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Effects of bubble coalescence and heater length scale on nucleate pool boiling

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Effects of bubble coalescence and heater length scale on nucleate pool boiling
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Chen, Tailian
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Boiling ( jstor )
Calibration ( jstor )
Data acquisition ( jstor )
Heat flux ( jstor )
Heat transfer ( jstor )
Heaters ( jstor )
Liquids ( jstor )
Nucleate boiling ( jstor )
Nucleation ( jstor )
Vapors ( jstor )

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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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EFFECTS OF BUBBLE COALESCENCE AND HEATER LENGTH SCALE ON
NUCLEATE POOL BOILING






I












By

TAILIAN CHEN


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


2002














ACKNOWLEDGMENTS


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

Chung, for his invaluable support and encouragement. Without his direction and support,

this work would not have been possible. Many thanks go to Dr. Jungho Kim for his help

build up the experimental setup and instructions in this research. I also greatly

acknowledge Dr. James F. Klausner for his invaluable suggestions in this research.

I have also had the privilege to work with Drs. William E. Lear, Jr., Zhuomin

Zhang and Ulrich H. Kurzweg as other members of my committee. Their suggestions and

encouragement have shaped this work considerably.

Finally, I feel indebted to my wife, Lu Miao, and my son, Matthew Chen. Without

their continuous support, this work would not have been possible.















TABLE OF CONTENTS

page

ACKN OW LEDGM ENTS................................................................................................... ii

LIST OF TABLES ............................................................................................................. vi

LIST OF FIGURES........................................................................................................... vii

NOM ENCLATURE........................................................................................................... xi

ABSTRACT .................................................................................................................... xiv

CHAPTER

1 INTRODUCTION ............................................................................................................ 1

1.1 Statem ent of the Problem .......................................................................................... 1
1.2 Research Objectives.................................................................................................. 2
1.3 Significance and Justification ................................................................................... 3

2 LITERATURE REVIEW AND BACKGROUND.......................................................... 5

2.1 Bubble Dynam ics and Nucleate Boiling................................................................... 5
2.2 Coalescence of Bubbles .......................................................................................... 15
2.3 Critical Heat Flux.................................................................................................... 21

3 EXPERIM ENT SYSTEM .............................................................................................. 24

3.1 M icroheaters and Heater Array............................................................................... 24
3.1.1 Heater Construction ......................................................................................... 24
3.1.2 Heater Specifications ....................................................................................... 25
3.2 Constant Temperature Control and Data Acquisition System................................ 27
3.2.1 Feedback Electronics Loop.............................................................................. 27
3.2.2 gProcessor Control Board and D/A Board....................................................... 28
3.2.3 A/D Data Acquisition Boards .......................................................................... 29
3.2.4 Heater Interface Board (Decoder Board) ......................................................... 29
3.2.5 Software ........................................................................................................... 29
3.3 Boiling Conditioin and Apparatus .......................................................................... 30
3.3.1 Boiling Condition............................................................................................. 30
3.3.2 Boiling Apparatus ............................................................................................ 30


iii








3.4 Experiment Procedure............................................................................................. 30
3.4.1 Heater Calibration............................................................................................ 30
3.4.2 Data Acquisition and Visualization ................................................................. 36
3.5 Heat Transfer Analysis and Data Reduction........................................................... 37
3.5.1 Qualitative Heat Transfer Analysis ................................................................. 37
3.5.2 Data Reduction Procedure................................................................................ 38
3.5.3 Determination of Natural Convection on the Microheaters............................. 40
3.5.4 Uncertainty Analysis........................................................................................ 44

4 SINGLE BUBBLE BOILING EXPERIMENT ............................................................ 52

4.1 Introduction............................................................................................................. 52
4.2 Experiment Results ................................................................................................. 54
4.2.1 Time-averaged Boiling Curve.......................................................................... 54
4.2.2 Time-resolved Heat Flux.................................................................................. 55
4.2.3 Time-resolved Heat Flux vs. Superheat AT..................................................... 58
4.2.4 Visualization Results and Bubble Growth Rate............................................... 63
4.3 Comparison and Discussion.................................................................................... 67
4.3.1 Bubble Departure Diameter............................................................................. 67
4.3.2 Size Effects on Boiling Curve and Peak Heat Flux ......................................... 68
4.3.3 Bubble Incipient Temperature.......................................................................... 72
4.3.4 Peak Heat Flux on the Microheater.................................................................. 72
4.4 Deviations from Steady Single Bubble Formation ................................................. 73
4.4.1 Discontinued Bubble Formation ...................................................................... 73
4.4.2 Bubble Jetting................................................................................................... 79

5 DUAL BUBBLE COALESCENCE.............................................................................. 86

5.1 Synchronized Bubble Coalescence......................................................................... 86
5.2 Dual Bubble Coalescence and Analysis.................................................................. 87
5.3 Heat Transfer Enhancement due to Coalescence.................................................... 93
5.4 Bubble Departure Frequency .................................................................................. 95

6 HEAT TRANSFER EFFECTS OF COALESCENCE OF BUBBLES FROM
VARIOUS SITE DISTRIBUTIONS .............................................................. 96

6.1 Coalescence of Dual Bubbles with a Moderate Separate Distance A Typical Case
......................................................................................................................... 9 6
6.2 Dual Bubble Coalescence from Heaters #11 and #14 at 100C Larger Separation
Distance Case................................................................................................ 103
6.3 Dual Bubble Coalescence from Heaters #11 and #14 at 130C Larger separation
Distance and Higher Heater Temperature Case............................................ 107
6.4 History of Time-resolved Heat Flux for Different Heater Separations................. 109
6.5 Time Period of a Bubbling Cycle.......................................................................... 109
6.6 Average Heat Flux of a Heater Pair Effects of Separation Distance.................. 113
6.7 Time-averaged Heat Flux from Heater #1 ............................................................ 113
6.8 Coalescence of Multiple Bubbles.......................................................................... 115








6.9 Heat Transfer Enhancement due to Coalescence Induced Rewetting................... 122

7 MECHANISTIC MODEL FOR BUBBLE DEPARTURE AND BUBBLE
COA LESCEN CE ......................................................................................... 126

7.1 Rew getting M odel................................................................................................... 127
7.2 Results from the Rewetting Model ....................................................................... 128

8 CONCLUSIONS AND FUTURE WORK ................................................................. 132

8.1 Summary and Conclusions.................................................................................... 132
8.2 Future W ork .......................................................................................................... 133

APPENDIX NOTES OF PROGRAMMING CODES FOR DATA ACQUISITION.. 135

REFEREN CES................................................................................................................ 146

BIOGRAPHICAL SKETCH........................................................................................... 150














LIST OF TABLES


Tables Page

3.1 The specifications of the D/A cards ........................................................................... 29

3.2 The uncertainty sources from calibration.................................................................... 46

4.1 Single bubble growth time and departure diameter ................................................... 68

4.2 Properties of FC-72 at 56C........................................................................................ 68

7.1 Effective thermal conductivity (w/m.K) used in the rewetting model...................... 129














LIST OF FIGURES


Figures Page

2.1 The numerical model and results given by Mei et al. (1995)........................................ 7

2.2 The numerical model and four growth domains by Robinson and Judd (2001)........... 8

2.3 Research on bubble coalescence by Li (1996)............................................................ 17

2.4 The coalescence research performed by Bonjour et al. (2000)................................... 20

3.1 Heaters and heater array ............................................................................................. 26

3.2 Wheatstone bridge with feedback loop....................................................................... 28

3.3 Boiling apparatus ........................................................................................................ 31

3.4 Schematic of calibration apparatus and temperature control loop.............................. 32

3.5 Part of the calibration results....................................................................................... 34

3.6 Comparison of calibrated resistances of heater #1 with the calculated resistances
from property relation........................................................................................... 35

3.7 The schematic showing the heat dissipation from a heater......................................... 39

3.8 Heat flux comparison from experimental and calculated results ................................ 41

3.9 Derived natural convection heat fluxes for different heater configurations................ 44

3.10 The circuit schematic for temperature control and voltage division......................... 47

3.11 The uncertainty at different temperatures................................................................. 50

4.1 The boiling curve of the single bubble boiling........................................................... 56

4.2 The heat flux variation during one bubble cycle......................................................... 57

4.3 Time-resolved heat flux variation at different heater superheats................................ 59








4.4 The trend of maximum and minimum heat fluxes during one bubble cycle with
various heater superheats ...................................................................................... 61

4.5 A hypothetical model for bubble departure from a high temperature heater.............. 62

4.6 Bubble images of a typical bubble cycle taken from the bottom................................ 64

4.7 Measured bubble diameters at different time.............................................................. 66

4.8 Bubble growth rate at different time ........................................................................... 66

4.9 The visualization result of bubble departure-nucleation process for heater #1 at 54C
............................................................................................................................... 69

4.10 The relationship between bubble departure diameter and growth time.................... 70

4.11 Comparison of boiling curves ................................................................................... 71

4.12 Comparison of peak heat fluxes................................................................................ 71

4.13 The process of vapor explosion together with onset of boiling ................................ 75

4.14 The ruler measuring the distance in figure 4.13 after vapor explosion..................... 75

4.15 The bottom images for vapor explosion and boiling onset process.......................... 76

4.16 The heat flux variation corresponding to the vapor-explosion and boiling onset
process................................................................................................................... 78

4.17 The chaotic bubble jetting process for heater #1 at 110C....................................... 81

4.18 The bottom images of chaotic bubble jetting process for heater #1 at 110C.......... 82

4.19 The heat flux traces corresponding to the bubble jetting process............................. 83

4.20 The heat flux traces for bubble jetting process from heater #1 at 105C ................. 84

4.21 The heat flux traces for bubble jetting process from heater #1 at 120C.................. 85

5.1 The heat flux variation for pair #1 with #11 and pair #1 and #12............................... 88

5.2 The heat flux variation of one typical bubble cycle for two configurations (a) and (b)
for heater #1 with #11, (c) and (d) for heater #1 with #12.................................... 89

5.3 The heater dry area before and after coalescence ...................................................... 90








5.4 The boiling heat flux for the two pairs (#1 with #11) and (#1 with #12) as they are set
at different temperatures to generate bubbles and coalesce .................................. 92

5.5 The heat flux increase due to coalescence.................................................................. 94

5.6 Comparison of bubble departure frequency from heater #1 for coalescence and non-
coalescence cases .................................................................................................. 95

6.1 The departing and nucleation process for heaters #11 and #13 at 100C ................... 99

6.2 The coalescence process (2 cycles of oscillation) for heaters #11 and #13 at 100C.
..... .. ....... ...... ............................................ .. .. .. .. ................ ...... ............ 100

6.3 The heat flux history for dual bubble coalescence .................................................... 101

6.4 Photographs showing the interface interaction ......................................................... 102

6.5 The side-view photographs of coalescence-departure-nucleation process for heaters
#11 and #14 at 100C .......................................................................................... 104

6.6 The bottom view of coalescence-departure-nucleation process for heaters #11 with
# 14 at l OOC ........................................................................................................ 105

6.7 The heat flux history from heater #11 when #11 and #14 are set at 100C .............. 106

6.8 The heat flux history for heaters #11 and #14 at 130C ........................................... 108

6.9 The heat flux history from heater #1 with time......................................................... 110

6.10 The bottom images for one bubble cycle and dryout changing (time in second) ... 111

6.11 The time duration of one bubble cycle at different superheats ............................... 112

6.12 The average heat fluxes from different pairs of heaters at different superheats..... 114

6.13 The average heat fluxes from heater #1 at different superheats.............................. 114

6.14 Four heater configurations for multiple bubble coalescence experiment ............... 115

6.15 The heat fluxes from each heater for case A (figure 6.14) vs. superheat................ 117

6.16 The heat fluxes from each heater for case C (figure 6.14) vs. superheat ................ 117

6.17 The average heat fluxes for different heater configurations vs. superheat.............. 118

6.18 The coalescence sequence for heaters #3, #5, #7, and #15 at 80C ........................ 120








6.19 The coalescence sequence for heaters #1, #3, #5, #7, and #15 at 80C.................. 120

6.20 The coalesced bubble formed on heaters #3, #5, #7, and #15 at 100C ................. 121

6.21 The coalesced bubble formed on heaters #1, #3, #5, #7, and #15 at 100C ........... 121

6.22 The heat fluxes from heater #11 when the other heaters are at various superheats. 123

6.23 The heat flux history from heater #11 during 0.8 second ....................................... 123

6.24 The heat flux history from heater #11 when the bubble formed on it is pulled
toward the primary bubble from heaters #1, #2, #3, and #4............................... 124

7.1 Typical heat flux spikes during bubble coalescence................................................. 126

7.2 The fluid flow induced by the bubble departure....................................................... 127

7.3 The fluid flow induced by the bubble coalescence................................................... 128

7.4 The results from the rewetting model for the bubble coalescence............................ 130

7.5 The results from the rewetting model for the bubble departure................................ 131

A. 1 The main interface to select heaters......................................................................... 135

A.2 Heaters temperature form......................................................................................... 137

A.3 The architecture for addressing the selected heaters................................................ 141

A.4 The pins layout of the D/A cards ............................................................................. 143

A.5 The data acquisition form......................................................................................... 144














NOMENCLATURE


A heater surface area (cm2)

C platinum constant coefficient (Q/f2C)

Cp,i specific heat (kJ/kg.K)

Db bubble departure diameter

Db dimensionless bubble departure diameter

Fo Fourier number

g gravitational acceleration (m/s2)

g(Pr) function of Prandtl number in Eq.(3.8)

GrL Grashof number defined in Eq.(3.7)

Hfg latent heat of vaporization (kJ/kg)

Ja Jacob number

k thermal conductivity (w/m.K)

keff effective thermal conductivity (w/m.K)

L heater characteristic length

Lo heater characteristic length

n constant

Nux Nusselt number

NuL average Nusselt number for a heater









NUL,- corrected Nusselt number for a heater

Phd hydrodynamic pressure

Pv vapor pressure inside a bubble

P.o bulk liquid pressure

Pr\ Prandtl number

q"t heat flux (w/cm2)

q"condi conductive heat transfer rate per unit area from a heater to substrate with
boiling (w/cm2)

q"cond2 conductive heat transfer rate per unit area from a heater to substrate
without boiling (w/cm2)

q"natural natural convection heat transfer rate per unit area from a heater (w/cm2)

q'radl radiation heat transfer rate per unit area from a heater with boiling (w/cm2)

q"rad2 radiation heat transfer rate per unit area from a heater without boiling
(w/cm2)

q"rawi total heat transfer rate per unit area supplied to a heater with boiling
(w/cm2)

q"raw2 total heat transfer rate per unit area supplied to a heater without boiling
(w/cm2)

q"s(t) heat transfer with time in the rewetting model(w/cm2)

q "top boiling heat transfer (w/cm2)

R electrical resistance at temperature T

Rb bubble diameter (mm)

Ro resistance at ambient temperature To

t time (seconds)

Ti bulk liquid temperature (C)

TS heater surface temperature (C)









ambient temperature (C)

voltage across the heater (V)

offset voltage of the Opamp (V)


Greek Symbols

e uncertainty associated with temperature (C)

w uncertainty associated with heat flux (w/cm2)

pA liquid density (kg/m3)

pv vapor density (kg/m3)

O1 thermal diffusivity (kJ/kg.K)

Teg dimensionless bubble growth time

Tg bubble growth time (seconds)

/9 coefficient of thermal expansion

v kinematic viscosity (m/s2)

1t liquid viscosity (N-s/m2)

ar surface tension (N/m)

ATe heater superheat (C)















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

EFFECTS OF BUBBLE COALESCENCE AND HEATER LENGTH SCALE ON
NUCLEATE POOL BOILING

By

Tailian Chen

August 2002


Chairman: Jacob N. Chung
Major Department: Mechanical Engineering

Nucleate boiling is one of the most efficient heat transfer mechanisms on earth.

For engineering applications, nucleate boiling is the mode of choice owing to its narrow

operating temperature range and high heat transfer coefficient. Though much effort has

been expended in numerous investigations over several decades, controversies persist,

and a complete understanding of the boiling mechanisms still remains elusive.

In this research, microscale array heaters have been utilized, where each heater

has a size of 270 gtm x 270 gim. The time and space-resolved heat fluxes from constant-

temperature heaters were acquired through a data acquisition system with side and

bottom images taken from the high speed digital visualization system. Together with the

heat fluxes from the heaters, we have been able to obtain much better new results.

For the single bubble boiling, we found that in the low superheat condition,

microlayer evaporation is the dominant heat transfer mechanism while in the high








superheat condition, conduction through a vapor film is dominant. During the bubble

departure, a heat flux spike was measured in the lower superheat regime whereas a heat

flux dip was found in the higher superheat regime. As the heater size is reduced in pool

boiling, the boiling curve shifts towards higher fluxes with corresponding increases in

superheats. Comparing with the single bubble boiling, two major heat flux spikes have

been recorded in dual bubble coalescence. One is due to the bubble departure from the

heater surface and the other one is due to the bubble coalescence. The overall heat

transfer is increased due to the rewetting of the heater surface as a result of bubble-bubble

interaction. A typical ebullition cycle includes nucleation, single bubble growth, bubble

coalescence, continued bubble growth and departure. We have found that in general the

coalescence enhances heat transfer as a result of creating rewetting of the heater surface

by colder liquid and turbulent mixing effects. The enhancement is proportional to the

ebullition cycle frequency and heater superheat. It was also measured that the longer the

heater separation distance is the higher the heat transfer rate is from the heaters. For the

multiple bubble coalescence, the key discovery is that the ultimate bubble that departs the

heater surface is the product of a sequence of coalescence by dual bubbles. For the heat

transfer enhancement, it was determined that the time and space averaged heat flux for a

given set of heaters increases with the number of bubbles involved and also with the

separation distances among the heaters. In particular, we found that the heat flux levels

for the internal heaters are relatively lower than those of the surrounding ones.













CHAPTER 1
INTRODUCTION

1.1 Statement of the Problem

In nucleate boiling from a heated surface, vapor bubbles generated tend to interact

with neighboring bubbles when the superheat is high enough to activate higher nucleation

site density. It is believed that bubble-bubble interaction and coalescence are responsible

mechanisms for achieving high heat transfer rates in heterogeneous nucleate boiling.

Bubble-bubble coalescence creates strong disturbances to the fluid mechanics and heat

transfer of the micro- and macro-layer beneath the bubbles. Because of the complicated

nature, the detailed physics and the effects of the bubble-bubble interaction process have

never been completely unveiled.

During the terrestrial pool boiling, the critical heat flux (CHF), which is the upper

heat transfer limit in the nucleate boiling, represents a state of balance. Because the

buoyancy force strength is relatively constant on earth, for heat fluxes lower than the

CHF, this force is more than that required for a complete removal of vapor bubbles

formed on the heater surface. At the CHF, the buoyancy force is exactly equal to the

force required for a total removal of the vapor bubbles. For heat fluxes greater than the

CHF, the buoyancy force is unable to remove all the bubbles, thus resulting in the

accumulation and merging of bubbles on the heater surface, which eventually leads to a

total blanketing of the heater surface by a layer of superheated vapor. Heat transfer

through the vapor film, so-called film boiling, is much less efficient than the nucleate

boiling and produces very high heater surface temperatures.








In many modem heat transfer applications, the length scale of heat source gets

smaller, where traditional boiling theory may not be applicable. How does the length

scale affect the boiling phenomenon? How do we maximize the heat transfer from a

limited heater surface? Those are frequent questions asked by industrial engineers. There

is no way to accurately answer these questions without the knowledge of microscale

boiling phenomenon.

1.2 Research Objectives

This research seeks to perform high-quality experiments to unmask the effects of

bubble coalescence and length scale of heaters on heterogeneous nucleate boiling

mechanisms. Through this research, we would be able to achieve the following:

1. To find the basic physics of bubble coalescence and its effects on fluid

mechanics and heat transfer in the micro- and macro-layers and to develop a simple

mechanistic model for this phenomenon.

2. To obtain a fundamental understanding of the effects of heater length scale on

the boiling mechanism and boiling heat transfer.

We intend to study the detailed physics of bubble formation on small heaters,

bubble coalescence and bubble dynamics, and heat and mass transport during bubble

coalescence. The purpose is to delineate through experiment and analysis the

contributions of the key mechanisms to total heat transfer. This includes micro/macro

layer evaporation on single and merged bubbles attached to a heated wall, and heat

transfer enhancement during coalescence of bubbles on the heater wall. We intend to

provide answers to the following:

How will the bubble coalescence affect the heat transfer from the heater surface?








What mechanisms are at play during bubble coalescence? In other words, how do
the thermodynamic force, surface tension force, and hydrodynamic force that are
associated with the merging process balance one another?

What controls the bubble nucleation, growth, and departure from the heater
surface in nucleate boiling when bubble coalescence is part of the process?

How does the heater surface superheating level affect the bubble coalescence?

How does the heater length scale affect the bubble inception and boiling heat
transfer?

1.3 Significance and Justification

Nucleate boiling has been recognized as one of the most efficient heat transfer

mechanisms. In many engineering applications, nucleate boiling heat transfer is the mode

of choice. Boiling heat transfer has the potential advantage of being able to transfer a

large amount of energy over a relatively narrow temperature range with a small weight to

power ratio. For example, boiling heat transfer has been widely used in microelectronics

cooling.

Apart from the engineering importance, there are science issues. Currently, the

mystery of critical heat flux remains unsolved. As a matter of fact controversies over the

basic transport mechanisms of bubble coalescence and its effects on the role of

microlayer and macrolayer, liquid resupply and heater surface property continue to

puzzle the heat transfer community. With the micro-array heaters, high speed data

acquisition system and high speed digital camera, we would have a better chance to

unlock the secrets of nucleate boiling. Boiling is also an extremely complex and elusive

process. Although a very large number of investigators have worked on boiling heat

transfer during the last half century, unfortunately, for a variety of reasons, far fewer

efforts have focused on the physics of boiling process. Most of the reported work has

been tailored to meeting the needs of engineering applications and as a result has led to






4


correlations involving several adjustable parameters. The correlations provide a quick

input to design, performance and safety issues; hence they are attractive on a short-term

basis. However, the usefulness of the correlations diminishes very rapidly as parameters

of interest start to lie outside the range for which the correlations were developed.













CHAPTER 2
LITERATURE REVIEW AND BACKGROUND

2.1 Bubble Dynamics and Nucleate Boiling

Boiling is an effective heat transfer mode because a large amount of heat can be

removed from a surface with a relatively small temperature difference between the

surface and the bulk liquid. Boiling bubbles have been successfully applied in ink-jet

printers and microbubble-powered acuators. The technologies still in the research and

development stage for possible applications include TIJ printers, optical cross-connect

(OXC) switch, micropumping in micro channels, fluid mixers for chemical analysis, fuel

mixers in combustion, prime movers in micro stem engines, and the heat pumps for

cooling of semiconductor chips in electronic devices. The boiling curve first predicted by

Nukiyama (1934) has been used to describe the different regimes of saturated pool

boiling. But until now, there are no theories or literature that exactly explains the

underlying heat transfer mechanisms. Forster and Grief (1959) assumed that bubbles act

as micropumping devices removing hot fluid from the wall, replacing it with cold liquid

from the bulk. The proposed equation for calculating the boiling heat transfer is


i=P T ---T,)f (2.1)

Mikic and Rohsenow (1969) developed a model whereby the departing bubble

scavenges away the superheated layer, initiating transient conduction into the liquid.

They also proposed the heat flux calculation by the expression








S.\1/2
= 4kplcp, [TwTf2 (2.2)


Mei et al. (1994) investigated the bubble formation and growth by considering

simultaneous energy transfer among the vapor bubbles, liquid microlayer, and the heater.

They presented the sketch for a growing bubble, microlayer and heating solid which is

shown in figure 2.1(a), where the bubble dome has the shape of a sphere of radius of

Rb(t), the microlayer has a wedge shape with a radius Rb(t), wedge angle 0 centered at r

=0.

They found that four dimensionless parameters governing the bubble growth rate

are Jacob number, Fourier number, thermal conductivity and diffusivity ratios of liquid

and solid. And the Jacob number is the most important one affecting c and cl, two

empirically determined constants that depict the bubble shape and microlayer wedge

angle. Using this model, they examined the effects of varying Ja, Fo, k, ac separately.

The results are shown in figure 2.1(b), and they claim that the effects of Ja, Fo, k, 04 on

the normalized growth rate Rb(t) are the following: (1) increasing Ja and ai will result in

an increasing Rb(t), and (2) increasing Fo and k will result in a decreasing Rb(t).

Recently, Robinson and Judd (2001) developed a theory to manifest the

complicated thermal and hydrodynamic interactions among the vapor, liquid and solid for

a single isolated bubble growing on a heated plane surface from inception. They use the

model shown in figure 2.2(a) to investigate the growth characteristics of a single isolated

hemispherical bubble growing on a plane heated surface with a negligible effect of an

evaporating microlayer. They demarcate the bubble growth into four regions, surface

tension controlled growth (ST), transition domain (T), inertial controlled growth (IC), and






















W ).


3~Q

a ct~


S" "i&a boo
WUPPW todr
W" ~or bdM i-aimaw


S()
(a) (b


1.2 1|- 1.B | ..- I

1.0 -0.01 -0.0 -
1-, 0.01
0.-a
0, 0.001-
S0.6 0.001-
0.6 0.0005
0.4
0.4

0.2 0.106 0.2

I I I 1.0 :. I I
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.6 02 0.4 0.6 04 1.0 1.2
T
(0) (4)

Parmetric depmndec of the nomnalized growth rate R(t). (a) Ja 1, 10,100 ad 1000 at (Fo. K.
a) -(, 000., 0.005); (b) Fo 0.01, 1, 10. 100, 1000 and 10000 at (Ja. a) (0. 0.005. 0.005); (c)
S- 0.0005. 0.001.0.01, 0.05 at (1a, PO. 2) (10. 1. 0.005) and (d) a 0.0005.0.001.0.01 and 005 at (A.,.
oa,. C)- (10, 1. 0.005).


(b)


Figure 2.1 The numerical model and results given by Mei et al. (1995). (a) The numerical
model; (b) The numerical results.





8


Z Liquid, P., T.





/Vapour "" (re. A)

\ lu Heatd Su&Nfe
rv






(a)


200 0.10
140 2.I 0.05
Plan "td Surfiooo




180 (a

S60 -0.05
400 / 1 100
180 .20 P \ /


0
-10 3.__ 2a |


-20 T T C t
640 0


0.000001 0.0001 0.01 1 100
Time (mIs)
(b)
Figure 2.2 The numerical model and four growth domains by Robinson and Judd (2001).
(a) The numerical model-Hemispherical bubble growing on a plane heated surface; (b)
The four growth domains with contiuent pressures at each domain.








heat transfer controlled growth (HT), which are shown in figure 2.2(b). During the

surface-controlled domain, they claim that energy is continuously transferred into the

bubble by conduction through liquid. But the average heat flux, thus the growth rate

dRb/dt, is so small that the contribution of the hydrodynamic pressure in balancing the

equation of motion is insignificant so that it essentially reduces to a static force balance,

Pv P. = 2o/Rb, as shown in figure 2.2(b). The bubble growth in this domain is

accelerated due to a positive feedback effect in which the increase in the radius, Rb, is

related to a decreasing interfacial liquid temperature. This corresponds to an increase in

q", through the increase in the magnitude of the local temperature gradient, which feeds

back by a proportional increase in the bubble growth rate aRb/t. In the earliest stage of

the surface tension domain, this feedback is not significant. However, in the latter stage,

it becomes appreciable as indicated by a noticeable increase in Rb away from Rb, a

significant decrease in both Tv and Pv and a sharp increase in q". At the transition

domain, the hydrodynamic force Phd rises sharply due to the significant liquid motion

outside of the bubble interface. Though q" and aRdat increase at the beginning of this

stage, they are shown to decrease in the latter stage and reach the maximum value. One of

the reasons for this decrease in spite of a positive feedback of surface-controlled growth

can be additional resistance associated with forcing the bulk liquid out radially. The other

reasons can be due to the conduction and advection occurring in the liquid adjacent to the

interface. Each of these heat transfer mechanisms acts in such a way as to diminish the

temperature gradients in the immediate vicinity of the vapor-liquid interface and thus has

a detrimental influence on the rate at which q" and aRblat increase. The inertial controlled

growth refers to the interval of bubble growth in which the rate of bubble expansion is

considered to be limited by the rate at which the growing interface can push back the








surrounding liquid (Carey, 1992). In this domain, the average heat flux into the bubble is

very high, so heat transfer to the interface is not the limiting mechanism of the growth.

The pressure difference, Pv P.o, is now balanced by the hydrodynamic pressure at the

interface. The hydrodynamic pressure comprises two "inertial" terms, i.e., the

acceleration term, plRb(d2Rb/dt2), and the velocity term, 3/2p1(dRb/dt)2. The two terms are

of differing signs and thus tend to have an opposite influence on the total liquid pressure,

and thus the force of the liquid on the bubble interface. This inertial controlled growth

domain is characterized by a decreasing average heat flux and a decelerating interface.

This signifies that the positive influence that the decreasing vapor temperature tends to

have on the local temperature gradient is not sufficient to compensate for the rate at

which advection and conduction serve to decrease the temperature gradient at the

interface. The heat transfer controlled growth domain refers to the interval of bubble

expansion and is considered to be limited by the rate at which liquid is evaporated into

the bubble, which is dictated by the rate of heat transfer by conduction through the liquid

(Carey, 1992). In this latter stage of bubble growth, the interface velocity has slowed

enough so that the hydrodynamic pressure, Phd, becomes insignificant compared with the

surface tension term, 2a/Rb, in balancing the pressure difference, P, Po.. This is shown

in figure 2.2(b). Because the liquid temperature at the interface is now constant, the

positive feedback effect, responsible for the rapid acceleration of the vapor-liquid

interface in the surface tension controlled region, does not occur in this domain of

growth. Conversely, the "shrinking" and "stretching" of the thermal layer in the liquid

due to conduction and advection are responsible for the continuous deceleration of the

interface due to the diminishing interfacial temperature gradients.








The steady cyclic growth and release of vapor bubbles at an active nucleation site

are termed an ebullition cycle. This bubble growth process begins immediately after the

departure of a bubble. Bulk fluid replaces the vapor bubble initially. A period of time,

called waiting period, then elapses during which transient conduction into the liquid

occurs but no bubble growth takes place. After this, the bubble begins to grow as the

thermal energy needed to vaporize the liquid at the interface arrives. This energy comes

from the liquid region adjacent to the bubble that is superheated during the waiting period

and from the heated surface. As the bubble emerges from the site, the liquid adjacent to

the interface is highly superheated and the transfer of heat is not a limiting factor.

However, the resulting rapid growth of the bubble is resisted by the inertia of the liquid

and, therefore, the bubble growth is considered to be inertia controlled. During the

inertia-controlled growth, the bubble generally grows radially in a hemispherical shape.

A thin microlayer (evaporation microlayer) is formed between the lower portion of the

bubble interface at the heated wall. Heat is said to transfer across the thin film from the

wall to the interface by directly vaporizing liquid at the interface. The liquid region

adjacent to the bubble interface (relaxation microlayer) is gradually depleted of its

superheat as the bubble grows. Therefore, as growth continues, the heat transfer to the

interface may become the limiting factor and the bubble is said to be heat transfer

controlled. It is easy to see that vapor bubbles grow in two distinct stages. Fast growth

emerges initially, followed by a slow growth period until detachment.

In general, very rapid, inertia controlled growth is more likely under the following

conditions which typically produce a build-up of high superheat levels during the waiting

period and/or cause rapid volumetric growth (Carey, 1992).

High wall superheat








High imposed heat flux

Highly polished surface having only very small cavities

Very low contact angle (highly wetting liquid)

Low latent heat of vaporization

Low system pressure (resulting in low vapor density)

Heat transfer controlled growth of a bubble is more likely for conditions which

result in slower bubble growth or result in a stronger dependence of bubble growth rate

on heat transfer to the interface. They include:

Low wall superheat

Low imposed heat flux

A rough surface having many large and moderately sized cavities

Moderate contact angle and moderately wetting liquid

High latent heat of vaporization

Moderate to high system pressures

The forces acting on a bubble can be a very complicated issue. It is highly

dependent on the bubble stages during its cyclic process. Among all forces, dominant

force can vary depending on the bubble stages, surface superheat, boiling condition, and

so forth. In general, the following major forces can be involved during boiling: surface

tension, buoyancy force, inertia of induced liquid flow, drag force, internal pressure,

adhesion force from the substrate, etc. In a flow boiling field, due to possible bubble slide

before the bubble lifts off, boiling becomes even more complicated. Klausner et al.

(1993) have studied bubble departure on an upward facing horizontal surface using R-113

as the test fluid. By balancing forces due to surface tension, quasi steady drag, liquid

inertia force due to bubble growth, buoyancy, shear lift force, hydrodynamic pressure and








contact pressure along and normal to the heater surface, they found that the bubble will

slide before lift-off. The predicted bubble diameter at the beginning of sliding motion was

found to agree well with their data. It was noted that liquid inertia force resulting from

the bubble growth played a more important role in holding the bubble adjacent to the

heater surface than the surface tension. However, such a conclusion is highly dependent

on the base diameter that is used in calculating the force due to surface tension. In a

subsequent study, Zeng et al. (1993) correlated both bubble diameter at departure and the

lift off diameter by assuming that the major axis of the bubble became normal to the

surface after the bubble began to slide. By balancing the components of buoyancy, liquid

inertia, and shear lift force in the direction of flow, they were able to predict bubble

diameter at departure. The bubble lift-off diameter was determined by balancing forces

due to buoyancy and liquid inertia associated with bubble growth. For the evaluation of

liquid inertia, the proportionality constant and the exponent in the dependence of bubble

diameter on time were obtained from the experiments. Mei et al. (1999) have included

the surface tension force, liquid inertia, shear lift force and buoyancy to determine the

bubble lift-off diameter. For the model the bubble lift off diameter was shown to decrease

with flow velocity and slightly increase with wall superheat. Maity and Dhir (2001)

experimentally investigated the bubble dynamics of a single bubble formed on a

fabricated micro cavity at different orientations of the heater surface with respect to the

horizontal surface. They found that under flow boiling conditions bubbles always slide

before lift off and the bubble departure diameter depends solely on the flow velocity and

is independent of the inclination of the surface. Bubble departure diameter decreases with

the flow velocity. Bubble lift-off diameter depends on both the flow velocity and the








angular position. Lift-off diameter increases with the angular position but decreases with

the flow velocity.

