IOP P
UBLISHING
J. Micromech. Microeng.
19 (2009) 095008 (10pp)
J
OURNAL OF
M
ICROMECHANICS AND
M
ICROENGINEERING doi:10.1088/0960-1317/19/9/095008
1
Department of Mechanical Engineering, Hong Kong University of Science and Technology,
Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China
E-mail: meqiu@ust.hk
Received 23 February 2009, in final form 23 June 2009
Published 24 August 2009
Online at stacks.iop.org/JMM/19/095008
Abstract
A micro heater array has been fabricated using a standard micromachining technique to study the micro thermal bubble dynamics on a horizontal downward-facing surface. Several different types of bubble dynamic phenomena, such as bubble sweeping, bubble departure / retraction and multibubbles interaction / coalescence, have been investigated utilizing a high-speed photography system. The effects of Marangoni force, buoyancy force and drag force on the bubble dynamic phenomena have been studied utilizing experimental data. The results obtained from this study are not only helpful for understanding the microscale thermal bubble dynamics but also useful for optimization of micro cooling equipment and development of novel thermal bubble-based MEMS (micro-electro-mechanical-system) devices.
(Some figures in this article are in colour only in the electronic version) y z u
T
M a
V
ν g
R t
R h
R
0
F b
F
D
F g
F
M p
acceleration due to gravity (9.8 m s
−
2 ) bubble radius (m) heater electrical resistance ( ) heater electrical resistance at 0 buoyancy force
◦
C drag force gravity force
Marangoni force (capillary force) pressure (N m
−
2 ) time (s) temperature (
◦
C)
Marangoni number volume velocity axial coordinate axial coordinate bubble velocity
λ
ρ
σ
μ
θ thermal conductivity (W mK
− 1
− 3 density (kg m ) surface tension (N m
− 1
) dynamic viscosity (N s m
−
2
)
) the azimuthal angle
l b
B c
C buoyancy bubble critical value
C
=
1 / 3 for the Hadamard–Rybczynski drag law and
C
=
2 / 9 for Stokes drag law liquid max maximum s stationary state w v wall vapor
α
α
thermal diffusivity of the liquid (m s
−
2 ) temperature coefficient of resistance (TCR) (
◦
C
−
1 )
1
Author to whom any correspondence should be addressed.
0960-1317/09/095008+10$30.00
1
Research on thermal bubble dynamics in microscale has numerous practical applications in many fields.
One of these applications is cooling of microelectronic components.
Nowadays, with the rapid development of IC (integrated
© 2009 IOP Publishing Ltd Printed in the UK

J. Micromech. Microeng.
19 (2009) 095008 circuit) technology, thermal management of electronic devices has become a vital issue and many different techniques
have been proposed to deal with this critical problem [ 1 – 5
].
Boiling heat transfer is one of these powerful approaches to thermal management of high power IC devices.
Other applications include thermal bubble inkjet printers, bubble pump, bubble actuator, and biological and chemical processes
[ 6 – 13
]. In these MEMS devices, thermal bubbles generated by micro heaters play a key role. To further optimize the microcooling devices and develop new functional MEMS devices, understanding thermal bubble dynamics in microscale is crucial.
Despite numerous researches on micro thermal bubble dynamics having been conducted, the mechanisms behind are not well understood yet, such as bubble dynamics on a horizontal downward-facing surface, which one can only find from following research.
Wasekar and Manglik
[ 14
] numerically investigated the dynamics of a single hemispherical bubble (1–100 μ m radius) on a downwardfacing wall, while their research was mainly focused on the effect of surfactant concentration on the initial short-timescale Marangoni convection. Another related research was conducted by Kasumi et al
[ 15 ], who computationally studied
the interaction between two bubbles on a downward-facing hot or cold wall. Apart from these theoretical researches, Peng et al
[ 16
] experimentally studied the boiling on a downward heating surface. They observed that a jet flow emerges from the bubble top and the nucleate boiling heat transfer efficiency is greatly enhanced by the jet flow. They attributed the formation of the jet flow to interfacial evaporation and condensation.
In this research, a micro heater array was designed and fabricated to investigate bubble dynamic processes on a downward-facing surface.
Different numbers of heater were applied to generate micro thermal bubbles.
Using this method, not only single-bubble but also multibubbles interaction phenomena were studied. These bubble dynamic phenomena were recorded by a high-speed photograph system and theoretical analysis based on these visual results was proposed.
X Qu and H Qiu
Figure 1.
Fabrication process flow of the micro heater array.
