Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 7.1.4 - A single bubble path instability in dilute surfactant solution
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00174
 Material Information
Title: 7.1.4 - A single bubble path instability in dilute surfactant solution Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tagawa, Y.
Funakubo, A.
Takagi, S.
Matsumoto, Y.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: single bubble
surfactant effect
zigzag/spiral motion
slip condition
3D measurement
 Notes
Abstract: Path instability of the single bubble is sensitive to the contamination of water. In this research, surfactant effects on bubble 3D motion in quiescent water are experimentally investigated. Using two high-speed digital cameras, measurements of 3D trajectories, velocities, and aspect ratios are carried out with a tank of 1.0m height filled with super purified water and a small amount of surfactant. Experimental parameters are bubble size for 1-4mm and surfactant concentration 0-150ppm which controls surface slip conditions of the bubble from free-slip to no-slip. Due to Marangoni effect, addition of surfactant in gas-water system yields immobilization of the bubble surface. First, results of bubbles in 1.9-2.1mm diameter without shape oscillation are analyzed. There is a one-to-one correspondence between bubble rise velocitiesand trajectories. It indicates that the slip condition decides not only the drag force but also the wake structure. The maximum amplitude of the horizontal projection of the spiral motion is 4.7 times as large as the minimum one and corresponds to not the maximum rise velocity but the maximum horizontal velocity. As a result of the comparison with simple models, the mechanism of the trajectory change by surfactant is explained by effects of drag force and the direction of motion affected by non-axisymmetric wake structure. Second, all measured trajectories are plotted on two dimensional field of bubble Reynolds number Re and instantaneous boundary slip condition. In free-slip and no-slip condition, bubble motions are dependent on Re. However, in half-slip condition, bubble motions are spiral and almost independent from Re. Therefore, bubbles in certain condition move along trajectories changing from spiral to zigzag. These interesting motions are caused by changing slip condition.
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: VID00174
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 714-Tagawa-ICMF2010.pdf

Full Text

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


A single bubble path instability in dilute surfactant solution


Yoshiyuki Tagawa, Ami Funakubo, Shu Takagi and Yoichiro Matsumoto

The University of Tokyo, Faculty of Engineering, Department of Mechanical Engineering
Hongo 7-3-1, Bunkyo-ku Tokyo, 1138656, Japan
tagawa@fel.t.u-tokyo.ac.jp


Keywords: Single bubble, Surfactant effect, Zigzag/Spiral motion, Slip condition, 3D measurement


Abstract

Path instability of the single bubble is sensitive to the contamination of water. In this research, surfactant effects on bubble 3D
motion in quiescent water are experimentally investigated. Using two high-speed digital cameras, measurements of 3D trajectories,
velocities, and aspect ratios are carried out with a tank of 1.0m height filled with super purified water and a small amount of
surfactant. Experimental parameters are bubble size for 1-4mm and surfactant concentration 0-150ppm which controls surface slip
conditions of the bubble from free-slip to no-slip. Due to Marangoni effect, addition of surfactant in gas-water system yields
immobilization of the bubble surface.
First, results of bubbles in 1.9-2.1mm diameter without shape oscillation are analyzed. There is a one-to-one correspondence
between bubble rise velocities and trajectories. It indicates that the slip condition decides not only the drag force but also the wake
structure. The maximum amplitude of the horizontal projection of the spiral motion is 4.7 times as large as the minimum one and
corresponds to not the maximum rise velocity but the maximum horizontal velocity. As a result of the comparison with simple
models, the mechanism of the trajectory change by surfactant is explained by effects of drag force and the direction of motion
affected by non-axisymmetric wake structure.
Second, all measured trajectories are plotted on two dimensional field of bubble Reynolds number Re and instantaneous
boundary slip condition. In free-slip and no-slip condition, bubble motions are dependent onRe. However, in half-slip condition,
bubble motions are spiral and almost independent from Re. Therefore, bubbles in certain condition move along trajectories changing
from spiral to zigzag. These interesting motions are caused by changing slip condition.