On the other hand, commercial success of bubble jet printers (Nielsen, 1985) has

inspired many researchers to apply bubble formation mechanisms as the operation

principle in microsystems. For this purpose, the bubble from a microheater should be

designed to present a stable, controllable behavior. Therefore, it is important to

understand the bubble formation mechanisms in microheaters before they may be

optimally designed and operated. Some previous work has been done in investigating

bubble formation mechanism. lida et al. (1994) used a 0.1mm x 0.25mm x 0.25tm film

heater subjected to a rapid heating (maximum 93 x 106 K/s). They measured the

temperature of heaters by measuring the electrical resistance. The temperature measured

at bubble nucleation suggested homogeneous bubble nucleation in their experiment. But

the heater they used does not ensure a uniformly heated surface. Lin et al. (1998) used a

line resistive heater 50 x 2 x 0.53 tm3 to produce microbubbles in Fluorinert fluids. By a

computational model and experimental measurements, they concluded that homogeneous

nucleation occurs on these micro line heaters. They also reported that strong Marangoni

effects prevent thermal bubbles from departing. Avedisian et al. (1999) performed

experiments on a heater (64.5ptm x 64.5tm x 0.2jm) used on the commercial thermal

inkjet printer (TIJ) by applying voltage pulses with short duration. They claimed that

homogeneous nucleation at a surface is the mechanism for bubble formation with an

extremely high heating rate (2.5 x 108 K/s), and this nucleation temperature increases as

the heating rate increases. Zhao et al. (2000) used a thin-film microheater of size of

100m x l lO0m to investigate the vapor explosion phenomenon. They placed the

microheater underside of a layer of water (about 6gm), and the surface temperature of the








heater was rapidly raised electronically well above the boiling point of water. By

measuring the acoustic emission from an expanding volume, the dynamic growth of the

vapor microlayer is reconstructed where a linear expansion velocity up to 17 m/s was

reached. Using the Rayleigh-Plesset equation, an absolute pressure inside the vapor

volume of 7 bars was calculated from the data of the acoustic pressure measurement. In a

heat transfer experiment, Hijikata et al. (1997) investigated the thermal characteristics

using two heaters of 50gm x 50gim and 100m x lO100m, respectively. They found that

70-80% of heat generated was released through a phase change process and heat is

initially conducted in the glass substrate, then, it is transferred to the liquid layer above

the heater and finally released through the evaporating process. Most of these works are

based on applying a constant current or voltage so that the heat flux on the heater is

maintained constant.

2.2 Coalescence of Bubbles

The suggested theory about boiling mechanism is that as the temperature of a

heater surface increases from the onset of nucleate boiling, more bubbles are nucleated

and coalesce simultaneously on the heater surface, which makes the heat flux higher and

higher until the critical heat flux point (CHF). It has been considered for a long time that

bubble-bubble coalescence plays an important, if not dominant, role in the high heat flux

nucleate boiling regime and during the CHF condition as well. Because of the

microscopic nature and complicated flow and heat transfer mechanisms, the research on

coalescence has not progressed very fast in both experimental and theoretical fronts.

Coalescence of bubbles on a surface is a highly complicated process that is involved with

a balance among surface tension, viscous force and inertia. The phenomenon is








intrinsically a fast transient event. For the above reasons, the research of coalescence

between bubbles has been rather limited.

Li (1996) claims when two small bubbles approach each other, a dimpled thin

liquid film is formed between them, as shown in figure 2.3(a). He developed a model for

the dynamics of the thinning film with mobile interfaces, in which the effects of mass

transfer and physical properties upon the drainage and rupture of the dimpled liquid film

are investigated. The model predicts the coalescence time, which is the time required for

the thinning and rupture of the liquid film, given only the radii of the bubbles and the

required physical properties of the liquid and the surface such as surface tension, London-

van der Waals constants, bulk and surface diffusion coefficients. The comparison of the

predicted time of coalescence and experimental results is shown in figure 2.3(b), which

shows that predicted coalescence is less than experimental results, and much less than the

results predicted when the immobile interface is considered. In his research, no heat

transfer is considered to affect the bubble coalescence.

Yang et al. (2000) performed a numerical study to investigate the characteristics

of bubble growth, detachment and coalescence on vertical, horizontal, and inclined

downward-facing surfaces. The FlowLab code, which is based on a lattice-Boltzmann

model of two-phase flows, was employed. Macroscopic properties, such as surface

tension and contact angle, were implemented through the fluid-fluid and fluid-solid

interaction potentials. The model predicted a linear relationship between the macroscopic

properties of surface tension and contact angle, and microscopic parameters.

Hydrodynamic aspects of bubble coalescence are investigated by simulating the growth

and detachment behavior of multiple bubbles generated on horizontal, vertical, and







17



z.


Phase I
(Phase C
Szh; (r'.lt)


h f(r hi't)-t!


h Z',t (rt) =



Phase 2




(a)




immobile interface (0)
pe- s ent study
a e000 experimmntol
/

.400 7
4oo-

m-- -
200 s







o. o- i iii ii .1
(b)
600, s
BOW

.400-



/
2 4oo. ,/.
'-yI
200 -s






oJ ,
OW.

600-

.5400-


*^ w
200 -


0.00 0.02 0.04 0.06
R; (cm)


(b)


Figure 2.3 Research on bubble coalescence by Li (1996). (a) The thin liquid film between

bubbles; (b) Comparison of the predicted results with experimental results.








inclined downward-facing surfaces. For the case of horizontal surface, three distinct

regimes of bubble coalescence were represented in the lattice-Boltzmann simulation:

lateral coalescence of bubbles situated on the surface; vertical coalescence of bubbles

detached in a sequence from a site; and lateral coalescence of bubbles, detached from the

surface. Multiple coalescence was predicted on the vertical surface as the bubble

detached from a lower elevation merges with the bubble forming on a higher site. The

bubble behavior on the inclined downward-facing surface was represented quite similarly

to that in the nucleate boiling regime on a downward facing surface.

Bonjour et al. (2000) performed an experimental study of the coalescence

phenomenon during nucleate pool boiling. Their work deals with the study of the

coalescence phenomenon (merging of two or more bubbles into a single larger one)

during pool boiling on a duraluminium vertical heated wall. Various boiling curves

characterizing boiling (with or without coalescence) from three artificial nucleation sites

with variable distance apart are presented. The heat flux ranges from 100 to 900 w/cm2

and the wall superheat from 5 to 35 K. They pointed out that the coalescence of bubbles

growing on three sites results in higher heat transfer coefficients than single-site boiling,

which is attributed to the supplementary microlayer evaporation shown in figure 2.4(a).

However, the highest heat transfer coefficients are obtained for an optimal distance

between the sites for which coalescence does not occur. They used different inter-site

distances (a = 0.26mm, 0.64mm, 1.05mm, 1.50mm, 1.82mm) to generate bubbles and

stated that for low and high intersite distances, the heat flux deviation is limited by the

seeding phenomenon and the intersite distance, respectively, whereas for moderate

intersite distances, the heat flux deviation is maximum because of the vicinity of the sites

and absence of seeding. They also showed that due to bubble coalescence there is a








noticeable change of the slope of the coiling curve. They claim that such a change is

attributed to coalescence and not to the progressive activation of the sites. They also

showed that the coalescence of two bubbles has a much lower effect on the slope of the

boiling curve, because the supplementary microlayer evaporation with two bubbles is

lower than with three bubbles and consequently has a lower effect on the heat transfer

coefficient. They used the influence area shown in figure 2.4(b) to depict the locations of

the influence areas for various intersite distances. For a = 0.26mm, the influence area is

overlapped for the three bubbles, thus a small overall influence area, which for the heater

of larger area results in a large heat transfer coefficient. They also proposed a map for

activation and coalescence that is shown in figure 2.4(c). In their experiment, it is also

shown that coalescence results in a decrease in the bubble frequency.

Haddad and Cheung (2000) found that the coalescence of bubbles is one of the

phases in a cyclic process during nucleate boiling on a downward-facing hemispherical

surface. Bubble coalescence follows the phase of bubble nucleation and growth but

precedes the large vapor mass ejection phase. A mechanistic model based on the bubble

coalescence in the wall bubble layer was proposed by Kwon and Chang (1999) to predict

the critical heat flux over a wide range of operating conditions for the subcooled and low

quality flow boiling. Comparison between the predictions by their model and the

experimental CHF data shows good agreement over a wide range of parameters. The

model correctly accounts for the effects of flow variables such as pressure, mass flux and

inlet subcooling in addition to geometry parameters. Ohnishi et al. (1999) investigated the

mechanism of secondary bubble creation induced by bubble coalescence in a drop tower

experiment. They also performed a two-dimensional numerical simulation study. They












)O. Q


(a)


\,' '''t6 i'-~~










j y
.1. ( %1
(b)







0
0 OS i i l
.11
t- p m.-..o

(c)


Figure 2.4 The coalescence research performed by Bonjour et al. (2000). (a) The
additional microlayer formed; (b) Schematic representation of influence-area; (c)
Coalescence and activation map.








reported that the simulation results agree well with the experimental data and indicate

that the size ratio and the non-dimensional surface tension play the most important role in

the phenomenon.


2.3 Critical Heat Flux

The boiling curve was first identified by Nukiyama (1934) more than sixty years

ago. Since then the critical heat flux (CHF) has been the focus of boiling heat transfer

research. A plethora of empirical correlations for the CHF are now available in the

literature, although each is applicable to somewhat narrow ranges of experimental

conditions and fluids. Recently a series of review articles (Lienhard 1988a,b, Dhir, 1990,

Katto, 1994, Sadasivan et al., 1995) have been devoted to the discussion of progress

made in the CHF research. The consensus is that a satisfactory overall mechanistic

description for the CHF in terrestrial gravity still remains elusive. The following are some

perspectives on issues in CHF modeling elucidated in a recent authoritative review by

Sadasivan et al. (1995).

1. CHF is the limiting point of nucleate boiling and must be viewed as linked to

high-heat-flux end of nucleate boiling region and not an independent pure hydrodynamic

phenomenon. The experiments dealing with CHF will be meaningful if only

measurements of the high heat-flux nucleate boiling region leading up to CHF are made

together with the CHF measurement. This would help resolve the issue of the role of dry

area formation and the second transition region on CHF. Simultaneous surface

temperature measurements are necessary.

2. Measurements of only averaged surface temperature in space or in time

actually mask the dynamics of the phenomena. An improved mechanistic explanation of

CHF also requires that experimental efforts be directed towards making high resolution








and high-frequency measurements of the heater surface temperature. Experiments

designed to make transient local point measurements of surface temperature (temperature

map) and near surface vapor content will help in developing a clearer picture of the

characteristics of the macrolayer and elucidating the role of liquid supply to the heater

surface. Microsensor technology appears to be one area that shows promise in this

respect.

3. Identifying the heater surface physical characteristics such as active nucleation

site distribution, static versus dynamic contact angles, and advancing versus receding

angles. These would help understand the heater surface rewetting behavior.

Sakashita and Kumada (1993) proposed that the CHF is caused by the dryout of a

liquid layer formed on a heating surface. They also suggested that a liquid macrolayer is

formed due to the coalescence of bubbles for most boiling systems, and that the dryout of

the macrolayer is controlled by the hydrodynamic behavior of coalesced bubbles on the

macrolayer. Based on these considerations, a new CHF model is proposed for saturated

pool boiling at higher pressures. In the model, they suggest that a liquid macrolayer is

formed due to coalescence of the secondary bubbles formed from the primary bubbles.

The detachment of the tertiary bubbles formed from the secondary bubbles determines

the frequency of the liquid macrolayer formation. The CHF occurs when the macrolayer

is dried out before the departure of the tertiary bubbles from the heating surface. One of

the formulations of the model gives the well-known Kutateladze or Zuber correlation for

CHF in saturated pool boiling.

The vast majority of experimental work performed to date utilized the heat flux-

controlled heater surface to generate bubbles. Rule and Kim (1999) were the first to

utilize the micro heaters to obtain a constant temperature surface and produced spatially








and temporally resolved boiling heat transfer results. Bae et al. (1999) used identical

micro heaters as those used by Rule and Kim (1999) to study single bubbles during

nucleate boiling. They performed heat transfer measurement and visualization of bubble

dynamics. In particular, it was found that a large amount of heat transfer was associated

with bubble nucleation, shrinking of dry spot before departure, and merging of bubbles.

In this research, identical micro heaters to those of Rule and Kim (1999) were used to

investigate the boiling microscopic mechanisms through the study of single bubbles

boiling and the coalescence of bubbles. For each experiment, the temperature of the

heaters was kept constant while the time-resolved and space-resolved heat fluxes and

bubble images were recorded.













CHAPTER 3
EXPERIMENT SYSTEM

3.1 Microheaters and Heater Array

3.1.1 Heater Construction

This section describes briefly the heater array construction. The details can be

referred to T. Rule, Design, Construction, and Qualification of a Microscale Heater

Array for Use in Boiling Heat Transfer, Master of Science thesis in mechanical

engineering at the Washington State University, 1997.

The heater array is constructed, as shown in figure 3.1(a), by depositing and

etching away layers of conductive and insulating material on a quartz substrate to form

conductive paths on the surface which will dissipate heat when electrical current is

passed through them. The basic element of the microscale heater array is the serpentine

platinum heater. The heater element, as shown in figure 3.1(b), is constructed by

depositing platinum onto the substrate surface, masking off the heater lines, and etching

platinum away from the unmasked areas. The terminal ends of each platinum heater are

connected to the edge of the chip with aluminum leads deposited on the chip. Substrate

conduction was reduced by using a quartz (k = 1.5 w/mK) substrate instead of a silicon (k

= 135 w/mK) substrate, since silicon is 90 times more thermally conductive than quartz.

A Kapton (k = 0.2 w/mK) would further reduce substrate conduction, but it has not yet

been tested as a substrate material. Quartz is an electrical insulator, so the substrate

cannot be used as an electrical ground, as it was when silicon was used. An aluminum

layer was deposited over the platinum heaters to serve as a common heater ground.








Something must be used to separate the platinum heaters from the aluminum layer. But

still the problem with the ground potential variation exists. The simplest way to eliminate

the problem with ground potential variations is to provide an individual ground lead for

each heater that connects to a ground bus bar. This bus bar must be large enough to

provide less than 100 tV voltage difference between individual heater ground

connections during all operating conditions. The construction steps are as follows:

1. A thin layer of titanium (Ti, 22) is first sputtered onto the quartz to enable the

platinum (Pt, 78) to adhere to surface.

2. A 2000 A layer of platinum is deposited on top of the titanium layer.

3. The platinum and titanium are etched away to leave the serpentine platinum

heaters and the power leads.

4. A layer of aluminum is then deposited and etched away to leave aluminum

overlapping the platinum for the power leads and the wire bonding pads.

5. Finally, a layer of silicon dioxide is deposited over the heater array to provide a

uniform energy surface across the heater. The area where wire-bond connections will

later be made is masked off to maintain a bare aluminum surface.

3.1.2 Heater Specification

The finished heater array measures approximately 2.7 mm square. It has 96

heaters on it, as shown in figure 3.1(c). Each individual heater is about 0.27 mm square.

The lines of the serpentine pattern are 5 jgm wide, with 5 gim spaces in between the lines.

The total length of the platinum lines in one heater is about 6000 pm, and the heater lines

about 2000 A thick. The nominal resistance of each heater's resistance is 750 ohm.








Aluminum Ground Lead


Silicon Dioxide
I


Aluminum Power Lead
Platinum Heater


I Quartz Substrate


U


l7 3l64 63E 1 60 11591158 3
IE 1 I Ji 141 56Ir
l~l 13 !55*I

|f42 J llo[I l 11 !5311

144 45[46 48 49 5o0515 IB

(c)

Figure 3.1 Heaters and heater array. (a) Heater construction; (b) Single serpentine
platinum heater; (c) Heater array with 96 heaters.








3.2 Constant Temperature Control and Data Acquisition System

The system is consisted of feedback electronics circuits, interface print board

connecting heaters array to the feedback electronics circuits, a D/A board used to set the

heater temperature, two A/D boards for data acquisition, and software made from Visual

Basics 6.0 in windows 95.

3.2.1 Feedback Electronics Loop

This experiment makes use of the relationship between platinum electrical

resistance and its temperature. We know that resistance of the platinum almost varies

linearly with its temperature by the following relationship:

(R-R IR=C(T-To) (3.1)

Where R is the electrical resistance at temperature T, Ro is the resistance at a

reference temperature To and C is the constant coefficient. For platinum, the value of C

is 0.002 Q/QC. The key part of the loop is the Wheatstone bridge with a feedback loop

where Rh is the platinum heater. Each heater has a nominal resistance 750Q. For a

temperature change of 1C, the heater's resistance would change by 1.5Q, while R2, R3

and R4 are regular metal film resistors which values are not sensitive to temperature. The

resistance of the digital potentiometer, Rc, can be set by the computer. Each heater has an

electronic loop to regulate and control the power across it. Wheatstone bridge shown in

figure 3.2 is used to carry out the constant temperature control. The bridge is said to be

balanced when V1 = V2. This occurs when the ratio between R4 and Rh is the same as that

between R2 and (Re+R3). The feedback loop maintains the heater at a constant

temperature by detecting imbalance and regulating the current through the bridge in order

to bring it back into balance. The amplifier will increase or decrease the electrical current








to the circuit until the heater reaches the resistance necessary for the bridge to maintain

balance. Therefore, the exact value of Rc corresponds to the temperature of the heater Rh.


Figure 3.2 Wheatstone bridge with feedback loop.


3.2.2 piProcessor Control Board and D/A Board

Each heater on the heater array can be individually controlled. g^Processor control

card programs each of the 96 feedback control circuits with correct control voltage.

Rather than having 96 separate wire connections from the computer control board, a

multiplexing scheme is used, where a single wire carries a train of voltage pulses to all

the boards and an address bus directs the voltage singles to the correct feedback circuit.

D/A board is used to connect the computer for the software to send the addressing

signals. The details can be referred to T. Rule, "Design, Construction, and Qualification

of a Microscale Heater Array for Use in Boiling Heat Transfer", Master of Science thesis

in mechanical engineering at Washing State University.








3.2.3 A/D Data Acquisition Boards

Each of the A/D data acquisition boards used in this experiment has 48 channels.

For 96 heaters, to acquire data simultaneously, we installed two A/D cards. But we just

need one of them because maximum eight heaters were selected for the purpose of this

research. The major parameters of the A/D cards have been shown in Table 3.1.



Table 3.1 The specifications of the D/A cards

# phanl 48 single ended, 24 differential or modified
differential

Resolution 12 bits, 4095 divisions of full scale
Accuracy 0.01% of reading +/-1 bit
Type successive approximation

Speed micro-seconds


3.2.4 Heater Interface Board (Docoder Board)

Heater interface board is used to interface the heater array with the feedback

control system. Since the heaters are independently grounded on the heater array, there

are 192 wires extended from the heater array to the interface board, which are accessed

by the feedback electronics loops.

3.2.5 Software

The software used in this experiment functions as following:

1. Address heaters so that heaters can be selected.

2. Send signals from the computer to the computer control board and D/A card to
set the heaters temperature.

3. Automatic and manual heaters calibration.








4. Data acquisition.

The software is developed in the Microsoft Visual Basic 6.0 environment under

windows 95 running in PC.

3.3 Boiling Condition and Apparatus

3.3.1 Boiling Condition

In this experiment, we choose FC-72 to be the boiling fluid. The reason for

choosing FC-72 is that it is dielectric, which makes it possible for each heater to be

individually controlled. The bulk fluid is at the room condition (1 atm, 25C), where its

saturation temperature is 56C, thus it is subcooled pool boiling.

3.3.2 Boiling Apparatus

Initially the boiling experiments were performed in an aluminum chamber. To

improve the visualization results, a transparent boiling chamber was built. Another

advantage of the new chamber is its flat glass walls that effectively prevent the image

distortion taken by the fast speed camera described in section 3.4.2. Figure 3.3 shows the

boiling experimental setup. In addition to heater array and electronics feedback system,

the computer is used to select the heaters and set their temperature through D/A card and

acquire data through A/D cards.

3.4 Experiment Procedure

3.4.1 Heater Calibration

3.4.1.1 Calibration apparatus

The calibration apparatus includes the constant temperature oil tank with oil-

circulating pump and temperature control system, as shown in figure 3.4. The constant oil

tank functions to impinge the constant oil into the heater array surface. The temperature

























on I-
Dfl--- Decodei



Digital camera
for bottom view


Figure 3.3 Boiling apparatus.

control system is used to keep the circulating oil at a constant temperature. Calibration is

the beginning of the experiment, and it is also a very important step since the following

boiling experiment will be based on the calibration data. Therefore, much more care

should be exercised to ensure the accuracy.

3.4.1.2 Calibration procedure

The calibration procedure is as follows:

1. Set the temperature controller at a certain temperature.

2. Circulating the fluids in the calibration tank. Power the heating components.
After this, several minutes or more are needed to maintain the temperature of the
circulating fluid at the stable temperature.

3. Start the calibration routine in PC and calibrate. The computer automatically
saves the calibration result.




















Lubricate Oil


Insulation


(b)

Figure 3.4 Schematic of calibration apparatus and temperature control loop. (a) The
calibration system; (b) The electrical loop to maintain the temperature of calibration oil.


4. Set the heater array at another temperature. Follow the first and second steps till
all calibration is completed.

5. Two calibration methods are included, automatic method and manual method.

Automatic method is for regular calibration use. We can select heaters to

calibrate, though, normally we calibrate all 96 heaters at one time. To find the

corresponding control voltage for the set temperature, progressive increment method was

used. Increment the control voltage gradually, and compare the voltage output across the









heater with last time value. If the voltage across the heater is different from the last time

value, we can say, the controlling system starts to regulate the circuit. Then the control

voltage is the corresponding value for the set temperature. It is worth mentioning that

how to set the difference to compare the voltage is important. Initially, the difference was

set as 0.01. The result proves the control voltage is a little bit higher than the actual value.

If the difference is set as 0.003, then the result is good. How to prove the result is the

correct value for the set temperature, manual calibration method is used to check it out.

Manual method is an alternative to the regular automatic method. It is designed to

check the accuracy of the automatic method. By referring to the figure 3.5(a), we can see

by increasing the control voltage, the heater's voltage starts to increase at about 91 axial

value. Below 91, the heater's temperature is at the set temperature; the voltage across the

heater is very small and at a relatively constant level. Starting at 91, increasing the

control voltage will increase the heater's voltage so that heater's temperature increases

accordingly. The starting value of 91 is the control voltage corresponding to the set

temperature. This method is much more viewable than automatic method. Its

disadvantage is slow, only one heater can be done at one time. But we can rely on its

result to verify the accuracy of automatic method.

3.4.1.3 Calibration results

Based on the relations between the heater resistance and temperature indicated in

Eq. (3.1). For each heater, its resistance almost linearly changes with temperature. Thus,

ideally, the resistance-temperature figure is an approximately straight line. The slope of

the line is determined by the material property. Thus the lines representing the resistance-

temperature relations have almost the same slope. On the other hand, the temperature

change also depends on heater's initial resistance values. This regard is shown on figure











3.5(b) for calibration results of heaters #1 through #9, where the slope of the lines for


different heaters.


s
2.5

I2

| 1.5
&


-- -- Voltage acquired from the heater vs. DQ values


DQ value (digital pot)


500

450

400

8.350

S300

* 250

200

o 150

100

50


Calibration results for heaters (1-9)
from50Cto 120C











#4
/- #5

#7
S- #8
----- #9


50 60 70 80 90 100 110
Impinging liquid temperature (C)


120


Figure 3.5 Part of the calibration results. (a) Result of the manual calibration method;
(b) The calibration results (only heaters #1 through #9 were shown).









The calibration results obtained for each heater will be used in boiling experiment

to set heater temperatures. For the present research, the heaters will be always set at the

same temperature in any experiment performed, thus nominally, there will not be any

temperature gradient among heaters.

3.4.1.4 Comparison of calibrated resistances with the calculated resistances

To validate the calibration results, i.e. the temperature of the heaters obtained by

calibration, we have measured the resistances of each heater at different temperatures and

then compare them with the resistances from calculation using the platinum property

relation given by Eq. (3.1), the result is shown in figure 3.6. From the above comparison,

we conclude that measured resistances match well with calculated resistance. It implies:

(1) The heater temperature is reliable.

(2) We can use calculated resistance to evaluate heat dissipation with only a small
uncertainty introduced.




1030

1000 U Calculated R
0 Measured R
S970

S940

S910

880

850
50 55 60 65 70 75 80 85 90 95 100 105 110 115 120
Temperature *C


Figure 3.6 Comparison of calibrated resistances of heater #1 with the calculated
resistances from property relation.








3.4.2 Data Acquisition and Visualization

To investigate the bubble coalescence, we need to generate bubbles with

appropriate separation distances. Since each of the 96 heaters on the heater array is

individually controlled by the electronic feedback control system, we can set active one

or more of the heaters by powering them individually so that they reach a certain

temperature while leaving all other heaters unheated. To obtain different cases of bubble

coalescence, all we need to do is to select heaters. In reference to figure 3.1, by powering

two heaters such as heaters #1 and #11, we obtain dual bubble coalescence. Also, if we

choose #1 and #3, we obtain dual bubble coalescence with a shorter separation distance.

However, by powering two heaters that are too far apart such as #1 and #25, two single

bubbles will be generated, but the bubble departure sizes are not large enough for them to

touch and merge before they depart. Therefore, for coalescence to take place, the active

heaters have to be close enough within a certain range. The power consumed by the

heater was acquired by the computer data acquisition system (figure 3.3). Data were

acquired at a sampling rate of 40,000 Hz for each channel of the A/D system, after

allowing the heater to remain at a set temperature for 15 minutes. The data were found to

be repeatable under these conditions. The acquired data were converted to heat flux from

the heater according to the following basic relationship:

q" = (V2 /R) I/A (3.2)

For each heater configuration, the heaters were always set at the same temperature

for the bubble coalescence experiment, and this temperature is varied to investigate the

effect of heater superheat on the bubble coalescence. For all cases, the dissipation from

heaters was acquired in sequence. Because steady state has been reached in all these








experiments, sequential data acquisition does not affect the data accuracy. The bubble

visualization includes both bottom and side views; though bottom views are more

suitable for multiple bubble coalescence. The semi-transparent nature of the heater

substrate made it possible to take images from below the heater. The setup of experiment

has been shown in figure 3.3. A high-speed digital camera (MotionScope PCI 8000S) was

used to take images at 2000 fps with a resolution of 240 x 210, with maximum 8 seconds

of recording time. The bubble visualization was performed using the shadowgraph

technique. In this technique, the bubbles were illuminated from one side while the images

were taken from the other side.

3.5 Heat Transfer Analysis and Data Reduction

3.5.1 Qualitative Heat Transfer Analysis

Each heater has a dimension of 0.27mm x 0.27mm. For such a small heater, the

heat transfer behavior is hardly similar to that for large heaters. Specifically, the edge

effects greatly affect the heat transfer. Since the heaters used in our experiment are

always kept at a constant temperature, the data reduction turns out to be much simpler.

Qualitatively, the heat dissipated from the heater at a certain temperature, by reference to

figure 3.7(a), is composed of the following components:

1. Boiling heat transfer from the heater in boiling experiment, when the heater is
superheated high enough.

2. Conduction to the substrate on which the heater is fabricated. This is due to the
temperature gradient between the heater and the ambient through the substrate.

3. Radiation heat transfer due to the temperature difference between the heater
and ambient.

4. Natural convection between the heater and air and FC-72 vapor mixture when
the heater array is positioned vertically to be separated from the liquid for data reduction








experiment. This natural convection is replaced by the boiling heat transfer from the
heater when the boiling occurs on the heater surface.

3.5.2 Data Reduction Procedure

To obtain the heat transfer rates due to boiling only, we conduct the experiments

by the following procedure:

1. Measure the total heat flux supplied to the heater during the boiling process at

different heater temperatures.

The total heat flux with boiling:

q"rawl = q"top + q"condl + q"radl. (3.3)

2. Tilt the boiling chamber 90, so that the heater is exposed to the air and FC-72

vapor, while separated from FC-72 liquid, and measure the total heat flux without boiling

at corresponding temperatures.

Therefore, the total heat flux without boiling:

q'raw2 = q"natural + q"cond2 + q"rad2 (3.4)

The q"condl in Eq.(3.3) and q"cond2 in Eq.(3.4) are the conduction to the substrate

and ambient through the substrate. Because the heater is held at a constant temperature,

they are independent of the state of fluid above the heater, thus we assume q"condji=q"cond2.

The same reasoning also goes with radiation. Thus, from Eq.(3.3) and Eq.(3.4) the heat

dissipated above the heater during boiling can be derived as the following:

q"top = q"rawl q"raw2 + q"natural (3.5)

where q"naturai is the contribution from natural convection with the mixture of air and FC-

72 vapor. To get a good estimate of the natural convection component in Eq.(3.5), we

need to pay special attention to the small size of the heater we used. The details for this

estimation are given in the following.











Bulk liquid


Ambient room
(a)


q a


SMixture of air
and vapor
^^^^^Bk ^(flnaftur

Ambient room 'aui



q'&nd2 4.
q'rd2

(b)


Figure 3.7 The schematic showing the heat dissipation from a heater. (a) The heat transfer
paths from the microheater during boiling experiment; (b) The heat transfer paths from
the heater during data reduction experiment.








3.5.3 Determination of Natural Convection on the Microheaters

We have done a significant amount of literature research in order to rationally

determine the natural convection on the heaters we were using. We first use the empirical

correlations to evaluate the heat dissipated from the heater, in which we use the results of

Ostrach (1953) to calculate this natural convection. Then the calculated heat dissipation is

used to compare with experimental results.

Conduction. We assume one dimensional conduction from the heater to the

ambient through the quartz substrate. The ambient has a constant temperature of 25C0(2.

Conductivity of the quartz substrate is ksub = 1.5 w/mK. For different heater temperatures

To, using Fourier law of conduction, we calculate the conduction heat flux. For

simplicity, we neglected the epoxy thickness that is used to seal the heater at the bottom.

Since we calculate the conduction based on quartz substrate only, neglecting the heat

transfer resistance of epoxy, the calculated conduction heat transfer should be larger than

that if the epoxy layer is accounted for.

Convection. When the liquid was separated from the heater, there is natural

convection heat transfer to the mixture of air and vapor from the heater. For this

calculation, the mixture of FC-72 vapor and air is approximated as ideal gas of air.

Radiation. With the approximation of black body, the radiation heat flux is

calculated as follows:

q"= ( T,4- To4) (3.6)

where cr is the Stefan-Boltzmann constant.

The calculation results for the above heat transfer modes have been shown in

figure (3.8). From this figure, obviously, the sum of convection, conduction and
























~60



---- Experimental heat flux from a heater
-0- Calculated heat flux from a heater
0 1 ., I [ | I .
60 90 120 150
Heat temperature (C)
Figure 3.8 Heat flux comparison from experimental and calculation results.


radiation is far less than the total heat flux q"raw2, when the heater is separated from the

liquid. This is sufficient to prove that since the heater size is much smaller than the

regular heater size, classical horizontal isothermal correlation is not applicable for this

heater. We need to find another approach to evaluate the natural convection occurring

from the heater for the data reduction.

Baker (1972) has investigated the size effects of heat source on natural

convection. He argued that as the heat source area decreases, the ratio of source perimeter

to surface area increases and since substrate conduction is proportional to the source

perimeter, the portion of the heat transferred by conduction into the substrate increases as

the surface area decreases. In our experiment, since the heater is kept at the same constant

temperature both in boiling and no-boiling conditions, the conduction to the substrate








should be the same regardless of the condition on the surface of the heater. However, this

small size effect does affect the natural convection calculation in our data reduction.

Baker (1972) used the experimental setup similar to that used in this research to study

the forced and natural convection of small size heat source of 2.00 cm2, 0.104 cm2

and 0.0106 cm2, respectively, smallest of which is over 10 times larger than the heater

used in this experiment. Therefore, we can not use Baker's data in our experiment. Also

according to Park and Bergles (1987) and, Kuhn and Oosthuizen (1988), due to the small

size, the edge effects are important. The approach to determining q"natur in this study for

a heater with height L and width W is that we first used the results of Ostrach (1953) for

two-dimensional laminar boundary layer over a vertical flat plate with a height of L. Then

the two-dimensional Nusselt number is corrected for the transverse width of W by the

correlation developed by Park and Bergles (1988). The following provides the details of

the procedure. The Grashof number, GrtL, at the trailing edge of a vertical plate with

height L is defined as

Gr gf(-T)L3
V 2 (3.7)


where fP is the coefficient of thermal expansion, Ts is the heater temperature, T, is

the ambient fluid temperature, L is the heater length, and v is the kinematic viscosity of

the fluid.

Based on Ostrach (1953), the local Nusselt number at the distance L from the

leading edge of the heater surface is given by:


NuL = Y g(Pr) (3.8)








where g(Pr) is a function of the Prandtl number, Pr, of the fluid and is given by

LeVevre (1956) as below:


g(Pr) -= 0.75Pr (3.9)
(0.609 +1.221Pr + 1.238Pr)Y

The average Nusselt number NuL of the heater surface with a height of L can be
obtained by:

4
NuL =-4NuL (3.10)
3

This two-dimension Nusselt number needs to be corrected to take into account the

finite width effects. This correction is based on the relation given by Kuan and

Oosthuizen (1988), which is repeated here:

0,4752
NuL =NuLx1+ 362.5 (3.11)
NuLxdge NL JQ0-73
lRaw j

In the above, Raw is the Rayleigh number based on the width W of the heater and

Raw is equal to Grw x Pr. This corrected Nusselt number NuL.,edge has been used to

evaluate the natural convection heat transfer from the microheaters.