2.1. Micro heater array fabrication
The micro heater array was designed and fabricated by a standard micromachining technique, as shown in figure
1 . The
heater array was fabricated on an N -type, single-side polished
1 0 0 oriented silicon wafer (4 inches in diameter and 500 μ m in thickness). After standard cleaning, the wafer was covered by a 0.5
μ m thick silicon dioxide film, which served as a thermal and electrical isolation layer. Then, a 0.4
μ m thick polysilicon layer was deposited on the oxide layer by a CVD
(chemical vapor deposition) technique (figure
1 (1)). After that,
the electrical resistivity of the polysilicon layer was changed by ion implantation of P at doses of 1.5
×
10
15 ions cm
− 2 and energy of 120 keV (figure
1 (2)). Following implantation, the
wafer was annealed at 900
◦
C for 30 min. Then, the heaters and leads were patterned by dry etching of the polysilicon
Figure 2.
Dimensions of the heater array (with enlargement of one heater).
layer (figure
1 (3)) and the second step of ion implantation
was carried out to increase the electrical conductivity of the connecting leads (figure
1 (4)). In this step, the dose amount
of P is 5
×
10 15 ions cm
−
2 and the injection energy is 80 keV.
After stripping off the protecting photoresist layer, the annealing process was taken at 900
◦
C for 30 min in an oven without oxygen. A photo taken during the fabrication process is shown in figure
2 , where there are 63 heaters
(7
×
9 array) on a single device chip. The dimensions of each heater are 8 × 23 μ m 2 and the distances between heaters are
93 μ m (in the horizontal direction) and 134 μ m (in the vertical direction). To connect the heaters with the electrical circuits on a PCB (printed circuit board), a 0.4
μ m thick Al film was coated and patterned to form the final metal leads (figure
1 (5)).
2

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu
Figure 4.
Micro heater chip integrated with the PCB and PMMA chamber.
Figure 3.
Calibration results of 15 heaters over a chip.
Because the micro heaters were designed to work in a liquid medium, a 0.2
μ m thick LTO (low temperature oxide) layer was deposited by CVD on the whole device as an electrical and chemical isolation layer to protect the devices. In the end, the connecting holes were dry etched through the LTO layer for wire bonding (figure
1 (6)). There were no obvious
defects found on the surface of the micro heaters when they were inspected with an optical microscope.
UV (ultraviolet) curving adhesive as shown in figure
4 . The
height and diameter of the mini chamber are 2 mm and 5 mm, respectively. During the experiment, the chamber was filled with working liquid and sealed with a small piece of glass plate. With this covering plate, the liquid can be prevented from fast evaporating and clear photos can be taken through the microscope.
2.2. Calibration of the micro heater array
After fabrication, 15 micro heaters evenly distributed over a single device chip were calibrated in a dark closed probe station using the HP 4145B semiconductor parameter analyzer. The calibration results are shown in figure
3 . The small variation
between heaters is mainly from the implantation process and the changing of contact resistance during calibration. The relationship between temperature and heater resistance ( R h
) can be expressed by the following equation as shown in figure
3 :
R h
(T )
=
R
0
( 1
−
α
·
T ), (1) where R
0
(
=
3250.12
) is the heater resistance at reference temperature (0
◦
C) and the temperature coefficient of the heater resistance is α (
=
0.0015
◦
C
−
1 ).
The calibration results indicate that the heater resistance decreases linearly with increasing temperature. This is the reason why some researchers used the heater as a temperature
sensor simultaneously in their experiments [ 10
,
17
]. In our experiment, the changing of the resistance during heating pulse was ignored and the power applied to each heater was assumed to be constant. This assumption is acceptable from previous
researches and practical MEMS applications [ 18
,
19 ].
2.3. Device integration
After fabrication of the micro heater array, the device chip was bonded on a PCB and a round chamber made of PMMA
(polymethyl methacrylate) was adhered to the heater chip by
2.4. Experimental setup
The experimental setup is illustrated in figure
5 . During the
experiment, the micro heater chip (as shown in figure
4 ) was
fastened upside down on the observation chuck of an inverse microscope (ECLIPSE TE2000-U, Nikon Co.).
A function generator (Global Specialties Co., Model
2003) was used to generate different levels of heating pulses.
The heating pulses were amplified by a power amplifier
(MS040 100 W Armour Symmetry Magnifier, Me Sing
Electronic Co.) and then supplied to the heaters.
In all experiments, the width of the heating pulse was kept as 50 ms, with an interval longer than 10 s in order to minimize the effect of residual heating. Because the pulse generated by the function generator is not high enough to trigger the camera, the signal was first fed into a PDA14 Waveform Digitizer
(Signatec, Inc.) and a synchronized standard pulse signal was then generated by the PDA14 to trigger the camera.
