Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P2.68 - Lateral Stability of a Bubble Chain
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00503
 Material Information
Title: P2.68 - Lateral Stability of a Bubble Chain Particle Bubble and Drop Dynamics
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Stanovsky, P.
Ruzicka, M.C.
Drahoš, J.
Sanada, T.
Watanabe, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: gas-liquid systems
bubble chain
lateral stability
 Notes
Abstract: In this work we present results of experimental studies on the bubble chain behaviour. The bubble chain represents a mezo-scale structure in multi-scale methodology of bubbly flow, which enables to go from pair-wise interactions to the macroscopic equations for bubble flow without the usual averaging (Ruzicka, 2005). Although some theoretical prediction was published (Harper, 1970), the assumption about the lateral stability of bubble chain need to be verified experimentally. The uniform bubble chain can be described by two parameters – initial dimensionless bubble spacing Si and bubble Reynolds number Re based on the terminal velocity of a solitary bubble. The bubble chains were produced using two devices of different construction. The mechanical bubble generator with a moving needle (Vejrazka et al., 2008) and the acoustical bubble generator with a pressure wave (Shirota et al., 2008). The chain was laterally stable at low Re, and stability was broken when Re exceed value 18 at low separations.
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: VID00503
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: P268-Stanovsky-ICMF2010.pdf

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


Lateral Stability of a Bubble Chain


Petr Stanovsky*, Marek C. Ruzicka*, JiNi DrahoS*, Toshiyuki Sanadat and Masao WatanabeT

Institute of Chemical Process Fundamentals ASCR, Rozvojova 135, 16502 Prague 6, Czech Republic
tDepartment of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561 Japan

Department of Mechanical and Space Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo, 060-8628 Japan
stanovsky@icpf.cas.cz


Keywords: gas-liquid systems, bubble chain, lateral stability


Abstract

In this work we present results of experimental studies on the bubble chain behaviour. The bubble chain represents a
mezo-scale structure in multi-scale methodology of bubbly flow, which enables to go from pair-wise interactions to the
macroscopic equations for bubble flow without the usual averaging (Ruzicka, 2005). Although some theoretical prediction
was published (Harper, 1970), the assumption about the lateral stability of bubble chain need to be verified experimentally.
The uniform bubble chain can be described by two parameters initial dimensionless bubble spacing Si and bubble Reynolds
number Re based on the terminal velocity of a solitary bubble. The bubble chains were produced using two devices of
different construction. The mechanical bubble generator with a moving needle (Vejrazka et al., 2008) and the acoustical
bubble generator with a pressure wave (Shirota et al., 2008). The chain was laterally stable at low Re, and stability was
broken when Re exceed value 18 at low separations.


Introduction

The bubble-bubble interactions and internal structure of
bubbly flow are still subject of the research due to still
incomplete understanding of regime transitions and
insufficient knowledge about dense bubbly flows. The
interactions between particles and the behaviour of the
particle clusters represent a mezzo-scale part in multi-scale
methodology used nowadays for a description of the
two-phase or multiphase systems. The information about
interaction between particles can be obtained from smallest
structural unit of the system pair or some structural units -
e.g. bubble chain. The literature reviewed below is focused
on clean bubbles which posses the free-slip condition at
their surfaces and they are spherical.
For the creeping flow conditions Harper (1983) analytically
derived a flow around a line of spherical bubbles. His
analysis shows that the second bubble rises faster than the
first, the second bubble catches the first and the pair rises
faster. This scenario (pairing-off and attraction of each even
bubble) is repeated again down the chain. The comparison
with experiment, as Omran and Foster (1977) is only
cursory. They studied experimentally a chain of spherical
bubbles rising in glycerol solution (0.2 < Re < 0.5) with a
separation ranging S= 3-20. They found an increase of
bubble velocity in the chain with decreasing separation.
Harper (1970) was first addressing the problem of bubbles
rising in the chain theoretically. He claimed that his result
for the bubble pair rising in line at Re ~ 0(102) could be
extended to the infinite vertical bubble chain. Even in this
case bubbles should be separated with the equilibrium


distance. Morrison (1973) made an analysis on the stability
of a bubble chain of spherical bubbles rising at low Re with
a shear-free condition at the surface. He concluded using the
nearest neighbour approximation that the infinite chain was
stable and pairing (grouping into pairs as they rise) did not
occur. The pairing occurs only for the finite or the
semi-infinite bubble chain.
Harper (1997) corrected his own analysis (1970) in a view
of a numerical computation of Yuan and Prosperetti (1994).
He corrected the approximation used in his previous work
(vorticity production and convection) by considering the
terms describing a viscous diffusion in the bubble wake at
finite Reynolds numbers to get the same qualitative results
as Yuan and Prosperetti. Further he suggested that the
difference from the results of Katz and Meneveau (1996)
could be explained by the necessity of consideration of
additional velocity caused by all the bubbles in line.
Nevertheless, it is needed to calculate the wake contribution
for a finite number of all the preceding bubbles. However,
the available solution, which had a form an infinite series,
diverges.
However, literature is quite poor regarding the experimental
data about bubble chains. Before mentioned Katz and
Meneveau (1996) studied experimentally a chain of
spherical bubbles in distilled water at 0.2 < Re < 35 (0.07 <
Dekv < 0.48 mm). They pointed that bubbles in the chain
grouped into the pairs and they coalesced in the contact.
They claimed that such process was observed for bubble
sizes up to Dekv = 0.8mm (Re ~ 140). However, after the
coalescence of larger bubbles Dekv ~ 0.35-0.48 mm, the
bubbles became misaligned. For such "big" bubbles, they