The derived natural convection heat fluxes for different heater configurations are

given in figure 3.9 and they were used in equation (3.3) to find the boiling heat transfer

flux, q"top. The order of magnitude of the derived natural convection heat fluxes using the

above approach has been found to be consistent with the results given by Kuan and

Oosthuizen (1988), where they investigated numerically the natural convection heat

transfer of a small heat source on a vertical adiabatic surface positioned in an enclosure

which is very similar to our experimental condition.










Natural convection heat flux derived for
10 heaters in this experiment

9 -A-- Single heater, L=0.027cm
-V-- Two heaters, L=0.038cm
8 ---- Three heaters, L=0.047cm .
-0-- Four heaters, L=0.054cm
S 7 -u---- Five heaters, L=0.061 cm
E










^O50 60 70 80 g0 100 110 120 130 140 150 160
Heater temperature (AT)


Figure 3.9 Derived natural convection heat fluxes for different heater configurations.


3.5.4 Uncertainty Analysis

Uncertainty analysis is the analysis of data obtained in experiment to determine

the errors, precision and general validity of experimental measurements.

For single sampled experiments, the methods introduced by Kline and

McClintock (1953) have been popularly used to determine the uncertainty. The theory of

the method is introduced in the following.

Assume R is a given function of the independent variables xs, x2, x3, ... x,, that is,

R = R(xl, x2, X3,.... Xn). Let wR be the uncertainty in the result of R, and wi, w2,4w3, ... wn,

be the uncertainties in the independent variables. If the uncertainties in the independent

variables are all given with the same odds, then the uncertainty in the result with these

odds is given as:
6
X

.4
3-
2


40 50 60 70 80 90 100 110 120 130 140 150 160
Heater temperature (AT)


Figure 3.9 Derived natural convection heat fluxes for different heater configurations.


3.5.4 Uncertainty Analysis

Uncertainty analysis is the analysis of data obtained in experiment to determine

the errors, precision and general validity of experimental measurements.

For single sampled experiments, the methods introduced by Kline and

McClintock (1953) have been popularly used to determine the uncertainty. The theory of

the method is introduced in the following.

Assume R is a given function of the independent variables x1, x2, X3, ... x,,, that is,

R = R(xj, x2, x3, ... x.). Let WR be the uncertainty in the result of R, and w1, W2, W3, ---..

be the uncertainties in the independent variables. If the uncertainties in the independent

variables are all given with the same odds, then the uncertainty in the result with these

odds is given as:









2 W) \(R 2 /1+ W)+.+ RW )2]1/2
[(aRY (QR Yf/ liY fa/ 1"
=WR -[ 2 a3 +n (3.12)
w axR+ -2 w -wax.

Because of the square propagation of the separate uncertainties, it is the larger

ones that predominate the final uncertainty. Thus any improvement in the overall

experimental result must be achieved by improving the instrumentation or technique

connected with these relatively large uncertainties. It should be noted that it is equally as

unfortunate to overestimate uncertainty as to underestimate it. An underestimate gives

false security, while an overestimate may make one discard important results, miss a real

effect or buy too much expensive instruments. The purpose of this exercise is to analyze

the possible sources of uncertainties and give a reasonable estimate of each uncertainty,

and finally obtain the overall uncertainty.

In each experiment, the heaters are always set at the same temperature, and this

temperature was increased to investigate how the boiling heat transfer changes with

heater temperature. The boiling data are always associated with the pre-set temperature.

Therefore, the uncertainties will include uncertainty for heater temperature and

uncertainty for boiling heat transfer.

The uncertainty sources come from calibration, boiling and data reduction

experiments. They have been summarized in the following.

The uncertainty sources from calibration. The uncertainty sources from

calibration basically include the oil fluctuation in the calibration chamber, heat loss due

to oil impinging on the heaters, discrete increment of control resistance and slew rate of

the opamp which is used to balance the wheat-stone bridge. Each uncertainty for these

has been estimated and given in table 3.2.








Table 3.2 The uncertainty sources from calibration


The uncertainty sources from boiling experiment. To have a better idea of

uncertainty sources from boiling experiment, figure 3.10 needs to be referred. They

include:

(1) Wiring resistance from heater to feedback system and from feedback system

to A/D card. Estimated total wiring resistance is about 50 ohm. Since heater's nominal

resistance is 1000 ohm. Thus uncertainty introduced is 5%.

(2) A/D card resolution, 2.44mV: 12 bits 4095 divisions of full scale (10V). For

present experiments, the average voltage is about 10V. Thus the uncertainty is

2.44mV/10V, which is less than 0.03%.

(3) Voltage division device. Mainly comes from the deviation of two division

resistors. They are metal film resistors (1% accuracy). Thus, the voltage division

uncertainty can be 101%/99% = 1.02%.

Summary of uncertainty sources in this experiment. The uncertainty sources

analyzed above can be divided into uncertainty sources for heater temperature and for

heat flux. They are summarized as follows.

(1) Uncertainty sources for temperature

Oil temperature fluctuation in calibration, eTI = +0.5C.


Sources of uncertainty Estimated uncertainty value
Oil temperature fluctuation eT, = +0.5C
Heat loss due to oil impinge en = +0.050C

Discrete increment of control resistance en = +0.1 C
Slew rate of Opamp Negligible











+24V


Qll
2N2222


OAuF


From
feedback
card


Output to
DQ- RI
CLK_ > .LOOK
4J



Figure 3.10 The circuit schematic for temperature control and voltage division.



Discrete increment of control resistance, EC2 = +0.05C.


Drift of Voff of the opamp, ET3 = +0.1 C.


Temperature fluctuation during boiling, especially during the vapor-liquid


exchange process, ET4 = +0.05C.


(2) Uncertainty sources for boiling heat transfer


Wiring resistance, Evi = 5%.


Resolution of A/D card, Ev2 =0.03%.


Voltage division device, Ev3 = 1.02%.


Natural convection, eHl = 15%.








Determination of overall temperature uncertainty. Since the individual

uncertainties given above are absolute values relative to one variable (temperature), the

overall temperature uncertainty can be obtained by simply summing up each of them, that

is: ET = ETI + ET2+ eT3 + eT4 = 0.5C + 0.1 C + 0.05 C + 0.05C = 0.7C.

Determination of overall heat transfer uncertainty. From the uncertainty

sources for boiling heat transfer analyzed above, the first three parts come from the

voltage measurements. Since they come from the single variable, the total uncertainty for

voltage can be obtained:

ev = evi + ev2 + ev3 = 5% + 0.03% + 1.02% = 6.05%

Now we are ready to calculate the overall uncertainty for boiling heat transfer.

V2 V2
rawl raw2 (1
qtop ~ p natural (3.13)
RA RA


From Eq. (3.7), the total boiling heat transfer is a function of voltages and natural

convection, neglecting the uncertainties contributed by R (resistance of heaters) and A

(area of the heaters).

From the uncertainty theory, the overall uncertainty can be written as
w-. _q w +( 9q'wv +( f ---w
11 .' = a- # W '. ) + W\- -- W ) I + --(- W ) ]
q #V I av V vq

that is,
7 V (2 1/'2



In this equation,
w, =e,xVr,w, =e,xV2 ,w. =e xq'








In this experiment, the temperatures of the heaters are set in a temperature range,

thus R is changing. To calculate uncertainty, we let R = 1000 ohm. Also the areas of the

heaters are given as A = 0.000731cm2. The averaged values for voltages during boiling

and data reduction are given at Vrawi = O10V, V,,2 = 4V. With these data, we can

calculate the overall uncertainty at different temperatures. As an example, at 100C single

bubble boiling: q, ,I = 40w/cm2.


The overall uncertainty can be obtained as wq. = 9.2w/cm2.

Also, at 100C, the boiling heat transfer can be read from the boiling curve:

q'= 65w/cm2.

Thus, the percent uncertainty for boiling heat transfer at 100C can be obtained

readily as:

Wov,, = 9.2/65 = 13.8%.

For other temperatures, the uncertainty can be calculated following the same

procedure. For the single bubble boiling, the boiling heat transfer uncertainties at

different temperatures have been calculated and shown in the figure 3.11 (a).

For dual bubble coalescence, we also calculated the overall uncertainty levels for

boiling heat transfer for temperatures from 100C to 140C, which are shown in the

figure 3.11(b) with the overall uncertainty values for single bubble boiling shown as well

for comparison.

As we have observed that in the dual-bubble coalescence boiling case, the overall

uncertainty is smaller than that for the single bubble boiling at corresponding

temperatures. The reason for this can come from two factors: (1) due to bubble




























100 105 110 115 120 125 130 135 140 145 150 155 160 165 170


(a)




17%

16%. *% Uncertainty for single bubble
S% Uncertainty for dual-bubble #1 with #11.
15%-

14%

13%

12%

11%1

10% 1 "
100 105 110 115 120 125 130 135 140 145 150 155 160 165 170

(b)



Figure 3.11 The uncertainty at different temperatures. (a) The uncertainty for single
bubble boiling at different temperatures; (b) The uncertainty for dual-bubble coalescence
together with single bubble boiling.








coalescence, the overall boiling heat transfer has been increased. (2) due to heater

interaction, the natural convection is smaller for the single heater case.

In summary, for temperatures, the oil temperature fluctuation during calibration

contributes to the main uncertainty, though opamp offset also has some contributions.

Natural convection is the main contributor to the boiling heat transfer uncertainty. The

overall uncertainty for heater temperature is estimated about 0.7C, and the overall

uncertainty of boiling heat flux is about 15% between 100C ~ 170C, and this

uncertainty is temperature dependent. The uncertainty of dual bubble boiling is smaller

than that of the single bubble boiling due to coalescence-enhanced heat transfer.













CHAPTER 4
SINGLE BUBBLE BOILING EXPERIMENT

4.1 Introduction

Applications of microtechnology must utilize components or systems with

microscale fluid flow, heat and mass transfer. As the size of individual component

shrinks and the length scale decreases drastically, the transport mechanisms involved go

beyond those covered by the traditional theories and understanding. The development of

the new theories and the fostering of up-to-date physical understanding have fallen

behind the progress of micro machining and manufacturing. Extensive survey papers

(Duncan and Peterson, 1994, Ho and Tai, 1998) of microscale single-phase heat transfer

and fluid mechanics noted that an investigation of the flow characteristics of small

channels has shown significant departure from the thermo-fluid correlations used for

conventional macroscale flows. For example, for turbulent flow of gases in microtubes

(with diameters of 3 mm to 81 mm), neither the Colbumrn analogy nor the Petukhov

analogy between momentum and energy transport (Duncan and Peterson, 1994) is

supported by the data. More recently Gad-el-Hak (1999) gave a complete review on the

fluid mechanics of microdevices. He concluded that the technology is progressing at a

rate that far exceeds our understanding of the transport physics in micro-devices.

Therefore the study of micro-scale transport has become an integral part of not only

understanding the performance and operation of miniaturized systems, but also designing

and optimizing new devices. The current chapter presents an experimental study and

analysis to provide a fundamental basis for boiling on a microheater and to investigate the









small size effect on boiling mechanisms. Microheaters have been found in many

applications, for example, inkjet printerhead, and actuators and pumps in microfluidic

systems.

Recently Yang et al. (2000) proposed a new model of characteristic length scale

and time scale to describe the dynamic growth and departure process of bubbles. A

correlation between bubble departure diameter and bubble growth time is established and

a predication formula for bubble departure diameter is suggested by considering the

analogue between nucleate boiling and forced convection. The predictions by the model

agree well with experimental results that were obtained with basically macro-scale pool

boiling conditions. Rainey and You (2001) reported an experimental study of pool

boiling behavior using flat, microporous-enhanced square heater surfaces immersed in

saturated FC-72. Flush-mounted 2cm x 2cm and 5cm x 5cm copper surfaces were tested

and compared to a 1cm x 1cm copper surface that was previously investigated. Heater

surface orientation and size effects on pool boiling performance were investigated under

increasing and decreasing heat-flux conditions for two different surface finishes: plain

and microporous material coated. Results of the plain surface testing showed that the

nucleate boiling performance is dependent on heater orientation. The nucleate boiling

curves of the microporous coated surfaces were found to collapse to one curve showing

insensitivity to heater orientation. The effects of heater size and orientation angle on CHF

were found to be significant for both the plain and microporous coated surfaces. Hijikata

et al. (1997) investigated boiling on small heaters to find the optimum thickness of the

surface deposited layer to enhance the heat removal from the heater in order to obtain the

best cooling effect for a semiconductor. The square heaters they used are 50 gm and 100








pm and they claimed that the deposited layer conduction dominates the heat transfer due

to the small sizes of the heater area. Also they presented the nucleate boiling curves for

the two heater sizes and different deposited layer thickness. Rule and Kim (1999) used a

meso-scale heater (2.7mm x 2.7mm) which consists of an array of 96 microheaters. Each

of the microheaters was individually controlled to maintain at a constant temperature that

enabled the mapping of the heat flux distributions during the saturated pool boiling of

FC-72 fluid. They presented space and time resolved data for nucleate boiling, critical

heat flux and transition boiling. Specifically, the outside edge heaters were found to have

higher heat fluxes than those of the inner heaters. For the materials in this chapter, only

one single microheater (marked as #1 in figure 3.1) is heated to produce bubbles. The

experiment starts with setting the microheater at a low temperature of 50C where only

natural convection occurs at this temperature. Then the temperature of the heater is

incremented by 5C at a time, and for each increment, the heat dissipation by the heater is

obtained by the data acquisition system until the superheat reaches 114C.

4.2 Experiment Results

For each series of the boiling experiment, the heater temperature was set at 50C

initially. After that the temperature was increased with 5C increments until it reached the

superheat of 114C. For each temperature setting, the voltage across the heater was

sampled at a rate of 4500 times per second. The time-resolved heat flux was obtained

based on the heater area and its electrical resistance.

4.2.1 Time-averaged Boiling Curve

Figure 4.1 shows the measured boiling curve in logarithmic and linear scales

where the superheat of the heater covers a range from -6C to 114C. As the degree of








superheat was increased to 54C, single bubbles were seen to nucleate. The onset of

nucleate boiling (ONB) for the single bubble experiment was found at the superheat ATe

of 54C to 59C. After the ONB, the degree of superheat for boiling dropped to 44C as

the minimum temperature for stable boiling on this heater. It is noted that the trend of

figure 4.1 remains very similar to that of the classical pool boiling curve predicted by

Nukiyama (1934) and this includes the ONB phenomenon. In figure 4.1, similar to the

classical macro-scale boiling, the entire boiling curve can be divided into three sections.

Regime I is due to natural convection. Regimes II and III are separated by the peak heat

flux (critical heat flux) which takes place at a heater superheat ATe of 90C. Also shown

in figure 4.1 are the boiling data from Rule and Kim (1999) for a meso-scale heater

(2.7mm x 2.7mm) which is composed of a 10 x 10 array of 96 microheaters. It is noted

that the boiling heat transfer rates for a micro heater (0.27 mm) in the current work are

more than twice higher than those for a meso-scale heater (2.7 mm) but the general trends

are similar for both heaters. Also, the peak heat flux for a micro heater takes place at a

higher heater temperature. These results are consistent with those of Baker (1972) for

forced convection and natural convection that as the heater size is decreased the heat

transfer increases.

4.2.2 Time-resolved Heat Flux

Figure 4.2 shows the heat flux history when the microheater was set at a degree of

superheat of 44C. In figure 4.2, we note that the heat flux is closely associated with the

bubble life cycle during the ebullition process. [A] corresponds to a large spike that takes

place during the bubble departure. When the preceding bubble departs, the heater is

rewetted by the cooler bulk fluid. The establishment of the microlayer for the succeeding













45
45 T peak heat flux

40
[II] *
35 X Before ONB_. ]
DRun I
|30. ARun 2
*Run 3
5 0 Meso heater (Rule and Kim, 19)

a % Xx U
20-' 00 [II
0o
00
1 5 0
100
10 ---- 0X0, -'--- 1-
-10 10 30 50 70 90 110 130
Superheat AT


(a)



100-
90 X Before ONB
80 ORun 1
70 ARun2
60 Run 3
5-. OMeso heater (Rule and Kim, 1999)
E5 .-k heat flux
I40 f

S30
= g
20f

0

X
10-- IX 0
1 10 100 1000
Superheat AT


(b)

Figure 4.1 The boiling curve of the single bubble boiling. (a) The boiling curve in
linear scale; (b) The boiling curve in logarithmic scale.













120 Heat flux trace for a typical bubble cycle from #1 at AT=44*C
100 [A]| [F]

~80

50
80[C] [E]

040

20

1.5 2 2.5 3 3.5
Time (seconds)

Figure 4.2 The heat flux variation during one bubble cycle.


new bubble on the heater surface and the turbulent micro-convection induced by this

vapor-liquid exchange lead to this large heat flux spike. [B] represents the moment when

the succeeding bubble starts to grow after the vapor-liquid exchange. As the new bubble

grows, the contact line that is the three-phase division expands outward. The bubble

growth results in a larger dry area on the heater surface, thus the heat flux is decreasing.

The low heat flux period indicated by [C], [D] and [El corresponds to the slow growth

stage of a bubble. As the bubble size reaches to a certain level, the buoyancy force starts

to become more important than the forces which hold the bubble to the surface, but it is

still not large enough to lift the bubble from the heater surface, causing the bubble to

neck. During the necking process, the contact line starts to shrink, then the dryout area is

starting to decrease, thus we have observed that the heat flux is starting to increase

slightly with some oscillation of a small-amplitude. Finally, the buoyancy force is large

enough to detach the bubble from the heater surface, and then another bubble ebullition

cycle begins.








4.2.3 Time-resolved Heat Flux vs. Superheat AT

Figure 4.3 shows the time-resolved heat flux at different heater superheats (44C

to 114C with increments of 10C) for a total of six-second data acquisition. Figure 4.4

shows the trends of two characteristic heat fluxes during a bubble life cycle (Point A -

Point E in figure 4.2) at various heater superheats. The curve with triangles represents the

peak heat flux of a spike or the minimum heat flux of a dip during the bubble departure

(point A). Based on figure 4.3, the bubble departure was recorded to produce a spike for

the heater temperature up to 84C, after that a heat flux dip was observed. In figure 4.4,

The curve with diamonds shows the heat flux level during bubble slow growth (point E).

It is clear that the two curves hold opposite trends, which is due to different controlling

mechanisms as explained next.

As we examine figures 4.1, 4.3 and 4.4 closely, all three figures consistently

indicate that Regimes II and III are dominated by two different transport mechanisms. In

figure 4.1, the heat flux increases with increasing heater superheat in Regime II while the

trend reverses in Regime III. In figure 4.3, we notice that a heat flux spike is associated

with the bubble departure in Regime II (heater superheat up to 84C) and a heat flux dip

is seen to accompany the bubble departure in Regime III. In figure 4.4, we found that the

two curves cross each other at the heater superheat of 90C which is the separating point

between Regimes II and III. We believe that in Regime II bubble growth is mainly

sustained by the heat transfer mechanism of microlayer evaporation that follows the

rewetting of the heater surface. This scenario is supported by the presence of a heat flux

spike recorded during the bubble departure. The spike is produced when the heater

surface is rewetted by the liquid with micro turbulent motion which in turn causes the

microlayer to form and the evaporation of the microlayer facilitates the bubble












at AT=44C Max: 105.6 w/cm2, I


110
100
90
"S80
70
|60
s50
X 40
30
20






110
100
S90
80
S70
60
50
T40
30
20
I




110
100
90
.g80
S70
S60
150
40
30
20





110
100

80
3, 70
S60
B50
Z 40
30
20


Time (second)


#1 at AT=64C Max: 84.6w/cm2, M in=48.9w/cm2


#1 atAT=74C Max: 74.8w/cm2, Min=51.4w/cm2





El .* . i . .


S 0.5 1 1.5 2 2.5 3 3.5
Time (second)


4 4.5 5 5.5 6


Figure 4.3 Time-resolved heat flux variation at different heater superheats.


#1 atAT=54C Max: 94.8w/cm2, Min=47.1 wlcm2













#1 atAT=84C Max: 65.6w/cm2, Min=53.2w/cm2











.. .. . .


1.5 2 2.5 3
Time (second)


3.5 4 4.5 5 5.5 6


#1 at AT=94C Max: 47.8.6w/cm2, Min=57.1w/cm2






'~ \^ ii*i- .,i~' -1 'V .x^^ ^. ii ^1 'i 1 ^ ^ -" "** i- ^ 1-^ *--* ( "


0.5 1 1.5 2 2.5 3
Time(second)


3.5 4 4.5 5 5.5 6


#1 atAT=104C Max: 39.2w/cm2, Min=47.9w/cm2











. .y . .'.. . m . .


0.5 1 1.5 2 2.5 3
Time(second)


3.5 4 4.5 5 5.5 6


#1 at AT=114C Max: 33.7w/cm2, M in=41.5w/cm2









. ..""* !"" -" **" .~^ i i |L* |- 1 .-- .*"**" '


0 0.5 1 1.5 2 2.5 3
Time (second)


3.5 4 4.5 5 5.5 6


Figure 4.3--continued Time-resolved heat transfer variation at different heater superheats.


0.5














120 A Departing moment
SMinimum Growth
100 Poly. ( Departing moment)
Poly. ( Minimum Growth)
-~80

~60-

||40-

20

0'
40 50 60 70 80 90 100 110 120
AT



Figure 4.4 The trend of maximum and minimum heat fluxes during one bubble cycle with
various heater superheats.




growth. While for Regime III, because of the higher heater superheat and the associated

higher surface tension, the heater is covered by a layer of vapor all the time, even during

the bubble departure. The heater surface is no longer wetted by liquid flow, which results

in the bubble growth controlled by conduction through the vapor layer. The conduction-

controlled scenario is supported by the presence of a heat flux dip recorded during the

bubble departure in Regime III. The reason for this heat flux dip is mainly due to the

necking process during the bubble departure. During the necking process, the top part of

the bubble exerts an upward pulling force to stretch the neck. After the bubble severs

from the base, the upward force disappears suddenly, which allows the lower part of the

neck to spread and cover more heater surface area as depicted in figure 4.5. This larger

dry area on the heater is responsible for the heat flux dip. Another support for the















S Before departure After departure


) k leftover vapor stem
Substrate Substrate






Figure 4.5 A hypothetical model for bubble departure from a high temperature heater.



conduction-controlled bubble growth in Regime III is that the heat flux level decreases

slightly with increasing heater surface temperature which is caused by the decrease of

FC-72 vapor thermal conductivity with increasing temperature.

From figure 4.3, where each spike or dip represents the departure of a bubble, we

can conclude that the bubble departure frequency increases with heater temperature. At a

heater superheat of 44C, the bubble departure frequency is about 0.43 Hertz, while at

84C, it is at 0.53 Hertz. Figure 4.3 also demonstrates the repeatability of the experiment.

We observed that the bubble departure size did not change much with

temperature. This is consistent with the results by Yang et al. (2000). Departure criteria

of the bubbles are totally determined by the forces acting on the bubbles. Buoyancy force,

besides the inertia force of the bubble, is the major player to render the bubble to depart.

The interfacial surface tension along the contact line invariably acts to hold the bubble in

place on the heater surface. Since this interfacial adhesive tension increases with








temperature, for departure to occur, it requires a larger bubble size to generate the

corresponding buoyancy force to overcome the adhesive force. At higher temperatures,

the thermal boundary layer that is due to transient heat conduction to the liquid is thicker

which allows the bubble to grow larger. However, we observed that as the heater

temperature was increased the bubble exhibited significant horizontal vibration that could

be due to the higher evaporation rate at higher superheat. This vibration promotes bubble

departure. On the other hand, due to the micro size of the heater, the natural convection

taking place around the outside of the contact line helps bubble detach from the surface.

Thus, these effects could cancel so that the bubble departure size does not change much

with heater superheat.

4.2.4 Visualization Results and Bubble Growth Rate

Figure 4.6 provides a sequence of bubble images during the life cycle of a typical

bubble on the microheater at superheat of 54C. The images were taken from beneath the

heater surface using a CCD camera of 30 fps. As shown by the images, as it grows, the

bubble displays the shape of an annulus. The outer circle is the boundary of the bubble,

which shows the diameter of the bubble. The inner circle represents the contact line

where solid, liquid and vapor meet which measures the bubble base area on the heater. In

this figure, we note that just before the departure, the micro heater is almost entirely

covered by the vapor, thus resulting to a very low heat flux (the portion between point D

and point E in figure 4.2), and at this point the bubble has a diameter of about 0.8 mm

which is three times the size of the micro heater. The corresponding bubble size history

and growth rate were estimated and plotted in figures 4.7 and 4.8, respectively. We note

that the characteristics of bubble growth dynamics shown in figures 4.7 and 4.8 agree

well with the theoretical prediction of Scriven (1959).

















0.0333 0.0667



B~~i^M. ft ^"^
,...s'* 9 .... 'V ..' nil i< j~f V '^' -




0.1667 0.2000








0.3000 0.3333








0.4333 0.4667








0.5667 0.6000
.. w i


0.7000


0.1000 0.1333


0.2333 0.2667


0.3667 0.4000


0.5000 0.5333


0.6333 0.6667


0.7667 0.8000


Figure 4.6 Bubble images of a typical bubble cycle taken from the bottom.




















0.8333 0.8667


0.9667


0.9000 0.9333


1.0000 1.0333


1.1000 1.1333


1.2333


1.1667 1.2000


1.2667 1.3000


1.3667


1.4000
,4:%


1.5000


1.4333


1.5667


1.5333


1.3333


1.4667










1.6000


Figure 4.6--continued Bubble images of a typical bubble cycle taken from the
bottom.


1.0667







66






Bubble diameter vs. Time





Heater #1(0.07136mm2) at AT=54C




0 Diameter (mm) reading
2nd order polynomial trendline


0.9
0.8
0.7
-, 0.6
e0.5
S0.4
S0.3
0.2
0.1
0.0
0


0.8 1.0 1.2
Time (seconds)


1.4 1.6 1.8


Figure 4.7 Measured bubble diameters at different time.


Growth speed of the single bubble at AT=54C


0 0.2 0.4 0.6 0.8


1 1.2 1.4 1.6 1.8
Time (seconds)


Figure 4.8 Bubble growth rate at different time.


.0 0.2 0.4 0.6


The initial growth speed
from 0 to 0.0333 seconds
is about 11.57mm/s.


o Growth Speed
- Logarithrric trendlne


0v

:: 0 Heater #1(0.07136mm2) at AT=54

0 o

o 0 0
0 0--- __


OC








A high-speed video camera has also been used to show the necking and bubble

departure process. Figure 4.9 displays the images taken from the side and bottom views

by the camera set at 1000 frames per second. Based on the side view images it is clear

that the embryo of the next bubble is formed as a result of the necking process. It is also

estimated that the bubble departs at a very high velocity of 0.16 m/s that causes a strong

disturbance to the heater surface. This departure force in turn produces turbulent mixing

and microlayer movement around the bubble embryo that are responsible for the spike of

heat flux denoted as Point A in figure 4.2. As shown by the bottom view images, the

bubble departure disturbance also produces microbubbles that stay near the bubble

embryo and eventually coalesce with it.

4.3 Comparison and Discussion

4.3.1 Bubble Departure Diameter

Recently Yang et al. (2000) proposed a dimensionless length scale and a

corresponding time scale to correlate the bubble departure diameter and growth time.

These scales are repeated in Eq. (4.1) and Eq. (4.2).


D = _AD, 1 ARl(AYr (4.1)
L0 B B)'

where = =2pATHA B= Ja12
A B =Ja -a,
V 3p,
(4.2)
and [= 1+1 +'
2(6Jaf 6Ja


For the current study, the measured bubble departure diameters and growth times at

various heater surface superheats are given in table 4.1. It is shown that the bubble











Table 4.1 Single bubble growth time and departure diameter

AT 49 54 59 64 69 74 79 84 89 94 99 104
Growth
time 2.352 2.054 1.922 1.873 1.747 1.611 1.483 1.403 1.335 1.237 1.128 1.024
(seconds)
Departure
diameter 0.823 0.824 0.829 0.833 0.832 0.836 0.839 0.843 0.850 0.859 0.866 0.875
(mm)

Table 4.2 Properties of FC-72 at 56C

Properties Pi (kg/m3) Pv (kg/m3) jHfg (kJ/kg) Cp, (kJ/kg) C4 (10m2/s)
Value 1680 11.5 87.92 1.0467 3.244


growth time is inversely proportional to the superheat while the departure size only

increases very slightly with the increasing superheat as discussed above.

In order to compare our data with the correlation of Yang et al. (2000), the data

were converted to dimensionless forms according to Eqs. (4.1) and (4.2) using thermal

properties given in table 4.2. Figure 4.10 shows the comparison. Part (a) of figure 4.10 is

the reproduced correlation curve from Yang et al. (2000) and part (b) shows our data

along with the correlation curve of part (a). It is seen that our data fall slightly lower than

the extrapolated correlation of Yang et al. (2000). Since the data given in part (a) are

from macro-scale heaters, we may conclude that on a microheater in the current study,

the bubble departure size is larger and they stay on the heater longer.

4.3.2 Size Effects on Boiling Curve and Peak Heat Flux

It is also of importance to examine the heater size effect on the boiling curve. We

plotted boiling curves for heater sizes ranging from 50 gtm, 100 gtm, 270 pgm, 2700 gtm, 1








































2ms


Figure 4.9 The visualization result of bubble departure-nucleation process for
heater #1 at 54C. (a) The side views; (b) The bottom views.


0 ms


3ms




























(a) (b)


Figure 4.10 The relationship between bubble departure diameter and growth time.
(a) Experimental data and correlation curve from Yang et al. (2000); (b) Data from
current study along with the correlation of Yang et al. (2000).


cm to 5 cm in figure 4.11. In order to ensure a meaningful comparison, all the curves in

figure 4.11 are based on fluids with similar thermal properties. The trend is very clear

that as the heater size decreases, the boiling curve shifts toward higher superheats and

higher heat fluxes. The peak heat fluxes for different size heaters have been plotted in

figure 4.12 for comparison. It is consistent that the peak heat flux increases sharply as the

heat size approaches the micro-scale. Actually, for heater sizes of 50 gtm and 100 gm

(Hijikata et al., 1997), even with a very high superheat of about 200C as shown in figure

4.11 the peak heat fluxes have not been reached.







71



Size effect on nucleate boiling curves



El

FP
E3


1000







100







10








I


100
Superheat(AT)


Figure 4.11 Comparison of boiling curves.


E
"'30

p20


CHF for Different Size Heaters




270 urn
present study





2700 urn



5 Cc
5Scm


Figure 4.12 Comparison of peak heat fluxes.


13h


A 50urn (Hijikata et al., 1997)

0 O1um (Hijikata etal., 1997)
g 0 Current study
+* X2700um (Rule and Kim, 1999)
+ 1cm (Chang and You, 1997)
+
+5cm (Rainey and You, 2001)
+ I I








4.3.3 Bubble Incipient Temperature

Bubble incipient temperature is relatively higher for the small size heater used in

this experiment. This is consistent with the results given by Rainey and You (2001),

where they observed that the incipient temperature is about 16-17C for 5 cm heater, 20-

35C for 2 cm heater, and 25-40C for 1cm heater. The incipient temperature observed in

our experiment is about 45-55C. The explanation for this phenomenon by Rainey and

You (2001) is that larger heaters are more likely to have more surface irregularities and

therefore wider size range for bubble to nucleate from.

4.3.4 Peak Heat Flux on the Microheater

As mentioned in Section 2.3, recently more research reports (Sakashita and

Kumada, 1993 and Sadasivan et al., 1995) have indicated their support of the macrolayer

dryout as the basic mechanism for CHF as opposed to the hydrodynamic instabilities

(Liehard, 1988a). In the current research with microheaters as suggested by Sadasivan et

al. (1995), the theory of macrolayer dryout has been verified further as the cause of the

CHF. The support based on the results of the current single bubble experiment is

summarized as follows:

1. As discussed in Section 4.2.3 Regimes II and III are separated by the CHF

point. Two different mechanisms were discovered for the two regimes, respectively. It is

clear that the CHF that is the starting point of the Regime III where the heat transfer is

through a layer of vapor film and the heater is no longer wettable, is corresponding to the

dryout of the macrolayer.

2. In the current microheater condition, there is no possibility for the formation of

Kelvin-Helmholtz instability nor Taylor instability.








4.4 Deviations from Steady Single Bubble Formation

For the single boiling experiment dedicated in this chapter, as the bubble incipient

temperature is reached, a steady bubbling process has been observed and analyzed as

above. With the help of a high speed digital camera and simultaneous data acquisition,

we have noticed some deviations from the steady single bubble bubbling process. In this

section, these deviations have been summarized. It must be noted that these deviations

are very random according to observations in the experiments. The physics behind these

phenomena requires much more experimental and analytical work. We have noticed there

are three possible phenomena associated with bubble formation that could occur. Firstly,

a long-waiting period is necessary before the onset of another bubble and a vapor

explosion always occurs before this onset of another bubble, we call this process

discontinued bubble formation. Discontinued bubble formation happens usually at lower

superheats and with a highly subcooled liquid. Secondly, the direct bubble formation is

the process during which another bubble forms immediately after a bubble departs.

Thirdly, the bubble jetting is a chaotic phenomenon with smaller bubbles ejected from the

heater surface without forming a single bubble. The direct bubble formation is the steady

bubble formation process that we have analyzed previously. This section is dedicated to

the other two deviations from the steady bubble formation process.

