Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 15.2.1 - Scaling and dynamics of microbubble generation in microfluidic T-junction
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00369
 Material Information
Title: 15.2.1 - Scaling and dynamics of microbubble generation in microfluidic T-junction Micro and Nano-Scale Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Miyazaki, R.
Ogasawara, O.
Takeuchi, S.
Takagi, S.
Matsumoto, Y.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: microchannel
microbubble
gas-liquid flow
Weber number
μ-PTV
 Notes
Abstract: A novel technique to generate micrometer-order bubbles is developed using a microchannel with a squeezed T-junction. The mechanism of bubble generation is investigated with observation with a high-speed camera and μ-PTV (micron-resolution Particle Tracking Velocimetry) method. The experiments are conducted by using several kinds of channels with the different cross-section size, and four kinds of liquid are selected as the liquid phase to examine the effect of the cross-section size of the channels and the physical properties of the liquid phase. μ-PTV is operated by seeding 1.0 μm particles and observing transmitted light. Using the periodicity of bubble generation, μ-PTV is conducted in iteration. Velocity of approximately 1 m/s is measured by this high-speed μ-PTV method. The experimental results show that the proposed technique realizes to generate 10 ~ 70 μm diameter bubbles with frequency of 1 ~ 102 kHz. The diameter of the generated bubble becomes smaller with an increase of the liquid velocity and with a decrease of the interfacial tension of the gas-liquid interface. The bubble diameter at the upper limit velocity is dominated by Weber number defined using an equivalent diameter of the channel and the mean velocity of the liquid phase. Besides, the high-speed observation indicates that the bubble generation consists of two stages; intruding stage and squeezing stage. Different kinds of flow field in front of bubble are observed for these two stages.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00369
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1521-Miyazaki-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Scaling and dynamics of microbubble generation in microfluidic T-junction


Ryoji Miyazaki, Toshiyuki Ogasawara, Shintaro Takeuchi, Shu Takagi and Yoichiro Matsumoto

Department of Mechanical Engineering, The University of Tokyo
7-3-1 Hongo, Bunkvo-ku, Tokyo, 113-8656, Japan
miyazaki~fel.t.u-tokyo.ac.jp


Keywords: microchannel, microbubble, gas-liquid flow, Weber number, pL-PTV



Abstract

A novel technique to generate micrometer-order bubbles is developed using a microchannel with a squeezed T-junction. The
mechanism of bubble generation is investigated with observation with a high-speed camera and pL-PTV (micron-resolution
Particle Tracking Velocimetry) method. The experiments are conducted by using several kinds of channels with the different
cross-section size, and four kinds of liquid are selected as the liquid phase to examine the effect of the cross-section size of the
channels and the plwsical properties of the liquid phase. pL-PTV is operated by seeding 1.0 pLm particles and observing
transmitted light. Using the periodicity of bubble generation, pL-PTV is conducted in iteration. Velocity of approximately 1 m/s
is measured by this high-speed pL-PTV method. The experimental results show that the proposed technique realizes to generate
10 ~ 70 pLm diameter bubbles with frequency of 1 ~ 102 kHz. The diameter of the generated bubble becomes smaller with an
increase of the liquid velocity and with a decrease of the interfacial tension of the gas-liquid interface. The bubble diameter at
the upper limit velocity is dominated by Weber number defined using an equivalent diameter of the channel and the mean
velocity of the liquid phase. Besides, the high-speed observation indicates that the bubble generation consists of two stages:
intruding stage and squeezing stage. Different kinds of flow field in front of bubble are observed for these two stages.


103 ~ 105 bubbles per second, under such high liquid
velocity. van Steijn et al. (2007) measured velocity field in a
800 pLm squared T-junction by using pL-PIV
(micron-resolution Particle Image Velocimery: Santiago et
al., 1998: Meinhart et al., 2000). However, to our
knowledge, no study has been presented on the transient
velocity distribution during such the high-frequency bubble
formation in a microchannel. We adopted pL-PTV
(micron-resolution Particle Tracking Velocimery) for the
measurement of flow field.