Introduction

Millimeter-sized bubbles in water follow not straight
trajectories but zigzag or spiral. These interesting motions
are shown in various industrial processes which require
better understanding (Fan & Tsuchiya 1990, Ohl et al. 2003).
However, due to complex coupled action of surfactant
effects, shape oscillation, and wake instability, the path
instability mechanism is not fully understood.
A small amount of surfactant is able to change bubble
behaviors drastically. For example, a bubble in aqueous
surfactant solution rises much slower than one in purified
water. This phenomenon is explained by the Marangoni
effect. Due to the gradient of surfactant surface
concentration, a variation of surface tension along the
bubble surface appears and causes a tangential shear stress.
This shear stress results in the decrease of the rising velocity
of the bubble. Here, the surface slip condition is changed
from free-slip condition (zero-shear stress along the surface)
to no-slip condition ( no slip velocity ). (Magnaudet and
Eames, 2000).
Using super purified water whose specific residence is
18.2MQcm and organic particles are less than 10 p.p.b.,
Duineveld (1995) found that the Marangoni effect
influences not only the rising velocity but also path
instability of bubbles in quiescent water. Critical reynolds
number which is threshold beyond occurrence of path


instability is reduced by a small amount of surfactant
impurities. Mougin & Magnaudet (2002) considered the
bubble as a spheroidal body of fixed shape and solved
numerically the coupled fluid-body system. The results are
agreed with experimental observations of Ellingesn & Risso
(2001). They found that without shape oscillation of bubbles,
the path instability occurs. The main factor is wake
instability which leads a double threaded wake. Lunde &
Perkins (1998) and de Vries (2001) visualized the
counter-rotating double threaded wake structure and pointed
out that 3D motion corresponds to the wake structure one by
one. The main difference between spiral motion and zigzag
motion is periodic vortex shedding. Yang & Prosperetti
(2007) carried out linear stability analysis of the flow past a
spheroidal bubble and Magnaudet & Mougin (2007) did
numerical simulation of fixed spheroidal bubble in uniform
flow. Both researches revealed that not surface slip
condition of the bluff body but the vorticity in a base flow
has an important role to decide the property of wake
structure.
However, 3D paths, velocities and shapes of freely
rising bubble in a surfactant solution are not investigated in
detail. The purpose of this study is experimental
investigation of the surfactant effect to path instability and
to get insight into instability mechanism of different
boundary conditions. Experimental Parameters are
surfactant concentration and bubble size.










Nomenclature

C Concentration of surfactant (ppm)
U Rise velocity of bubble (mm/s)
V Horizontal velocity of bubble (mm/s)
Uto, Bubble speed (mm/s)
Ro Volume equivalent radius (mm)
f Frequency of periodic bubble motion (1/s)
T Periodic time of bubble motion (s)
A Amplitude of periodic bubble motion (mm)
Re Reynolds number (Re=2plURo/i1)
Eo E6tv6s number (Eo=4g(pi-pg)(Ro)2/r)
Mo Morton number (Mo=g u4(pl-pg)/ p 2a)
St Strouhal number (St=2fRo /U)
We Weber number ('. =,- rfRo /a)
CD Drag coefficient
ka Absorption rate constant (m3/(mol s))

Greek letters
p Density (kg/m3)
p Viscosity (Pa s)
,P Desorption rate constant (mol/m3)
F Surface concentration of surfactant (mol/ m2)