4.4.1 Discontinued Bubble Formation

As we have observed, discontinued bubble formation actually occurs similarly to

the initial onset of boiling on the heater. For the microheater used in out experiment,

onset of nucleate boiling starts actually with vapor explosion, a physical event in which

the volume of vapor phase expands at the maximum rate in a volatile liquid. During this

process, the liquid vaporizes at high pressures and expands, performing mechanical work








on its surroundings and emitting acoustic pressure waves. According to previous

investigators, for large heaters rapid introduction of energy is necessary to initiate and

sustain the vapor volume growth at the high rate. For the microheater used in this

experiment, vapor explosion always occurs prior to the nucleation of small bubbles on the

heater. This could be due to the limited energy the microheater can supply from the solid

surface into the liquid though the superheat is well beyond the required superheat for

nucleating bubbles. We recorded the vapor explosion process together with the onset of

boiling, as shown in figure 4.13 for side-view images and figure 4.15 for bottom-view

images. When the heater reaches about 110C, vapor explosion occurs. Following this

process, small bubbles start to nucleate and coalesce almost right after. With the

existence of noise due to the acoustic pressure waves, a layer of vapor is ejected with

high speed up into the liquid exhibiting a shape of mushroom (about 1.0ms). The vapor

enclosed in the mushroom is loose due to the rapid expansion, and then starts to shrink to

form a round bubble and moves up. On top of the heater, the cool liquid replenishes the

vacancy and small bubbles nucleate and coalesce to a single bubble. The high energy

stored before the ONB is released suddenly to overcome all kinds of forces including the

Van der Waals force from the solid surface, hydrostatic force due to the liquid depth, etc.

A typical application of this process is the commercial success of thermal ink jet printers.

The key to the thermal ink-jet technology is the action of exploding micro bubbles, which

propel tiny ink droplets through the openings of an ink cartridge.

Zhao et al. (1999) used a thin-film microheater of size of 0l0m x llOpm to

investigate the vapor explosion phenomenon. They placed the microheater underside of a

layer of water and the surface temperature of the heater was rapidly raised (about 6gm)




























Figure 4.13 The process of vapor explosion together with onset of boiling.


Figure 4.14 The ruler measuring the distance in figure 4.13 after vapor explosion.


o 0 0 8 07









J hLmi


!-
wi -


MUM


** ii -1*R ITV Wpm
M~iiSw ^6L l jL41


Figure 4.15 The bottom images for vapor explosion and boiling onset process.


I .









electronically well above the boiling point of water. By measuring the acoustic emission

from an expanding volume, the dynamic growth of the vapor microlayer is reconstructed

where a linear expansion velocity up to 17m/s was reached. Using the Rayleigh-Plesset

equation, an absolute pressure inside the vapor volume of 7 bars was calculated from the

data of the acoustic pressure measurement. In this experiment, we also measured the

bubble velocity when vapor was exploded. By referring the heater size shown in figure

4.14 the distance the bubble was ejected up from the heater surface can be measured. The

result is the average velocity during the first 7 milliseconds is about 0.2m/s which is well

below that measured by Zhao et al. (1999). The low velocity measured in this experiment

is not surprising due to the following reasons. One of the reasons is that only a layer of

water was used in their experiment while pool boiling experiment was used in this

experiment. Also in this experiment the boiling liquid FC-72 with a lower saturation

temperature is used.

Figure 4.16 illustrates the heat flux traces corresponding to the vapor explosion

and boiling onset process. In figure 4.16(a) during the 6-second data acquisition, it starts

at a lower level where boiling is not present with natural convection to be the heat

transfer mode. All of a sudden, the vapor explosion exists and we recorded a sharp heat

flux spike that is supposed to correspond to the vapor explosion process as shown in

figure 4.16(b). For present data recording speed about 4,500 data points per second, we

recorded the vapor explosion occurs only in a mini-second related to the heat flux

variation from the heater. Following this vapor explosion, small bubbles start to nucleate

and heat flux increases.







78


PrllM1 I SO ftM I
no The Heat Flux History Recording Onset of Boiling Process
100
SVapor explosion and onset of boiling

S00


so
Natural convection nglebubble formed
40
30 1I 1
0 1 2 3 4 8 1
Seconds


(a)


F-061I 20p*m I
The Heat Flux History During Vapor Explosion and Onset of Boiling

4. 1 ^ I I
onst p () Te ht fx vOnset o1 bonlln o


pces 7 b Th hea lxvaporexpiIatio d th -e b o pr
40-

30-


'2.01 15 2.02 2.02. 203 2.036 2.04
S~oomwo


(b)


Figure 4.16 The heat flux variation corresponding to the vapor-explosion and boiling
onset process. (a) The heat flux variation recording the vapor-explosion and boiling onset
process; (b) The heat flux variation during the vapor-explosion and boiling onset process.








4.4.2 Bubble Jetting

During the single bubble boiling process, we observed that periodically there is

bubble jetting after two or three bubbling cycles. This bubble jetting lasts about 0.2

second each time before a new single bubble is formed on the heater. Images taken with

the high speed camera in figure 4.17 and figure 4.18 show the bubble jetting process, and

figure 4.19(a) is the heat flux traces for a six-second data acquisition which includes three

bubble cycles of the departing-nucleation process. Figure 4.19(b) and 4.19(c) are the

close-up views of two heat flux encircled in figure 4.19(a). Through a close observation,

we find figure 4.19(b) is the heat flux variation corresponding to this bubble-jetting

process shown in figure 4.17 and figure 4.18. We notice that during the bubble-jetting

process, the heat flux stays much higher and drops sharply as a single bubble grows on

the heater. We also observed the single bubble boiling at 105C and 120C. At these two

temperatures, we also noticed the same phenomenon of bubble jetting. Figure 4.20 shows

the heat flux variation from the heater when it is set at 105C, and figure 4.21 shows the

heat flux variation from the heater when it is set at 120C. For both these two cases at

105C and 120C, we also observed the bubble-jetting after bubble's departure. The

bubble jetting process is a characteristic of chaotic bubble nucleation, merging, and

departing process with the company of acoustic waves. During the bubble jetting process,

small bubbles on the heater keeps merging and departing. And all of a sudden a merged

bubble stays and merges with all other small bubbles around it, then a single bubble is

formed. The single bubble formation and growth also inhibits the bubble-jetting process,

and at the same time dries out the microlayer around the bubble for this particular heater

configuration used in this experiment. Thus the heat flux drops quickly as the single

bubble grows. The possible reason for this bubble jetting phenomenon is due to the high






80


superheat of the heater, the evaporation rate is very high on top of and around the edge of

the heater. The small bubbles do not have enough liquid to replenish the microlayer

region for them to grow. Clearer explanation of these phenomena needs further

observation and numerical approach.


















1~ei
-011O 1.. 1LA 69.00. -421 jPOi *3W -&* .


4 L-bI ..4.
I ,a' *I a ,,a "m .*


qii .6aL--"i a a, v


_* -,- I "s, 7" -41 to-J


... -.> -J- -jif- '* .jafr** .^.<


An m d W d P


. Z :A :: <
..,WO wim Md*


6*" 0-% i


Figure 4.17 The chaotic bubble jetting process for heater #1 at 110C.


dadgmw-mlmws AMW W
-.. 0.% -OOMMM -- a. Ak % --1- 04 4k


m







56 ms 58ms 59ms 60ms 61 ms




61.5m 62 62. 5ms 63m 63.5ms




64.5 ms 67ms 70 5 ms 77 Is .At h. 8055 E





I 06fma 1265 ms




128 ms 164.5ms 165ms 165.5ms 166.5ms


0* l _4__ of

167.5ms 168ms 169ms 170ms 171.5mg

O- 0 of0 of 0
9 #9 .9 :9 o

173ms 173.5m 174ms 175ms 176mS




Figure 4.18 The bottom images of chaotic bubble jetting process for heater #1 at 1 10C.



































Heat Flux
- i




/ 1 ,t,


Variation during Nucleation-Departing Process

.. -- I .


-,-- \ .- ... .
Buotle jetting process about 0 12 seconds





i Bub lede rting si ng bubble is omed


0 0.01 0.02 0.03 0.04 0.05 0.06 0


.07 0.08 0.09 0.1 C
Seconds


1.11 ....0.12 0.13 0.14 0.15 0.16 0.17 0.1 0.1... 0....2
.11 0.'12 0.'13 0.'14 0.15 0.16 0.17 0.18 0.'19 0.2


FmO041 IMN r----2-
13 The heat flux variation with invisible bubble jetting

130
120 -- -- -- --- -- -- -- -- -- -- -- -- -- __ __ __ __ __ __
110 --
S100 _
9.0


X 70 .._




40
3.1 3.2 3.3 3.4
Seconds



(c)
Figure 4.19 The heat flux traces corresponding to the bubble jetting process. (a) 6-second
data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view of (a)
for direct bubble formation.


F t- 1 I FPOMI I
Typical heat flux variation #1 at 110 IOC
130. __I__ I I I I I I I l __ I I_ I J I I I

,,o .- 1 1 ... .IhJ! p o : n m .b u. J r = ..... ....
Visible e letting Invisible bubble jetIng after depalture __
110 .. .. .





X 70 .... .. .. ...
o .. ^ .. ^ ... .. ... .

: 0I t -i i i i, i iT _-' l r -

0 1 2 3 4 5 6
Seconds


I- 1 7 ft202 1


120

110

100

190

180

1 70

60


I
I










l3 Typical heat flux variation #1 at 105C
12D L H t I I I i t- 1 1 1 1 1 1 1 1
--i i i j_ _-..111. i

i Invisible bubbW eting VIb bbble n




X~ 70



40 P I I iI I I
j. -' F ... i .: .... i -+- ^ + IL __ .i,






Seconds


f- ," I O... I, ,


Typical heat flux variation #1 at 105C

VI i5blebubl I el9ng
M A .... ... ... ... W,


5.8
Second*


Figure 4.20 The heat flux traces for bubble jetting process from heater #1 at 105C. (a) 6-
second data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view
of (a) for direct bubble formation.


130
120
110
if100

9D0
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1 70)
60
SO

50
405.


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130
120
110
100
90
1 90

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50


130
120
110
100
190
19.0
X 70
S0
50
40


0


0.9


2.9
Seconds


Scnd
Secnd


Figure 4.21 The heat flux traces for bubble jetting process from heater #1 at 120C. (a) 6-
second data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view
of (a) for direct bubble formation.


Typical heat flux variation #1 at 120C

1:! i 1 L1 L I I I I I I 1
Invilble bubble jetting Visible bubble Jetting
110..




z ... ........... .......-
if


0 T I _

0 1 2 3 4 5 4
Seconds


Typical heat flux variation #1 at 120'C

Visble bubble'jet__ .A



..... I^--"--- i ,
. -. .



.. .. I "
I I i .... -1- --i ... T i


Typical heat flux variation #1 at 120C
__I 1 1 1 t I .1 1_ l L i!..
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I








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7




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FILES


EFFECTS OF BUBBLE COALESCENCE AND HEATER LENGTH SCALE ON
NUCLEATE POOL BOILING
By
TAILIAN CHEN
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
2002

ACKNOWLEDGMENTS
I would like to express my sincere appreciation to my advisor, Dr. Jacob N.
Chung, for his invaluable support and encouragement. Without his direction and support,
this work would not have been possible. Many thanks go to Dr. Jungho Kim for his help
build up the experimental setup and instructions in this research. I also greatly
acknowledge Dr. James F. Klausner for his invaluable suggestions in this research.
I have also had the privilege to work with Drs. William E. Lear, Jr., Zhuomin
Zhang and Ulrich H. Kurzweg as other members of my committee. Their suggestions and
encouragement have shaped this work considerably.
Finally, I feel indebted to my wife, Lu Miao, and my son, Matthew Chen. Without
their continuous support, this work would not have been possible.
li

TABLE OF CONTENTS
gage
ACKNOWLEDGMENTS ii
LIST OF TABLES vi
LIST OF FIGURES vii
NOMENCLATURE xi
ABSTRACT xiv
CHAPTER
1 INTRODUCTION 1
1.1 Statement of the Problem 1
1.2 Research Objectives 2
1.3 Significance and Justification 3
2 LITERATURE REVIEW AND BACKGROUND 5
2.1 Bubble Dynamics and Nucleate Boiling 5
2.2 Coalescence of Bubbles 15
2.3 Critical Heat Flux 21
3 EXPERIMENT SYSTEM 24
3.1 Microheaters and Heater Array 24
3.1.1 Heater Construction 24
3.1.2 Heater Specifications 25
3.2 Constant Temperature Control and Data Acquisition System 27
3.2.1 Feedback Electronics Loop 27
3.2.2 ^Processor Control Board and D/A Board 28
3.2.3 A/D Data Acquisition Boards 29
3.2.4 Heater Interface Board (Decoder Board) 29
3.2.5 Software 29
3.3 Boiling Conditioin and Apparatus 30
3.3.1 Boiling Condition 30
3.3.2 Boiling Apparatus 30
in

3.4 Experiment Procedure 30
3.4.1 Heater Calibration 30
3.4.2 Data Acquisition and Visualization 36
3.5 Heat Transfer Analysis and Data Reduction 37
3.5.1 Qualitative Heat Transfer Analysis 37
3.5.2 Data Reduction Procedure 38
3.5.3 Determination of Natural Convection on the Microheaters 40
3.5.4 Uncertainty Analysis 44
4 SINGLE BUBBLE BOILING EXPERIMENT 52
4.1 Introduction 52
4.2 Experiment Results 54
4.2.1 Time-averaged Boiling Curve 54
4.2.2 Time-resolved Heat Flux 55
4.2.3 Time-resolved Heat Flux vs. Superheat AT 58
4.2.4 Visualization Results and Bubble Growth Rate 63
4.3 Comparison and Discussion 67
4.3.1 Bubble Departure Diameter 67
4.3.2 Size Effects on Boiling Curve and Peak Heat Flux 68
4.3.3 Bubble Incipient Temperature 72
4.3.4 Peak Heat Flux on the Microheater 72
4.4 Deviations from Steady Single Bubble Formation 73
4.4.1 Discontinued Bubble Formation 73
4.4.2 Bubble Jetting 79
5 DUAL BUBBLE COALESCENCE 86
5.1 Synchronized Bubble Coalescence 86
5.2 Dual Bubble Coalescence and Analysis 87
5.3 Heat Transfer Enhancement due to Coalescence 93
5.4 Bubble Departure Frequency 95
6 HEAT TRANSFER EFFECTS OF COALESCENCE OF BUBBLES FROM
VARIOUS SITE DISTRIBUTIONS 96
6.1 Coalescence of Dual Bubbles with a Moderate Separate Distance - A Typical Case
96
6.2 Dual Bubble Coalescence from Heaters #11 and #14 at 100°C - Larger Separation
Distance Case 103
6.3 Dual Bubble Coalescence from Heaters #11 and #14 at 130°C - Larger separation
Distance and Higher Heater Temperature Case 107
6.4 History of Time-resolved Heat Flux for Different Heater Separations 109
6.5 Time Period of a Bubbling Cycle 109
6.6 Average Heat Flux of a Heater Pair - Effects of Separation Distance 113
6.7 Time-averaged Heat Flux from Heater #1 113
6.8 Coalescence of Multiple Bubbles 115
IV

6.9 Heat Transfer Enhancement due to Coalescence Induced Rewetting
122
7 MECHANISTIC MODEL FOR BUBBLE DEPARTURE AND BUBBLE
COALESCENCE 126
7.1 Rewetting Model 127
7.2 Results from the Rewetting Model 128
8 CONCLUSIONS AND FUTURE WORK 132
8.1 Summary and Conclusions 132
8.2 Future Work 133
APPENDIX NOTES OF PROGRAMMING CODES FOR DATA ACQUISITION.. 135
REFERENCES 146
BIOGRAPHICAL SKETCH 150
v

LIST OF TABLES
Tables Page
3.1 The specifications of the D/A cards 29
3.2 The uncertainty sources from calibration 46
4.1 Single bubble growth time and departure diameter 68
4.2 Properties of FC-72 at 56°C 68
7.1 Effective thermal conductivity (w/m-K) used in the rewetting model 129
vi

LIST OF FIGURES
Figures Page
2.1 The numerical model and results given by Mei et al. (1995) 7
2.2 The numerical model and four growth domains by Robinson and Judd (2001) 8
2.3 Research on bubble coalescence by Li (1996) 17
2.4 The coalescence research performed by Bonjour et al. (2000) 20
3.1 Heaters and heater array 26
3.2 Wheatstone bridge with feedback loop 28
3.3 Boiling apparatus 31
3.4 Schematic of calibration apparatus and temperature control loop 32
3.5 Part of the calibration results 34
3.6 Comparison of calibrated resistances of heater #1 with the calculated resistances
from property relation 35
3.7 The schematic showing the heat dissipation from a heater 39
3.8 Heat flux comparison from experimental and calculated results 41
3.9 Derived natural convection heat fluxes for different heater configurations 44
3.10 The circuit schematic for temperature control and voltage division 47
3.11 The uncertainty at different temperatures 50
4.1 The boiling curve of the single bubble boiling 56
4.2 The heat flux variation during one bubble cycle 57
4.3 Time-resolved heat flux variation at different heater superheats 59
vii

4.4 The trend of maximum and minimum heat fluxes during one bubble cycle with
various heater superheats 61
4.5 A hypothetical model for bubble departure from a high temperature heater 62
4.6 Bubble images of a typical bubble cycle taken from the bottom 64
4.7 Measured bubble diameters at different time 66
4.8 Bubble growth rate at different time 66
4.9 The visualization result of bubble departure-nucleation process for heater #1 at 54°C
69
4.10 The relationship between bubble departure diameter and growth time 70
4.11 Comparison of boiling curves 71
4.12 Comparison of peak heat fluxes 71
4.13 The process of vapor explosion together with onset of boiling 75
4.14 The ruler measuring the distance in figure 4.13 after vapor explosion 75
4.15 The bottom images for vapor explosion and boiling onset process 76
4.16 The heat flux variation corresponding to the vapor-explosion and boiling onset
process 78
4.17 The chaotic bubble jetting process for heater #1 at 110°C 81
4.18 The bottom images of chaotic bubble jetting process for heater #1 at 110°C 82
4.19 The heat flux traces corresponding to the bubble jetting process 83
4.20 The heat flux traces for bubble jetting process from heater #1 at 105°C 84
4.21 The heat flux traces for bubble jetting process from heater #1 at 120°C 85
5.1 The heat flux variation for pair #1 with #11 and pair #1 and #12 88
5.2 The heat flux variation of one typical bubble cycle for two configurations (a) and (b)
for heater #1 with #11, (c) and (d) for heater #1 with #12 89
5.3 The heater dry area before and after coalescence 90

5.4 The boiling heat flux for the two pairs (#1 with #11) and (#1 with #12) as they are set
at different temperatures to generate bubbles and coalesce 92
5.5 The heat flux increase due to coalescence 94
5.6 Comparison of bubble departure frequency from heater #1 for coalescence and non¬
coalescence cases 95
6.1 The departing and nucleation process for heaters #11 and #13 at 100°C 99
6.2 The coalescence process (2 cycles of oscillation) for heaters #11 and #13 at 100°C.
100
6.3 The heat flux history for dual bubble coalescence 101
6.4 Photographs showing the interface interaction 102
6.5 The side-view photographs of coalescence-departure-nucleation process for heaters
#11 and #14 at 100°C 104
6.6 The bottom view of coalescence-departure-nucleation process for heaters #11 with
#14 at 100°C 105
6.7 The heat flux history from heater #11 when #11 and #14 are set at 100°C 106
6.8 The heat flux history for heaters #11 and #14 at 130°C 108
6.9 The heat flux history from heater #1 with time 110
6.10 The bottom images for one bubble cycle and dryout changing (time in second)... 111
6.11 The time duration of one bubble cycle at different superheats 112
6.12 The average heat fluxes from different pairs of heaters at different superheats 114
6.13 The average heat fluxes from heater #1 at different superheats 114
6.14 Four heater configurations for multiple bubble coalescence experiment 115
6.15 The heat fluxes from each heater for case A (figure 6.14) vs. superheat 117
6.16 The heat fluxes from each heater for case C (figure 6.14) vs. superheat 117
6.17 The average heat fluxes for different heater configurations vs. superheat 118
6.18 The coalescence sequence for heaters #3, #5, #7, and #15 at 80°C 120
IX

6.19 The coalescence sequence for heaters #1, #3, #5, #7, and #15 at 80°C 120
6.20 The coalesced bubble formed on heaters #3, #5, #7, and #15 at 100°C 121
6.21 The coalesced bubble formed on heaters #1, #3, #5, #7, and #15 at 100°C 121
6.22 The heat fluxes from heater #11 when the other heaters are at various superheats. 123
6.23 The heat flux history from heater #11 during 0.8 second 123
6.24 The heat flux history from heater #11 when the bubble formed on it is pulled
toward the primary bubble from heaters #1, #2, #3, and #4 124
7.1 Typical heat flux spikes during bubble coalescence 126
7.2 The fluid flow induced by the bubble departure 127
7.3 The fluid flow induced by the bubble coalescence 128
7.4 The results from the rewetting model for the bubble coalescence 130
7.5 The results from the rewetting model for the bubble departure 131
A.l The main interface to select heaters 135
A.2 Heaters temperature form 137
A.3 The architecture for addressing the selected heaters 141
A.4 The pins layout of the D/A cards 143
A.5 The data acquisition form 144
x

NOMENCLATURE
A
C
Cp.l
Db
D\
Fo
8
g(Pr)
GrL
Hig
Ja
k
keff
L
L0
n
Nux
heater surface area (cm2)
platinum constant coefficient (Q/£2°C)
specific heat (kJ/kg-K)
bubble departure diameter
dimensionless bubble departure diameter
Fourier number
gravitational acceleration (m/s2)
function of Prandtl number in Eq.(3.8)
Grashof number defined in Eq.(3.7)
latent heat of vaporization (kJ/kg)
Jacob number
thermal conductivity (w/m-K)
effective thermal conductivity (w/m-K)
heater characteristic length
heater characteristic length
constant
Nusselt number
Nu,
average Nusselt number for a heater

Nul+.
corrected Nusselt number for a heater
Phd
hydrodynamic pressure
PV
vapor pressure inside a bubble
bulk liquid pressure
Pn
Prandtl number
q"
heat flux (w/cm2)
I»
H condl
conductive heat transfer rate per unit area from a heater to substrate with
boiling (w/cm )
tl
H cond2
conductive heat transfer rate per unit area from a heater to substrate
without boiling (w/cm2)
»!
q natural
natural convection heat transfer rate per unit area from a heater (w/cm2)
q radl
radiation heat transfer rate per unit area from a heater with boiling (w/cm )
q rad2
radiation heat transfer rate per unit area from a heater without boiling
(w/cm2)
II
q rawl
total heat transfer rate per unit area supplied to a heater with boiling
(w/cm2)
q raw2
total heat transfer rate per unit area supplied to a heater without boiling
(w/cm2)
q" s(t)
heat transfer with time in the rewetting model(w/cm2)
rr
q top
boiling heat transfer (w/cm2)
R
electrical resistance at temperature T
Rb
bubble diameter (mm)
Ro
resistance at ambient temperature T0
t
time (seconds)
Ti
bulk liquid temperature (°C)
Ts
heater surface temperature (°C)
Xll

T0 ambient temperature (°C)
V voltage across the heater (V)
Voff offset voltage of the Opamp (V)
Greek Symbols
w
Pi
Pv
a,
P
v
Pi
uncertainty associated with temperature (°C)
uncertainty associated with heat flux (w/cm2)
liquid density (kg/m3)
vapor density (kg/m3)
thermal diffusivity (kJ/kg-K)
dimensionless bubble growth time
bubble growth time (seconds)
coefficient of thermal expansion
kinematic viscosity (m/s2)
liquid viscosity (N-s/m2)
surface tension (N/m)
ATe
heater superheat (°C)
xm

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
EFFECTS OF BUBBLE COALESCENCE AND HEATER LENGTH SCALE ON
NUCLEATE POOL BOILING
By
Tailian Chen
August 2002
Chairman: Jacob N. Chung
Major Department: Mechanical Engineering
Nucleate boiling is one of the most efficient heat transfer mechanisms on earth.
For engineering applications, nucleate boiling is the mode of choice owing to its narrow
operating temperature range and high heat transfer coefficient. Though much effort has
been expended in numerous investigations over several decades, controversies persist,
and a complete understanding of the boiling mechanisms still remains elusive.
In this research, microscale array heaters have been utilized, where each heater
has a size of 270 pm x 270 pm. The time and space-resolved heat fluxes from constant-
temperature heaters were acquired through a data acquisition system with side and
bottom images taken from the high speed digital visualization system. Together with the
heat fluxes from the heaters, we have been able to obtain much better new results.
For the single bubble boiling, we found that in the low superheat condition,
microlayer evaporation is the dominant heat transfer mechanism while in the high

superheat condition, conduction through a vapor film is dominant. During the bubble
departure, a heat flux spike was measured in the lower superheat regime whereas a heat
flux dip was found in the higher superheat regime. As the heater size is reduced in pool
boiling, the boiling curve shifts towards higher fluxes with corresponding increases in
superheats. Comparing with the single bubble boiling, two major heat flux spikes have
been recorded in dual bubble coalescence. One is due to the bubble departure from the
heater surface and the other one is due to the bubble coalescence. The overall heat
transfer is increased due to the rewetting of the heater surface as a result of bubble-bubble
interaction. A typical ebullition cycle includes nucleation, single bubble growth, bubble
coalescence, continued bubble growth and departure. We have found that in general the
coalescence enhances heat transfer as a result of creating rewetting of the heater surface
by colder liquid and turbulent mixing effects. The enhancement is proportional to the
ebullition cycle frequency and heater superheat. It was also measured that the longer the
heater separation distance is the higher the heat transfer rate is from the heaters. For the
multiple bubble coalescence, the key discovery is that the ultimate bubble that departs the
heater surface is the product of a sequence of coalescence by dual bubbles. For the heat
transfer enhancement, it was determined that the time and space averaged heat flux for a
given set of heaters increases with the number of bubbles involved and also with the
separation distances among the heaters. In particular, we found that the heat flux levels
for the internal heaters are relatively lower than those of the surrounding ones.
xv

CHAPTER 1
INTRODUCTION
1.1 Statement of the Problem
In nucleate boiling from a heated surface, vapor bubbles generated tend to interact
with neighboring bubbles when the superheat is high enough to activate higher nucleation
site density. It is believed that bubble-bubble interaction and coalescence are responsible
mechanisms for achieving high heat transfer rates in heterogeneous nucleate boiling.
Bubble-bubble coalescence creates strong disturbances to the fluid mechanics and heat
transfer of the micro- and macro-layer beneath the bubbles. Because of the complicated
nature, the detailed physics and the effects of the bubble-bubble interaction process have
never been completely unveiled.
During the terrestrial pool boiling, the critical heat flux (CHF), which is the upper
heat transfer limit in the nucleate boiling, represents a state of balance. Because the
buoyancy force strength is relatively constant on earth, for heat fluxes lower than the
CHF, this force is more than that required for a complete removal of vapor bubbles
formed on the heater surface. At the CHF, the buoyancy force is exactly equal to the
force required for a total removal of the vapor bubbles. For heat fluxes greater than the
CHF, the buoyancy force is unable to remove all the bubbles, thus resulting in the
accumulation and merging of bubbles on the heater surface, which eventually leads to a
total blanketing of the heater surface by a layer of superheated vapor. Heat transfer
through the vapor film, so-called film boiling, is much less efficient than the nucleate
boiling and produces very high heater surface temperatures.
1

2
In many modem heat transfer applications, the length scale of heat source gets
smaller, where traditional boiling theory may not be applicable. How does the length
scale affect the boiling phenomenon? How do we maximize the heat transfer from a
limited heater surface? Those are frequent questions asked by industrial engineers. There
is no way to accurately answer these questions without the knowledge of microscale
boiling phenomenon.
1.2 Research Objectives
This research seeks to perform high-quality experiments to unmask the effects of
bubble coalescence and length scale of heaters on heterogeneous nucleate boiling
mechanisms. Through this research, we would be able to achieve the following:
1. To find the basic physics of bubble coalescence and its effects on fluid
mechanics and heat transfer in the micro- and macro-layers and to develop a simple
mechanistic model for this phenomenon.
2. To obtain a fundamental understanding of the effects of heater length scale on
the boiling mechanism and boiling heat transfer.
We intend to study the detailed physics of bubble formation on small heaters,
bubble coalescence and bubble dynamics, and heat and mass transport during bubble
coalescence. The purpose is to delineate through experiment and analysis the
contributions of the key mechanisms to total heat transfer. This includes micro/macro
layer evaporation on single and merged bubbles attached to a heated wall, and heat
transfer enhancement during coalescence of bubbles on the heater wall. We intend to
provide answers to the following:
How will the bubble coalescence affect the heat transfer from the heater surface?

3
What mechanisms are at play during bubble coalescence? In other words, how do
the thermodynamic force, surface tension force, and hydrodynamic force that are
associated with the merging process balance one another?
What controls the bubble nucleation, growth, and departure from the heater
surface in nucleate boiling when bubble coalescence is part of the process?
How does the heater surface superheating level affect the bubble coalescence?
How does the heater length scale affect the bubble inception and boiling heat
transfer?
1.3 Significance and Justification
Nucleate boiling has been recognized as one of the most efficient heat transfer
mechanisms. In many engineering applications, nucleate boiling heat transfer is the mode
of choice. Boiling heat transfer has the potential advantage of being able to transfer a
large amount of energy over a relatively narrow temperature range with a small weight to
power ratio. For example, boiling heat transfer has been widely used in microelectronics
cooling.
Apart from the engineering importance, there are science issues. Currently, the
mystery of critical heat flux remains unsolved. As a matter of fact controversies over the
basic transport mechanisms of bubble coalescence and its effects on the role of
microlayer and macrolayer, liquid resupply and heater surface property continue to
puzzle the heat transfer community. With the micro-array heaters, high speed data
acquisition system and high speed digital camera, we would have a better chance to
unlock the secrets of nucleate boiling. Boiling is also an extremely complex and elusive
process. Although a very large number of investigators have worked on boiling heat
transfer during the last half century, unfortunately, for a variety of reasons, far fewer
efforts have focused on the physics of boiling process. Most of the reported work has
been tailored to meeting the needs of engineering applications and as a result has led to

4
correlations involving several adjustable parameters. The correlations provide a quick
input to design, performance and safety issues; hence they are attractive on a short-term
basis. However, the usefulness of the correlations diminishes very rapidly as parameters
of interest start to lie outside the range for which the correlations were developed.

CHAPTER 2
LITERATURE REVIEW AND BACKGROUND
2.1 Bubble Dynamics and Nucleate Boiling
Boiling is an effective heat transfer mode because a large amount of heat can be
removed from a surface with a relatively small temperature difference between the
surface and the bulk liquid. Boiling bubbles have been successfully applied in ink-jet
printers and microbubble-powered acuators. The technologies still in the research and
development stage for possible applications include TIJ printers, optical cross-connect
(OXC) switch, micropumping in micro channels, fluid mixers for chemical analysis, fuel
mixers in combustion, prime movers in micro stem engines, and the heat pumps for
cooling of semiconductor chips in electronic devices. The boiling curve first predicted by
Nukiyama (1934) has been used to describe the different regimes of saturated pool
boiling. But until now, there are no theories or literature that exactly explains the
underlying heat transfer mechanisms. Forster and Grief (1959) assumed that bubbles act
as micropumping devices removing hot fluid from the wall, replacing it with cold liquid
from the bulk. The proposed equation for calculating the boiling heat transfer is
4 = P,cpl
f7n\
, 3 ,
Ri
ÍT -T
ls ll
-T,
f
(2.1)
Mikic and Rohsenow (1969) developed a model whereby the departing bubble
scavenges away the superheated layer, initiating transient conduction into the liquid.
They also proposed the heat flux calculation by the expression
5

6
1/2
[T„-Tjfm (2.2)
Mei et al. (1994) investigated the bubble formation and growth by considering
simultaneous energy transfer among the vapor bubbles, liquid microlayer, and the heater.
They presented the sketch for a growing bubble, microlayer and heating solid which is
shown in figure 2.1(a), where the bubble dome has the shape of a sphere of radius of
Rb(t), the microlayer has a wedge shape with a radius Rb(t), wedge angle 0 centered at r
= 0.
They found that four dimensionless parameters governing the bubble growth rate
are Jacob number, Fourier number, thermal conductivity and diffusivity ratios of liquid
and solid. And the Jacob number is the most important one affecting c and ci, two
empirically determined constants that depict the bubble shape and microlayer wedge
angle. Using this model, they examined the effects of varying Ja, Fo, k, a\ separately.
The results are shown in figure 2.1(b), and they claim that the effects of Ja, Fo, k, «i on
the normalized growth rate Rb(t) are the following: (1) increasing Ja and a.\ will result in
an increasing Rb(t), and (2) increasing Fo and k will result in a decreasing R\,(t).
Recently, Robinson and Judd (2001) developed a theory to manifest the
complicated thermal and hydrodynamic interactions among the vapor, liquid and solid for
a single isolated bubble growing on a heated plane surface from inception. They use the
model shown in figure 2.2(a) to investigate the growth characteristics of a single isolated
hemispherical bubble growing on a plane heated surface with a negligible effect of an
evaporating microlayer. They demarcate the bubble growth into four regions, surface
tension controlled growth (ST), transition domain (T), inertial controlled growth (IC), and

7
(a)
Parametric dependence of the normalized growth rate £(r). (a) Ja - I, 10, 100 and 1000 at (Fo. k.
a) - (I, 0.005, 0.005); (b) Fo - 0.01, I, 10, 100, 1000 and 10000 at (/a, k, a) - (10. 0.005, 0.005); (c)
K - 0.0005,0.001.0.01,0.05 at (Jo, Fo. i) - (10,1.0.005) and (d) » - 0.0005,0.001.0 01 and 0.05 at (Jo,
Fo.k) - (10, 1,0.005).
(b)
Figure 2.1 The numerical model and results given by Mei et al. (1995). (a) The numerical
model; (b) The numerical results.

8
(a)
Time (ms)
(b)
Figure 2.2 The numerical model and four growth domains by Robinson and Judd (2001).
(a) The numerical model-Hemispherical bubble growing on a plane heated surface; (b)
The four growth domains with contiuent pressures at each domain.

