Thats because with a higher flow rate the gas has a larg er force to push the liqu id and resist the liquid pressure at the neck, so both of the expansion and collapse time te and tc increase which leads to a longer bubble. While from Fig. 5-10b) we can see at a fixed gas flow rate L decreases with the 99

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liquid flow rate. The same physics can be applied here. The increasing liquid momentum cuts the neck quickly and shortens the time of both stages which results in a bubble with a short length. Fig. 5-11 shows the data of L/w at the gas-liquid flow rate ra tio ranging from 0.01 2 with one gas flow rate 5ml/h and three different liq uid flow rates chosen as 21ml/h, 42ml/h, and 63ml/h respectively. It was found that under curre nt experimental conditions, except for the high gas to liquid ratio data shown as the hollow triangles in the figure where the gas flow rate was kept constant at Qg = 5ml/h, the rest of the data can be co rrelated successfully by Eq. (5-1) with = 1, which is based on fitting with the experimental data in a T-channel which is shown as the solid line in Fig. 511 and expressed as: l gQ Q wL 1 / (5-4) The reason why the hollow triangle data deviate from Eq. (5-4) is given as follows: From Fig. 5-8, we know that the bubble break-up physics is similar to that in a T-junction as the bubble break-up requires a vertical liqui d velocity component to pinch off the neck. Oak et al. (2004) demonstrated that in the co-flowing micro-channe l, when the liquid flow rate is increased, around the barrier there is a corres pondingly higher vertic al component that is used to form the bubble. So when the liquid flow rate is larger than the critical va lue, the flow dynamics is almost identical to the T-junction case. Wh en the liquid flow rate is less than the critical value, only a portion of the liquid velocity is used in the bubble formation, which lowers the effectiveness of Ql, As a result, the L/W is increased from that predicted by Eq. (5-4). 5.4.3 Bubble Frequency For the macro channel, the bubble velocity is related with the mi xture mean velocity Ug+Ul and the mean drift velocity Ugl, which can be given by (Zuber and Findlay 1965): 100

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gllGUUUCU 0 (5-5) C0 is the distribution parameter. The mean drift velocity Ugl can be neglected in micro-channels due to the inability of the bubbles to rise through the stagnant li quid (Ali et al. 1993) and Cubaud et al. (2005) found C0 1 in micro-channels. Hence hw QQ Ugl (5-6) Assume T is the total time of formation of one bubble, then cettUUTD (5-7) Assume the left and right side of the bubble is nearly spherical and the small volume of the film thickness ( 1%-3% of the total bubble volume from the image) can be neglected, then the gas volume in a bubble is approximately estimated to be ((L-w)w+w2/4)h According to the mass conversation, the relationship between L and D can be written as w L w LD w Lw w wLD Q Qg l 4 1 4 1 4 1 4 12 2 (5-8) Combine Eqs. (5-4) (5-8), and the b ubble frequency can be calculated as: 4 112lg gl ceQQhw QQ ttT fre (5-9) Fig. 5-12 shows the experimental bubble freque ncies and the theoretical one expressed by Eq. (5-9). The experimental values are calculated by checking the video a nd getting the time of bubble formation in one period. Fr om Fig. 5-12, we can see the experimental data agree well with the predicted one at the low frequency regi on. But there is an underestimation at the high 101

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frequency region since in this region the gas fl ow rate is high and th e bubble shape at the interface shows an elliptical shap e. When Eq. (5-8) is applied, the gas volume is underestimated which results in the underestimation of frequency. 5.4.4 Effect of Viscosit y and Surface Tension Mixtures of water-glycerol and water-Tween 20 were used to obt ain the effects of viscosity and surface tension on the bubble generation respectively. The recorded data shows that the bubble formation still can be steady and period ic as the pure water under the same operating conditions. However, we have f ound some changes on the bubble shapes at different viscosities and surface tensions. Fig. 5-13 shows the bubble sh apes with different viscosities and surface tensions at QL = 21ml/h and QL = 42ml/h. With the increasing of the viscosity, the film thickness is obviously increased. A typical example is th at the bubble shape changes from a slug to an approximately spherical bubble at the lower Qg/Ql. At this time, we can not use the channel width w to be the bubble width wb. Hence a modified equation can be obtained by using wb to replace w in Eq. (5-4). Fig. 5-14 shows the measured L/wb at different ratios of gas to liquid flow rate. The experimental data shows a good agreem ent with the ones pred icted by the modified equation. If w was still used here, the bubble length would be overestimated by around 6%, 18.7%, and 31.2% respectively. From Fig. 5-13, we also see the bubble changes to a tadpole-like shape due to the decrease of surface tension. The tail of the bubble decreases with gas and liquid flow rates. The reason may be at the interface th at the increasing inertia forces push and shorten the tail. To compare the bubble le ngth with the former results, we define an equivalent bubble length Le for the tadpole-like bubbles, which can be approximately calculated by: width channel by the covered Pixels area bubble by the covered Pixels w A Lb e (5-10) 102