Nomenclature


Introduction

Bubbles less than about hundred micro meters in diameter
are called microbubbles. Microbubbles have various
features, such as a good response to ultrasound, efficient
energy transfer from acoustic into thermal, and so on, so
microbubbles are expected to be applied for biomedical field.
For example, contrast agent for ultrasonic diagnosis, heating
promoter for high-intensity focused ultrasound therapy
(Kaneko et al., 2006), or micro capsules for drug delivery
systems(Soetanto & Watarai, 2000). For these applications,
bubbles are required to be small enough, roughly several
micro meters, so that they can go through blood capillaries.
In addition, the uniformity in the size and the selectivity of
liquid, gas and shell components are important.
One of the methods for generating microbubbles is using
T-shaped microchannel. Monodisperse and bubbles of
controllable diameter can be obtained by joining liquid and
gas at a microfluidic T-junction (Garstecki et al., 2005; Xu
et al. 2006). Furthermore, any liquid or any gas can be
chosen at some extent, and bubble surface can be coated
with some chemicals easily. However, it is difficult to
generate several-micro-meter bubbles with T-shaped
microchannel.
Our objective of this study is to produce smaller bubbles
and we developed a method of generating microbubbles in
microchannels with squeezing, large-aspect-ratio T-junction.
Process of bubble generation under high liquid velocity was
investigated and flow-field of liquid phase was measured.
Frequency of the bubble generation becomes extremely high,


width of bubble neck [pLm]
diameter of generated bubble [pLm]
twdraulic equivalent diameter of channel [pLm]
frequency of bubble generation [kHz]
channel height [pLm]
gas pressure [kPa]
period of bubble generation [pLs]
time [pLs]
duration of intruding stage [pLs]
duration of squeezing stage [pLs]
mean liquid velocity [m/s]
channel width [pLm]
Weber number [-]
viscosity [mPa/s]
density [g/cm ]
surface tension [mN/m]






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Four different types of channels were prepared (Table 1),
which have different cross-section shapes at the T-junction.
Note that the cross-sectional aspect ratio (W/H) of every
channel is larger than 5.
The liquid was driven by a syringe pump and controlled
in flow rate, and the gas was controlled in pressure by a
regulator. Both were supplied onto the channel chip through
capillary tubes (inner diameter 260 pLm). Four kinds of
fluids were used for liquid phase; pure water, 99.5 %
ethanol and two kinds of silicon oil. Table 2 shows the
properties of the fluids. Nitrogen was used for the gas phase.
There was a silicon pressure sensor on each capillary tube to
measure the pressure.


Table 2: Properties of the liquid fluids at 200C. p, a and pu
represent density, surface tension and viscosity of the fluids,
respectively.
p [g/cm3] a [mN/m] pu [mPa/s]
Pure water 0.998 72.7 1.00
99.5% Ethanol 0.789 22.4 1.20
Silicon oil 0.65cs 0.760 15.9 0.494
Silicon oil 2cs 0.837 18.3 2.29


rH


Figure 2: Geometries of the microchannel. (a) Schematic
geometry of the T-junction. W is channel width and H is
channel height of both the main channel and the side
channel. (b) Cross-section of the channel.

Table 1: Channel size of T-junction of the four different
channels. Dh meaHS a hydraulic equivalent diameter of the
channel.
W [Cpm] H [Cpm] Dh [Cpm]
Channel A 110 20 34
Channel B 50 11 18
Channel C 50 7 12
Channel D 24 2 4


Paper No


Experimental Facility

Figure 1 shows a schematic of the whole experimental
apparatus. The experiments were conducted by controlling
liquid flow rate and gas pressure at room temperature. The
bubble generation was recorded with a high-speed video
camera.

Microfluidic device
The microfluidic channel was fabricated in a flat plate of
borosilicate glass by wet etching method, and sealed by a
thin borosilicate cover glass (Institute of Microchemical
Technology Corp.). Figure 2(a) illustrates schematically the
geometry of a T-junction. An actual cross-section was not
completely square-shaped (Figure 2(b)) because the
channels were fabricated with a wet etching process. The
main channel carries the liquid and the side channel supplies
the gas. The channels were broadened at the upstream and
the downstream of the T-junction. This was to decrease the
pressure drop in the main channel.


Regulator


Light source


Figure 1: A schematic illustration
apparatus.


for the experimental


~;S~Z~


Figure 4: An image of the generation of the bubble at the
T-junction. Channel B, ethanol, U= 0.68 m/s, P, = 29 kPa.