Subsripts
1 Liquid
g Gas


Experimental Facility

Experimental apparatus is shown in Fig.l. A single
nitrogen gas bubble is generated at the bottom of test section
of 100xl00xl000mm3. Its 3D trajectory is measured by two
cameras (MotionPro 10000, Redlake co.) following up the
bubbles with Z-Axis stages (KT-45A-B20-100, THK Co.).
Views of two cameras are at right angles to each other.
Super-purified water ( Milli-RX 12a, Milli-Q SP,
Millipore co.) and teflon tubes are used to avoid any
impurities as far as possible. Specific resistance of the water
is more than 18.2 MQcm and less than 20 ppb of total
organic carbon (TOC). Surfactants we used are Triton
X-100 and 1-Pentanol. Properties are shown in table 1. The
concentration of solution is set from 0 ppm 150 ppm.
Bubble generator is constructed with an audio speaker
(F-200 Technics co), a pressure controller and an electric
valve. This equipment can change bubble sizes for 1-5mm
by adjusting frequency of the speaker. Tomiyama et al.
(2002) pointed out that the bubble path depends on the
initial shape. In this experiment, we observed "large initial
shape deformation" type bubbles.
Telecentric lenses (59LGG950 59LGH416) are used to
prevent the difference of bubble images due to the different
position in depth-wise direction. A small space between a
camera and lenses causes high frequency image vibration.
To remove the noise, we put a certain marking behind test
section and calculated vibration of lenses. The bubble
position and diameter are represented by its centroid and
volume equivalent diameter, respectively. We set camera
conditions as shutter speed: 1/2000sec, frame rate: 250fps,


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

and spatial resolution: 22pm/pixel. About 2mm diameter
bubbles in 1-Pentanol solution, Mo number is 2.6x10-11and
Eo number is 0.54.
Measurement error of trajectories is 0.1mm, that of
velocity is 2.2mm/s. Aspect ratio y of bubble is the ratio of
major axis and minor axis.
Before 3D motion observation, we measured rise
velocity of straight rising bubbles to check surfactant effects
in purified water. Drag coefficient is calculated by
following equation.


SRsg
CD 83
3U2


Ro is equivalent bubble radius, g is gravity acceleration,
U is rise velocity. We compared our results with Moor
(1965), Mei et al.(1994), Duineveld(1995), Sanada et al
(2007) and Takagi et al. (2003) shown in Fig.2. In Re<250,
our results agree with results of Mei et al.(1994). However
in Re>250, our results become more close to the
Moore(1965)'s result. It is because Mei et al.(1994)
considered a bubble as a spherical shape while Moore
considered it as an ellipsoidal one. Around Re=500 (bubble
diameter is around 1.5mm), our results agree with other
experimental datas within 5%. Generally, the more bubble
diameter increases, the less Marangoni effect affects bubble
motions. Therefore, our results show that bubbles of more
than 2mm diameter in super purified water have a free-slip
boundary condition.


Diffuser


Back
Light


Z-Axis stage


Z-Axis


x


Fig. Experimental apparatus


1-Pentanol TritonX-100
Molecular
Molecular 88.15 '647
mass
Molecular CH(CH 4H C8H17C6H4(OC2
formula CH3(CH2)40H
formula H5)xOH(x 10)
Density 0.814 1.07
Diffusivity 1.1 10-10m2/s 3.5 10-10m2/s
Solubility Dissolve well Dissolve well
k, [m'/(mol s)] 5.08 50
fo [mol / m3] 21.7 6.6x10-4
F,,a[mol/m2] 5.9x10-6 2.9x10-6

Tablel Property of 1-Pentanol and TritonX-100

























0.0 L
100


0 . . ,
200 300


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

(Fig.7). It means that surfactant absorption on the free-slip surface
causes larger horizontal movement while rising speed decreases.
The maximum value of the amplitude is larger as 4.7 times as the
minimum value.
The frequency of the trajectory is shown in Fig. 8. As a
contrary to the amplitude, a minimum value is taken around U=
280 mm/s. The maximum value is larger as 2.1 times as the
minimum.
Each value has the extreme value at rise velocity U=280 mm/s,
changes most greatly in 230-260 mm/s, and has the flexion point
in this section if it is thought one curve. The width of the change
becomes small in 190-230 mm/s. Therefore, it is expected that
there is a similar change in the flow structure around bubbles.