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where Ab is the bubble area obtained from the flow image. It is the area enclosed by the bubble interface. This interface can be detected by an image processing function in the commercial software ImageJ, Edge Detecti on Function, which uses the grad ient of the pixel values around the interface to detect it. Fig. 5-15 shows the Le/w at different surface tensions. The data also have a good agreement with the predict ones. The conclusion can be made that under current operating conditions, the bubble length can still be predicted by a modified equation which uses the real bubble width wb or an equivalent bubble length Le. Fluid viscosity and surface tension have a major effect on the bubble shape. 5.4 Summary In this chapter, we experimentally and numeri cally investigated the formation of bubbles in a simple co-flowing micro-chan nel, which has a compact size to be easily scaled up or multiplexed and can generate micro-bubbles roughly from 0.1 L to 0.6 L under current operating conditions. The break-up process, bubble length, bubble frequency, and effects of viscosity and surface tension were comprehensiv ely studied. The following conclusions can be made: Bubble break-up is obtained by the velocity di stribution change around the barrier. It is periodic under certai n operating conditions, and it become s unsteady and nonperiodic when Ql is less than some critical values or Qg/Ql is too large. The process has two steps: gas ligament expansion and collapse. The bubble length L is dependent on Qg and Ql, and has a quantitativ e relationship with channel width w and Qg/Ql, which is the same as that used for the T-junction since the break-up process becomes similar with that of T-junction under th e operating conditions. At the low frequency region, bubble generation frequency is a function of channel width w channel depth h and QlQg/(Qg+Ql/4) This functional relations hip provides a very good prediction at the low frequency region. The liquid viscosity affects the film thickness while the surface tens ion changes the bubble shape. The dimensionless bubble length L/w can still be predicted by a modified equation which uses the real bubble width wb or an equivalent bubble length Le. 103

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A) B) Figure 5-1. Schematic of the co-flowi ng micro-channel: A) 3-D and B) 2-D Figure 5-2. 3-D image and depth m easurement by the optical profiler 104

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Figure 5-3. Schematic of the experi mental flow visualization apparatus Figure 5-4. Schematic of micro-PIV measurement for micro-bubble dispenser 105

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Figure 5-5. Schematic of 3D CFD mesh t = 0s t = 0s t = 0.04s t = 0.04s t = 0.15s t = 0.15s t = 0.20s t = 0.20s t = 0.23s t = 0.23s t = 0.26s t = 0.26s Figure 5-6. Time evolution of th e periodic bubble generation process ( Qg = 6.3ml/h, Ql = 21ml/h, Air+Water) and the prediction by CFD simulation 106

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A B C Figure 5-7. Unsteady break-up proce ss at different flow rates: A) Qg = 2.4ml/h, Ql = 3ml/h B) Qg = 105ml/h, Ql = 42ml/h and C) Qg = 37.5ml/h, Ql = 15ml/h A B Figure 5-8. Instantaneous micro-PIV measurements around the barrier ( Ql = 21ml/h, Qg = 6.3ml/h) 107

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C D Figure 5-8. Continued 108

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E F Figure 5-8. Continued 109

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A B C D Figure 5-9. Bubble distribution along the channel at different flow rates: A) Qg/Ql = 0.01 ( Ql = 21ml/h, Qg = 0.21ml/h) B) Qg/Ql = 0.1 ( Ql = 21ml/h, Qg = 2.1ml/h) C) Qg/Ql = 0.5 ( Ql = 21ml/h, Qg = 10.5ml/h) D) Qg/Ql = 1 ( Ql = 21ml/h, Qg = 21ml/h) A Figure 5-10. Dependence of the bubble length L on the A) gas flow rate ( Ql = 18ml/h) and B) liquid flow rate ( Qg = 5ml/h) 110

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B Figure 5-10. Continued Figure 5-11. Dimensionless ratio ( L/w ) with the ratio of ga s and liquid flow rates 111

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Figure 5-12. Bubble frequency with different liquid and gas flow rates (Air +water) Figure 5-14. Dimensionless ratio ( L/wb) with the ratio of gas and liquid flow rates 112