9
heat transfer controlled growth (HT), which are shown in figure 2.2(b). During the
surface-controlled domain, they claim that energy is continuously transferred into the
bubble by conduction through liquid. But the average heat flux, thus the growth rate
d/?b/dt, is so small that the contribution of the hydrodynamic pressure in balancing the
equation of motion is insignificant so that it essentially reduces to a static force balance,
Pv - Poo = 2o//?b, as shown in figure 2.2(b). The bubble growth in this domain is
accelerated due to a positive feedback effect in which the increase in the radius, Rb, is
related to a decreasing interfacial liquid temperature. This corresponds to an increase in
q", through the increase in the magnitude of the local temperature gradient, which feeds
back by a proportional increase in the bubble growth rate dRJdt. In the earliest stage of
the surface tension domain, this feedback is not significant. However, in the latter stage,
it becomes appreciable as indicated by a noticeable increase in R¡, away from Rbc, a
significant decrease in both Tv and Pv and a sharp increase in q". At the transition
domain, the hydrodynamic force Phd rises sharply due to the significant liquid motion
outside of the bubble interface. Though q" and 3/?b/3t increase at the beginning of this
stage, they are shown to decrease in the latter stage and reach the maximum value. One of
the reasons for this decrease in spite of a positive feedback of surface-controlled growth
can be additional resistance associated with forcing the bulk liquid out radially. The other
reasons can be due to the conduction and advection occurring in the liquid adjacent to the
interface. Each of these heat transfer mechanisms acts in such a way as to diminish the
temperature gradients in the immediate vicinity of the vapor-liquid interface and thus has
a detrimental influence on the rate at which q" and dRJdt increase. The inertial controlled
growth refers to the interval of bubble growth in which the rate of bubble expansion is
considered to be limited by the rate at which the growing interface can push back the

10
surrounding liquid (Carey, 1992). In this domain, the average heat flux into the bubble is
very high, so heat transfer to the interface is not the limiting mechanism of the growth.
The pressure difference, Pv - Poo, is now balanced by the hydrodynamic pressure at the
interface. The hydrodynamic pressure comprises two “inertial” terms, i.e., the
acceleration term, pi/?b(d2/?b/dt2), and the velocity term, 3/2pi(d/?b/dr)2- The two terms are
of differing signs and thus tend to have an opposite influence on the total liquid pressure,
and thus the force of the liquid on the bubble interface. This inertial controlled growth
domain is characterized by a decreasing average heat flux and a decelerating interface.
This signifies that the positive influence that the decreasing vapor temperature tends to
have on the local temperature gradient is not sufficient to compensate for the rate at
which advection and conduction serve to decrease the temperature gradient at the
interface. The heat transfer controlled growth domain refers to the interval of bubble
expansion and is considered to be limited by the rate at which liquid is evaporated into
the bubble, which is dictated by the rate of heat transfer by conduction through the liquid
(Carey, 1992). In this latter stage of bubble growth, the interface velocity has slowed
enough so that the hydrodynamic pressure, Pm, becomes insignificant compared with the
surface tension term, 2a//?b, in balancing the pressure difference, Pv - Poo. This is shown
in figure 2.2(b). Because the liquid temperature at the interface is now constant, the
positive feedback effect, responsible for the rapid acceleration of the vapor-liquid
interface in the surface tension controlled region, does not occur in this domain of
growth. Conversely, the “shrinking” and “stretching” of the thermal layer in the liquid
due to conduction and advection are responsible for the continuous deceleration of the
interface due to the diminishing interfacial temperature gradients.

11
The steady cyclic growth and release of vapor bubbles at an active nucleation site
are termed an ebullition cycle. This bubble growth process begins immediately after the
departure of a bubble. Bulk fluid replaces the vapor bubble initially. A period of time,
called waiting period, then elapses during which transient conduction into the liquid
occurs but no bubble growth takes place. After this, the bubble begins to grow as the
thermal energy needed to vaporize the liquid at the interface arrives. This energy comes
from the liquid region adjacent to the bubble that is superheated during the waiting period
and from the heated surface. As the bubble emerges from the site, the liquid adjacent to
the interface is highly superheated and the transfer of heat is not a limiting factor.
However, the resulting rapid growth of the bubble is resisted by the inertia of the liquid
and, therefore, the bubble growth is considered to be inertia controlled. During the
inertia-controlled growth, the bubble generally grows radially in a hemispherical shape.
A thin microlayer (evaporation microlayer) is formed between the lower portion of the
bubble interface at the heated wall. Heat is said to transfer across the thin film from the
wall to the interface by directly vaporizing liquid at the interface. The liquid region
adjacent to the bubble interface (relaxation microlayer) is gradually depleted of its
superheat as the bubble grows. Therefore, as growth continues, the heat transfer to the
interface may become the limiting factor and the bubble is said to be heat transfer
controlled. It is easy to see that vapor bubbles grow in two distinct stages. Fast growth
emerges initially, followed by a slow growth period until detachment.
In general, very rapid, inertia controlled growth is more likely under the following
conditions which typically produce a build-up of high superheat levels during the waiting
period and/or cause rapid volumetric growth (Carey, 1992).
- High wall superheat

12
- High imposed heat flux
- Highly polished surface having only very small cavities
- Very low contact angle (highly wetting liquid)
- Low latent heat of vaporization
- Low system pressure (resulting in low vapor density)
Heat transfer controlled growth of a bubble is more likely for conditions which
result in slower bubble growth or result in a stronger dependence of bubble growth rate
on heat transfer to the interface. They include:
- Low wall superheat
- Low imposed heat flux
- A rough surface having many large and moderately sized cavities
- Moderate contact angle and moderately wetting liquid
- High latent heat of vaporization
- Moderate to high system pressures
The forces acting on a bubble can be a very complicated issue. It is highly
dependent on the bubble stages during its cyclic process. Among all forces, dominant
force can vary depending on the bubble stages, surface superheat, boiling condition, and
so forth. In general, the following major forces can be involved during boiling: surface
tension, buoyancy force, inertia of induced liquid flow, drag force, internal pressure,
adhesion force from the substrate, etc. In a flow boiling field, due to possible bubble slide
before the bubble lifts off, boiling becomes even more complicated. Klausner et al.
(1993) have studied bubble departure on an upward facing horizontal surface using R-113
as the test fluid. By balancing forces due to surface tension, quasi steady drag, liquid
inertia force due to bubble growth, buoyancy, shear lift force, hydrodynamic pressure and

13
contact pressure along and normal to the heater surface, they found that the bubble will
slide before lift-off. The predicted bubble diameter at the beginning of sliding motion was
found to agree well with their data. It was noted that liquid inertia force resulting from
the bubble growth played a more important role in holding the bubble adjacent to the
heater surface than the surface tension. However, such a conclusion is highly dependent
on the base diameter that is used in calculating the force due to surface tension. In a
subsequent study, Zeng et al. (1993) correlated both bubble diameter at departure and the
lift off diameter by assuming that the major axis of the bubble became normal to the
surface after the bubble began to slide. By balancing the components of buoyancy, liquid
inertia, and shear lift force in the direction of flow, they were able to predict bubble
diameter at departure. The bubble lift-off diameter was determined by balancing forces
due to buoyancy and liquid inertia associated with bubble growth. For the evaluation of
liquid inertia, the proportionality constant and the exponent in the dependence of bubble
diameter on time were obtained from the experiments. Mei et al. (1999) have included
the surface tension force, liquid inertia, shear lift force and buoyancy to determine the
bubble lift-off diameter. For the model the bubble lift off diameter was shown to decrease
with flow velocity and slightly increase with wall superheat. Maity and Dhir (2001)
experimentally investigated the bubble dynamics of a single bubble formed on a
fabricated micro cavity at different orientations of the heater surface with respect to the
horizontal surface. They found that under flow boiling conditions bubbles always slide
before lift off and the bubble departure diameter depends solely on the flow velocity and
is independent of the inclination of the surface. Bubble departure diameter decreases with
the flow velocity. Bubble lift-off diameter depends on both the flow velocity and the

14
angular position. Lift-off diameter increases with the angular position but decreases with
the flow velocity.
On the other hand, commercial success of bubble jet printers (Nielsen, 1985) has
inspired many researchers to apply bubble formation mechanisms as the operation
principle in microsystems. For this purpose, the bubble from a microheater should be
designed to present a stable, controllable behavior. Therefore, it is important to
understand the bubble formation mechanisms in microheaters before they may be
optimally designed and operated. Some previous work has been done in investigating
bubble formation mechanism. Iida et al. (1994) used a 0.1mm x 0.25mm x 0.25pm film
heater subjected to a rapid heating (maximum 93 x 106 K/s). They measured the
temperature of heaters by measuring the electrical resistance. The temperature measured
at bubble nucleation suggested homogeneous bubble nucleation in their experiment. But
the heater they used does not ensure a uniformly heated surface. Lin et al. (1998) used a
line resistive heater 50 x 2 x 0.53 pm3 to produce microbubbles in Fluorinert fluids. By a
computational model and experimental measurements, they concluded that homogeneous
nucleation occurs on these micro line heaters. They also reported that strong Marangoni
effects prevent thermal bubbles from departing. Avedisian et al. (1999) performed
experiments on a heater (64.5pm x 64.5pm x 0.2pm) used on the commercial thermal
inkjet printer (TIJ) by applying voltage pulses with short duration. They claimed that
homogeneous nucleation at a surface is the mechanism for bubble formation with an
extremely high heating rate (2.5 x 108 K/s), and this nucleation temperature increases as
the heating rate increases. Zhao et al. (2000) used a thin-film microheater of size of
100pm x 110pm to investigate the vapor explosion phenomenon. They placed the
microheater underside of a layer of water (about 6pm), and the surface temperature of the

15
heater was rapidly raised electronically well above the boiling point of water. By
measuring the acoustic emission from an expanding volume, the dynamic growth of the
vapor microlayer is reconstructed where a linear expansion velocity up to 17 m/s was
reached. Using the Rayleigh-Plesset equation, an absolute pressure inside the vapor
volume of 7 bars was calculated from the data of the acoustic pressure measurement. In a
heat transfer experiment, Hijikata et al. (1997) investigated the thermal characteristics
using two heaters of 50pm x 50pm and 100pm x 100pm, respectively. They found that
70-80% of heat generated was released through a phase change process and heat is
initially conducted in the glass substrate, then, it is transferred to the liquid layer above
the heater and finally released through the evaporating process. Most of these works are
based on applying a constant current or voltage so that the heat flux on the heater is
maintained constant.
2.2 Coalescence of Bubbles
The suggested theory about boiling mechanism is that as the temperature of a
heater surface increases from the onset of nucleate boiling, more bubbles are nucleated
and coalesce simultaneously on the heater surface, which makes the heat flux higher and
higher until the critical heat flux point (CHF). It has been considered for a long time that
bubble-bubble coalescence plays an important, if not dominant, role in the high heat flux
nucleate boiling regime and during the CHF condition as well. Because of the
microscopic nature and complicated flow and heat transfer mechanisms, the research on
coalescence has not progressed very fast in both experimental and theoretical fronts.
Coalescence of bubbles on a surface is a highly complicated process that is involved with
a balance among surface tension, viscous force and inertia. The phenomenon is

16
intrinsically a fast transient event. For the above reasons, the research of coalescence
between bubbles has been rather limited.
Li (1996) claims when two small bubbles approach each other, a dimpled thin
liquid film is formed between them, as shown in figure 2.3(a). He developed a model for
the dynamics of the thinning film with mobile interfaces, in which the effects of mass
transfer and physical properties upon the drainage and rupture of the dimpled liquid film
are investigated. The model predicts the coalescence time, which is the time required for
the thinning and rupture of the liquid film, given only the radii of the bubbles and the
required physical properties of the liquid and the surface such as surface tension, London-
van der Waals constants, bulk and surface diffusion coefficients. The comparison of the
predicted time of coalescence and experimental results is shown in figure 2.3(b), which
shows that predicted coalescence is less than experimental results, and much less than the
results predicted when the immobile interface is considered. In his research, no heat
transfer is considered to affect the bubble coalescence.
Yang et al. (2000) performed a numerical study to investigate the characteristics
of bubble growth, detachment and coalescence on vertical, horizontal, and inclined
downward-facing surfaces. The FlowLab code, which is based on a lattice-Boltzmann
model of two-phase flows, was employed. Macroscopic properties, such as surface
tension and contact angle, were implemented through the fluid-fluid and fluid-solid
interaction potentials. The model predicted a linear relationship between the macroscopic
properties of surface tension and contact angle, and microscopic parameters.
Hydrodynamic aspects of bubble coalescence are investigated by simulating the growth
and detachment behavior of multiple bubbles generated on horizontal, vertical, and

17
(a)
(b)
Figure 2.3 Research on bubble coalescence by Li (1996). (a) The thin liquid film between
bubbles; (b) Comparison of the predicted results with experimental results.

18
inclined downward-facing surfaces. For the case of horizontal surface, three distinct
regimes of bubble coalescence were represented in the lattice-Boltzmann simulation:
lateral coalescence of bubbles situated on the surface; vertical coalescence of bubbles
detached in a sequence from a site; and lateral coalescence of bubbles, detached from the
surface. Multiple coalescence was predicted on the vertical surface as the bubble
detached from a lower elevation merges with the bubble forming on a higher site. The
bubble behavior on the inclined downward-facing surface was represented quite similarly
to that in the nucleate boiling regime on a downward facing surface.
Bonjour et al. (2000) performed an experimental study of the coalescence
phenomenon during nucleate pool boiling. Their work deals with the study of the
coalescence phenomenon (merging of two or more bubbles into a single larger one)
during pool boiling on a duraluminium vertical heated wall. Various boiling curves
characterizing boiling (with or without coalescence) from three artificial nucleation sites
with variable distance apart are presented. The heat flux ranges from 100 to 900 w/cm2
and the wall superheat from 5 to 35 K. They pointed out that the coalescence of bubbles
growing on three sites results in higher heat transfer coefficients than single-site boiling,
which is attributed to the supplementary microlayer evaporation shown in figure 2.4(a).
However, the highest heat transfer coefficients are obtained for an optimal distance
between the sites for which coalescence does not occur. They used different inter-site
distances (a = 0.26mm, 0.64mm, 1.05mm, 1.50mm, 1.82mm) to generate bubbles and
stated that for low and high intersite distances, the heat flux deviation is limited by the
seeding phenomenon and the intersite distance, respectively, whereas for moderate
intersite distances, the heat flux deviation is maximum because of the vicinity of the sites
and absence of seeding. They also showed that due to bubble coalescence there is a

19
noticeable change of the slope of the coiling curve. They claim that such a change is
attributed to coalescence and not to the progressive activation of the sites. They also
showed that the coalescence of two bubbles has a much lower effect on the slope of the
boiling curve, because the supplementary microlayer evaporation with two bubbles is
lower than with three bubbles and consequently has a lower effect on the heat transfer
coefficient. They used the influence area shown in figure 2.4(b) to depict the locations of
the influence areas for various intersite distances. For a = 0.26mm, the influence area is
overlapped for the three bubbles, thus a small overall influence area, which for the heater
of larger area results in a large heat transfer coefficient. They also proposed a map for
activation and coalescence that is shown in figure 2.4(c). In their experiment, it is also
shown that coalescence results in a decrease in the bubble frequency.
Haddad and Cheung (2000) found that the coalescence of bubbles is one of the
phases in a cyclic process during nucleate boiling on a downward-facing hemispherical
surface. Bubble coalescence follows the phase of bubble nucleation and growth but
precedes the large vapor mass ejection phase. A mechanistic model based on the bubble
coalescence in the wall bubble layer was proposed by Kwon and Chang (1999) to predict
the critical heat flux over a wide range of operating conditions for the subcooled and low
quality flow boiling. Comparison between the predictions by their model and the
experimental CHF data shows good agreement over a wide range of parameters. The
model correctly accounts for the effects of flow variables such as pressure, mass flux and
inlet subcooling in addition to geometry parameters. Ohnishi et al. (1999) investigated the
mechanism of secondary bubble creation induced by bubble coalescence in a drop tower
experiment. They also performed a two-dimensional numerical simulation study. They

20
\ \ x ' y T
(b)
(c)
Figure 2.4 The coalescence research performed by Bonjour et al. (2000). (a) The
additional microlayer formed; (b) Schematic representation of influence-area; (c)
Coalescence and activation map.

21
reported that the simulation results agree well with the experimental data and indicate
that the size ratio and the non-dimensional surface tension play the most important role in
the phenomenon.
2.3 Critical Heat Flux
The boiling curve was first identified by Nukiyama (1934) more than sixty years
ago. Since then the critical heat flux (CHF) has been the focus of boiling heat transfer
research. A plethora of empirical correlations for the CHF are now available in the
literature, although each is applicable to somewhat narrow ranges of experimental
conditions and fluids. Recently a series of review articles (Lienhard 1988a,b, Dhir, 1990,
Katto, 1994, Sadasivan et al., 1995) have been devoted to the discussion of progress
made in the CHF research. The consensus is that a satisfactory overall mechanistic
description for the CHF in terrestrial gravity still remains elusive. The following are some
perspectives on issues in CHF modeling elucidated in a recent authoritative review by
Sadasivan et al. (1995).
1. CHF is the limiting point of nucleate boiling and must be viewed as linked to
high-heat-flux end of nucleate boiling region and not an independent pure hydrodynamic
phenomenon. The experiments dealing with CHF will be meaningful if only
measurements of the high heat-flux nucleate boiling region leading up to CHF are made
together with the CHF measurement. This would help resolve the issue of the role of dry
area formation and the second transition region on CHF. Simultaneous surface
temperature measurements are necessary.
2. Measurements of only averaged surface temperature in space or in time
actually mask the dynamics of the phenomena. An improved mechanistic explanation of
CHF also requires that experimental efforts be directed towards making high resolution

22
and high-frequency measurements of the heater surface temperature. Experiments
designed to make transient local point measurements of surface temperature (temperature
map) and near surface vapor content will help in developing a clearer picture of the
characteristics of the macrolayer and elucidating the role of liquid supply to the heater
surface. Microsensor technology appears to be one area that shows promise in this
respect.
3. Identifying the heater surface physical characteristics such as active nucleation
site distribution, static versus dynamic contact angles, and advancing versus receding
angles. These would help understand the heater surface rewetting behavior.
Sakashita and Kumada (1993) proposed that the CHF is caused by the dryout of a
liquid layer formed on a heating surface. They also suggested that a liquid macrolayer is
formed due to the coalescence of bubbles for most boiling systems, and that the dryout of
the macrolayer is controlled by the hydrodynamic behavior of coalesced bubbles on the
macrolayer. Based on these considerations, a new CHF model is proposed for saturated
pool boiling at higher pressures. In the model, they suggest that a liquid macrolayer is
formed due to coalescence of the secondary bubbles formed from the primary bubbles.
The detachment of the tertiary bubbles formed from the secondary bubbles determines
the frequency of the liquid macrolayer formation. The CHF occurs when the macrolayer
is dried out before the departure of the tertiary bubbles from the heating surface. One of
the formulations of the model gives the well-known Kutateladze or Zuber correlation for
CHF in saturated pool boiling.
The vast majority of experimental work performed to date utilized the heat flux-
controlled heater surface to generate bubbles. Rule and Kim (1999) were the first to
utilize the micro heaters to obtain a constant temperature surface and produced spatially

23
and temporally resolved boiling heat transfer results. Bae et al. (1999) used identical
micro heaters as those used by Rule and Kim (1999) to study single bubbles during
nucleate boiling. They performed heat transfer measurement and visualization of bubble
dynamics. In particular, it was found that a large amount of heat transfer was associated
with bubble nucleation, shrinking of dry spot before departure, and merging of bubbles.
In this research, identical micro heaters to those of Rule and Kim (1999) were used to
investigate the boiling microscopic mechanisms through the study of single bubbles
boiling and the coalescence of bubbles. For each experiment, the temperature of the
heaters was kept constant while the time-resolved and space-resolved heat fluxes and
bubble images were recorded.

CHAPTER 3
EXPERIMENT SYSTEM
3.1 Microheaters and Heater Array
3.1.1 Heater Construction
This section describes briefly the heater array construction. The details can be
referred to T. Rule, Design, Construction, and Qualification of a Microscale Heater
Array for Use in Boiling Heat Transfer, Master of Science thesis in mechanical
engineering at the Washington State University, 1997.
The heater array is constructed, as shown in figure 3.1(a), by depositing and
etching away layers of conductive and insulating material on a quartz substrate to form
conductive paths on the surface which will dissipate heat when electrical current is
passed through them. The basic element of the microscale heater array is the serpentine
platinum heater. The heater element, as shown in figure 3.1(b), is constructed by
depositing platinum onto the substrate surface, masking off the heater lines, and etching
platinum away from the unmasked areas. The terminal ends of each platinum heater are
connected to the edge of the chip with aluminum leads deposited on the chip. Substrate
conduction was reduced by using a quartz (k = 1.5 w/mK) substrate instead of a silicon (k
= 135 w/mK) substrate, since silicon is 90 times more thermally conductive than quartz.
A Kapton (k = 0.2 w/mK) would further reduce substrate conduction, but it has not yet
been tested as a substrate material. Quartz is an electrical insulator, so the substrate
cannot be used as an electrical ground, as it was when silicon was used. An aluminum
layer was deposited over the platinum heaters to serve as a common heater ground.
24

25
Something must be used to separate the platinum heaters from the aluminum layer. But
still the problem with the ground potential variation exists. The simplest way to eliminate
the problem with ground potential variations is to provide an individual ground lead for
each heater that connects to a ground bus bar. This bus bar must be large enough to
provide less than 100 pV voltage difference between individual heater ground
connections during all operating conditions. The construction steps are as follows:
1. A thin layer of titanium (Ti, 22) is first sputtered onto the quartz to enable the
platinum (Pt, 78) to adhere to surface.
2. A 2000 Á layer of platinum is deposited on top of the titanium layer.
3. The platinum and titanium are etched away to leave the serpentine platinum
heaters and the power leads.
4. A layer of aluminum is then deposited and etched away to leave aluminum
overlapping the platinum for the power leads and the wire bonding pads.
5. Finally, a layer of silicon dioxide is deposited over the heater array to provide a
uniform energy surface across the heater. The area where wire-bond connections will
later be made is masked off to maintain a bare aluminum surface.
3.1.2 Heater Specification
The finished heater array measures approximately 2.7 mm square. It has 96
heaters on it, as shown in figure 3.1(c). Each individual heater is about 0.27 mm square.
The lines of the serpentine pattern are 5 pm wide, with 5 pm spaces in between the lines.
The total length of the platinum lines in one heater is about 6000 pm, and the heater lines
about 2000 Á thick. The nominal resistance of each heater's resistance is 750 ohm.

26
Aluminum Ground Lead Silicon Dioxide Aluminum Power Lead
(a)
(b)
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Figure 3.1 Heaters and heater array, (a) Heater construction; (b) Single serpentine
platinum heater; (c) Heater array with 96 heaters.

27
3.2 Constant Temperature Control and Data Acquisition System
The system is consisted of feedback electronics circuits, interface print board
connecting heaters array to the feedback electronics circuits, a D/A board used to set the
heater temperature, two A/D boards for data acquisition, and software made from Visual
Basics 6.0 in windows 95.
3.2.1 Feedback Electronics Loop
This experiment makes use of the relationship between platinum electrical
resistance and its temperature. We know that resistance of the platinum almost varies
linearly with its temperature by the following relationship:
(.R-R)/R = C(T-T) (3.1)
Where R is the electrical resistance at temperature T, R0 is the resistance at a
reference temperature T0 and C is the constant coefficient. For platinum, the value of C
is 0.002 Q/Q°C. The key part of the loop is the Wheatstone bridge with a feedback loop
where Rh is the platinum heater. Each heater has a nominal resistance 750Q. For a
temperature change of 1°C, the heater’s resistance would change by 1.5Q, while R2, R3
and R4 are regular metal film resistors which values are not sensitive to temperature. The
resistance of the digital potentiometer, Rc, can be set by the computer. Each heater has an
electronic loop to regulate and control the power across it. Wheatstone bridge shown in
figure 3.2 is used to carry out the constant temperature control. The bridge is said to be
balanced when Vt = V2. This occurs when the ratio between R4 and Rh is the same as that
between R2 and (Rc+R3). The feedback loop maintains the heater at a constant
temperature by detecting imbalance and regulating the current through the bridge in order
to bring it back into balance. The amplifier will increase or decrease the electrical current

28
to the circuit until the heater reaches the resistance necessary for the bridge to maintain
balance. Therefore, the exact value of Rc corresponds to the temperature of the heater Rh.
Figure 3.2 Wheatstone bridge with feedback loop.
3.2.2 ^Processor Control Board and D/A Board
Each heater on the heater array can be individually controlled. ^Processor control
card programs each of the 96 feedback control circuits with correct control voltage.
Rather than having 96 separate wire connections from the computer control board, a
multiplexing scheme is used, where a single wire carries a train of voltage pulses to all
the boards and an address bus directs the voltage singles to the correct feedback circuit.
D/A board is used to connect the computer for the software to send the addressing
signals. The details can be referred to T. Rule, "Design, Construction, and Qualification
of a Microscale Heater Array for Use in Boiling Heat Transfer", Master of Science thesis
in mechanical engineering at Washing State University.

29
3.2.3A/D Data Acquisition Boards
Each of the A/D data acquisition boards used in this experiment has 48 channels.
For 96 heaters, to acquire data simultaneously, we installed two A/D cards. But we just
need one of them because maximum eight heaters were selected for the purpose of this
research. The major parameters of the A/D cards have been shown in Table 3.1.
Table 3.1 The specifications of the D/A cards
# channels
48 single ended, 24 differential or modified
differential
Resolution
12 bits, 4095 divisions of full scale
Accuracy
0.01% of reading +/-1 bit
Type
successive approximation
Speed
micro-seconds
3.2.4 Heater Interface Board (Docoder Board)
Heater interface board is used to interface the heater array with the feedback
control system. Since the heaters are independently grounded on the heater array, there
are 192 wires extended from the heater array to the interface board, which are accessed
by the feedback electronics loops.
3.2.5 Software
The software used in this experiment functions as following:
1. Address heaters so that heaters can be selected.
2. Send signals from the computer to the computer control board and D/A card to
set the heaters temperature.
3.Automatic and manual heaters calibration.

30
4. Data acquisition.
The software is developed in the Microsoft Visual Basic 6.0 environment under
windows 95 running in PC.
3.3 Boiling Condition and Apparatus
3.3.1 Boiling Condition
In this experiment, we choose FC-72 to be the boiling fluid. The reason for
choosing FC-72 is that it is dielectric, which makes it possible for each heater to be
individually controlled. The bulk fluid is at the room condition (1 atm, 25°C), where its
saturation temperature is 56°C, thus it is subcooled pool boiling.
3.3.2 Boiling Apparatus
Initially the boiling experiments were performed in an aluminum chamber. To
improve the visualization results, a transparent boiling chamber was built. Another
advantage of the new chamber is its flat glass walls that effectively prevent the image
distortion taken by the fast speed camera described in section 3.4.2. Figure 3.3 shows the
boiling experimental setup. In addition to heater array and electronics feedback system,
the computer is used to select the heaters and set their temperature through D/A card and
acquire data through A/D cards.
3.4 Experiment Procedure
3.4.1 Heater Calibration
3.4.1.1 Calibration apparatus
The calibration apparatus includes the constant temperature oil tank with oil-
circulating pump and temperature control system, as shown in figure 3.4. The constant oil
tank functions to impinge the constant oil into the heater array surface. The temperature

31
Not to Scale
Digital camera
for bottom view
Figure 3.3 Boiling apparatus.
control system is used to keep the circulating oil at a constant temperature. Calibration is
the beginning of the experiment, and it is also a very important step since the following
boiling experiment will be based on the calibration data. Therefore, much more care
should be exercised to ensure the accuracy.
3.4.1.2 Calibration procedure
The calibration procedure is as follows:
1. Set the temperature controller at a certain temperature.
2. Circulating the fluids in the calibration tank. Power the heating components.
After this, several minutes or more are needed to maintain the temperature of the
circulating fluid at the stable temperature.
3. Start the calibration routine in PC and calibrate. The computer automatically
saves the calibration result.

32
(a)
(b)
Figure 3.4 Schematic of calibration apparatus and temperature control loop, (a) The
calibration system; (b) The electrical loop to maintain the temperature of calibration oil.
4. Set the heater array at another temperature. Follow the first and second steps till
all calibration is completed.
5. Two calibration methods are included, automatic method and manual method.
Automatic method is for regular calibration use. We can select heaters to
calibrate, though, normally we calibrate all 96 heaters at one time. To find the
corresponding control voltage for the set temperature, progressive increment method was
used. Increment the control voltage gradually, and compare the voltage output across the

33
heater with last time value. If the voltage across the heater is different from the last time
value, we can say, the controlling system starts to regulate the circuit. Then the control
voltage is the corresponding value for the set temperature. It is worth mentioning that
how to set the difference to compare the voltage is important. Initially, the difference was
set as 0.01. The result proves the control voltage is a little bit higher than the actual value.
If the difference is set as 0.003, then the result is good. How to prove the result is the
correct value for the set temperature, manual calibration method is used to check it out.
Manual method is an alternative to the regular automatic method. It is designed to
check the accuracy of the automatic method. By referring to the figure 3.5(a), we can see
by increasing the control voltage, the heater’s voltage starts to increase at about 91 axial
value. Below 91, the heater’s temperature is at the set temperature; the voltage across the
heater is very small and at a relatively constant level. Starting at 91, increasing the
control voltage will increase the heater’s voltage so that heater’s temperature increases
accordingly. The starting value of 91 is the control voltage corresponding to the set
temperature. This method is much more viewable than automatic method. Its
disadvantage is slow, only one heater can be done at one time. But we can rely on its
result to verify the accuracy of automatic method.
3.4.1.3 Calibration results
Based on the relations between the heater resistance and temperature indicated in
Eq. (3.1). For each heater, its resistance almost linearly changes with temperature. Thus,
ideally, the resistance-temperature figure is an approximately straight line. The slope of
the line is determined by the material property. Thus the lines representing the resistance-
temperature relations have almost the same slope. On the other hand, the temperature
change also depends on heater’s initial resistance values. This regard is shown on figure

34
3.5(b) for calibration results of heaters #1 through #9, where the slope of the lines for
different heaters.
(a)
(b)
Figure 3.5 Part of the calibration results, (a) Result of the manual calibration method;
(b) The calibration results (only heaters #1 through #9 were shown).

35
The calibration results obtained for each heater will be used in boiling experiment
to set heater temperatures. For the present research, the heaters will be always set at the
same temperature in any experiment performed, thus nominally, there will not be any
temperature gradient among heaters.
3.4.1.4 Comparison of calibrated resistances with the calculated resistances
To validate the calibration results, i.e. the temperature of the heaters obtained by
calibration, we have measured the resistances of each heater at different temperatures and
then compare them with the resistances from calculation using the platinum property
relation given by Eq. (3.1), the result is shown in figure 3.6. From the above comparison,
we conclude that measured resistances match well with calculated resistance. It implies:
(1) The heater temperature is reliable.
(2) We can use calculated resistance to evaluate heat dissipation with only a small
uncertainty introduced.
Figure 3.6 Comparison of calibrated resistances of heater #1 with the calculated
resistances from property relation.

36
3.4.2 Data Acquisition and Visualization
To investigate the bubble coalescence, we need to generate bubbles with
appropriate separation distances. Since each of the 96 heaters on the heater array is
individually controlled by the electronic feedback control system, we can set active one
or more of the heaters by powering them individually so that they reach a certain
temperature while leaving all other heaters unheated. To obtain different cases of bubble
coalescence, all we need to do is to select heaters. In reference to figure 3.1, by powering
two heaters such as heaters #1 and #11, we obtain dual bubble coalescence. Also, if we
choose #1 and #3, we obtain dual bubble coalescence with a shorter separation distance.
However, by powering two heaters that are too far apart such as #1 and #25, two single
bubbles will be generated, but the bubble departure sizes are not large enough for them to
touch and merge before they depart. Therefore, for coalescence to take place, the active
heaters have to be close enough within a certain range. The power consumed by the
heater was acquired by the computer data acquisition system (figure 3.3). Data were
acquired at a sampling rate of 40,000 Hz for each channel of the A/D system, after
allowing the heater to remain at a set temperature for 15 minutes. The data were found to
be repeatable under these conditions. The acquired data were converted to heat flux from
the heater according to the following basic relationship:
q"=(V2/¡i)/A (3.2)
For each heater configuration, the heaters were always set at the same temperature
for the bubble coalescence experiment, and this temperature is varied to investigate the
effect of heater superheat on the bubble coalescence. For all cases, the dissipation from
heaters was acquired in sequence. Because steady state has been reached in all these

37
experiments, sequential data acquisition does not affect the data accuracy. The bubble
visualization includes both bottom and side views; though bottom views are more
suitable for multiple bubble coalescence. The semi-transparent nature of the heater
substrate made it possible to take images from below the heater. The setup of experiment
has been shown in figure 3.3. A high-speed digital camera (MotionScope PCI 8000S) was
used to take images at 2000 fps with a resolution of 240 x 210, with maximum 8 seconds
of recording time. The bubble visualization was performed using the shadowgraph
technique. In this technique, the bubbles were illuminated from one side while the images
were taken from the other side.
3.5 Heat Transfer Analysis and Data Reduction
3.5.1 Qualitative Heat Transfer Analysis
Each heater has a dimension of 0.27mm x 0.27mm. For such a small heater, the
heat transfer behavior is hardly similar to that for large heaters. Specifically, the edge
effects greatly affect the heat transfer. Since the heaters used in our experiment are
always kept at a constant temperature, the data reduction turns out to be much simpler.
Qualitatively, the heat dissipated from the heater at a certain temperature, by reference to
figure 3.7(a), is composed of the following components:
1. Boiling heat transfer from the heater in boiling experiment, when the heater is
superheated high enough.
2. Conduction to the substrate on which the heater is fabricated. This is due to the
temperature gradient between the heater and the ambient through the substrate.
3. Radiation heat transfer due to the temperature difference between the heater
and ambient.
4. Natural convection between the heater and air and FC-72 vapor mixture when
the heater array is positioned vertically to be separated from the liquid for data reduction

38
experiment. This natural convection is replaced by the boiling heat transfer from the
heater when the boiling occurs on the heater surface.
3.5.2 Data Reduction Procedure
To obtain the heat transfer rates due to boiling only, we conduct the experiments
by the following procedure:
1. Measure the total heat flux supplied to the heater during the boiling process at
different heater temperatures.
The total heat flux with boiling:
q rawl = q top "I" fl condl + q radl. (3.3)
2. Tilt the boiling chamber 90°, so that the heater is exposed to the air and FC-72
vapor, while separated from FC-72 liquid, and measure the total heat flux without boiling
at corresponding temperatures.
Therefore, the total heat flux without boiling:
q raw2 — q natural "I” q cond2 "t" q rad2 (3.4)
The q"condi in Eq.(3.3) and q"COnd2 in Eq.(3.4) are the conduction to the substrate
and ambient through the substrate. Because the heater is held at a constant temperature,
they are independent of the state of fluid above the heater, thus we assume q"Condi=q"cond2.
The same reasoning also goes with radiation. Thus, from Eq.(3.3) and Eq.(3.4) the heat
dissipated above the heater during boiling can be derived as the following:
n" n" n" , n"
4 top — 4 rawl “ 4 raw2 ' 4 natural
(3.5)
where q"naturai is the contribution from natural convection with the mixture of air and FC-
72 vapor. To get a good estimate of the natural convection component in Eq.(3.5), we
need to pay special attention to the small size of the heater we used. The details for this
estimation are given in the following.