400 500


Fig.2 Plots of Re-Drag coefficient CD (V: Our experimental
results, ---: Moore(1965) --:Mei et al. (1994) 0:
Duineveld(1995) D: Sanada et a/.(1995), o: Takagi et al.
(2003))


Results and Discussion
Trajectories, velocities, and shapes of 1.9-2.1 mm bubbles in
1-Pentanol solution are shown in Figure 3-5. In this diameter
range, shape oscillation does not affect bubble motions (Ellingsen
& Risso, 2001)
In super purified water, or 0 ppm solution, bubbles of free-slip
condition move along spiral path (Fig.3(a)) or transition path
from zigzag to spiral while there are no reverse transitions. The
rise velocity is constant at 356mm/s which agrees with the results
of Duineveld(1995). In 1-Pentanol 150ppm solution, bubbles
always move along zigzag path (Fig.3(d)). The rise velocity
decreases immediately. After the velocity drop, it becomes
periodic around 167mm/s. The frequency of velocity fluctuation
is twice as much as that of path fluctuation. The shape of bubble
takes almost spheres (Fig.5(d)). When we put more surfactant
into the solution (200ppm), velocity and shape of bubble is same
as the result in 150ppm. Therefore, the slip condition is supposed
to be no-slip.
In 1-Pentanol 25-100 ppm solution, Fig.4 shows that the rise
velocities are depend on surfactant concentration. The thicker
concentration becomes, the smaller rise velocity becomes and the
more shape becomes spherical. The slip condition becomes close
to no-slip when surfactant concentration is high. In these slip
conditions, bubble motions are spiral.
Tsuge & Hibino (1977) found the following important relation
available in both purified water and surfactant solution


1000


5 5
E 0 E


-0- - ~0-m5 10 1 5 0 5 10
x[mm] x[mm]
(a) Oppm (b) 25ppm


1000o

800-

600
n400

200,

10
0 10
10 10 o
x[mm] y[mm]


St = 0.100CO 734


According to their results, the experimental data in purified
water and surfactant solution must be plotted within 30% of
equation(2). Fig.6 shows the line of equation(2) and our results.
Note that these data plots are around z=150mm as same as Tsuge
& Hibino(1977). All of our results satisfy this relation.
To reveal the relation between a slip condition and bubble
behavior, the amplitude and the frequency of bubble path in
rising distance more than 400 mm were plotted in Fig.7 and Fig.8,
respectively.
The maximum value of the amplitude is taken not at the
highest rise velocity U=360 mm/s but around U=280 mm/s


10 10

5 5

-5 5

o0 -5 0 5 1o 1-9 -5 0 5 10
x[mm] x[mm]
(c) 75ppm (d) 150ppm


Fig. 3 Experimental results of trajectories; upper: whole view,
lower: horizontal projection ((a) Oppm (b) 25ppm (c)75ppm (d)
150ppm)





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


400

300

200

100


0 200 400 600 800
Z [mm]
Fig. 4 Experimental results of rise velocities


150 200 250 300
U [mm/s]


Fig. 7 Rise speed U (mm/s) v.s. trajectory amplitude A (mm)


C


0


0


(a) Oppm (b) 25ppm (c) 75ppm (d) 150ppm



2.4 -

2.0 igzag | Spiral
O Oppm
2 0 25ppm
1.6 5ppm
V 50ppm
A 75ppm
1.2- 4i t l Oppm
S150ppm
0.8- I


150 200 250
U [mm/s]


8

, 6


150 200 250 300
U [mm/s]


350 400


Fig. 8 Rise speed U(mm/s) v.s. trajectory frequencyf(1/s)


300 350 400


Fig. 5 Pictures of bubbles and aspect ratios


To analyze these changes of trajectories, the relation between
amplitude and frequency is modeled first. Spiral motion bubble
moves on a circular trajectory in horizontal plane while zigzag
bubble goes on a line trajectory. Therefore,