C ... d~







Figure 3: The process of obtaining velocity vectors using
pL-PTV. (a) An image taken by the high-speed video camera.
(b) A retouched image which is subtracted background
image and masked the gas phase and the outside of the
channel. (c) Vector plot of the liquid velocity obtained by
pL-PTV. (d) High-density vector field obtained by overlaying
five vector fields in the same phase of the bubble
generation.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


-e U = 0.74 m/s (a)
+ U =1.5 m/s (b)

I ~P = 56 kPa


t/ T = 0


t/T = 0.17




t/T = 0.33





t/T = 0.5




C/T = 0.67




t/T = 0.83


Intruding
stage


Squeezing
stage


1.0 f-----~ IBreak-lup
0 10 20 30 40
d [plm]

Figure 6: The neck width d as a function
of time since the start of a bubble
generation, using channel A. The liquid
phase is water. d = 0 means that a
breakup occurs.


t/T = 1 I3 Cr 100 lm


Figure 5: Snapshots of the bubble generation for one period. The time is shown
scaled with the period T. Characteristic width d of the bubble neck is defined as
a length from the channel corner to the interface at an angle of 450. (a) Channel
A, water, P, = 56 kPa, U = 0.74 m/s, Ait = 28 pLs. (b) Channel A, water, P, = 56
kPa, U= 1.5 m/s, At= 56 pLs.


Image acquisition
The image recording system was composed of a
high-speed video camera (SHIMADZU, HyperVision
HPV-1), an inverted microscope (Nikon, ECLIPSE Ti-U),
an objective lens (Nikon, Plan Apo 40XA/Plan Apo 60XA)
and a mercury lamp (OSRAM, HBO 103W/2 N). The
channel on the microscope stage was exposed to the light
source, and transmitted light was observed by the
high-speed video camera fixed to the microscope. The
maximum frame-rate and the resolution of the high-speed
video camera were 1 Mfps and 312 x 260 pix2, respectively.
The optical resolution was 1.63 pLm/pix and 1.12 pLm/pix in
the cases of using the 40 x objective lens and the 60 x
objective lens, respectively.

pL-PTV and flow visualization
Flow-field measurements were performed by seeding the
carrier fluid with 1.0 pLm diameter tracer particles
(Invitrogen Corp, FluoSpheres F8823.) into pure water and
observing bright-field image. Generally, pL-PIV or pL-PTV is
often operated by fluorescent observation because of the
smallness of seeding particles. However, in present study


the particle image was obtained by transmitted light in order
to acquire high light intensity. The particle image was
recorded in the frame-rate 500 kfps in this way. 1.0 pLm
diameter particles were adopted as tracer particles, limited
by the diffraction limit. A volume concentration of the
particles was 0.06 %.
Because images of a sufficient particle concentration for a
pL-PIV could not be obtained in this volume concentration,
the flow field was measured by a pL-PTV in this study. A
dynamic thresholding method was used for detection of the
particles. The interrogation window size was 20 x 7 pix2.
Because of the small number of particles (Figure 3(a)),
the velocity field obtained by the pL-PTV was of low density
(Figure 3(c)). Therefore, using the periodicity of the bubble
generation, the pL-PTV was operated in iteration, and a
high-density flow field was obtained by overlaying the
vectors in the same phase of the bubble generation. Figure
3(d) shows a result of overlaying five velocity fields in the
same phase.
A high-speed pL-PTV system succeeded to be developed
by adopting transmitted-light observation and iteration,
which enables flow-field measurement of velocity ~ 1 m/s.







































































' '1111 ""'111 '1111 "" ' "' "


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

as time until d reaches its maximal value, and time while d
decreases and finally bubble breaks up is regarded as a
squeezing stage. Figure 7 shows the duration of intruding
stage (T,,) and the one of squeezing stage (T,,) as a
function of the mean liquid velocity U at the T-junction. The
whole period of the bubble generation has a minimal value
to the liquid velocity, which is because T,, increases and Ts,
decreases monotonically with the increase of the liquid
velocity. This ensures that the bubble generation consists of
these two stages.

Scaling analysis for the bubble diameter
The diameter Db Of the generated bubble became smaller
with an increase of the liquid velocity under constant gas
pressure P, (Figure 8). Furthermore, smaller bubbles were
generated in the case of using ethanol as liquid phase than
the case of water. This can be thought to be an effect of
surface tension.


Paper No


Results and Discussion

Process of the bubble generation
Figure 4 is a snapshot of the bubble generation at the
T-junction. Monodisperse microbubbles are generated
constantly. The flow was highly periodic with a frequency f
of 1 ~ 102 kHz and a period T of 10 ~ 103 pLS. Figure 5
shows the growth process during one period.