Before the experiment, the chamber was cleaned thoroughly with DI water (deionized water) and dried with nitrogen gas.
Pure ethanol was used as a medium liquid because of its relatively low boiling point (351.6 K) and minimum toxicity.
The ethanol liquid was not degassed, so during the experiment, it was found that after heating pulse the boiling bubble would not collapse very quickly but remain on the substrate for a relatively long time before it finally disappeared. The experiments were carried out at room temperature (23
◦
C) and under 1 atmospheric pressure. The bubble dynamics phenomena were all recorded by a highspeed camera (Redlake Motion Xtra HG-100 K) and the results were downloaded into a PC for theoretical analysis.
3

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu
Figure 5.
Experimental setup.
Figure 6.
Bubble sweeping along the heater (33 mW).
The minimum power needed to generate a thermal bubble was determined by gradually increasing the pulse voltage until a bubble was nucleated. The minimum power was measured to be 8.33 mW. In the experiment, it was found that the bubble dynamic phenomena were different according to different power level applied. They are bubble sweeping / oscillating along the heater surface and bubble departure / return inside the liquid which will be discussed below.
3.1. Single bubble sweeping and oscillating
When the power was relatively low, which was set to be
33 mW, the typical bubble dynamic process is shown in figures
6 (
A )–( J ). It is found that the behavior of bubble dynamics can be divided into several phases.
First, just after the power was turned on for 1.6 ms, the heater was covered with a blanket thermal bubble as shown in figure
6 (
B ).
This blanket thermal bubble is attributed to a highly localized near-homogeneous boiling. This phenomenon is termed the cavitation phase. At 3.6 ms, the thermal bubble collapsed to form a smaller single bubble which attached on the heater surface as shown in figure
6 (
C ). This collapsing process was very fast, which exceeded the limitation of our high-speed camera (in this research, the camera was set to be 2500 fps).
At the same time, the bubble began to move along the heater very quickly, which is called the bubble sweeping movement as shown in figures
6 (
C ) and ( D ). As the small bubble reached the end of the heater, it would return in the reverse direction and sweep to the other end. This kind of bubble sweeping forth and back along the heater surface is called oscillating movement.
During the experiment, the bubble oscillated for tens of cycles until the power was turned off. There are four cycles shown in figure
6 , where the little arrow beside the bubble indicates the
direction of the sweeping movement. According to a series of photographs taken by a high-speed camera, the period of the bubble oscillating cycle is estimated to be 1.2–1.6 ms under this condition. Figures
6 (
E ), ( G ) and ( I ) show the transient states.
In those figures, there are not two bubbles coexisting on the heater but only one bubble existing continuously on two frames of high-speed photographs. From the high-speed photograph results, during the whole heating period, the oscillating cycles are counted to be 70 to 80 times.
The multiboiling bubbles sweeping phenomenon has been studied intensively by a relatively large-scale experimental
setup [ 20 – 25 ]. In those researches, a wire heater located in
a liquid pool was applied to generate multithermal bubbles.
With this kind of experimental device, more than one mini thermal bubble was generated randomly on the wire heater.
The obvious advantage of our experimental setup in this paper is that a single micro thermal bubble can be generated repeatedly and accurately on a micro heater. So it provides the special opportunity to investigate the single sweeping bubble phenomenon more clearly. Another advantage of our experimental setup is that it can mimic the real case of MEMS application.
The temperature field across the micro heater is uneven
[ 19 ] as described in figures
7 (
A ) and ( B ). Because the temperature at the center of the heater ( T
2
) is known to be higher than the temperature at the end of the heater ( T
1
) [ 19 ],
the direction of the Marangoni force ( F
M
) [ 26 , 27 ], which is
4

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu
( A ) ( B )
Figure 7.
Illustration of the thermal bubble sweeping phenomenon.
induced by the temperature gradient, is toward the center of the heater as shown in figure
7 .
For a bubble existing in a liquid where there is a temperature gradient along the z direction, the Marangoni
force acting on the bubble can be given as [ 28
]
F
M
=
2 π μ l
αM a
= −
2 π R
2
∂σ
∂T
∂T
∂z
, (2) where μ l is the fluid viscosity and σ is the surface tension.
M a is the Marangoni number which can be described as
M a
= −
∂σ
∂T
∂T
∂z
R 2
μα
.
(3)
Because in general, ∂σ/∂T < 0, the direction of the
Marangoni force is the same as the temperature gradient
( ∂T /∂z ).