V
Spiral : A= ,
27 f


Zigzag : A =-
4f


V(mm/s) is horizontal velocity of bubble. When V is regarded as
constant, amplitude A is inversely proportional to frequency
Fig.9 shows the plot of experimental data and 3 curve lines of
constant V=80,120,160mm/s of equation(3).
When concentration changes from Oppm to 25ppm,
amplitude A is 1.6 times as large as amplitude calculated by
inverse curve of equation(3) of constant V Therefore, the
horizontal velocity Vincreases. However, the case in 25-150ppm,
amplitudes are smaller than that calculated from equation(3). In
these concentrations, Vdecreases as concentration increases.
All of our results and previous results show that rise velocity
decreases when surfactant concentration increases. We focused
on surfactant effect to horizontal velocity.


c


350 400


0.1 C 1
Fig.6 Drag coefficient vs. Stroual number St
Fig.6 Drag coefficient CD v.s. Strouhal number St






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


Fig.10 shows the relation between rise velocity U(mm/s) and
horizontal velocity V(mm/s). When rise velocity increases,
horizontal velocity increases in U>280mm/s while it decreases in
U<280mm/s. The maximum value of V(mm/s) corresponds to
the maximum value of amplitude A(mm) and minimum value of
frequency( 1/s).
To discuss about wake structure and drag force, two models
about the spiral motion in U>190mm/s are shown below. In the
first model, horizontal velocity is described as


V = ,i-U2


(U,, =-to U2 +V2 ) (4)


U,,a is the bubble speed. If U,, is constant, V increases as U
decreases. This model assumes that only the direction of bubble
motion changes while the bubble speed is constant. The direction
is affected by non-axisymmetric property of double-threaded
wake but not by drag force. Therefore, this model assume that the
drag force is unchanged but only the non-axisymmetric property
of wake changes.
The second model consider the direction of motion as a
constant value;


V = UtanO


0 is an angle between the direction of bubble motion and
vertical direction. This model assumes that the speed of bubble
changes but the direction is constant.
To compare these models with experimental data, several
curves of equation(4) and (5) are plotted on fig.10.
In U>280mm/s, experimental data Vis 0.9 times as big as
V calculated by equation(4). However, compared with
equation(5), V is twice as large as V calculated from constant 0.
Therefore, in this region, growth of Vis mainly caused by change
of 0. Therefore maximum value of V and A, and minimum value
off are occurred by the change of non-axisymmetry of the wake
structure.
In U<280mm/s, compared with equation(5), V is smaller
than Vfrom the equation(5). This is because decrease of 0. Both
U,ta and 0 decrease. Therefore, amplitude A decreases because
drag increases and the direction of motion becomes more
vertical.


4 6 8 10 12
f[1/s]

Fig. 9 trajectory amplitude A(mm) v.s. trajectory frequencyf(1/s)


150 200 250 300 350
U [mm/s]
Fig. 10 Rise speed U (mm/s) v.s. Horizontal speed V(mm/s)



Let us discuss the relation between the slip conditions,
Reynolds number Re and bubble motion modes (straight,
spiral, or zigzag).
To evaluate surface slip condition quantitatively,
normalized drag coefficient CD is defined as follows.


C -C
S D,xp Dean
C. -C.


CD, clean and CD, rigd mean drag coefficient of clean bubble
and rigid sphere with the same volume, respectively. CD,,x
is instantaneous drag coefficient calculated by experimental
data from equation(l). CD = 0 and 1 means free-slip
condition and no-slip condition respectively.
Fig.11 shows the map of bubble motion modes on
Re-CD field. Bubble motions of clean bubble (CD =0) in
600 consistent with previous investigations (Clift et al. 1978,
Magnaudet and Eames, 2000). Those of no-slip bubbles
(CD =1), zigzag motions are shown 280 consistent with results of rigid spheres (Jenny et al., 2004).
In free-slip and no-slip condition, bubble motions are
dependent on Re. However, bubble motions in half-slip
condition 0.4 spiral motions are stable and independent from Re. Results
in 1-pentanol and tritonX-100 solutions are consistent.
Therefore, slip condition changes Re-dependency of bubble
motion modes.
Fig.12 shows typical single bubble trajectories. Fig.
12(a) shows a trajectory changing from zigzag to spiral in
super purified water. This motion has been reported by
previous researches (Ellingsen and Risso, 2001). We also
observed a motion changing from spiral to zigzag in Triton
X-100 0.27 ppm solution (Fig.12(b)). As previously
described, this transition has never been observed in
purified water. To analyze the mechanism of the change, we
focused on boundary condition on the bubble surface. The
condition is related to bubble rise velocity. Fig. 13 shows
rise velocities of same size of bubbles in 3 kinds of
solutions. In super purified water, rise velocity becomes
constant and bubble motion is spiral. In Triton X-100 2.7
ppm solution, rise velocity decreases and becomes constant
but bubble motion is zigzag. In Triton X-100 0.27 ppm
solution, around 130 mm distance, rise velocity is almost