Garstecki et al. (2005) explained as follows about a
squeezing mechanism of a two phase flow at a T-junction.
First, the tip of the discontinuous phase penetrates into the
main channel until it hits the opposite wall, which leads to
the increase of the upstream pressure of the continuous
phase. Second, by the pressure difference between the
upstream and the downstream pressure of the continuous
phase, the neck of the discontinuous phase is squeezed and
consequently breaks up. van Steijn et al. (2007) named these
two stages "the filling stage" and "the squeezing stage",
respectively.
On the contrary, the gas phase does not fill up the main
channel in the present study. There is no filling stage. In this
respect, it can be said that this bubble generation has
different mechanism from the other studies. Therefore, the
gas phase need not grow until filling up the main channel,
so the bubble whose diameter is smaller than the channel
width could be formed. This difference of the mechanisms
can be thought to be due to the quite high aspect ratio of the
cross-section. The fairy large pressure difference exists
between the upstream and the downstream of the liquid
phase without the gas phase blocking the main channel.
Hence the breakup occurs with no filling stage.

We divided the process of the bubble generation into two
stages that suits the present mechanism; the intruding stage
and the squeezing stage (Figure 5). The intruding stage is set
by the time required for an emerging bubble to intrude into
the junction. In the second stage, referred to as the
squeezing stage, the receding interface is squeezed by the
insurgent liquid until the bubble pinches off. These stages
are defined by characteristic width d of the bubble neck. In
Figure 6, d is plotted as a function of time since the start of a
bubble generation. Duration of an intruding stage is defined


35



S25

S20

is


1 .o o.s to 1.5 2.0
u [mis]
Figure 8: The bubble diameter as a function of the mean
liquid velocity, using channel C. The liquid phase is water.
The diameter decreases with the increase of the liquid
velocity, until upper limit for the bubble generation.


*Channel A
o Channel B
x ChannelC
n Channel D

[LIM IT]


naa
a

a"


2.5


2.0

1.5

1.0

0.5


500


400


S300


200


100


0.001


0 0 '


0.01 0.1 1


We
Figure 9: The bubble diameter normalized with the
hydraulic diameter of the channel as a function of the Weber
number at the limit points of the bubble generation. One
kind of plot represents data with several liquid fluids with
one channel.


0.9 1.0 1.1 1.2 1.3 1.4 1.5
v [m/s]
Figure 7: The duration of both intruding stage and
squeezing stage as a function of the mean liquid velocity U
at the T-junction, using channel A. The liquid phase is water.
































-.--i


__ ___~ __ __ _T


~c~-- 'rY
b
~'P :;
i-~t-3 a
=a


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


t/T = 0.21


t/T = 0.47


t/T = 0.74


t/T = 1


t/T = 0.80


t/T = 0.86


t/T = 0.93


t/T = 1


S5 m/s


- 50 lm


Figure 10: Vector field in the liquid phase for one period obtained by using pL-PTV in iteration. (a) Channel A, P, = 56 kPa, U
= 0.74 m/s, Ait = 52 pLs. The camera frame-rate is 250 kfps. (b) Channel A, P, = 56 kPa, U = 1.5 m/s, Ait = 24 pLs. The camera
frame-rate is 500 kfps.


When the liquid velocity exceeded a certain value, the gas a
phase was pushed back and the bubble generation stopped. t T:.
Here we describe this value as "the upper limit velocity" and ,
such the state as "the limit point of the bubble generation".
The bubble diameter takes a minimum value at this upper
limit~ velocity and-~-~ wihteices fth a rsue h
upper limit velocity becomes large (Figure 8). In short,
under a certain gas pressure, the bubble generation stops
when the liquid velocity exceeds the upper limit. Then the .. 0.
bubble diameter takes the minimum value under that gas- .
pressure. t/T = 0.27 t/T = 0.69


We focused on the bubble diameter on these bubble
generation and conducted scaling analysis using Weber
number We: the ratio of the inertia force and the interfacial
tension. Here the Weber number is defined as

We =pU 2Dhl 1

In Figure 9, the nonnalized diameter (Db/Dh) iS plotted as a
function of the Weber number. Note that there are plotted
only the diameters at the limit points of the bubble
generation. With the four different channels, and with a
variety of liquid phase, the dimensionless diameter is well
represented as a function of the Weber number. This strong
correlation was found over a wide range of Weber number.
Therefore, it can be said that the inertia force and the
interfacial tension are both the dominant factors in the
bubble generation.

Effect of the flow field
Figure 10 shows the velocity field inside the liquid phase
during one period of bubble fonnation. Figure 10(a) is the
one where the liquid velocity is substantially low, and in
Figure 10(b), the liquid velocity is close to the upper limit


t/T = 0.81


t/T = 0.89
1 m/s


- 20 lm


Figure 11: Velocity field of nonnal components to the
interface of the bubble neck. Gray vectors mean the original
vectors. (a) and (b) correspond the ones in Figure 10,
respectively. The left side shows velocity field at the early
intruding stage, and the right side shows at the transition
stage from the intruding to the squeezing.