Therefore, when a single bubble was formed by a pulse, the Marangoni force acting on the bubble would drive it to move toward the heater center. Once the bubble began to move in the liquid, the drag force would also act on the bubble. With the assumption of μ
B
μ l
, the drag force ( F
D
) is expressed
as [ 28
]
F
D
=
2 π μ l
Ru
3 μ
B
μ
B
+ 2 μ l
+ μ l
∼
4 π μ l
Ru, (4) where u is the bubble velocity.
At the moment when the bubble reached the heater center, the net Marangoni force acting on the bubble became zero because of the symmetry of the temperature field.
While under the inertia effect, the bubble would not stop at the center area but keep sweeping toward the end of the heater. During this sweeping process from the center to the end of the heater, the Marangoni force and drag force were both toward the heater center, so the bubble would decelerate and finally stop at the end of the heater. After that under the effect of the
Marangoni force, which was directed to the center of the heater, the bubble accelerated again in the reverse direction to move toward the heater center. Then, the second cycle of the sweeping process started. From the above analysis, it can be found that the balance between the Marangoni force and the drag force induces the bubble to sweep along the heater surface with acceleration or deceleration.
If the power was lower than a critical value (48–56 mW), the oscillating cycles and sweeping velocity of the micro thermal bubble increased with the heating power. Because it is very hard to measure the sweeping velocity accurately, only the oscillating cycles were counted from the visual recording. The
Figure 8.
Relation between the power and the sweeping cycle times.
relation between oscillating cycles and four different powers are shown in figure
8 . Clearly, there is a linear relationship
between the power supplied and the cycle times of the bubble oscillating. It can be found from the figure, with increasing power, that the oscillating cycles become larger in the constant heating pulse duration, which means the velocity of bubble sweeping became faster with increasing power.
Bubble oscillating and sweeping may be used in mixing of micro fluid or actuator in MEMS devices. It also increases the heat transfer coefficient.
Because of bubble sweeping and oscillating along the heater surface, the convective heat transfer from the heater to the surrounding liquid medium is significantly intensified, which has been found in normal
scale experiment [ 20
]. In comparison with the wire heater, this experimental design has some advantages. First, with this experimental design, the real situation of boiling heat transfer can be mimicked and studied. Instead of using a heater immersed in a liquid, this experimental device with micro heaters located on the substrate is similar to the practical boiling heat transfer condition.
The second advantage of this design is that the boiling bubble can be repeatedly generated on one or several positions with high precision, which is almost impossible for the wire heater. Third, the heater array around the nucleation points on the substrate can be applied as a temperature sensor to characterize the thermal bubble dynamics. So, the temperature field around the sweeping bubble can be measured, which will be useful for understanding the sweeping bubble dynamics. Because of these advantages, this experimental design will be helpful for investigation of boiling heat transfer under special conditions, such as boiling on horizontal downward-facing surfaces and boiling in microgravity. The Marangoni effect on the quick motion of boiling bubbles between different temperature regions on a heated surface can be investigated.
After the power was switched off, the bubble dynamics were different according to different power levels applied. For a relatively low level of power applied, the micro bubble would stop sweeping and shrink to disappear. While for a relatively high level of power applied, the thermal bubble would break away from the heater surface and dive into the liquid volume
5

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu
Figure 9.
Bubble departs from the heater (33 mW).
Figure 11.
Single bubble dynamics downward from a surface.
Figure 10.
Thermal bubble departure and return processes.
as shown in figure
9 , where the shadow of the bubble projected
on the substrate indicates the bubble departure.
Figure 12.
Bubble growth, force balance and temperature field during the heating pulse.
3.2. Single bubble departure and return
A high power experiment was carried out with a pulse heating power of 103 mW and the results are shown in figures
10 (
A )–
( L ). From this figure, it can be seen that the bubble dynamics is different in two ways in comparison with previous low power experiments.
First, the bubble grew very fast and almost no sweeping phenomenon could be observed. Second, after departure from the heater, the bubble would return to the heater in 400–500 ms.
Because the microscope was focused on the heater substrate, when the bubble was attached on the heater, its contour was distinct and clear, such as those photos shown in figures
10 (
A )–( C ). While when the bubble lifted off and got out of the focus plane, the contour of the bubble became blurry and obscure, such as in figures
10 (
E )–( I ). Therefore, according to the change of the bubble contour, the whole dynamic processes can be illustrated in figure
11 .
In figure
11 , the vertical coordinate is the distance from
the heater substrate to the position of the bubble center and the horizontal coordinate is the time. The whole dynamic process is divided into four different phases according to different bubble phenomena. The first phase, t
1
, is the pulse heating phase, where there are two substeps: t
11 is the bubble nucleation step, where the bubble was generated and began to grow; t
12 is the bubble pulsating step, where the bubble pulsated several times and kept growing until the power was cut off. Then, in the second phase, t
2
, without heating, the big thermal bubble detached from the heater and dived into the liquid. When the bubble reached the longest distance, the thermal bubble shrank slowly and floated up toward the heater.