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


same as that in super purified water and
similar spiral. Around 550 mm distance
decreases and is same as that in 2.7 ppm
solution. Its motion is similar zigzag. This g
of velocity along distance indicates that
gradually changes from free-slip to no-s
phenomenon had been reported by Zhang an
about smaller bubbles. Therefore, the cha
boundary condition from free-slip to no-sl
bubble motion from spiral to zigzag.


1J- + *-* *+
legion Zigzag region
D + **
O. -
o
0.6 I
S Zigzag -
I Straight n Spiral region
0.4 Spiral 0 -


02
%

0.0 Straightregion j
200 400 600
Re

Fig. 11 Motion modes in Re v.s. CD


IO0
600,


-400


200


0

0 10
0 -10
y[mm] -10 -10 x[mm]


800


the motion is
, the velocity


Conclusions


STriton X-100 Surfactant effects on path instability is experimentally
radual decrease analyzed. Measurements of 3D trajectories, velocities, and
slip condition aspect ratios are carried out with a tank of 1.0m height filled
lip. The same with super purified water and a small amount of surfactant.
id Finch (2001) Due to Marangoni effect, surfactant concentration controls
nge of surface surface slip conditions of the bubble from free-slip to no-slip.
ip changes the First, we discussed about bubbles in 1.9-2.1mm diameter.
Our result indicates that the slip condition decides not only the
drag force but also the wake structure. The maximum
amplitude of the horizontal projection of the spiral motion is
4.7 times as large as the minimum one. The maximum value
Corresponds to not the maximum rise velocity but the
maximum horizontal velocity. As a result of the comparison
with simple models, the mechanism of the trajectory change by
surfactant is explained by effects of drag force and the direction
of motion affected by non-axisymmetric wake structure.
Second, all measured trajectories which are categorized
Sin straight, spiral or zigzag mode are plotted on two
S* dimensional field of Reynolds number Re and normalized
Sdrag coefficient CD*. While free-slip and no-slip bubble
Zlgzagregion motions are strongly dependent on Re, half-slip bubble
*t motions of 0.4 800 1000
on Re. Bubbles in certain condition move along trajectories
changing from spiral to zigzag. These interesting motions
Smap are caused by surfactant accumulation on bubble surface
which change surface boundary condition from free-slip to
no-slip. Comparing this transitional motion to spiral motion
of free-slip bubble in super purified water and to zigzag
motion of no-slip one, we deduced that instantaneous slip
L condition on a bubble surface also decides bubble motion.


400

200-


10
0 10


y[mm] -1


(a) Zigzag to spiral in super purified water
(b) Spiral to zigzag in 0.27 ppm Triton X-
Fig.12 Transitional motion of a single
quiescent water


-0---- Spiral path
400- Super purified water
-0- -- ......<... ........ -........- ....
S300 I s-i
I I. TritonX-
S200 AAAA A -

100 --A-- Zizag Path
TritonX-100 2.7 ppm


0 100 200 300
Distance (mm)
Fig. 13 Velocity profiles of bubbles in Supe
Triton X-100 0.27 ppm solution, and Triton
solution


Acknowledgements

This research is supported by Grant-in-Aid for JSPS
Fellows.

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

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