:1.
1 i '
~:" ~
., ~~ c
5~____
~C --w
1 ~e ---e
= s-- ~f~T~
,~=~L;, ~cg=_
~I- ~h~L~2~- ~t-a- ~
15 -a.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

(5) With the growth of the bubble in the main channel, the
liquid becomes to flow into the side channel. Velocity
component normal to neck interface was not depending
on the liquid flow rate at the transition stage from the
intruding to the squeezing.



References

Kaneko, Y., lida, N., et al., "Effective heat therapy
controlling heat deposition of microbubbles in the
ultrasound field", Proc. 6th ISTU, 157-163 (2006)

Soetanto, K. & Watarai, H.,. "Development of magnetic
microbubbles for drug delivery system", Japanese Joumnal of
Applied Physics, Vol. 39, 3230-3232 (2000)

Garstecki, P., Fuerstman, M. J., Stone, H. A. & Whitesides,
G. M., "Formation of droplets and bubbles in a microfluidic
T-junction--scaling and mechanism of brak-up", Lab on a
Chip, 6, 437-446 (2006)

Xu, J. H., Li, S. W., Chen, G. G. & Luo, G. S., "Formation of
Monodisperse microbubbles in a microfluidic device",
AlChE Joumnal, Vol. 52, No. 6, 2254-2259 (2006)

van Steijn, V., Kreutzer, M. T. & Kleijn, C. R., "pL-PIV study
of the formation of segmented flow in microfluidic
T-junction", Chemical Engineering Science, 62, 7505-7514
(2007)

Santiago, J. G, Wereley, S.T., Meinhart, C. D., Beebe, D. J.
& Adrian, R. J., "A particle image velocimetry system for
microfluidics", Experiments in Fluids, 25, 316-319 (1998)

Meinhart, C. D., Wereley, S. T. & Santiago, J. G, "A PIV
algorithm for estimating time-averaged velocity fields",
Journal of Fluids Engineering, Vol. 122, 285-289 (2000)


Paper No


for the bubble generation.
From Figure 10(a), it is observed that the liquid flow is
blocked by the bubble growing in the main channel and
flows into the side channel under low liquid velocity. On the
other hand, according to Figure 10(b), the effect of the
gas-liquid interface on the liquid flow is small near the limit
point of the bubble generation. Almost constant flow field is
observed from the intruding stage to the squeezing stage.
Figure 11 shows the velocity component normal to the
neck interface near the channel corner in each condition.
Under the substantially low liquid velocity compared with
the upper limit velocity, small velocity is toward the
interface of the bubble neck at first because of the small
mean velocity, but with the growth of the bubble in the main
channel, the liquid flow becomes blocked and flows into the
side channel. Thus, the velocity component normal to the
neck interface increases during the intruding stage. For these
two cases, the velocity components normal to the neck
interface become comparable at the transition stage from the
intruding to the squeezing. This fact indicates that the force
of breaking up the bubble is derived from the liquid velocity
component normal to the interface of the bubble neck.

As already discussed, the inertial force and the interfacial
tension both seem to be the dominant factors in the bubble
generation. This can be explained as follows. The transition
from the intruding stage to the squeezing stage is caused by
the inertia force of the liquid which pushes the interface of
the bubble neck exceeds the opposite force, interfacial
tension. Hence, the larger the inertia force is and the smaller
the interfacial tension is, the earlier the intruding stage
finishes. The bubble diameter consequently becomes
smaller as the increase of the Weber number.



Conclusions

Monodisperse microbubbles were generated using a
microchannel with a squeezed, large-aspect-ratio T-junction,
and the effect of liquid velocity was investigated by
observation with a high-speed camera. High-speed pL-PTV
system was developed by adopting transmitted-light
observation and iteration, which enables flow-field
measurement of velocity ~ 1 m/s.
The following facts and conclusions were obtained.

(1) Bubbles smaller than channel width was generated by
using squeezed, large-aspect-ratio T-junction and under
high (~ 1 m/s) liquid velocity.
(2) Under an assumption that the bubble generation is
divided into intruding stage and squeezing stage, the
intruding stage becomes longer and the squeezing stage
becomes shorter monotonically with the increase of the
liquid velocity.
(3) The diameter of the generated bubble became smaller
with the increase of liquid velocity under constant gas
pressure, until the liquid velocity reached upper limit
for the bubble generation.
(4) The bubble diameter at the limit point of the bubble
generation is dominated by Weber number. This
indicates that the inertia force and the interfacial tension
are both dominant factors in the bubble generation.




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