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A QL/Qg Air + Water = 72mN/m, = 0.92 mPa s Air + Water-Glycerol (10%) = 72mN/m, = 1.19 mPa s Air + Water-Glycerol (30%) = 72mN/m, = 2.68 mPa s Air + Water-Glycerol (50%) = 72mN/m, = 7.31 mPa s Air + Water-Tween20 = 37mN/m, = 0.92 mPa s 0.1 0.5 1 B QL/Qg Air + Water = 72mN/m, = 0.92 mPa s Air + Water-Glycerol (10%) = 72mN/m, = 1.19 mPa s Air + Water-Glycerol (30%) = 72mN/m, = 2.68 mPa s Air + Water-Glycerol (50%) = 72mN/m, = 7.31 mPa s Air + Water-Tween20 = 37mN/m, = 0.92 mPa s 0.1 0.5 1 Figure 5-13. Bubble shapes at different viscosities and surface tensions: A) Ql = 21ml/h B) Ql = 42ml/h 113

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Figure 5-15. Dimensionless ratio ( Le/w ) with the ratio of gas and liquid flow rates 114

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CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS In this research, many features of the singl eand two-phase pre ssure-driven flows in micro-channels were experimentally and numerically investigated. Major accomplishments and recommendations for future research are provided in the following. 6.1 Accomplishments and Findings 1. For straight micro-channels, the experimental Poiseuille numbers show agreement with standard laminar incompressibl e flow predictions when the Re is less than a value around 1500. The discrepancy observed by the former researchers is the result of unaccounted bias in experiment setups, such as not accounting for increased pressure drop in the entrance region or unreliable inlet and outlet losses. 2. The flow micro structures around the bend of a se rpentine micro-channel can be divided into three categories depending on the flow Reynolds number. When Re<100, there is no induced flow recirculation and flow se paration. When Re>100, vortice s and flow separation appear and further develop. The outer corner vortex develops along th e wall of the channel, and the vortex center moves slightly from the upper stream to the down stream with the increasing of the Re number. The inner wall vortex due to flow separation develops immediately after the flow makes the turn. When Re>1000-1500, the shap e and size of the outer and inner vortices become almost constant. 3. In serpentine micro-channels, the additional pressure drop due to miter bends can be divided into two groups. The first group is for Re<100 where there is no eddies and the additional pressure drop is very small for all of the channels. The other group is for flows with the Reynolds numbers exceeding the th reshold values that are in the range of 100-300. When the Reynolds is higher than the thre shold value, we found the flow separation and formation of vortices that appear on the inner and outer wall around the miter bend. These vortices increase in strength with increasing Re numbe r that causes the bend pressure drop to increase sharply with the Re number. The experimental results also show the bend pressure drop increases with decreasing hydraulic diameters. Bend loss coefficient Kb is a function of the Re number only when Re<100, a function of th e Re number and channel size when Re>100, and almost keeps constant and changes in the range of 10% when Re is larger than some value in 1000-1500. The trend of the experimental pressure drop is consistent with the flow structure change. 4. The phenomenon that micro-channel flow pattern changes with time at a fixed location under a certain gas and liquid superficial velocity was found, which can be attributed to the density wave oscillation in the microchannel. According to the appearance of the transition flow patterns such as liquid ring flow liquid lump flow and disr uption tail of the slug, four flow patterns can be defined fo r micro-channels with the hydraulic diam eters of 0.412 mm and 0.622 mm: bubbly-slug flow, sl ug-ring flow, dispersed-churn flow and annular flow. For the micro-channel with the hydraulic diamet ers of 0.209 mm, the bubbly-slug flow became 115