This step is shown as t
3 in figure
11
and is named the floating and return phase. When the bubble reached the substrate, it approached the heater and stayed on the heater surface until it finally disappeared after several seconds, which is termed the diminish and disappear phase and the duration of this phase is t
4 as shown in figure
11 . The time and length scales in figure 11
are just for illustration but not according to the real scale accurately.
The mechanism of bubble growth and departure processes is analyzed as follows. When the heater was powered, the temperature field and force balance on the bubble are both illustrated in figure
12 .
At this moment, the maximum temperature was located at the heater substrate as shown in the subfigure of figure
12
(z
=
0 , T w
=
T max
) , while in the liquid volume far away from the wall ( z is much larger than the characteristic dimension of the heater), the liquid temperature remained at room temperature ( T
0
). In this state, all the forces acting on the bubble, such as buoyancy force ( F b
),
Marangoni force ( F
M
) and gravity force ( F g
), were balanced in the vertical direction and no obvious bubble movement was observed except bubble growth and pulsation.
In figures
10
and
11 , the bubble departed and lifted off
after the heating pulse was over. The temperature field and forces acting on the bubble during this process are illustrated
6

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu moment, u
=
0, so the stationary radius of the bubble can be calculated to be
R
S
=
∂σ
∂T
∂T
∂z
1
2 Cρ l g
.
(7)
After the temporary resting in the liquid, the temperature gradient became smaller and the Marangoni force became less important than the buoyancy force. So, the bubble would finally float up to the heater substrate under the effect of the new force balance between the buoyancy force and the Marangoni force.
Figure 13.
Bubble departure, force balance and temperature field after the heating pulse.
in figure
13 . When the heating power was shut down, the
temperature of the heater substrate dropped more quickly than that of the liquid because the thermal conductivity of the silicon substrate (149 W mK
−
1 ) is much higher than that of the working liquid (ethanol, 0.14–0.17 W mK
−
1
) [ 29
,
30
].
So the temperature of the heater substrate would become lower than that of the liquid volume in a short time. Then, the temperature gradient in the liquid reversed compared with the heating condition. The temperature field across the liquid is sketched in the right subfigure of figure
13 , where it shows
that the maximum temperature ( T max
) is located in the liquid volume but not on the heater surface where the temperature is T w
.
With this newly formed temperature gradient, the direction of the Marangoni force would change to downward and would play a more important role than the buoyancy force in determining the bubble movement direction. So the thermal bubble would move downward against the buoyancy force in this new condition.
During the downward movement, there were four forces acting on the bubble, which are buoyancy ( F b
), drag force ( F
D
), Marangoni force ( F
M
) and gravity force ( F g
).
Drag force and Marangoni force have been expressed as
equations ( 2 ) and ( 4 ). With the assumption of
ρ
B and μ
B
μ l
, the balance of these four forces ( F
G
ρ l
) in the
, vertical direction can be described as
F
G
= F g
− F b
+ F
M
− F
D
∼ −
4
3
π R
3
ρ l g
−
2 π R
2
∂σ
∂T
∂T
∂z
−
4 π μ l
Ru.
(5)
With these forces acting on the bubble, the velocity of the
bubble can be expressed as [ 31
] u
= u
B
+ u
M
= −
C
R 2 ρ l g
μ l
−
∂σ
∂T
∂T
∂z
R
2 μ l
, (6) where C
=
1 / 3 and 2 / 9 for the Hadamard–Rybczynski and
Stokes drag laws, respectively; u
B is the velocity induced by
F g
, F b and F
D
, when there is no temperature gradient existing in the liquid.
u
M is the velocity induced by the Marangoni force. When the bubble reached the maximum distance in the liquid, it would remain stationary instantaneously. For that
Micro thermal bubbles interaction and coalescence on an upward-facing surface have been investigated by Chen and
Chung [ 32
]. They used micro heaters to generate two micro thermal bubbles on a substrate side by side. The coalescence took place when these two bubbles had grown to a certain size that allowed them to touch each other and combined to form a single bigger thermal bubble. By that experiment, they found the heat transfer was highly improved because of rewetting of the dry heater surface and turbulent mixing induced by the bubbles coalescence. In our research, dynamics of multithermal bubbles on a downward-facing substrate were investigated. We found that the bubble dynamic phenomena under this special condition are much more complicated than what happened in Chen and Chung’s experiment. The interactions of two bubbles, three bubbles and four bubbles were studied separately.