39
Figure 3.7 The schematic showing the heat dissipation from a heater, (a) The heat transfer
paths from the microheater during boiling experiment; (b) The heat transfer paths from
the heater during data reduction experiment.

40
3.5.3 Determination of Natural Convection on the Microheaters
We have done a significant amount of literature research in order to rationally
determine the natural convection on the heaters we were using. We first use the empirical
correlations to evaluate the heat dissipated from the heater, in which we use the results of
Ostrach (1953) to calculate this natural convection. Then the calculated heat dissipation is
used to compare with experimental results.
Conduction. We assume one dimensional conduction from the heater to the
ambient through the quartz substrate. The ambient has a constant temperature of 25°C.
Conductivity of the quartz substrate is kSUb = 1.5 w/mK. For different heater temperatures
T0, using Fourier law of conduction, we calculate the conduction heat flux. For
simplicity, we neglected the epoxy thickness that is used to seal the heater at the bottom.
Since we calculate the conduction based on quartz substrate only, neglecting the heat
transfer resistance of epoxy, the calculated conduction heat transfer should be larger than
that if the epoxy layer is accounted for.
Convection. When the liquid was separated from the heater, there is natural
convection heat transfer to the mixture of air and vapor from the heater. For this
calculation, the mixture of FC-72 vapor and air is approximated as ideal gas of air.
Radiation. With the approximation of black body, the radiation heat flux is
calculated as follows:
q” = <* (Ts4- To4) (3.6)
where <7 is the Stefan-Boltzmann constant.
The calculation results for the above heat transfer modes have been shown in
figure (3.8). From this figure, obviously, the sum of convection, conduction and

41
Figure 3.8 Heat flux comparison from experimental and calculation results.
radiation is far less than the total heat flux q"raw2, when the heater is separated from the
liquid. This is sufficient to prove that since the heater size is much smaller than the
regular heater size, classical horizontal isothermal correlation is not applicable for this
heater. We need to find another approach to evaluate the natural convection occurring
from the heater for the data reduction.
Baker (1972) has investigated the size effects of heat source on natural
convection. He argued that as the heat source area decreases, the ratio of source perimeter
to surface area increases and since substrate conduction is proportional to the source
perimeter, the portion of the heat transferred by conduction into the substrate increases as
the surface area decreases. In our experiment, since the heater is kept at the same constant
temperature both in boiling and no-boiling conditions, the conduction to the substrate

42
should be the same regardless of the condition on the surface of the heater. However, this
small size effect does affect the natural convection calculation in our data reduction.
Baker (1972) used the experimental setup similar to that used in this research to study
the forced and natural convection of small size heat source of 2.00 cm2, 0.104 cm2
and 0.0106 cm , respectively, smallest of which is over 10 times larger than the heater
used in this experiment. Therefore, we can not use Baker’s data in our experiment. Also
according to Park and Bergles (1987) and, Kuhn and Oosthuizen (1988), due to the small
size, the edge effects are important. The approach to determining ^"natural in this study for
a heater with height L and width W is that we first used the results of Ostrach (1953) for
two-dimensional laminar boundary layer over a vertical flat plate with a height of L. Then
the two-dimensional Nusselt number is corrected for the transverse width of W by the
correlation developed by Park and Bergles (1988). The following provides the details of
the procedure. The Grashof number, Gr¿, at the trailing edge of a vertical plate with
height L is defined as
Cr _gP(Ts-T,)L3
v2
(3.7)
where P is the coefficient of thermal expansion, Ts is the heater temperature, T, is
the ambient fluid temperature, L is the heater length, and v is the kinematic viscosity of
the fluid.
Based on Ostrach (1953), the local Nusselt number at the distance L from the
leading edge of the heater surface is given by :
GrL
f n-
Nul =
v 4 ,
S(Pr)
(3.8)

43
where g(Pr) is a function of the Prandtl number, Pr, of the fluid and is given by
LeVevre (1956) as below :
g(Pr) =
0.75 Pr^
(0.609 +1.221 Pr^ +1.238 Pr)X
(3.9)
The average Nusselt number NuL of the heater surface with a height of L can be
obtained by :
NUl=-Nul
(3.10)
This two-dimension Nusselt number needs to be corrected to take into account the
finite width effects. This correction is based on the relation given by Kuan and
Oosthuizen (1988), which is repeated here :
10.4752
362.5
Nu, , = Nu, x
L.edge L
1 +
Ral
(3.11)
In the above, Raw is the Rayleigh number based on the width W of the heater and
Raw is equal to Grw x Pr. This corrected Nusselt number NuL edge has been used to
evaluate the natural convection heat transfer from the microheaters.
The derived natural convection heat fluxes for different heater configurations are
given in figure 3.9 and they were used in equation (3.3) to find the boiling heat transfer
flux, q"top. The order of magnitude of the derived natural convection heat fluxes using the
above approach has been found to be consistent with the results given by Kuan and
Oosthuizen (1988), where they investigated numerically the natural convection heat
transfer of a small heat source on a vertical adiabatic surface positioned in an enclosure
which is very similar to our experimental condition.

44
Natural convection heat flux derived for
- heaters in this experiment
IQ
0)
X
10
9
8
7
6
5
4
3
2f-
1 -
0 h m 1111111
40 50 60
Single heater, L=0.027cm
Two heaters, L=0.038cm
Three heaters, L=0.047cm
Four heaters, L=0.054cm
Five heaters, L=0.061 cm
11111 1 1111 1111 â– 1 1111i11111111''111i'111 J ' 11' J >i I
70 80 90 100 110 120 130 140 150 160
Heater temperature (AT)
Figure 3.9 Derived natural convection heat fluxes for different heater configurations.
3.5.4 Uncertainty Analysis
Uncertainty analysis is the analysis of data obtained in experiment to determine
the errors, precision and general validity of experimental measurements.
For single sampled experiments, the methods introduced by Kline and
McClintock (1953) have been popularly used to determine the uncertainty. The theory of
the method is introduced in the following.
Assume R is a given function of the independent variables x¡, X2, xj, ... xn, that is,
R = R(xi, X2, X3,... xn). Let vvR be the uncertainty in the result of R, and wi, W2, W3,... wn,
be the uncertainties in the independent variables. If the uncertainties in the independent
variables are all given with the same odds, then the uncertainty in the result with these
odds is given as:

45
1/2
dx, 1
dx.
w2 + —W,
dx.
(3.12)
Because of the square propagation of the separate uncertainties, it is the larger
ones that predominate the final uncertainty. Thus any improvement in the overall
experimental result must be achieved by improving the instrumentation or technique
connected with these relatively large uncertainties. It should be noted that it is equally as
unfortunate to overestimate uncertainty as to underestimate it. An underestimate gives
false security, while an overestimate may make one discard important results, miss a real
effect or buy too much expensive instruments. The purpose of this exercise is to analyze
the possible sources of uncertainties and give a reasonable estimate of each uncertainty,
and finally obtain the overall uncertainty.
In each experiment, the heaters are always set at the same temperature, and this
temperature was increased to investigate how the boiling heat transfer changes with
heater temperature. The boiling data are always associated with the pre-set temperature.
Therefore, the uncertainties will include uncertainty for heater temperature and
uncertainty for boiling heat transfer.
The uncertainty sources come from calibration, boiling and data reduction
experiments. They have been summarized in the following.
The uncertainty sources from calibration. The uncertainty sources from
calibration basically include the oil fluctuation in the calibration chamber, heat loss due
to oil impinging on the heaters, discrete increment of control resistance and slew rate of
the opamp which is used to balance the wheat-stone bridge. Each uncertainty for these
has been estimated and given in table 3.2.

46
Table 3.2 The uncertainty sources from calibration
Sources of uncertainty
Estimated uncertainty value
Oil temperature fluctuation
Ej\ = +0.5°C
Heat loss due to oil impinge
6n = +0.05°C
Discrete increment of control resistance
Ej2 = +0.1 °C
Slew rate of Opamp
Negligible
The uncertainty sources from boiling experiment. To have a better idea of
uncertainty sources from boiling experiment, figure 3.10 needs to be referred. They
include:
(1) Wiring resistance from heater to feedback system and from feedback system
to A/D card. Estimated total wiring resistance is about 50 ohm. Since heater’s nominal
resistance is 1000 ohm. Thus uncertainty introduced is 5%.
(2) A/D card resolution, 2.44mV: 12 bits 4095 divisions of full scale (10V). For
present experiments, the average voltage is about 10V. Thus the uncertainty is
2.44mV/10V, which is less than 0.03%.
(3) Voltage division device. Mainly comes from the deviation of two division
resistors. They are metal film resistors (1% accuracy). Thus, the voltage division
uncertainty can be 101%/99% = 1.02%.
Summary of uncertainty sources in this experiment. The uncertainty sources
analyzed above can be divided into uncertainty sources for heater temperature and for
heat flux. They are summarized as follows.
(1) Uncertainty sources for temperature
- Oil temperature fluctuation in calibration, eTi = +0.5°C.

47
+24V
S R1
> LOOK
R2
200K
Signal output
to A/D
2N2222 LOOK
Q)
H<—
O.luF
+ 15V
R8
12.0K
JT
V
/
KST
DQ
CLI
T I"
¿i
Figure 3.10 The circuit schematic for temperature control and voltage division.
- Discrete increment of control resistance, Erz = +0.05°C.
- Drift of V0ff of the opamp, £t3 = +0.1°C.
- Temperature fluctuation during boiling, especially during the vapor-liquid
exchange process, Ej4 = +0.05°C.
(2) Uncertainty sources for boiling heat transfer
- Wiring resistance, eVi = 5%.
- Resolution of A/D card, £y2 = 0.03%.
- Voltage division device, £v3 = 1.02%.
- Natural convection, £hi = 15%.

48
Determination of overall temperature uncertainty. Since the individual
uncertainties given above are absolute values relative to one variable (temperature), the
overall temperature uncertainty can be obtained by simply summing up each of them, that
is; £t = £ti + £t2 + £n + £t4 = 0.5°C + 0.1 °C + 0.05 °C + 0.05°C = 0.7°C.
Determination of overall heat transfer uncertainty. From the uncertainty
sources for boiling heat transfer analyzed above, the first three parts come from the
voltage measurements. Since they come from the single variable, the total uncertainty for
voltage can be obtained:
£v — £vi + £v2 + £v3 = 5% + 0.03% + 1.02% = 6.05%
Now we are ready to calculate the overall uncertainty for boiling heat transfer.
(3.13)
From Eq. (3.7), the total boiling heat transfer is a function of voltages and natural
convection, neglecting the uncertainties contributed by R (resistance of heaters) and A
(area of the heaters).
From the uncertainty theory, the overall uncertainty can be written as
1/2
that is,
In this equation,

49
In this experiment, the temperatures of the heaters are set in a temperature range,
thus R is changing. To calculate uncertainty, we let R = 1000 ohm. Also the areas of the
heaters are given as A = 0.000731cm . The averaged values for voltages during boiling
and data reduction are given at Vrawi = 10V, Kaw2 = 4V. With these data, we can
calculate the overall uncertainty at different temperatures. As an example, at 100°C single
bubble boiling: q'alura, = 40w/cra2.
The overall uncertainty can be obtained as wq- = 9.2w/cm2.
Also, at 100°C, the boiling heat transfer can be read from the boiling curve:
q" = 65w/cm2.
Thus, the percent uncertainty for boiling heat transfer at 100°C can be obtained
readily as:
Woverall = 9.2/65 = 13.8%.
For other temperatures, the uncertainty can be calculated following the same
procedure. For the single bubble boiling, the boiling heat transfer uncertainties at
different temperatures have been calculated and shown in the figure 3.11(a).
For dual bubble coalescence, we also calculated the overall uncertainty levels for
boiling heat transfer for temperatures from 100°C to 140°C, which are shown in the
figure 3.11(b) with the overall uncertainty values for single bubble boiling shown as well
for comparison.
As we have observed that in the dual-bubble coalescence boiling case, the overall
uncertainty is smaller than that for the single bubble boiling at corresponding
temperatures. The reason for this can come from two factors: (1) due to bubble

50
(a)
(b)
Figure 3.11 The uncertainty at different temperatures, (a) The uncertainty for single
bubble boiling at different temperatures; (b) The uncertainty for dual-bubble coalescence
together with single bubble boiling.

51
coalescence, the overall boiling heat transfer has been increased. (2) due to heater
interaction, the natural convection is smaller for the single heater case.
In summary, for temperatures, the oil temperature fluctuation during calibration
contributes to the main uncertainty, though opamp offset also has some contributions.
Natural convection is the main contributor to the boiling heat transfer uncertainty. The
overall uncertainty for heater temperature is estimated about 0.7°C, and the overall
uncertainty of boiling heat flux is about 15% between 100°C ~ 170°C, and this
uncertainty is temperature dependent. The uncertainty of dual bubble boiling is smaller
than that of the single bubble boiling due to coalescence-enhanced heat transfer.

CHAPTER 4
SINGLE BUBBLE BOILING EXPERIMENT
4.1 Introduction
Applications of microtechnology must utilize components or systems with
microscale fluid flow, heat and mass transfer. As the size of individual component
shrinks and the length scale decreases drastically, the transport mechanisms involved go
beyond those covered by the traditional theories and understanding. The development of
the new theories and the fostering of up-to-date physical understanding have fallen
behind the progress of micro machining and manufacturing. Extensive survey papers
(Duncan and Peterson, 1994, Ho and Tai, 1998) of microscale single-phase heat transfer
and fluid mechanics noted that an investigation of the flow characteristics of small
channels has shown significant departure from the thermo-fluid correlations used for
conventional macroscale flows. For example, for turbulent flow of gases in microtubes
(with diameters of 3 mm to 81 mm), neither the Colburn analogy nor the Petukhov
analogy between momentum and energy transport (Duncan and Peterson, 1994) is
supported by the data. More recently Gad-el-Hak (1999) gave a complete review on the
fluid mechanics of microdevices. He concluded that the technology is progressing at a
rate that far exceeds our understanding of the transport physics in micro-devices.
Therefore the study of micro-scale transport has become an integral part of not only
understanding the performance and operation of miniaturized systems, but also designing
and optimizing new devices. The current chapter presents an experimental study and
analysis to provide a fundamental basis for boiling on a microheater and to investigate the
52

53
small size effect on boiling mechanisms. Microheaters have been found in many
applications, for example, inkjet printerhead, and actuators and pumps in microfluidic
systems.
Recently Yang et al. (2000) proposed a new model of characteristic length scale
and time scale to describe the dynamic growth and departure process of bubbles. A
correlation between bubble departure diameter and bubble growth time is established and
a predication formula for bubble departure diameter is suggested by considering the
analogue between nucleate boiling and forced convection. The predictions by the model
agree well with experimental results that were obtained with basically macro-scale pool
boiling conditions. Rainey and You (2001) reported an experimental study of pool
boiling behavior using flat, microporous-enhanced square heater surfaces immersed in
saturated FC-72. Flush-mounted 2cm x 2cm and 5cm x 5cm copper surfaces were tested
and compared to a 1cm x 1cm copper surface that was previously investigated. Heater
surface orientation and size effects on pool boiling performance were investigated under
increasing and decreasing heat-flux conditions for two different surface finishes: plain
and microporous material coated. Results of the plain surface testing showed that the
nucleate boiling performance is dependent on heater orientation. The nucleate boiling
curves of the microporous coated surfaces were found to collapse to one curve showing
insensitivity to heater orientation. The effects of heater size and orientation angle on CHF
were found to be significant for both the plain and microporous coated surfaces. Hijikata
et al. (1997) investigated boiling on small heaters to find the optimum thickness of the
surface deposited layer to enhance the heat removal from the heater in order to obtain the
best cooling effect for a semiconductor. The square heaters they used are 50 pm and 100

54
pm and they claimed that the deposited layer conduction dominates the heat transfer due
to the small sizes of the heater area. Also they presented the nucleate boiling curves for
the two heater sizes and different deposited layer thickness. Rule and Kim (1999) used a
meso-scale heater (2.7mm x 2.7mm) which consists of an array of 96 microheaters. Each
of the microheaters was individually controlled to maintain at a constant temperature that
enabled the mapping of the heat flux distributions during the saturated pool boiling of
FC-72 fluid. They presented space and time resolved data for nucleate boiling, critical
heat flux and transition boiling. Specifically, the outside edge heaters were found to have
higher heat fluxes than those of the inner heaters. For the materials in this chapter, only
one single microheater (marked as #1 in figure 3.1) is heated to produce bubbles. The
experiment starts with setting the microheater at a low temperature of 50°C where only
natural convection occurs at this temperature. Then the temperature of the heater is
incremented by 5°C at a time, and for each increment, the heat dissipation by the heater is
obtained by the data acquisition system until the superheat reaches 114°C.
4.2 Experiment Results
For each series of the boiling experiment, the heater temperature was set at 50°C
initially. After that the temperature was increased with 5°C increments until it reached the
superheat of 114°C. For each temperature setting, the voltage across the heater was
sampled at a rate of 4500 times per second. The time-resolved heat flux was obtained
based on the heater area and its electrical resistance.
4.2.1 Time-averaged Boiling Curve
Figure 4.1 shows the measured boiling curve in logarithmic and linear scales
where the superheat of the heater covers a range from -6°C to 114°C. As the degree of

55
superheat was increased to 54°C, single bubbles were seen to nucleate. The onset of
nucleate boiling (ONB) for the single bubble experiment was found at the superheat ATe
of 54°C to 59°C. After the ONB, the degree of superheat for boiling dropped to 44°C as
the minimum temperature for stable boiling on this heater. It is noted that the trend of
figure 4.1 remains very similar to that of the classical pool boiling curve predicted by
Nukiyama (1934) and this includes the ONB phenomenon. In figure 4.1, similar to the
classical macro-scale boiling, the entire boiling curve can be divided into three sections.
Regime I is due to natural convection. Regimes II and III are separated by the peak heat
flux (critical heat flux) which takes place at a heater superheat ATe of 90°C. Also shown
in figure 4.1 are the boiling data from Rule and Kim (1999) for a meso-scale heater
(2.7mm x 2.7mm) which is composed of a 10 x 10 array of 96 microheaters. It is noted
that the boiling heat transfer rates for a micro heater (0.27 mm) in the current work are
more than twice higher than those for a meso-scale heater (2.7 mm) but the general trends
are similar for both heaters. Also, the peak heat flux for a micro heater takes place at a
higher heater temperature. These results are consistent with those of Baker (1972) for
forced convection and natural convection that as the heater size is decreased the heat
transfer increases.
4.2.2 Time-resolved Heat Flux
Figure 4.2 shows the heat flux history when the microheater was set at a degree of
superheat of 44°C. In figure 4.2, we note that the heat flux is closely associated with the
bubble life cycle during the ebullition process. [A] corresponds to a large spike that takes
place during the bubble departure. When the preceding bubble departs, the heater is
rewetted by the cooler bulk fluid. The establishment of the microlayer for the succeeding

56
45
40
35
£
-S30
=25
s
x
20 --
15
10
,NBd“
/
peak heat flux
'V
X Before ONB,
â–¡ Run 1
A Run 2
ORun 3
O Meso heater (Rule and Kim, l^jp)
°* m
oXo
num
D
L-H
‘-H
-10 10 30 50 70 90 110 130
Superheat AT
(a)
100
—
90
X Before ONB
80
â–¡ Run 1
70
A Run 2
60
ORun 3
OMeso heater (Rule and Kim, 1999)
g DU
-j)eak heat flux
- 40
X
â„¢/n
& aim]
g 30
X
a
20
*â– "
3<°
X
0
10
X
1 10 100 1000
Superheat AT
(b)
Figure 4.1 The boiling curve of the single bubble boiling, (a) The boiling curve in
linear scale; (b) The boiling curve in logarithmic scale.

57
Figure 4.2 The heat flux variation during one bubble cycle.
new bubble on the heater surface and the turbulent micro-convection induced by this
vapor-liquid exchange lead to this large heat flux spike. [B] represents the moment when
the succeeding bubble starts to grow after the vapor-liquid exchange. As the new bubble
grows, the contact line that is the three-phase division expands outward. The bubble
growth results in a larger dry area on the heater surface, thus the heat flux is decreasing.
The low heat flux period indicated by [C], [D] and [E] corresponds to the slow growth
stage of a bubble. As the bubble size reaches to a certain level, the buoyancy force starts
to become more important than the forces which hold the bubble to the surface, but it is
still not large enough to lift the bubble from the heater surface, causing the bubble to
neck. During the necking process, the contact line starts to shrink, then the dryout area is
starting to decrease, thus we have observed that the heat flux is starting to increase
slightly with some oscillation of a small-amplitude. Finally, the buoyancy force is large
enough to detach the bubble from the heater surface, and then another bubble ebullition
cycle begins.

58
4.2.3 Time-resolved Heat Flux vs. Superheat AT
Figure 4.3 shows the time-resolved heat flux at different heater superheats (44°C
to 114°C with increments of 10°C) for a total of six-second data acquisition. Figure 4.4
shows the trends of two characteristic heat fluxes during a bubble life cycle (Point A -
Point E in figure 4.2) at various heater superheats. The curve with triangles represents the
peak heat flux of a spike or the minimum heat flux of a dip during the bubble departure
(point A). Based on figure 4.3, the bubble departure was recorded to produce a spike for
the heater temperature up to 84°C, after that a heat flux dip was observed. In figure 4.4,
The curve with diamonds shows the heat flux level during bubble slow growth (point E).
It is clear that the two curves hold opposite trends, which is due to different controlling
mechanisms as explained next.
As we examine figures 4.1, 4.3 and 4.4 closely, all three figures consistently
indicate that Regimes II and III are dominated by two different transport mechanisms. In
figure 4.1, the heat flux increases with increasing heater superheat in Regime II while the
trend reverses in Regime III. In figure 4.3, we notice that a heat flux spike is associated
with the bubble departure in Regime II (heater superheat up to 84°C) and a heat flux dip
is seen to accompany the bubble departure in Regime III. In figure 4.4, we found that the
two curves cross each other at the heater superheat of 90°C which is the separating point
between Regimes II and III. We believe that in Regime II bubble growth is mainly
sustained by the heat transfer mechanism of microlayer evaporation that follows the
rewetting of the heater surface. This scenario is supported by the presence of a heat flux
spike recorded during the bubble departure. The spike is produced when the heater
surface is rewetted by the liquid with micro turbulent motion which in turn causes the
microlayer to form and the evaporation of the microlayer facilitates the bubble

Heat flux (w/cm2) Heat flux (w/cm2) Heat flux (w/cm2) Heat flux (w/cm2)
59
110
100
90
80
70
60
50
40
30
20
#1 at AT=74°C Max: 74.8w/cm2, Min=51.4w/cm2
../fy—- ..Jw.
i i i
0.5 1
1.5
2.5 3 3.5
Time (second)
4.5
5.5
Figure 4.3 Time-resolved heat flux variation at different heater superheats.

Heat flux (w/cm2) Heat flux (w/cm2) Heat flux (w/cm2) Heat flux (w/cm2)
60
110
100
90
80
#1 at AT=84°C Max: 65.6w/cm2, Min=53.2w/cm2
70
60
50
40
k
30 -
20 -
i_i_i â–  ' â–  â–  L
0.5 1
1.5 2 2.5 3 3.5 4 4.5
Time (second)
-i_ ...â– â– â–  i
5 5.5 6
110
100
90
80
70
60
50
40
30
20
#1 at AT=94°C Max: 47.8.6w/cm2, Min=57.1 w/cm2
vy~
■"•vy"
â– V-y-
0.5
1.5
2 2.5 3 3.5
Time (second)
4.5
5.5 6
110
100
90
80
70
60
50
40
â– 
30
i
20
-L
1
#1 at AT=104°C Max: 39.2w/cm2, Min=47.9w/cm2
1.5 2 2.5 3 3.5 4 4.5
Time (second)
â– VY
5.5
110
100
90
80
70
60
50
40
30
20
0.5
#1 at AT=114°C Max: 33.7w/cm2, Min=41.5w/cm2
i i ..iii.. .... i . . .i.. . i
1.5 2 2.5 3 3.5 4 4.5
Time (second)
vy
-J 1 I I I I J 1 I
5 5.5 6
Figure 4.3-continued Time-resolved heat transfer variation at different heater superheats.

61
AT
Figure 4.4 The trend of maximum and minimum heat fluxes during one bubble cycle with
various heater superheats.
growth. While for Regime III, because of the higher heater superheat and the associated
higher surface tension, the heater is covered by a layer of vapor all the time, even during
the bubble departure. The heater surface is no longer wetted by liquid flow, which results
in the bubble growth controlled by conduction through the vapor layer. The conduction-
controlled scenario is supported by the presence of a heat flux dip recorded during the
bubble departure in Regime III. The reason for this heat flux dip is mainly due to the
necking process during the bubble departure. During the necking process, the top part of
the bubble exerts an upward pulling force to stretch the neck. After the bubble severs
from the base, the upward force disappears suddenly, which allows the lower part of the
neck to spread and cover more heater surface area as depicted in figure 4.5. This larger
dry area on the heater is responsible for the heat flux dip. Another support for the

62
Figure 4.5 A hypothetical model for bubble departure from a high temperature heater.
conduction-controlled bubble growth in Regime III is that the heat flux level decreases
slightly with increasing heater surface temperature which is caused by the decrease of
FC-72 vapor thermal conductivity with increasing temperature.
From figure 4.3, where each spike or dip represents the departure of a bubble, we
can conclude that the bubble departure frequency increases with heater temperature. At a
heater superheat of 44°C, the bubble departure frequency is about 0.43 Hertz, while at
84°C, it is at 0.53 Hertz. Figure 4.3 also demonstrates the repeatability of the experiment.
We observed that the bubble departure size did not change much with
temperature. This is consistent with the results by Yang et al. (2000). Departure criteria
of the bubbles are totally determined by the forces acting on the bubbles. Buoyancy force,
besides the inertia force of the bubble, is the major player to render the bubble to depart.
The interfacial surface tension along the contact line invariably acts to hold the bubble in
place on the heater surface. Since this interfacial adhesive tension increases with

63
temperature, for departure to occur, it requires a larger bubble size to generate the
corresponding buoyancy force to overcome the adhesive force. At higher temperatures,
the thermal boundary layer that is due to transient heat conduction to the liquid is thicker
which allows the bubble to grow larger. However, we observed that as the heater
temperature was increased the bubble exhibited significant horizontal vibration that could
be due to the higher evaporation rate at higher superheat. This vibration promotes bubble
departure. On the other hand, due to the micro size of the heater, the natural convection
taking place around the outside of the contact line helps bubble detach from the surface.
Thus, these effects could cancel so that the bubble departure size does not change much
with heater superheat.
4.2.4 Visualization Results and Bubble Growth Rate
Figure 4.6 provides a sequence of bubble images during the life cycle of a typical
bubble on the microheater at superheat of 54°C. The images were taken from beneath the
heater surface using a CCD camera of 30 fps. As shown by the images, as it grows, the
bubble displays the shape of an annulus. The outer circle is the boundary of the bubble,
which shows the diameter of the bubble. The inner circle represents the contact line
where solid, liquid and vapor meet which measures the bubble base area on the heater. In
this figure, we note that just before the departure, the micro heater is almost entirely
covered by the vapor, thus resulting to a very low heat flux (the portion between point D
and point E in figure 4.2), and at this point the bubble has a diameter of about 0.8 mm
which is three times the size of the micro heater. The corresponding bubble size history
and growth rate were estimated and plotted in figures 4.7 and 4.8, respectively. We note
that the characteristics of bubble growth dynamics shown in figures 4.7 and 4.8 agree
well with the theoretical prediction of Scriven (1959).

64
0.0333
0.0667
áP
0.2000
0.3000
0.3333
0.4333
0.4667
0.1000 0.1333
0.6333 0.6667
0.7000
0.7333
0.7667
0.8000
Figure 4.6 Bubble images of a typical bubble cycle taken from the bottom.

65
# tst-
0.9667
1.0333
1.0667
1.2000
1.3333
1.3667
1.4333
1.4667
1.5000
1.5333
1.5667
1.6000
Figure 4.6-continued Bubble images of a typical bubble cycle taken from the
bottom.

66
Bubble diameter vs. Time
Time (seconds)
Figure 4.7 Measured bubble diameters at different time.
Growth speed of the single bubble at AT=54CC
Figure 4.8 Bubble growth rate at different time.

67
A high-speed video camera has also been used to show the necking and bubble
departure process. Figure 4.9 displays the images taken from the side and bottom views
by the camera set at 1000 frames per second. Based on the side view images it is clear
that the embryo of the next bubble is formed as a result of the necking process. It is also
estimated that the bubble departs at a very high velocity of 0.16 m/s that causes a strong
disturbance to the heater surface. This departure force in turn produces turbulent mixing
and microlayer movement around the bubble embryo that are responsible for the spike of
heat flux denoted as Point A in figure 4.2. As shown by the bottom view images, the
bubble departure disturbance also produces microbubbles that stay near the bubble
embryo and eventually coalesce with it.
4.3 Comparison and Discussion
4.3.1 Bubble Departure Diameter
Recently Yang et al. (2000) proposed a dimensionless length scale and a
corresponding time scale to correlate the bubble departure diameter and growth time.
These scales are repeated in Eq. (4.1) and Eq. (4.2).
where
D* = — = ■ADi
L0 B'-
T+ =-
‘ 0
A= 2PAT.H,
V w,
B = JaJ—a,
n
and
0 =
iA
( n ^
2/3
n
+
2
6 Ja
6 Ja
(4.1)
(4.2)
For the current study, the measured bubble departure diameters and growth times at
various heater surface superheats are given in table 4.1. It is shown that the bubble

68
Table 4.1 Single bubble growth time and departure diameter
AT
49
54
59
64
69
74
79
84
89
94
99
104
Growth
time
(seconds)
2.352
2.054
1.922
1.873
1.747
1.611
1.483
1.403
1.335
1.237
1.128
1.024
Departure
diameter
(mm)
0.823
0.824
0.829
0.833
0.832
0.836
0.839
0.843
0.850
0.859
0.866
0.875
Table 4.2 Properties of FC-72 at 56°C
Properties
Pi (kg/m3)
Pv (kg/m3)
7/fg (kJ/kg)
Cpi (kJ/kg)
«1 (108m7s)
Value
1680
11.5
87.92
1.0467
3.244
growth time is inversely proportional to the superheat while the departure size only
increases very slightly with the increasing superheat as discussed above.
In order to compare our data with the correlation of Yang et al. (2000), the data
were converted to dimensionless forms according to Eqs. (4.1) and (4.2) using thermal
properties given in table 4.2. Figure 4.10 shows the comparison. Part (a) of figure 4.10 is
the reproduced correlation curve from Yang et al. (2000) and part (b) shows our data
along with the correlation curve of part (a). It is seen that our data fall slightly lower than
the extrapolated correlation of Yang et al. (2000). Since the data given in part (a) are
from macro-scale heaters, we may conclude that on a microheater in the current study,
the bubble departure size is larger and they stay on the heater longer.
4.3.2 Size Effects on Boiling Curve and Peak Heat Flux
It is also of importance to examine the heater size effect on the boiling curve. We
plotted boiling curves for heater sizes ranging from 50 pm, 100 pm, 270 pm, 2700 pm, 1

69
3 ms
©
7ms
€)
4
0
5 ms
8 ms
©
1
2
Figure 4.9 The visualization result of bubble departure-nucleation process for
heater #1 at 54°C. (a) The side views; (b) The bottom views.

70
4
/
f4
â–¡a
0 Cola.WItaiâ„¢ .
0 col», ecu"
0 Cola. Toluana" _
v Cola, n-Panttna"
o Cola. MaOianal'
o Han, Watai"
9 Stialan, Witai'"
* Stanilakl Watar1'11
9 «annul, Uatena"
* Slajal, Watai1*1 ”
l-l.l.l.
/
"*-2 >1 0 1 2 3 4 5 •
(a)
(b)
Figure 4.10 The relationship between bubble departure diameter and growth time.
(a) Experimental data and correlation curve from Yang et al. (2000); (b) Data from
current study along with the correlation of Yang et al. (2000).
cm to 5 cm in figure 4.11. In order to ensure a meaningful comparison, all the curves in
figure 4.11 are based on fluids with similar thermal properties. The trend is very clear
that as the heater size decreases, the boiling curve shifts toward higher superheats and
higher heat fluxes. The peak heat fluxes for different size heaters have been plotted in
figure 4.12 for comparison. It is consistent that the peak heat flux increases sharply as the
heat size approaches the micro-scale. Actually, for heater sizes of 50 pm and 100 pm
(Hijikata et al., 1997), even with a very high superheat of about 200°C as shown in figure
4.11 the peak heat fluxes have not been reached.