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the slug-flow and the dispersed flow disappear ed. The current flow regime maps show the transition boundary lines shift to high WeGS or gas superficial velocity with the decreasing of the hydraulic diameter. It can be explaine d by the strong surface tension effect in micro-channels. The micro-channel flow maps were compared with the mini-channel flow map based on the Weber number model, which showed poor agreement. 5. Time-averaged void fractions of each micro-cha nnel were measured for 22 runs to cover the whole range of homogeneous void fraction. Th e data of each run were obtained from the analysis of 8000 flow pattern images captured at a certain gas and liqui d superficial velocity. With the decreasing of the hydraulic diamet er, the time-average void fraction showed a non-linear relationship with the homogeneous void fraction. A new empirical correlation was proposed to predict the non-linear relationship, and most of the current experimental data and Kawarahas (2002) data fall with in % of the new correlati on. The uncertainty of this measurement method was analyzed and the uncer tainty range was approximately from 3.1% to 9.8% under the current expe rimental conditions. The results of this study provide basic information of the effects of length scale reduction on nitrogen-water two-phase flow characteristics in micro-scale channels that would be useful for the design of gas-liquid transport and their separation encounte red in low-temperature fuel cells. 6. In a micro-bubble dispenser w ith co-flowing struct ure, bubble break-up is obtained by the pressure drop resulting from the sudden velocity distribution change arou nd the barrier. It is periodic under certai n operating conditions, and it become s unsteady and nonperiodic when Ql is less than some critical values or Qg/Ql is too large. The process has two steps: gas ligament expansion and collapse. 7. The bubble length L is dependent on Qg and Ql, and has a quantitativ e relationship with channel width w and Qg/Ql, which is the same as that used for the T-junction since the break-up process becomes similar with that of T-junction under the op erating conditions. At the low frequency region, bubble generation fre quency is a function of channel width w, channel depth h and QlQg/(Qg+Ql /4). This functional re lationship provides a good prediction at the low frequency region. The li quid viscosity affects the film thickness while the surface tension changes the bubble shape. The dimensionless bubble length L/w can still be predicted by a modified equation which uses the real bubble width wb or an equivalent bubble length Le. 6.2 Future Research Future research to further understand the micro-scale pr essure-driven flow can be performed both experime ntally and numerically. 6.2.1 Experimental Study 1. Segmented bubble transport in serpentine micr o-channels to compare with gas-liquid two-phase flow motion and transpor t in straight micro-channels. 2. Rapid micro-T-junction mixer. 116

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3. Droplet transport in micro-T-junctio n and serpentine micro-channels. 6.2.2 Numerical Study 1. A general micro-scale two-phase flow model in corporate the inertia force, viscous force, surface tension force to predict the flow pattern s, void fraction and fric tional pressure drop. 2. A new model to predict the enhanced mixing induced by the segmente d micro-bubble/droplet 117

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APPENDIX TIMING PROGRAM FOR MICRO-PARTICLE IMAGE VELOCIMETRY The timing controller LC880 needs to be pr ogrammed to synchronize the laser and CCD camera. The following channels refer to: Channel A: Reference clock Channel B: Control the CCD Camera Channel C: Control the Flashlamp of laser 1 Channel D: Control th e Q-Switch of laser 1 Channel E: Control the Flashlamp of laser 2 Channel F: Control th e Q-Switch of laser 2 Overall LC880 settings: Programming preset A, Using 40 MHz internal clock. Channel A: Free-running clock: High duration: 1.000000 ms; low duration: 1.000000 ms. Channel B: Delayed pulse: Delay after trigger 50.000000 ns then pulse output 1.000000 ms. Invert output (pulse from high to low). Triggering options: Trigger on rising edge Skip 100 triggers before triggering. Trigger Input Logic: inB = outA; Channel C: Delayed pulse: Delay after trigger 0. 853800 ms then pulse output 15.000000 us. Triggering options: Trigger on rising edge. Unlimited retriggering. Trigger Input Logic: inC = not outB; Channel D: Delayed pulse: Delay afte r trigger 152.000000 us then pulse output 15.000000 us. Triggering options: Trigger on rising edge. Unlimited retriggering. Trigger Input Logic: inD = outC; Channel E: Delayed pulse: Delay after trigger 0. 856300 ms then pulse output 15.000000 us. Triggering options: Trigger on rising edge. Unlimited retriggering. Trigger Input Logic: inE = not outB; Channel F: Delayed pulse: Delay afte r trigger 152.000000 us then pulse output 15.000000 us. Triggering options: Trigger on rising edge. Unlimited retriggering. Trigger Input Logic: inF = outE; 118

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BIOGRAPHICAL SKETCH Renqiang Xiong was born in 1978, in China. He grew up predominantly in Jingdezhen city, Jiangxi Province, China, and rece ived his Bachelor of Science in energy engineering and Master of Science in optical engineering from Zhe jiang University in June 1999 and May 2002, respectively. Renqiang moved to the Sunshine state in Sp ring 2003 and enrolled in the Department of Mechanical and Aerospace Engineer ing at the University of Florida where he received a Master of Science in mechanical engi neering with minor in st atistics in August 2005. He then continued to pursue his PhD degree a nd worked as a research assistant on a part-time basis with Dr. Jacob N Chung. In the meantime, he is also pursuing a Master of Science in electrical and computer engineer ing. His research interests include microfluidics, micro-PIV, MEMS, and cryogenics. 125