The results obtained from these experiments are introduced in the following sections.
4.1. Two bubbles interaction mode
Two bubbles interaction mode was studied by two heaters which were simultaneously powered. The distance between these two heaters is 186.7
μ m.
The power applied on each heater is 105 mW. A series of photographs, shown in figure
14 , depict the two bubbles interaction process. The
force analysis of the whole dynamic process is illustrated in figure
15 , where the bubbles’ movement is shown by moving
paths and the arrows denote the moving directions. This two bubbles interaction phenomenon is analyzed and explained as follows.
First, the bubble nucleation and departure processes are similar to the case introduced in section
3.2
.
So these processes will not be explained in detail in this section. The difference compared with single bubble dynamics is shown in figure
14 (
B ), which illustrates that after departure from the heaters simultaneously, these two bubbles moved toward each other in the liquid volume. The force balance during the approaching movement is illustrated in figure
15 (
A ). In this case, the temperature gradient existed not only in the vertical direction, as analyzed in section
3.2
, but also in the
horizontal direction, which was induced by the existence of a neighbor thermal bubble. The combination of these two temperature gradients determined the bubbles to move along the direction of the Marangoni force ( F
M
), which is shown in figure
15 (
A ). Because the thermal bubbles moved in the
7

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu
Figure 14.
Two bubbles interaction dynamics process.
Figure 16.
Three thermal bubbles interaction.
single bubble. This bubbles coalescence phenomenon will be studied in the following sections.
Figure 15.
Path tracks of micro bubbles during interaction.
liquid, their temperature kept dropping during the approaching movement.
While the Marangoni force is proportional to
the temperature gradient, as described in equation ( 2 ), so
during the approaching movement, the Marangoni force also decreased with the dropping temperature of the thermal bubble.
This can explain why the bubbles stopped approaching and temporarily stopped in figure
14 (
F ), which happened at about
344 ms.
The force analysis at that moment is shown in figure
15 (
B ), where we can find that there was no force acting in the horizontal directions. So after that moment, these two bubbles returned in the reverse directions and floated upward to approach their heaters, respectively. The dynamic analysis of the floating process is shown in figure
15 (
C ), where it illustrates that the Marangoni force is toward the heater area because the temperature around the heater was still higher than that in the other area on the substrate. At about 1.13 s, shown in figure
14 (
G ), these two bubbles reached the substrate surface.
This experiment investigated the interaction between two thermal bubbles which were separated over a long distance.
No coalescence phenomenon occurred in the experiment. If the power applied on the heaters is further increased or the distance between the bubbles is reduced, these two bubbles will finally combine with each other and merge to form a
4.2. Three bubbles interaction mode
Three kinds of coalescence were studied in this and the following sections. The first kind of coalescence is termed as primary coalescence, which occurred between two original thermal bubbles. Original thermal bubble means the bubble is generated by the heater, while the thermal bubble generated by the primary coalescence is called the newborn thermal bubble.
The second kind of coalescence is termed as semi-primary coalescence, which occurred between one original thermal bubble and one newborn thermal bubble.
The third kind of coalescence is termed as secondary coalescence, which occurred between two newborn thermal bubbles.
In this section, the first two kinds of coalescence were investigated.
For that purpose, three heaters were powered simultaneously to generate thermal bubbles, and the interaction between these bubbles was studied. The relative positions of these heaters applied in this research are shown in figure
16 , where we can see these heaters are designated as [a],
[b] and [c]. The average power applied on these heaters was
120 mW. A series of photos show that the bubble interaction process is also exhibited in figure
16 . The bubbles interaction
and coalescence processes are introduced as follows.
For the first tens of microseconds, the phenomena of the bubbles nucleation, growth and pulsation are almost the same as introduced in section
3.2
.
The difference compared with two bubbles mode is shown in figures
16 (
D ) and ( H ), which show the first two kinds of bubbles coalescence phenomena. The primary coalescence is shown in
8

J. Micromech. Microeng.
19 (2009) 095008 X Qu and H Qiu
Figure 18.
Schematic drawings of bubble dynamics and three phases—A: departure; B: coalescence; C: floating.
Figure 17.
Four thermal bubbles interaction.
figure
16 (
D ), where two original thermal bubbles, which were generated by heater [a] and heater [b], approached each other and merged at about 59.4 ms. After the primary coalescence, the newborn thermal bubble approached and attracted the third original thermal bubble, which just departed from the heater [c]. The relative positions and movement directions are illustrated in figure
16 (
E ), which shows that the newborn thermal bubble is located almost at the center of the heater [a] and heater [b]. The distance between the newborn bubble and the third original bubble is about 165 μ m. At about 88.2 ms, the semi-primary coalescence occurred between the newborn thermal bubble and the original bubble, which is shown in figure
16 (
H ). All these coalescence processes took place in the liquid medium but not on the heater surface, because the contours of these bubbles are blurry which means the bubbles are out of the focus plane and move inside the liquid medium.