71
1000
100
B
i
x
3
c
10
Size effect on nucleate boiling curves
♦
â–¡
♦
♦ □
♦ cP
V
“A
10
♦ 50um (Hijikata et al., 1997)
â–¡ lOOum (Hijikata et al., 1997)
O Current study
X2700um (Rule and Kim, 1999)
01cm (Chang and You, 1997)
+ 5cm (Rainey and You, 2001)
100
Superheat(AT)
1000
Figure 4.11 Comparison of boiling curves.
CHF for Different Size Heaters
Figure 4.12 Comparison of peak heat fluxes.

72
4.3.3 Bubble Incipient Temperature
Bubble incipient temperature is relatively higher for the small size heater used in
this experiment. This is consistent with the results given by Rainey and You (2001),
where they observed that the incipient temperature is about 16-17°C for 5 cm heater, 20-
35°C for 2 cm heater, and 25-40°C for 1cm heater. The incipient temperature observed in
our experiment is about 45-55°C. The explanation for this phenomenon by Rainey and
You (2001) is that larger heaters are more likely to have more surface irregularities and
therefore wider size range for bubble to nucleate from.
4.3.4 Peak Heat Flux on the Microheater
As mentioned in Section 2.3, recently more research reports (Sakashita and
Kumada, 1993 and Sadasivan et al., 1995) have indicated their support of the macrolayer
dryout as the basic mechanism for CHF as opposed to the hydrodynamic instabilities
(Liehard, 1988a). In the current research with microheaters as suggested by Sadasivan et
al. (1995), the theory of macrolayer dryout has been verified further as the cause of the
CHF. The support based on the results of the current single bubble experiment is
summarized as follows:
1. As discussed in Section 4.2.3 Regimes II and III are separated by the CHF
point. Two different mechanisms were discovered for the two regimes, respectively. It is
clear that the CHF that is the starting point of the Regime III where the heat transfer is
through a layer of vapor film and the heater is no longer wettable, is corresponding to the
dryout of the macrolayer.
2. In the current microheater condition, there is no possibility for the formation of
Kelvin-Helmholtz instability nor Taylor instability.

73
4.4 Deviations from Steady Single Bubble Formation
For the single boiling experiment dedicated in this chapter, as the bubble incipient
temperature is reached, a steady bubbling process has been observed and analyzed as
above. With the help of a high speed digital camera and simultaneous data acquisition,
we have noticed some deviations from the steady single bubble bubbling process. In this
section, these deviations have been summarized. It must be noted that these deviations
are very random according to observations in the experiments. The physics behind these
phenomena requires much more experimental and analytical work. We have noticed there
are three possible phenomena associated with bubble formation that could occur. Firstly,
a long-waiting period is necessary before the onset of another bubble and a vapor
explosion always occurs before this onset of another bubble, we call this process
discontinued bubble formation. Discontinued bubble formation happens usually at lower
superheats and with a highly subcooled liquid. Secondly, the direct bubble formation is
the process during which another bubble forms immediately after a bubble departs.
Thirdly, the bubble jetting is a chaotic phenomenon with smaller bubbles ejected from the
heater surface without forming a single bubble. The direct bubble formation is the steady
bubble formation process that we have analyzed previously. This section is dedicated to
the other two deviations from the steady bubble formation process.
4.4.1 Discontinued Bubble Formation
As we have observed, discontinued bubble formation actually occurs similarly to
the initial onset of boiling on the heater. For the microheater used in out experiment,
onset of nucleate boiling starts actually with vapor explosion, a physical event in which
the volume of vapor phase expands at the maximum rate in a volatile liquid. During this
process, the liquid vaporizes at high pressures and expands, performing mechanical work

74
on its surroundings and emitting acoustic pressure waves. According to previous
investigators, for large heaters rapid introduction of energy is necessary to initiate and
sustain the vapor volume growth at the high rate. For the microheater used in this
experiment, vapor explosion always occurs prior to the nucleation of small bubbles on the
heater. This could be due to the limited energy the microheater can supply from the solid
surface into the liquid though the superheat is well beyond the required superheat for
nucleating bubbles. We recorded the vapor explosion process together with the onset of
boiling, as shown in figure 4.13 for side-view images and figure 4.15 for bottom-view
images. When the heater reaches about 110°C, vapor explosion occurs. Following this
process, small bubbles start to nucleate and coalesce almost right after. With the
existence of noise due to the acoustic pressure waves, a layer of vapor is ejected with
high speed up into the liquid exhibiting a shape of mushroom (about 1 .Oms). The vapor
enclosed in the mushroom is loose due to the rapid expansion, and then starts to shrink to
form a round bubble and moves up. On top of the heater, the cool liquid replenishes the
vacancy and small bubbles nucleate and coalesce to a single bubble. The high energy
stored before the ONB is released suddenly to overcome all kinds of forces including the
Van der Waals force from the solid surface, hydrostatic force due to the liquid depth, etc.
A typical application of this process is the commercial success of thermal ink jet printers.
The key to the thermal ink-jet technology is the action of exploding micro bubbles, which
propel tiny ink droplets through the openings of an ink cartridge.
Zhao et al. (1999) used a thin-film microheater of size of 100pm x 110pm to
investigate the vapor explosion phenomenon. They placed the microheater underside of a
layer of water and the surface temperature of the heater was rapidly raised (about 6pm)

75
oms V
0.5 ms M
1.0 ms •
s
1.5 ms i
s
2.0 ms I
2.5 ms *
o
3.0 ms -
«>
a -
3.5 ms r
o
o-
4.0 ms •
**
o-
4.5 ms |
A
0
5.0 ms 1
5.5 ms ijj
(6t
6.0 ms |
ms
7.0ms^H^
o
0
0
0
0
”“■£3
8.0 ms
““ €7)
9.0ms ,4*..,^
Q-
r
0
0
0
0
Figure 4.13 The process of vapor explosion together with onset of boiling.
Figure 4.14 The ruler measuring the distance in figure 4.13 after vapor explosion.

76
6.0 ms 6.5 ms 7.0 ms 7.5 ms
m í »> »
8.0 ms
8.5 ms
[1
9.0 ms
9.5 ms
th §& i©
Figure 4.15 The bottom images for vapor explosion and boiling onset process.

77
electronically well above the boiling point of water. By measuring the acoustic emission
from an expanding volume, the dynamic growth of the vapor microlayer is reconstructed
where a linear expansion velocity up to 17m/s was reached. Using the Rayleigh-Plesset
equation, an absolute pressure inside the vapor volume of 7 bars was calculated from the
data of the acoustic pressure measurement. In this experiment, we also measured the
bubble velocity when vapor was exploded. By referring the heater size shown in figure
4.14 the distance the bubble was ejected up from the heater surface can be measured. The
result is the average velocity during the first 7 milliseconds is about 0.2m/s which is well
below that measured by Zhao et al. (1999). The low velocity measured in this experiment
is not surprising due to the following reasons. One of the reasons is that only a layer of
water was used in their experiment while pool boiling experiment was used in this
experiment. Also in this experiment the boiling liquid FC-72 with a lower saturation
temperature is used.
Figure 4.16 illustrates the heat flux traces corresponding to the vapor explosion
and boiling onset process. In figure 4.16(a) during the 6-second data acquisition, it starts
at a lower level where boiling is not present with natural convection to be the heat
transfer mode. All of a sudden, the vapor explosion exists and we recorded a sharp heat
flux spike that is supposed to correspond to the vapor explosion process as shown in
figure 4.16(b). For present data recording speed about 4,500 data points per second, we
recorded the vapor explosion occurs only in a mini-second related to the heat flux
variation from the heater. Following this vapor explosion, small bubbles start to nucleate
and heat flux increases.

78
Figure 4.16 The heat flux variation corresponding to the vapor-explosion and boiling
onset process, (a) The heat flux variation recording the vapor-explosion and boiling onset
process; (b) The heat flux variation during the vapor-explosion and boiling onset process.

79
4.4.2 Bubble Jetting
During the single bubble boiling process, we observed that periodically there is
bubble jetting after two or three bubbling cycles. This bubble jetting lasts about 0.2
second each time before a new single bubble is formed on the heater. Images taken with
the high speed camera in figure 4.17 and figure 4.18 show the bubble jetting process, and
figure 4.19(a) is the heat flux traces for a six-second data acquisition which includes three
bubble cycles of the departing-nucleation process. Figure 4.19(b) and 4.19(c) are the
close-up views of two heat flux encircled in figure 4.19(a). Through a close observation,
we find figure 4.19(b) is the heat flux variation corresponding to this bubble-jetting
process shown in figure 4.17 and figure 4.18. We notice that during the bubble-jetting
process, the heat flux stays much higher and drops sharply as a single bubble grows on
the heater. We also observed the single bubble boiling at 105°C and 120°C. At these two
temperatures, we also noticed the same phenomenon of bubble jetting. Figure 4.20 shows
the heat flux variation from the heater when it is set at 105°C, and figure 4.21 shows the
heat flux variation from the heater when it is set at 120°C. For both these two cases at
105°C and 120°C, we also observed the bubble-jetting after bubble’s departure. The
bubble jetting process is a characteristic of chaotic bubble nucleation, merging, and
departing process with the company of acoustic waves. During the bubble jetting process,
small bubbles on the heater keeps merging and departing. And all of a sudden a merged
bubble stays and merges with all other small bubbles around it, then a single bubble is
formed. The single bubble formation and growth also inhibits the bubble-jetting process,
and at the same time dries out the microlayer around the bubble for this particular heater
configuration used in this experiment. Thus the heat flux drops quickly as the single
bubble grows. The possible reason for this bubble jetting phenomenon is due to the high

80
superheat of the heater, the evaporation rate is very high on top of and around the edge of
the heater. The small bubbles do not have enough liquid to replenish the microlayer
region for them to grow. Clearer explanation of these phenomena needs further
observation and numerical approach.

81
Figure 4.17 The chaotic bubble jetting process for heater #1 at 110°C.

82
56 ms
o
58 ms
o
59 ms
o
60 ms
61 ms
A
IBr
61.5 ms
o
62 ms
©
62.5 ms
63 ms
63.5 ms
©
64.5 ms
0
67 ms
70.5 ms
&
“jWlllfc
O
HUI ML1
Jf
TT^
94 ms
6J»
a
106 ms
.4
126.5 ms
' fP
*
128 ms
• m
*■ C *o °
164.5 ms
°*r
~ â– 
165 ms
if
165.5 ms
wr •
166.5 ms
if
167.5 ms
° gg
168 ms
if
169 ms
; 170 ms
°<3F
♦ •
171.5 ms
173 ms
173.5 ms
&
174 ms
175 ms
.9
176 ms
Figure 4.18 The bottom images of chaotic bubble jetting process for heater #1 at 110°C.

83
FfWwOOl I 06 F»to 2002 T
(a)
(c)
Figure 4.19 The heat flux traces corresponding to the bubble jetting process, (a) 6-second
data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view of (a)
for direct bubble formation.

84
Frwm» 001 | 0«F*>2002 I
(a)
(b)
(c)
Figure 4.20 The heat flux traces for bubble jetting process from heater #1 at 105°C. (a) 6-
second data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view
of (a) for direct bubble formation.

85
(a)
(b)
(c)
Figure 4.21 The heat flux traces for bubble jetting process from heater #1 at 120°C. (a) 6-
second data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view
of (a) for direct bubble formation.

CHAPTER 5
DUAL BUBBLE COALESCENCE
To obtain bubble coalescence, a single bubble was generated from heater #1, at
the same time one more bubble was generated from another heater. In the experiment, by
referring to figure 3.1, if the other heater is too far apart like heaters #25, #29, no matter
how high the heater temperatures are set, the bubbles will not be large enough to coalesce
before they depart. And if the bubbles are too close like heaters #2, #3, #4, the bubble
coalescence will not be distinguishable because the first stage of nucleation process is so
fast that the two bubbles coalesce right after they are nucleated. In this experiment we use
heaters #11 and #12 to generate the other bubble. The purpose of selecting this two pairs
of heaters is to obtain stable bubble coalescence and investigate how heat transfer from
the heaters can be affected due to the interaction of the bubbles on the heaters.
5.1 Synchronized Bubble Coalescence
In this experiment, for heaters #1 and #11, when we set two heaters at 90°C to
95°C, the two bubbles depart without coalescence, and they are not syncronized. We
increase the temperature of the two heaters to 100°C, they coalesced and was
synchronized. For heaters #1 and #12, we observed the same situation except that the
required stable coalescence temperature is lower, 95°C. We notice that the higher the
heater temperature, the larger the departure size of the bubbles. This implies that to obtain
the coalescence the departure size of the bubble has to be greater than the distance of two
nucleation sites. And we conclude that coalescence not only enhances the heat transfer
86

87
which we will see shortly, the bubbles also interact with each other by retarding or
promoting their nucleation and growth rate.
5.2 Dual Bubble Coalescence and Analysis
For two configurations #1 with #11, and #1 with #12, figure 5.1 shows the heat
flux variations from each heater when the bubbles experience coalescence with that from
the other heater at the same temperature. Figure 5.2 shows heat flux of one typical
ebullition cycles for each heater in two configurations. Together with visualization
results, we observed that one ebullition bubble for coalescence includes from [A] to [F],
where [A] to [C] is the single bubble period before coalescence. [D] corresponds to the
bubbles coalescence moment. After this point, the newly-coalesced bubble grows till the
departing point [F], After this, another cycle starts. The detail is as follows:
[A]: This point corresponds to the nucleation of the new bubble and departing of
the old bubble. As in the single bubble boiling, the embryo left from the departed bubble
helps the next cycle and there is a heat flux spike.
[B], [C]: The two individual bubbles are growing and gaining in size on their
respective heaters. The mechanism is the same as in single bubble boiling at the same
stage.
[D]: It corresponds to the moment when the two bubbles coalesce. There is
another major heat flux spike due to the coalescence. When the two bubbles grow to a
certain size where their interfaces contact each other, the two bubbles merge together and
form a new bubble. It is suggested that this coalescence be mainly due to the effect of
surface tension between the vapor and liquid. It is also due to the interfacial surface
tension that makes the newly coalesced bubble sitting on the top of two heaters. Because

88
100
90
| 80
i 70
I 60
8 50
z
40
30
20
Heat flux variation from #1, when coalesce with #11 at 110°C
1/
1
V
V
L
V.
V.
V.
8 10
Time (seconds)
12
16
(a)
Figure 5.1 The heat flux variation for pair #1 with #11 and pair #1 and #12. (a) The heat
flux variation for #1, when coalesce with #11 at 110°C; (b) The heat flux variation for
#12, when coalesce with #1 at 100°C; (c) The heat flux variation for #12, when coalesce
with #1 at 100°C; (d) The heat flux variation for #12, when coalesce with #1 at 100°C.

89
Figure 5.2 The heat flux variation of one typical bubble cycle (a) and (b) for heater #1
with #11, (c) and (d) for heater #1 with #12.

90
the power sources are from two single heaters, the new bubble forms an oval shape with
its long axis in the direction of two heaters. The heaters are rewetted with liquid again
and part of heaters is in the micro-layer region, thus resulting in the heat flux spike. To
make it clearer the coalescence process, we take a look at the heaters arrangement in
figure 5.3. Just before coalescence as figure 5.3(a) shows, the bubbles are sitting on their
respective heaters. The dry area indicated by the contact line covers most of heater area.
Only a small portion of heater area is wetted with liquid in the micro region. After
coalescence, as figure 5.3(b) shows, a large portion of heaters is rewetted with liquid
again, which results in high evaporation rate, thus heat flux maintains at much higher
level.
(a) (b)
Figure 5.3 The heater dry area before and after coalescence.
[E]: The new bubble is growing. The heat flux tends to decrease after
coalescence, which is due to the increase of heater dry area, as in the single bubble
boiling. Comparing with the heat flux before coalescence, the heat flux is higher. We also
noticed from figure 5.2 that there is a substantial heat flux fluctuation after coalescence.

91
The large volume of the coalesced bubble experiences a force unbalance that makes the
bubble oscillate back and forth. This oscillation makes the heater dry area change, thus
resulting in the heat transfer fluctuation.
[F]: This corresponds to the moment when the coalesced bubble departs from the
heater surface, and new bubbles are nucleated on the heater. There is another
corresponding heat flux spike as discussed above.
From the foregoing analysis and comparison with the case without coalescence, it
is clear that during the bubble life cycle the bubble nucleation results in one major heat
flux spike, whereas for the case with coalescence, it is obvious that there are two major
spikes during an ebullition cycle. The first is due to the nucleation of new bubbles and the
second is due to the coalescence of the bubbles. For the case without coalescence, the
bubble experiences nucleation, growth, detachment, and departure stages, whereas, for
the coalescence case, the bubbles experience nucleation, growth, coalescence,
detachment and departure. After coalescence, the heat flux maintains at a much higher
level than that before the coalescence.
Figure 5.4(a) and figure 5.4(b) show the average heat flux when two heaters,
which are set at the same temperature, generate bubbles that coalesce during the
ebullition cycle at different temperatures. Figure 5.4(a) is for configuration #1 with #11,
and figure 5.4(b) is for #1 with #12. These results were obtained by dividing the total
power dissipation by the two heaters total area. We have the following observations:
The average heat flux tends to increase with heater temperature. As temperature
increases, due to the shorter waiting period between ebullition cycles and higher
evaporation rate, the bubbles grow faster before they are large enough to coalesce. Thus,

92
(a)
(b)
Figure 5.4 The boiling heat flux for the two pairs (#1 with #11) and (#1 with #12) as they
are set at different temperatures to generate bubbles and coalesce, (a) The pair #1 with
#11; (b) The pair #1 with #12.
they coalesce earlier to allow longer time of higher heat flux during one bubble ebullition
cycle.
There are deflective heat fluxes at AT = 55°C for both heaters in configuration #1
with #11, and AT = 50°C for #1 while AT = 65°C for #12 in configuration #1 with #12.

93
Close observation of heat flux variations in figure 5.1 for different temperatures, we
found that the sudden drop of average heat flux is because the dryout area is larger so that
the heat flux valley point before coalescence is lower and makes the average heat flux
lower.
We also noticed that for configuration #1 with #12, the deflective heat flux is not
as apparent as #1 with #11, and occurs at different temperatures. Because #1 and #12
have shorter distance than that for #1 with #11, they coalesce much more stably. On the
other hand, different surface areas for #1 and #12 probably are the reasons for different
temperatures when deflective heat flux occurs. Heater #12 (0.0748mm2) has a larger area
than #1 (0.07316mm2), while #1 and #11 (0.0732mm2) are much closer in surface areas.
5.3 Heat Transfer Enhancement due to Coalescence
To quantitatively compare the heat transfer between the single bubble boiling and
dual bubble boiling with coalescence, we use the same method to obtain the average heat
flux for single bubble boiling at the same boiling conditions. Figure 5.5 shows the heat
transfer enhancement for the two configurations, in which figure 5.5(a) is for heater #1
with #11 and figure 5.5(b) is for the configuration #1 with #12. For configuration #1
with #11, the heat transfer enhancement changes substantially with the temperatures of
two heaters, while for #1 with #12, the heat transfer enhancement is relatively stable
within the temperatures of interest.
Comparing the heat transfer characteristics during coalescence with those for the
single bubble case, we offer the following summary and conclusions:
1. There are two major heat flux spikes for the case with coalescence as compared
to only one single major spike for the non-coalescence case. Through a quantitative
analysis, coalescence results in a heat transfer enhancement.

94
(a)
(b)
Figure 5.5 The heat flux increase due to coalescence, (a) The pair #1 with #11; (b) The
pair #1 with #12.
2. The bubble departure frequency increases due to coalescence of bubbles by
comparing with the single bubble case at the same boiling condition.
3. The heat transfer from the heaters is closely associated with the bubble contact
line movement and dry area on the heater surface.

95
4. We also suggest that the interfacial surface force is the determinant factor to
render the bubbles coalescence.
5. Degree of heat transfer enhancement depends on the configuration and
temperature of two heaters.
5.4 Bubble Departure Frequency
Figure 5.6 is plotted to compare the bubble departure frequencies for the
coalescence case with that without coalescence. It illustrates the heat flux variation
during a 10-second period, which also indicates the bubble life cycles for the single
bubble case and the bubble-bubble coalescence case. It is clear that when two bubbles
coalesce, the departure frequency increases as a result of enhanced heat transfer.
Figure 5.6. Comparison of bubble departure frequency from heater #1 for coalescence
and non-coalescence cases.

CHAPTER 6
HEAT TRANSFER EFFECTS OF COALESCENCE OF BUBBLES FROM VARIOUS
SITE DISTRIBUTIONS
6.1 Coalescence of Dual Bubbles with a Moderate Separation Distance - A Typical
Case
The relative locations of the two heaters #11 and #13 are depicted in figure 3.1.
The distance between the centers of the two heaters is about the size of two heaters, i.e.
0.56mm. When the two heaters were set at 100°C, we obtained stable bubble
coalescence. The visualization results are shown in figure 6.1 and figure 6.2, where figure
6.1 provides the departure and nucleation process and figure 6.2 covers the coalescence
process. In each figure, both the bottom images and side images have been given. We can
conclude that a typical ebullition cycle is characterized by the following stages:
nucleation, single bubble growth, coalescence, continued growth of the coalesced bubble,
and departure of the coalesced bubble. Also these stages have been clearly shown in heat
flux traces plotted in figure 6.3.
Bubble departure and nucleation process. According to figure 6.1, the bubble
departure and the ensuing bubble embryo formation are virtually a continuous process.
The succeeding bubble nucleation is taking place while the proceeding bubble is leaving
the heater surface. As a bubble grows large enough in size, the buoyancy force lifts the
bubble so that the contact line shrinks (this is visible from the bottom images). The
surface tension force from the heater surface that is part of the forces responsible for
holding the bubble in place decreases accordingly so that the bubble moves horizontally
to one heater. As this happens, the other heater is rewetted and the first bubble nucleation
96

97
begins as shown at 4 ms in figure 6.1. This horizontal move promotes one bubble’s
nucleation and inhibits the other bubble’s nucleation, thus resulting in a time delay for the
nucleation of the second bubble. At 6 ms the coalesced bubble departs, and the second
bubble is nucleated at 7 ms. Therefore, there is about a 3 ms delay between the nucleation
of the two bubbles. The heat flux history given in figure 6.3 shows there is a heat flux
spike associated with this process. Just prior to this heat flux spike due to departure and
nucleation, we noticed that the heat flux exhibits wave-like fluctuations with a period
about 0.42 ms. These fluctuations as observed are due to the size oscillation of the
coalesced bubble. After the departure/nucleation heat flux spike, the heat flux drops
sharply as the new bubbles grow. This heat flux drop is a direct result of bubble growth
that produces more dry area on the heater surface. As seen in figure 6.3(b), we found that
it takes about 0.01 second for the heat flux to decay to the lower level. After this, the heat
flux still drops as the bubble grows, but the drop rate is much slower. During the slow
growth period, conduction through the vapor is the main heat transfer mechanism.
Bubble coalescence process. As the bubbles grow large enough to touch each
other, they coalesce. The coalescence process starts with the touching of the interface of
the two bubbles, shown in figure 6.2 (at 163 ms). At the next millisecond (164 ms), the
common area of the liquid-vapor interface of the two bubbles ruptured, thus resulting in a
strong surface tension force acting on the ruptured area. Figure 6.4 is used to illustrate
this point. Before the rupture of the interface of the bubble, the surface tension keeps the
bubble as it is. After rupture, the peripheral of the rupture area is occupied by the
remaining surface tension, and this force pulls the rupture area of the bubble outward.
And this pulling draws the bubble toward each other with a large initial speed. This

98
inertia makes the new bubble oscillates several cycles (about 4 to 5 cycles) before it
settles into its final shape. Each time it stretches, some energy is dissipated; thus the
strength lessens after each stretch. The first stretch is the strongest. The bubble is pulled
in oval shape with the major axis perpendicular to centerline of the two heaters, thus
resulting in the minimum dry area on the two heaters as shown in figure 6.4. This point
should be responsible for the heat flux peak during the merging process as shown in
figure 6.3(b). As we have observed, this heat flux peak is not attributed to the interface
interaction when the two bubbles touch because at this moment, the bubbles themselves
are still held at their original place, thus the dry areas have not been changed
substantially. Before the new bubble settles, its size oscillates several cycles. These
oscillatory motions lead to the secondary heat flux spikes following the first heat flux
spike. In figure 6.3(c), there are five heat flux spikes that correspond to the five
oscillations during the bubble coalescence process. The dry area variation during the
coalescence process has been shown in figure 6.2(b). Figure 6.4(b) corresponds to the
image at time 164 ms in figure 6.2(a) when the interface area ruptures. Figure 6.4(c)
corresponds to the minimum dry area at time 167 ms in figure 6.2(a) at the time of the
first and largest spike. We also observed from the images in figure 6.2(a) that the
coalescence results in higher convection heat transfer, and natural convection heat
transfer around the bubbles due to the subcooled liquid used in this experiment.

99
0 ms * 1 ms 2 ms * 3 ms '
.o .o .o .o
4 ms «
5 ms •
6 ms *
7 ms •
.O O .0 .©
8ms • 9ms • 10ms 11 ms •
.o o © o
(b)
Figure 6.1 The departing and nucleation process for heaters #11 and #13 at 100°C. (a)
The side views; (b) The bottom views.

100
(a)
163 ms*
8-
164 ms*
8-
165 ms'
166 ms'
r>
167ms •
168 ms*
169 ms*
170 ms •
»
. 0*
0-
171 ms'
172 ms'
173 ms'
174 ms'
0
O-
O'
O-
(b)
Figure 6.2 The coalescence process (2 cycles of oscillation) for heaters #11 and #13 at
100°C. (a) The side views; (b) The bottom views.

Heat flux (w/cm2) Heat flux (w/cm2) Heat flux (w/cm2)
101
(b)
Figure 6.3 The heat flux history for dual bubble coalescence, (a) 6-second data
acquisition of heat fluxes including 5 cycles; (b) Close-up heat flux variation from (a) for
one typical ebullition process; (c) Close-up heat flux variation from (b) for coalescence
process.

102
Bubble shape just before coalescence
Bubble shape after first stretch
(b)
(c)
Figure 6.4 Photographs showing the interface interaction, (a) Schematic showing the
coalescence procedure; (b) Two touching bubbles; (c) The coalesced bubble.

103
6.2 Dual Bubble Coalescence from Heaters #11 and #14 at 100°C - Larger
Separation Distance Case
The relative locations of the two heaters #11 and #14 are given in figure 3.1. The
distance between the centers of the two heaters is about three-heater size, i.e. 0.84 mm.
When the two heaters are set at 100°C, we can obtain stable bubble coalescence. Unlike
the case for heaters #11 and #13, from the images shown in figure 6.5 and figure 6.6, we
found that a typical ebullition cycle is characterized by different stages: nucleation, single
bubble growth, coalescence, and departure. Comparing with the cycle of heaters #11 and
#13 both held at 100°C, the stage of continued growth after coalescence is absent.
Instead, the coalesced bubble departs right after they coalesced. These stages can be seen
from the visualization results provided in figure 6.5 and figure 6.6, and also have been
clearly shown in the heat flux traces plotted in figure 6.7.
The main reason for the immediate departure after coalescence comes from the
balance between the lifting force and the holding force of a sessile bubble. The lifting
force is basically the buoyancy force that is proportional to the volume of the bubble,
while the holding force consists of contact pressure, hydrodynamic pressure, drag and
surface tension. The holding force is dominated by the contact pressure and the drag
force which are proportional to the square of the radius. As the ratio of the lifting force to
the holding force is proportional to the radius of the bubble, the radius of a bubble must
be greater than the critical radius for the buoyancy force to over-power the holding force
to lift the bubble. For the case of #11 and #14 coalescence, the two individual bubbles
grow to larger sizes before they touch each other and coalesce because of the larger
heater separation distance. Therefore the radius of the coalesced bubble in the #11 and

104
23 ms |
Figure 6.5 The side-view photographs of coalescence-departure-nucleation process
for heaters #11 and #14 at 100°C.

105
3 ms
•O
6 ms
O O O O
9 ms
10 ms
11 ms
6 0-06
12 ms
13 ms
14 ms
15 ms
17 ms
18 ms
19 ms
O 0 0 0
20 ms
22 ms
23 ms
0 0 0 0
Figure 6.6 The bottom view of coalescence-departure-nucleation process
for heaters #1 lwith #14 at 100°C.

106
(a)
(b)
Figure 6.7 The heat flux history from heater #11 when #11 and #14 are set at 100°C. (a)
6-second data acquisition of heat fluxes from #11; (b) Close-up heat flux variation at
coalescence-departing process.
#14 case is greater than the critical radius which facilitates the immediate departure while
for the case of #11 and #13, the radius of the coalesced bubble is below the critical
radius, thus it needs to grow further before departure.
The heat transfer enhancement from coalescence is due to the following
mechanisms: (1) The bubble departure frequency increases because the bubble departs
right after coalescence. For single bubble boiling, one bubbling cycle takes about 2

107
seconds, while for this case, due to the coalescence, one bubbling cycle takes about 1
second. This can be seen in both figure 6.5 and figure 6.6. (2) The coalescing process
promotes other transfer modes such as the convection and conduction heat transfer.
The heat flux history shown in figure 6.7 carries some similarity to that from
single bubble boiling without coalescence. But some important aspects have
distinguished them from each other. Firstly, the bubbling cycle frequency is almost
doubled for the coalescence case, which definitely enhances the heat transfer. Secondly,
the departure mechanism for the coalesced bubble is different from that for the single
bubble boiling. From the heat flux history in figure 6.7(b), we can see, due to
coalescence, that the bubble departure from each heater is pretty straightforward. But for
the single bubble case, the bubble always experiences some heat flux fluctuation before
the buoyancy force lifts the bubble from the heater.
6.3 Dual Bubble Coalescence from Heaters #11 and #14 at 130°C - Larger
Separation Distance and Higher Heater Temperature Case
When the two heaters are set at 130°C, we can also obtain stable bubble
coalescence. Due to an increased temperature from 100°C to 130°C, the bubbles exhibit
different behavior. The heat flux history corresponding to each stage has been shown in
figure 6.8. We can see one typical ebullition cycle is characterized by the following
different stages: nucleation, single bubble growth, coalescence, short growth and
departure. In this case, the bubbles experience almost the same stages as those of the case
for #11 with #14 at 100°C. The only difference is that due to the different heater
temperature, the coalesced bubble did not depart right after coalescence. Instead, the
coalesced bubble oscillated few cycles and then departed, which is different from the

108
(a)
(b)
Figure 6.8 The heat flux history for heaters #11 and #14 at 130°C. (a) 6-second data
acquisition of heat fluxes from #11; (b) Close-up heat flux variation from heater #11
during coalescence and departing process.
after-coalescence slow growth observed for the case of coalescence from #11 and #13.
This difference can be further illustrated by figure 6.3 and figure 6.8. The reason that the
coalesced bubble did not depart immediately is thought due to the effect of temperature
on the densities of the FC-72 boiling fluid. As a result of the heater temperature increase
from 100°C to 130°C, the buoyancy force is reduced by 15% accordingly as the liquid
density decreases with temperature while the vapor density increase with temperature.

109
6.4 History of Time-resolved Heat Flux for Different Heater Separations
Next, we focus on the effects of the separation distance between the heaters.
Three cases were performed where heater #1 with heater #4 (0.281 mm), heater #1 with
heater #13 (0.541 mm), and heater #1 with heater #11 (0.770 mm) were investigated.
Figure 6.9 shows the time resolved heat fluxes for the three cases. Figure 6.10 shows the
corresponding images taken from the bottom of the heaters. In our previous work (Chen
and Chung 2002), we found that in general there are two heat flux spikes in the
coalescence of two identical bubbles. One is due to the combined process of departure
and nucleation, and the other one is due to the coalescence. From figure 6.9 and figure
6.10, we have the following observations: For the shortest separation distance (0.281
mm) among the three cases, there is only one clear spike for each boiling cycle which is
definitely due to the bubble departure/nucleation process. There is no apparent
coalescence observed either from the heat flux measurement or visualized images. It is
believed that simply there is no room for two individual bubbles to develop. From the
time-resolved heat flux traces where the heat flux fluctuates very much indicates that the
bubble experiences significant vibration over the heaters. At the separation distances of
0.451 mm and 0.770 mm, coalescence of bubbles can be clearly observed both from the
heat flux trace and the visualized images. Also obviously, at the shorter distance of 0.451
mm, bubbles coalesce earlier than that at the longer distance of 0.770 mm during a
bubbling cycle. As explained before, this phenomenon is due to the fact that bubbles
touch each other earlier for the shorter separation distance case.
6.5 Time Period of a Bubbling Cycle
It is interesting to study the periods of bubbling cycles for heater pairs with
different separation distances. Usually we found that the longer the period the lower the

Heat flux (w/cm!) Heat flux (w/cm2) Heat flux (w/cm2)
110
Heat flux with time from heater #1, when both #1 and #4 at 110°C
(a)
(b)
(c)
Figure 6.9. The heat flux history from heater #1 with time, (a) Heat flux from #1 with
time when #1 and #4 are set at 110°C; (b) Heat flux from #1 with time when #1 and #13
are set at 110°C; (c) Heat flux from #1 with time when #1 and #11 are set at 110°C.

Ill
Figure 6.10 The bottom images for one bubble cycle and dryout changing (time in
second), (a) One bubbling cycle for #1 with #4 set at 110°C; (b) One bubbling cycle for
#1 with #13 set at 110°C; (c) One bubbling cycle for #1 and #11 set at 110°C.

112
average heat fluxes. Figure 6.11 shows the time period of a bubbling cycle as a function
of the heater superheat for five pairs of heater arrangement. These five pairs represent a
range of heater separation distance between 0.280 mm to 0.770 mm. There is a common
trend for the period curves among all pairs. For each heater pair, the period of the
bubbling cycle initially increases until the superheat reaches to 45°C ~ 50°C, then it
decreases monotonously. This phenomenon can be explained by the competition between
two mechanisms. It should be pointed out that every bubbling cycle ends with the
departure of a single bubble if no coalescence occurs or the departure of the coalesced
bubble. Therefore the earlier the bubble departs the shorter the period is. For a given pair
of heaters, as the temperature of the heaters is increased, the buoyancy force decreases as
explained before, which is the mechanism that retards the bubble departure. While on the
Time duration of one coalescence cycle
Figure 6.11 The time duration of one bubble cycle at different superheats.