After the semi-primary coalescence, the finally formed bubble floated to the heater substrate and gradually vanished in several seconds. The whole bubbles coalescence processes took about 36 ms from ( B ) to ( H ) in figure
16 , which
is relatively fast compared to the duration of the whole dynamic process. During the experiment, it was found that the bubbles velocities increased when they approached each other. This
phenomenon has been predicted by theoretical analysis [ 15
].
The reason is that when these bubbles approach each other, the
Marangoni force ( F
M
) acting on the bubble increases because the temperature gradient is enhanced by the approaching of the neighbor thermal bubble. So the Marangoni force is larger than the hydrodynamic drag ( F
D
), the bubbles accelerate to approach each other and combine in the end.
108 mW to generate four original thermal bubbles. A series of photographs taken during four bubbles interaction and coalescence process are shown in figure
17 , where we can
find that primary and secondary coalescences occurred during this process.
When the power was just cut off, these four original thermal bubbles had grown to their maximum size and began to depart from their heaters separately, which happened at about 52 ms as shown in figure
17 (
B ). After departure from their original positions almost simultaneously, these bubbles approached each other in two groups, which is shown in figure
17 (
C ). At about 58 ms, in figure
17 (
E ), two newborn bubbles were formed by two primary coalescences, which happened between four original thermal bubbles in two groups.
After that, these two newborn thermal bubbles attracted and moved toward each other, which is shown in figure
17 (
F ).
Then, at about 76 ms, in figure
17 (
H ), secondary coalescence happened between these two newborn thermal bubbles. After that the finally generated thermal bubble floated upward to the substrate surface and slowly disappeared. The whole bubble coalescences process took about 24 ms as shown in figure
17
( B ) to ( H ).
Although there are three different kinds of coalescence investigated in sections
4.2
and
4.3
, the mechanism and
dynamic process of these bubble coalescences are almost the same, which is illustrated in figure
18 . From the analysis in
that figure, we can see that the balance between the Marangoni force and the drag force is still the main effect to drive these bubbles to approach and combine.
4.3. Four bubbles interaction mode
The secondary coalescence, which occurred between two newborn thermal bubbles, was studied in this case.
For that purpose, in this experiment, four symmetrical heaters were activated simultaneously with an average power of
The combination of MEMS-fabricated micro heater array and high-speed photography system provides a powerful experimental method to explore the microscale thermal bubble dynamics under special conditions. In this paper, we presented the experimental results of several kinds of different bubble
9

J. Micromech. Microeng.
19 (2009) 095008 dynamic phenomena induced by a micro heater array located on a horizontal downward-facing surface. Both single bubble dynamics on heater surface and multi bubble interaction in the liquid medium were studied.
For single bubble dynamics, two kinds of phenomena were investigated, which are bubble sweeping / oscillating along the heater and bubble departure / return in the liquid volume, while for multibubbles dynamics, several complicated dynamic phenomena were studied by experiments of two bubbles, three bubbles and four bubbles. These dynamic phenomena are two bubbles interaction and several different coalescence processes, which are primary coalescence, semi-primary coalescence and secondary coalescence.
Through these studies, it was found that the relative balance of several forces acting on the bubble determined different bubble dynamic phenomena.
The experimental design applied in this research was proved powerful for the investigation of thermal bubble dynamics. The experimental results are not only significant for better understanding of thermal bubble dynamics under special conditions but also helpful for optimization and development of some new micro fluid devices, including a bubble mixer or bubble actuator in
MEMS technology.
This work was supported by the Hong Kong Government and
Hong Kong University of Science and Technology under the
RGC / ERG grant no 618805 and 618806.
[1] Bahadur V and Garimella S V 2008 Energy minimizationbased analysis of electrowetting for microelectronics cooling applications Microelectron. J.
39 957–65
[2] Zhang H Y et al 2007 Development and characterization of thermal enhancement structures for single-phase liquid cooling in microelectronics systems Heat Transfer Eng.
28 997–1007
[3] Wang Y et al 2005 Active cooling substrates for thermal management of microelectronics IEEE Trans. Compon.
Pack. Technol.
28 477–83
[4] Phelan P E, Chiriac V A and Lee T Y T 2002 Current and future miniature refrigeration cooling technologies for high power microelectronics IEEE Trans. Compon. Pack.
Technol.
25 356–65
[5] Oconnor J P, You S M and Price D C 1995 A dielectric surface coating technique to enhance boiling heat-transfer from high-power microelectronics IEEE Trans. Compon. Pack.
Manuf. Technol.
A 18 656–63
[6] Takahashi K et al 2001 Novel applications of thermally controlled microbubble driving system 14th IEEE Int. Conf.
on Micro Electro Mechanical Systems
[7] Baek S S, Choi B and Oh Y 2004 Design of a high-density thermal inkjet using heat transfer from CVD diamond
J. Micromech. Microeng.
14 750–60
[8] Yin Z Z and Prosperetti A 2005 ‘Blinking bubble’ micropump with microfabricated heaters J. Micromech. Microeng.
15 1683–91
X Qu and H Qiu
[9] Deng P G, Lee Y K and Cheng P 2005 Measurements of micro bubble nucleation temperatures in DNA solutions
J. Micromech. Microeng.
15 564–74
[10] van den Broek D M and Elwenspoek M 2008 Bubble nucleation in an explosive micro-bubble actuator
J. Micromech. Microeng.
18 064003
[11] Shikida M et al 2008 Fabrication of a bubble-driven arrayed actuator for a tactile display J. Micromech. Microeng.
18 065012
[12] Wu X S et al 2008 Kinematically stabilized microbubble actuator arrays J. Microelectromech. Syst.
17 124–32
[13] Takahashi K, Weng J G and Tien C L 1999 Marangoni effect in microbubble systems Microscale Therm. Eng.
3 169–82
[14] Wasekar V M and Manglik R N 2003 Short-time-transient surfactant dynamics and Marangoni convection around boiling nuclei ASME J. Heat Trans.
125 858–66
[15] Kasumi H, Sides P J and Anderson J L 2004 Interactions between two bubbles on a hot or cold wall J. Colloid Interf.
Sci.
276 239–47
[16] Peng X F, Huang Y J and Lee D J 2001 Transport phenomenon of a vapour bubble attached to a downward surface Int. J. Therm. Sci.
40 797–803
[17] Deng P G, Lee Y K and Cheng P 2005 Measurements of micro bubble nucleation temperatures in DNA solutions
J. Micromech. Microeng.
15 564–74
[18] Li J and Peterson G P 2005 Microscale heterogeneous boiling on smooth surfaces—from bubble nucleation to bubble dynamics Int. J. Heat Mass Transfer 48 4316–32
[19] Lin L W, Pisano A P and Carey V P 1998 Thermal bubble formation on polysilicon micro resistors ASME J. Heat
Trans.
120 735–42
[20] Wang H et al 2003 Bubble sweeping and jet flows during nucleate boiling of subcooled liquids Int. J. Heat Mass
Transfer 46 863–9
[21] Wang H et al 2004 Bubble-top jet flow on microwires Int. J.
Heat Mass Transfer 47 2891–900
[22] Wang H et al 2005 Investigation of bubble-top jet flow during subcooled boiling on wires Int. J. Heat Fluid Flow
26 485–94
[23] Christopher D M, Wang H and Peng X F 2006 Numerical analysis of the dynamics of moving vapor bubbles Int. J.
Heat Mass Transfer 49 3626–33
[24] Wang H et al 2007 Microbubble return phenomena during subcooled boiling on small wires Int. J. Heat Mass Transfer
50 163–72
[25] Lu J F and Peng X F 2008 Bubble oscillation on thin wire during subcooled boiling Int. J. Heat Mass Transfer
51 4461–69
[26] Carey V P 2008 Liquid-Vapor Phase-Change Phenomena: an
Introduction to the Thermophysics of Vaporization and
Condensation Processes in Heat Transfer Equipment (New
York: Taylor and Francis)
[27] Young N O, Goldstein J S and Block M J 1959 The motion of bubbles in a vertical temperature gradient J. Fluid Mech.
6 350–6
[28] Nepomnyashchy Alexander A, Velarde Manuel G and Colinet
Pierre 2002 Interfacial Phenomena and Convection (Boca
Raton, FL: Chapman & Hall / CRC)
[29] Adrian B and Allan D K 2003 Heat Transfer Handbook (New
York: Wiley)
[30] Warren M R, James R H and Yound I C 1998 Handbook of
Heat Transfer (New York: McGraw-Hill)
[31] Ramos J I 1997 Lumped models of gas bubbles in thermal gradients Appl. Math. Model.
21 371–86
[32] Chen T L and Chung J N 2002 Coalescence of bubbles in nucleate boiling on microheaters Int. J. Heat Mass Transfer
45 2329–41
10