113
other hand, we anticipate that the higher the heater temperature the higher the heat
transfer to the bubble which causes the bubble to grow faster and therefore promotes
bubble departure. We suggest that the retarding mechanism prevails before the peak
period and after that the promoting mechanism dominates. At a given heater superheat,
the longer the separation distance is between the heaters, the shorter the period of
bubbling cycle is measured. This is explained by the larger rewetted area and higher
induced convection due to more violent coalescence when the two heaters are separated
at a larger distance.
6.6 Average Heat Flux of a Heater Pair - Effects of Separation Distance
As discussed in the above, the two-phase condition on one heater of a heater pair
during the coalescence experiment is not identical to that of the other heater. From
practical point of view, it is useful to examine the average heat flux for a given pair of
heaters at various superheats. Figure 6.12 shows the average heat flux of a boiling cycle
for seven heater pairs with the separation distance ranging from 0.280 mm to 0.810 mm.
These data were derived by dividing the sum of the two heat transfer rates over the total
area of two heaters. The results are relatively very consistent which show the heat flux
increasing linearly with the superheat. For a given superheat, the heat flux increases with
increasing separation distance. With a larger separation distance, more of an individual
heater surface would be rewetted by the surrounding liquid that facilitates higher heat
transfer rates.
6.7 Time-averaged Heat Flux from Heater #1
Figure 6.13 is used to illustrate the effects of heater pair configuration on the heat
transfer. Here heater #1 is chosen as the reference heater and therefore, in figure 6.13, the

114
Superheat (AT)
Figure 6.12 The average heat fluxes from different pairs of heaters at different
superheats.
Superheat (AT)
Figure 6.13 The average heat fluxes from heater #1 at different superheats.

115
time-averaged heat flux of this heater is plotted as a function of the heater superheat for
five cases where the second heater is placed at various positions relative to heater #1. In
general, figure 6.13 is very similar to figure 6.12, which means that the time averaged
heat fluxes from the two heaters are very close to each other.
6.8 Coalescence of Multiple Bubbles
In this experiment, we use four different heater configurations to perform multiple
bubble coalescence: A. triangle - three bubbles from #1, #12, and #14, B. tight square -
four bubbles from #1, #2, #3 and #4, C. loose square plus center - five bubbles from #1,
#15, #3, #5 and #7 and D. loose square - four bubble from #15, #3, #5 and #7. Figure
17
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7
2
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11
Case A: three heaters 1-12-13
17
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18
5
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6
1
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13
20
7
2
3
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21
8
9
10
11
Case C: five heaters 1-3-5-7-15
17
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33
18
5
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15
14
19
6
1
4
13
20
7
2
3
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Case B: four heaters 1-2-3-4
17
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6
1
4
13
20
7
2
3
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8
9
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11
Case D: Four heaters 3-5-7-15
Figure 6.14 Four heater configurations for multiple bubble coalescence experiment.

116
6.14 provides the schematic of these four cases, where the selected heaters were
highlighted for each case. For the multibubble experiment, the heaters were all kept at the
same temperature during each run. The heater temperature was varied with superheats
ranging from 34°C to 84°C in 5°C increments. For each superheat, the heaters were set
and maintained at that temperature. The detailed coalescence process recorded by a high
speed camera was obtained for visualization.
Average heat fluxes of individual heaters vs. superheat. First we present time-
averaged heat fluxes for Case A - three-bubble coalescence in figure 6.15. The same
experiment was repeated three times and the results show an excellent repeatability. In
general, the heat fluxes increase monotonically with the superheat for all three heaters.
Concerning the individual heaters, heat fluxes from #12 and #14 are supposed to be
identical to each other because of geometric symmetry. In reality, the level of heat flux
depends strongly on where the coalesced bubble is located which determines the rewetted
and dry area ratio for a particular heater. For the results given in figure 6.15, it is apparent
that the coalesced bubble is located closer to #12. The reason for which the coalesced
bubble is located near #12 is given later in the section of visualization. To further
demonstrate the relationship between the heat flux level and the location of coalesced
bubble, we present figure 6.16 where the time-averaged heat fluxes are plotted for all five
heaters for Case C - loose square with center. For Case C, the coalesced bubble
inevitably is located near the center heater # 1 which also turned out to have not only the
lowest but substantially lower heat flux level than those of the four comer heaters. This
finding is consistent with that reported by Rule and Kim (1999), where 96 heaters in a 10

117
x 10 square array have been used in pool boiling experiment and they found that the
surrounding heaters exhibit higher heat fluxes than those from the inner heaters.
Figure 6.15 The heat fluxes from each heater for case A (figure 6.14) vs. superheat.
Figure 6.16 The heat fluxes from each heater for case C (figure 6.14) vs. superheat.

118
Comparison of heat transfer enhancement from various multibubble
coalescence configurations. For the purpose of quantitatively evaluating the
multibubble coalescence effects on boiling heat transfer, we have selected six
configurations : Cases A, B, C, and D defined above together with Case E - heaters #1
and #3 and Case F - heaters #1 and #13. Cases E and F provide the base cases for
coalescence of twin bubbles. The summary of the results is plotted in figure 6.17 where
each curve represents the averaged heat flux for a particular set of heaters as a function of
the superheat. The heat flux levels in descending order are D, A, C, F, E, and B. Let us
first focus on Cases D, A, and F as they represent four-bubble, three-bubble and two-
bubble coalescences, respectively, with approximately equal separation distances
between any two heaters. As discussed earlier, the separation distance is an important
parameter because it determines the portion of rewetted area on a heater. With the
Figure 6.17 The average heat fluxes for different heater configurations vs. superheat.

119
separation distance removed as a factor, we may conclude that the more bubbles
participate in the formation of a single coalesced bubble, the higher the average heat flux
level would result among the heaters involved. The reason that the enhancement is
proportional to the number of bubbles is thought due to that the number of individual
coalescences before the formation of a single coalesced bubble increases with increasing
number of participating bubbles. For the rest of cases, the reason that Case C results in
higher heat fluxes than Case E is also due to more bubbles participating in coalescence
for Case C than for Case E. Case B has shortest distances among heaters, thus lowest heat
flux levels. The reason is mainly due to the lack of room for coalescence resulting in
virtually no rewetting and little induced convection.
Flow visualization of coalescence mechanism. We selected Cases C and D for
the flow visualization study. The images were obtained for the bottom view of the
heaters. The basic difference between the two cases is that the average separation
distance for Case D is larger because it does not have the center heater. Figures 6.18 and
6.19 provide the coalescence sequence for both cases at a heater superheat of 80°C. In
general, the bubble that departs eventually is a product of multistage coalescences.
During each stage, there is a single coalescence between two adjacent bubbles. For
example in Case D (figure 6.18), the two bubbles on the right-hand-side merge first, then
the coalesced bubble from the first stage merges with the lower one on the left-hand-side,
after that the coalesced bubble from the second stage merges with the left upper one to
complete the third stage of coalescence. After the third coalescence, the combined overall
bubble departs. It is noted that by the time the overall bubble departed, the next

120
Figure 6.18 The coalescence sequence for heaters #3, #5, #7, and #15 at 80°C.
Figure 6.19 The coalescence sequence for heaters #1, #3, #5, #7, and #15 at 80°C.

121
generation bubbles have already grown to medium sizes. The main reason for the
multistage process is that all the bubbles would be at somewhat slightly different sizes at
any instant, therefore, they do not touch one another at the same time. Whenever any pair
that grows closer enough would coalesce first. For Case C (figure 6.19), the coalescence
mechanism is similar, but with the extra bubble in the center, there are four stages rather
than three as in Case D. Based on figures 6.18 and 6.19, we may conclude that for Case D
with a larger separation distance, the overall bubble departs much quicker and thus it
results in a shorter cycle period. Also the size of the overall bubble is smaller for Case D
which gives rise to larger rewetted area. The combination of a shorter cycle and more
rewetted area is believed to be responsible for the higher time-averaged heat flux shown
in figure 6.17. Figures 6.20 and 6.21 show the coalescence sequences for Cases C and D
at a superheat of 100°C. At a higher superheat, the coalescence mechanism remains
similar to that of the lower superheat. The major differences are that the pace is faster and
the overall bubble size is larger.
Figure 6.20 The coalesced bubble formed on heaters #3, #5, #7, and #15 at 100°C.
Figure 6.21 The coalesced bubble formed on heaters #1, #3, #5, #7, and #15 at 100°C.

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6.9 Heat Transfer Enhancement due to Coalescence Induced Re wetting
In Chen and Chung (2002) and in previous sections of this paper, we have
attributed higher heat transfer rates to the coalescence-induced rewetting of a heater
surface. In this section, we have designed an experiment to further clarify this heat
transfer enhancement phenomenon. Two heater configurations have been used to
compare the heat fluxes. The first one is composed of #1, #2, #3, #4 and #11 heaters.
The second one is composed of just #3 and #11 heaters. For all the results obtained, #11
heater was always kept at 80°C, while for the first configuration #1, #2, #3 and #4 have
been allowed to vary with superheats ranging from 25°C to 80°C. The same superheat
range was applied to #3 heater in the second configuration for all the experimental runs.
As a result of the above settings, the heat flux registered on the #11 heater will provide an
unbiased comparison because it is kept at a single temperature at all times. The time-
averaged heat fluxes of #11 heater are plotted in figure 6.22 for both heater
configurations. For each configuration, three runs were performed to ensure the
repeatability. It is clear that the heat flux level for the first configuration is approximately
20% higher than that of the second configuration. For the first configuration, heaters #1,
#2, #3 and #4 always produce a single but larger bubble as shown in figure 6.23. The
bubble produced by the #11 heater is smaller and therefore is absorbed by the larger
bubble on heaters #1, #2, #3 and #4 as seen in figure 6.23 which results in a rewetting of
the entire surface on the #11 heater. While for the second configuration, bubbles
produced on heaters #3 and #11, respectively, are roughly equal in size and the coalesced
bubble is located in the middle between the two heaters which results in only a partial
rewetting of the #11 heater. Figure 6.24 is a plot of the heat flux history for #11 heater.

123
Superheat(AT)
Figure 6.22 The heat fluxes from heater #11 when the other heaters are at various
superheats.
Figure 6.23 The heat flux history from heater #11 during 0.8 second.

124
Figure 6.24 The heat flux history from heater #11 when the bubble formed on it is pulled
toward the primary bubble from heaters #1, #2, #3, and #4.
The history shows a mixture of short and long cycles, approximately a long cycle is
followed by three short cycles. Each spike in the short cycle corresponds to the rewetting
of the heater surface as the bubble is absorbed by the larger bubble. The long cycle is
produced due to growing of the larger bubble on heaters #1, #2, #3 and #4. After the
departure of the larger bubble, the smaller bubble on heater #11 would stay longer on the
heater and grow slowly waiting for the larger bubble to grow to the appropriate size for
merging. In other words, the large bubble would absorb three small bubbles before
departure.
Based on the experimental work and analysis given in this chapter, some
conclusions can be drawn in the following.
An experimental work has been performed to investigate the heat transfer
enhancement from the coalescence of multiple bubbles at various separation distances.
The individual bubbles were formed and positioned by powering selected microheaters in
a heater array. A series of bubble coalescence interactions then took place as the
individual bubbles grew large enough to touch one another.

125
A typical ebullition cycle which includes the coalescence of two bubbles is
characterized by the following stages: nucleation and growth of two single bubbles,
coalescence of dual bubbles, relatively long continued slow growth of the coalesced
bubble, and finally departure of the coalesced bubble. There are also possibilities that the
coalesced bubble would depart immediately or stay for a short growth period before
departure.
We have found that in general the coalescence enhances heat transfer as a result
of creating rewetting of the heater surface by colder liquid and turbulent mixing effects.
The enhancement is proportional to the ebullition cycle frequency and heater superheat. It
was also predicted that the longer the heater separation distance is the higher the heat
transfer rates would be enhanced.
For the multibubble coalescence study, the key discovery is that the ultimate
bubble that departs the heater surface is the product of a sequence of coalescences by
dual bubbles. For heat transfer enhancement, it was determined that the time and space
averaged heat flux for a given set of heaters increases with the number of bubbles
involved and also with the separation distances among the heaters. In particular, we
found that the heat flux levels for the internal heaters are relatively lower.

CHAPTER 7
MECHANISTIC MODEL FOR BUBBLE DEPARTURE AND BUBBLE
COALESCENCE
As presented in previous chapters, both the bubble departure/nucleation and
coalescence result in heat flux spikes as shown in figure 7.1. These spikes were found to
be the major contributions to heat transfer enhancement. Therefore, it is important to
further our understanding of the heat transfer process by building mechanistic models.
Following the flow visualization and physical understanding, the models developed in
Figure 7.1 Typical heat flux spikes during bubble coalescence.
this section are based on the transient process of rewetting heat transfer between the
heater surface and colder liquid. The physical process is further explained in figure 7.2
and figure 7.3 for the departure and coalescence, respectively. In figure 7.2(a), we see a
sessile bubble during slow growth. When the buoyancy force is ready to lift the bubble as
126

127
shown in figure 7.2(b), the necking process starts, which causes the liquid to initiate the
downward motion. In figure 7.2(c), the bubble lifts off and accelerates upward which also
gives the colder fluid more momentum to rush down to rewet the heater surface. For the
coalescence as shown in figure 7.3, the coalesced bubble tends to be a vertical oval that
results in rewetting of most of the surface area of the two heaters #1 and #13.
Figure 7.2 The fluid flow induced by the bubble departure.
7.1 Re wetting Model
Based on the physical illustration given above, the rewetting model adopts the
following assumptions:
(1) The colder fluid with a temperature of T„ covers the previously dry surface
instantaneously at / = 0.
(2) The fluid at T«, is a semi-infinite medium which is suddenly exposed to a
constant interface temperature of Ts which corresponds to the heater temperature.
(3) An effective conductivity Ktg is used to account for the convection and
turbulent mixing effects.

128
3y
\>
>#<
>4
V
29
11
28
Bubble outer profile
Contact line
34
\
1
)
/
s ✓
9
10
11
(a)
(b)
Figure 7.3 The fluid flow induced by the bubble coalescence, (a) The model for heaters
#1 and #13 completely wetted after coalescence, (b) The fluid flow induced by the bubble
coalescence.
For the semi-infinite solid transient conduction, Equation (5.58) given in
Incropera and DeWitt (1996) is used and it is repeated here as follows
KM-tj
(7.1)
7.2 Results from the Rewetting Model
The results from the re wetting model for two heater temperatures (100°C and
110°C) have been shown in figure 7.4 and figure 7.5, where figure 7.4 is for bubble
coalescence and figure 7.5 is for the departure process. In both figures 7.4(a) and 7.5(a), a

129
smaller plot is inserted to show relatively where the modeled portion is located in the
entire ebullition cycle. From these figures, we can see that the predicted heat flux levels
from the rewetting model agree well with the measured values. As the re wetting model is
only valid for the heat flux spikes, it is therefore not adequate for the bubble slow growth
periods that follow the departure and coalescence.
Table 7.1 provides a list of the actual thermal conductivities and effective thermal
conductivities. The ratio of the effective thermal conductivity to actual thermal
conductivity is given in parentheses. It is clear that the effective thermal conductivity that
accounts for the convection and turbulence is not sensitive to whether it is bubble
departure or coalescence (3.5 vs. 3.63 at 100°C and 2.31 vs. 2.49 at 110°C) because the
rewetting processes are similar for both cases. Whereas for different heater temperatures,
the change of the effective thermal conductivity is quite substantial (2.31 vs. 3.5 for
coalescence and 2.49 vs. 3.63 for departure). The reason is that both the departure and
coalescence depend on the thermal properties and the surface tension that vary with the
temperature.
Table 7.1 Effective thermal conductivity (w/m-K) used in the rewetting model
100°C
110°C
Actual thermal conductivity
0.052
0.051
Effective thermal conductivity (departure)
0.182 (3.5)
0.118 (2.31)
Effective thermal conductivity (coalescence)
0.189 (3.63)
0.127 (2.49)

Heat flux (w/cm2) Heat flux (w/cm2)
130
(a)
(b)
Figure 7.4 The results from the rewetting model for the bubble coalescence, (a) Heaters at
100°C; (b) Heaters at 110°C.

131
(a)
(b)
Figure 7.5 The results from the rewetting model for the bubble departure, (a) Heaters at
100°C; (b) Heaters at 110°C.

CHAPTER 8
CONCLUSIONS AND FUTURE WORK
8.1 Summary and Conclusions
A heater array consisting of 96 microheaters was used in this research. Each
heater on the array can be selected and individually controlled and maintained at constant
temperature by the electronics feedback system. By generating a single bubble on a
microheater at different temperatures, an experimental study of miniature-scale pool
boiling heat transfer has been performed to provide a fundamental understanding on the
heater size effect. The heat transfer history during the lifetime of a single bubble, which
includes nucleation, growth, detachment and departure, has been measured at different
heater temperatures. A major discovery is that for the heater size used in the current
study, the boiling curve is composed of two regimes which are separated by a peak heat
flux. In the lower superheat regime, the boiling is dominated by liquid rewetting and
microlayer evaporation. While in the higher superheat regime, conduction through the
vapor film and micro-convection play the key heat transfer role as the heater is covered
by vapor all the time. In general, as the heater size decreases, the boiling curve moves
towards higher heat fluxes with corresponding higher superheats. At a low AT, boiling is
controlled by the microlayer evaporation and at a high AT, conduction dominates the heat
transfer. We also observed that the bubble departure frequency increases with the
superheat, but the departure size changes only very slightly.
By selecting two or multiple heaters bubble coalescence experiments were
performed to investigate the bubble coalescence phenomenon and its effect on boiling
132

133
heat transfer. For bubble coalescence experiments, the individual bubbles were formed
and positioned by powering selected microheaters in a heater array. A series of bubble
coalescence interactions then took place, as the individual bubbles grew large enough to
touch one another. A typical ebullition cycle which includes the coalescence of two
bubbles is characterized by the following stages: nucleation and growth of two single
bubbles, coalescence of dual bubbles, relatively long continued slow growth of the
coalesced bubble, and finally departure of the coalesced bubble. There are also
possibilities that the coalesced bubble would depart immediately or stay for a short
growth period before departure. We have found that in general the coalescence enhances
heat transfer as a result of creating rewetting of the heater surface by colder liquid and
turbulent mixing effects. The enhancement is proportional to the ebullition cycle
frequency and heater superheat. It was also predicted that the longer the heater separation
distance is the higher the heat transfer rates would be from the heaters. For the
multibubble coalescence study, the key discovery is that the ultimate bubble that departs
the heater surface is the product of a sequence of coalescence by dual bubbles. For the
heat transfer enhancement, it was determined that the time and space averaged heat flux
for a given set of heaters increases with the number of bubbles involved and also with the
separation distances among the heaters. In particular, we found that the heat flux levels
for the internal heaters are relatively lower.
8.2 Future Work
Since boiling is a highly complicated heat transfer mode, its research is far from
complete. The suggested future work following this research are listed in the following.
1. Use the constant heat flux heater instead of a constant temperature heater.

134
2. Incline the heater surface at different orientations to study bubble coalescence
effects.
3. Perform a more detailed study on the microlayer and macrolayer of bubbles
during growth period using optical methods.
4. Investigate the subcooling effects on boiling heat transfer and on bubble
coalescence.
5. Study the bubble formation mechanism on a microheater when the heater is
subjected to different heating rates.

APPENDIX A
NOTES OF PROGRAMMING CODES FOR DATA ACQUISITION
A.l Friendly Interface to Select Heaters - frmMain.frm
The interface with 96 heaters in the array on which heaters can be selected
according to experiment requirements has been utilized to facilitate the heaters selection.
The form is shown in figure A.l. In this form, the following functions are to be realized:
1. Initiate the D/A board (board 0) to output signals and the two A/D boards
(board 1 and board 2) for data acquisition. The installation and configuration of the
computerboards are accomplished.
Figure A.l The main interface to select heaters.
2. Select heaters. Maximum 8 heaters can be selected. The heater code and
number of selected heaters are stored in public variables that can be used by other forms
135

136
and procedures. HeatersInfo.Heater(i) is the different heaters selected, and
HeatersInfo.Num is the total number of heaters selected.
3. Zero heaters. Set all digital pots to zero before turn on the 24 V power supply
to the control circuits.
Also in this form, the technology of WindowsAPI was used to obtain the screen
color of the mouse pointer.
Code A-l
Private Declare Function GetPixel& Lib "gdi32" (ByVal hdc As Long, ByVal X As Long, ByVal
Y As Long)
Private Declare Function GetDC Lib "user32" (ByVal hwnd As Long) As Long
Private Declare Function GetCursorPos Lib "user32" (IpPoint As POINTAPI) As Long
Private Type POINTAPI
X As Long
Y As Long
End Type
Code A-2
Private Sub form_MouseMove(Button As Integer, Shift As Integer, X As Single, Y As Single)
Dim dsDC As Long
Dim screenColour As Long
Dim cp As POINTAPI
'check the screen size
'get desktop device context- to copy from
GetCursorPos cp
dsDC = GetDC(0&)
screenColour = GetPixel(dsDC, cp.X, cp.Y)
Label2.Caption = cp.X
Label3.Caption = cp.Y
‘Note: the position is cp.X and cp.Y, which are the absolute coordinates on the screen. But the
return ‘values X, Y of _MouseMove are relative position values of the
current form.
If screenColour <> 65280 Then
Lblcolor (previousColor).Caption = screenColour
End If
End Sub
The selected heaters on the array have been programmed to exhibit the
temperature corresponding to that set in the form frmAnimate.form.

137
A.2 Set the Temperature for Selected Heaters - (frmAnimate.frm)
Multiple document interface (MDI) was used to individually set the heater
temperature. Initial consideration was that we set the selected heaters temperature at the
same time by setting the Dq values. In this experiment, we always set the heaters at the
same temperature. For different heaters at the same temperature, Dq values are different.
Therefore, the best way is to set the heaters temperature individually. From the
frmMain.frm form, heaters were selected. In this form shown in figure A.2, we
dynamically build the menu for all selected heaters that is under the menu: “Heaters”.
The code is given as follows.
Code A-3
Private Sub Addltems()
'To show which heaters are selected.
Dim i As Integer
For i = 1 To HeatersInfo.Num
Load mnultems(i) ‘**Dynamic adding items of the menu.
mnultems(i).Caption = "#" + Str(HeatersInfo.Heater(i) + 1)
Next i
End Sub
Figure A.2 Heaters temperature form.

138
Special notes are that we need to add an dummy submenu to load the menus
dynamically, as in this case mnultem with index as 0, which is a separation bar. Thus the
index starts with the menu is actually 1. With the click the each other under menu of
“Heaters”, the child form corresponding to the heater is opened. Note that variable
“Mark(i)” is used to mark whether the child form corresponding to the heater is opened
or not to avoid to be opened twice.
Code A-4
Private Sub mnultems_click(index As Integer)
Dim i As Integer
If Mark(index) = False Then
Dim frmDumm As New frmTemplate
frmDumm.Show
frmDumm.Caption = Str(index) + "-Heater" + Str(HeatersInfo.Heater(index) + 1)
'Note: I put index in front of the Caption, so that we can index the children forms
'when we unload them, in frmTemplate.
Mark(index) = True
For i = 0 To 7 'set a mark for ActiveForm
If i = index Then
ActiveMark(i) = True
Else
ActiveMark(i) = False
End If
Next i
' Label5.Caption = index
End If
End Sub
The major function of this form is to set the heater temperature individually in its
child form. Each child form corresponds to a horizontal scroll bar: hscDqValue(i). Only
the hscDqValue that corresponds to the active child form is set visible. In this way, the
scroll bar can be used to set the heater temperature of the active child form. The control
Timer used in this form is used to detect the active child form and set the corresponding
scroll bar. This use is not very efficient because use of Timer always slows the program

139
down, thus decrease the speed of data acquisition. The Child Form caption was used to
distinguish them by adding the index number, as shown in the following.
Code A-5
Private Sub mnultems_click(index As Integer)
Dim i As Integer
If Mark(index) = False Then
Dim frmDumm As New frmTemplate
frmDumm.Show
frmDumm.Caption = Str(index) + "-Heater " + Str(HeatersInfo.Heater(index) + 1)
'Note: I put index in front of the Caption, so that we can index the children forms
'when we unload them, in frmTemplate.
End Sub
Private Sub Timerl_Timer()
'This is used to detect which is Me.ActiveForm, so that it can be menu
Dim i, j As Integer
For i = 0 To 7 'To obtain the index of the ActiveForm.
If Mark(i) = True Then
j = Val(Left$(frmAnimate.ActiveForm.Caption, 2))
End If
Next I
End Sub
A.3 Programming the Digital Potentiometer
The kernel of programming the temperature control is included in this form code.
This kernel includes control of the circuit and inputting the Dq values to the circuit to set
the digital potentiometer: DS1267-10. Its value ranges from 0 to 10k ohms. It contains
two wipers, each of them has 8 bits to be set, thus 2x28=512 positions (from 0 to 511).
Note there is extra bit bO that is used distinguish which wiper is being set.
Communication and control of DS1267 is accomplished through a 3-wire serial port
interface that drives an internal control logic unit. The 3-wire serial interface consists of
the three input signal: RST, CLK, and Dq. The RST control signal is used to enable the 3-

140
wire serial port operation of the device. It is an active high input and is required to begin
any communication to the DS1267. The CLK signal input is used to provide timing
synchronization for data input and output. The DQ signal line is used to transmit
potentiometer wiper settings and the stack select bit configuration bO to the 17-bit I/O
shift register of the DS1267.
Code A-6
Sub SetPotValue(ByVal dq)
Dim dqbit( 17) As Byte
‘The variable dqbit( 17) is used to hold the converted dq values, which dqbit(O) is for bO
for stack select.
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 34, 1) 'set reset high ‘RST
signal is set high.
If ulStat <> 0 Then Stop
For i = 0 To 16
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 33, dqbit(i)) 'set dq
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 32, 1) ’ set clock
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 33, 0)' set clock
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 32, 0)' set clock
Next i
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 34, 0)' set reset low
End Sub
A.4 Individual Heater Control
The architecture of the system for the control of the circuits on the feedback cards
is shown in the figure A.3. The multiplexers were used to realize the signal decoding.
One multiplexer (MC74HC138A) is on the mother card. It is a one of eight decoder or
demultiplexer. It decodes a three-bit Address to one-of-eight active-low outputs. The 8
outputs are respectively sent to each card so that only one card accepts the high signal.
(In this system there are only 6 cards, thus only 6 signals are used.) The other multiplexer

141
(MC74HC4514) is used to select the circuit on the card. The signal to each card is
connected to the Chip select pin to enable the multiplexer on the card, while the other
mulitiplexers on other cards are not enabled. The selected heater is converted to a 7-bit
signal. The first 3 bits are output to the 74HC138A to select the card, the last 4 bits are
output to the 74HC4514 to select the circuits. The following two lines are used to address
the selected heater.
Figure A.3 The architecture for addressing the selected heaters.

142
Code A-7
Addr = CircuitSelect(SelHeater)
ulStat = cbDOut(DACBoardNum, SECONDPORTA, Addr)
Data acquisition is simply accomplished by using the computerboards library
function “cbAIn”, which is shown as follows.
Code A-8
Function GetHeaterVoltage(PortNum, CardNum)
Dim voltage
ulStat% = cbAIn(CardNum, PortNum, UNIIOVOLTS, voltage)
'value must be defined,
voltage = voltage * 10 / 4096
GetHeaterVoltage = voltage
End Function
For data acquisition, an important thing is that the pins on the A/D cards are not
consistent with the heater numbers (from 0 to 95). Therefore a function is required to
convert this inconsistency, which is done by “DAS48PortNum”. The figure A.4 is used to
illustrate this inconsistency.
CodeA-9
Function DAS48PortNum(Heater) As Integer
Dim PortNum As Integer
If Heater Mod 2=1 Then
PortNum = (Heater - 1) / 2
PortNum = PortNum + 24
Else
PortNum = Heater / 2
End If
DAS48PortNum = PortNum
End Function

Channel
Number
Pin
Number
Figure A.4 The pins layout of the D/A cards.
A.5 Data Acquisition - (frmADConv.frm)
The major function of this form shown in figure A.5 is data acquisition in which
the acquisition time and output file can be selected. The heater temperature needs to be
set before starting the acquisition. The main feature used in this form is the use of SQL.
The database that is built using “Visual Data Manager” contains the information of each
heater including heater area, heater resistance values. These data are accessed in this form
after the voltage across the heater have been acquired, then used to calculate the heat flux
dissipated by the heater. The control “data” is included in this form to realize the access
by using SQL language.
The following is the code to access the data stored in the database.
Code A-10
Datal.Recordset.Move SelectedHeater - Data 1.Recordset.AbsolutePosition
143
View From Component Side of Board
UGNO SO
• •
49 LLOND
CH47N/CH23LOW 40
• •
4 7 CH HI 23
CH 4« H)/CH 22 LOW 46
• •
45 CH HI 22
CH 45 Hi/CM 21 LOW 44
• •
4 3 CH HI 21
CH 44 HI /CH ?0LOW 4?
• •
41 CH HI 20
CM 43 Ml/CM 19 LOW 40
• •
39 CH HI 19
CH 42 HI/CM 18 LOW 38
• •
3 7 CH HI IB ^
CH4IM/CNI7LOW 36
• •
35 CH HI 1 ’jék
CH 40 HI / CH 16 LOW 34
• •
33 CH HI 16
CM 30 Hi/CH 15 LOW 32
• •
3i CH Ml 15
CH 38 HI/CM 14 LOW 30
• •
29 CH HI 14
CH 37 HI/CM 13 LOW 28
• •
27 CH HI 13
CH 36 HI/CH 12 LOW 26
• •
25 CH HI 12
CM 35 HI/CH 11 LOW 24
• •
23 CH HI 11
CH 34 HI/CH 10LOW 22
• •
21 CH HI 10
CH 33 HI / CH 9 LOW 20
• •
19 CM HI 9
CM 32 HI / CH » LOW 18
• •
17 CH HI3X'’
CH3I HI/CH 7LOW >6
• •
15*pW^Hi 7
CH 30 HI / CH 6 LOW 14
• •
I^CH HI 6
CM 29 HI / CM 5 LOW 12
• •
11 CH HI 5
CH 26 HI/CH 4 LOW 10
• •
9 CH HI 4
CM 27 Ml / CH 3 LOW 8
• •
7 CH HI 3
CH 26 HI / CH 2 LOW 6
• •
5 CM Ml 2
CH 25 HI/CH 1 LOW 4
• •
3 CH Ml 1
CH 24 HI / CM 0 LOW 2
• •
1 CH HI 0

144
RMResist = Datal.Recordset.Fields("Resistance").Value
realResist = RMResist / (1 - 0.002 * (HeatersInfo.Temperature - 25))
HeaterArea = Datal.Recordset.Fields("Area").Value
Three combo controls have been implemented in this form. One is the control
"cmbSelect" which is used to contain the heaters selected in the Main Form. By selecting
one of them, the heater can be accessed for data acquisition. The control "cmbDuration"
is used to choose the time for data acquisition. The control "cmbTemp" is used to select
the temperature that the heater is set, which has to be same as the actual temperature the
heater is set.
Figure A.5 The data acquisition form.
A.6 Child Form Template - (frmTemplate.frm)
This form is built to set up the template child form so that each child form has the
same format. In this form, the unloading of the ActiveForm of the child forms is detected

145
by checking the index associated with the form caption, which is shown in the following
code. After this unloading, the Timer control in frmAnimate.frm automatically detects
the current ActiveForm.
Code A-11
Private Sub Form_unLoad(index As Integer)
'The whole idea is to reopen the child form after it is open and closed,
by using the using index in front of the Caption.
Dim strlndex As String
Dim sstrlndex As Integer
'frmAnimate.Labell. Caption = Me.Caption
strlndex = Left$(Me.Caption, 2)
'For some reason, if Left$(me.caption, 1) is used, the result is blank.
' frmAnimate.Label2.Caption = strlndex
sstrlndex = Val(strlndex)
Mark(sstrlndex) = False
End Sub
Actually, Timer control does not have to be always enabled since its sole function
is to detect the current ActiveForm. Here, we can modify the code so that only when
there is a change of ActiveForm, the Timer is enabled.
In addition to the Forms described above, this software also includes the
following modules: DataStructure.bas, ModDAC.bas, ModADC.bas, Heatersinfo.bas,
Cbw.bas, PubConst.bas, PubVariables.bas. Among these, Cbw.bas is the module
included to enable the computerboards functions.

REFERENCES
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BIOGRAPHICAL SKETCH
Tailian Chen received his bachelor’s degree in mechanical engineering in 1990,
and continued his study in automotive engineering. He finished his Master of Science
degree in 1993 at Jiangsu University of Science and Technology in Zhenjiang, China.
After that, he joined Panda Motors (China) Corporation to be an electro-mechanical
engineer until December 1998. During his tenure in PMCC his responsibilities included
technical, engineering work and project management.
In January 1999, he moved to Gainesville, Florida, USA, to pursue his Ph.D
degree in mechanical engineering. His research is on microscale boiling heat transfer. His
archival publications have appeared in the International Journal of Heat and Mass
Transfer.
150

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
A/.
Jacob N. Chung, Chair v
Professor of Mechanical Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
F. Klausner
bssor of Mechanical Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
William E. Lear, Jr. /
Associate Professor of Mechanical
Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
ihuomin Zhang
Associate Professor of Mechanical
Engineering

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
V\.
Ulrich H. Kurzweg
Professor of Aerospace Engineering,
Mechanics and Engineering Science
This dissertation was submitted to the Graduate Faculty of the College of
Engineering and to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
August 2002
Pramod P. Khargonekar
Dean, College of Engineering
Winfred M. Phillips
Dean, Graduate School

LD
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UNIVERSITY OF FLORIDA
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