did not observe any deceleration prior to coalescence as for
the smaller bubbles Dekv < 0.16. Unfortunately, the terminal
velocity of solitary bubbles was assumed as the velocity of
bubbles when separation of the bubble chain was uniform.
Moreover, a theoretical model of motion of one bubble pair
based on Oseen flow or alternatively far-wake
approximation fairly matches with the experimental results.
Also Martin and Chandler (1982) measured the velocity of
bubbles rising in the chain of spherical bubbles with a
diameter Dekv = 0.3 1 mm in distilled water and Polyox
solution. They reported an increase of the bubble velocity
with a decreasing separation between the bubbles for
separation lower than 20-fold of bubble radius.
Ruzicka (2000) developed a simple model describing the
dynamic behaviour of equal-sized spherical bubbles in the
vertical chain or in the group with finite number of bubbles.
The Model description is limited for Reynolds number in
the range from 50 to 200 because the drag force correction
for bubbles hindered by a previously rising bubble is based
on the work of Yuan and Prosperetti (1994). Besides others,
this model predicted pairing-off in the initially uniform
chain of bubbles, what was observed experimentally by
Katz and Menaveau. In addition, Ruzicka improved the
Harper's (1997) result for wake profile in the chain of
spherical bubbles assuming a viscous decay of velocity
disturbances along the chain. Newly, he introduced the
effect of the distant forces between the father bubbles
(non-local interactions) and studied their influence on the
basic dynamic pattern generated by the nearest-neighbour
(local) interactions. Interesting results were obtained, on
how the distant coupling affects the chain behaviour. In the
sequel paper, Ruzicka (2005) studied the vertical stability of
bubble chains in a detail, on three different length scales (a
discrete bubble chain, a continuous bubble chain bubble
"string", a macroscopic 1D bubbly flow). He developed a
multis-cale methodology that enables to go from the
pairwise interaction between two discrete bubbles to the
macroscopic equations for bubbly mixtures without the need
for any kind of averaging. He considered both the local and
the distant coupling of the bubbles, on the all three scales.
The introduction clearly shows a lack of experimental data
about bubble chains with low separation between bubbles to
verify some theoretical predictions.


Nomenclature


bubble diameter (mm)
bubble velocity (mm.s 1)
dimensionless bubble centre to centre spacing (-)
gravity acceleration (m.s-2))


Greek letters
c surface tension (N.m 1)
v kinematic viscosity (Pa.s)
p Density (kg.m-3)

Subsripts
i initial
ekv sphere of equivalent volume
T terminal


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

Experimental Facility

Two experimental arrangements were used for a 3D
observation of the bubble chains.

Experimental setup 1
An experimental tank, made of glass, had a size
0.11 x 0.11 x 0.25 m3 and it had both ends opened. This
tank was fixed by bolts between two stainless steel plates
into a groove with white rubber sealing. In the bottom plate,
an orifice was made for the mounting of a device for
controlled production; an upper plate had an orifice for tank
filling.

1 2
3
PC 4


i o






.-------- -- .
". 10 9 .- -




-- ---------- - - - -


Figure 1: The experimental set-up in the experiments with
the bubble generator with a moving needle. 1-glass tank,
2-system of mirrors (in experiments with bubble chains),
3-light diffuser, 4-speedlight, 5-SLR digital camera,
6-bubble generator, 7-amplifier, 8-solenoid valves,
9-pressure controller, 10-gas filter.

The bubbles were produced using the bubble generator
described in Vejra2ka et al. (2008). The pressure controller
in the range 5-160 kPa regulated the pressure of incoming
gas. The bubble was created at a fused silica capillary
glued inside the hypodermic needle. The capillary with
inner diameter 20 gm (and outer 140 gm) was 8 mm long.
The inner part of the capillary was coated with the paraffin
layer.
With regard to a credible classification of bubble chains
behaviour, a pair of thin tall mirrors was installed inside
the tank to ensure a side view of the bubble chain. Their
position is schematically depicted on the Fig 1 and from
the top view with a visualized optical path on Fig. 2.


1

2
+----
--


Figure 2: The top view of experimental set-up for the two
sidview measurement. -glass tank, 2-system of mirrors,
3-light diffuser, 4-speedlight, 5-SLR digital camera.









The driving signals for the bubble generator were created
in LabVIEW environment. The signals were generated by
a D/A converter of data acquisition card (National
Instruments) and amplified by an external amplifier
(BITTNER Basic 200). The LabVIEW environment and
the data acquisition card were used for triggering of a
speedlight (Nikon SB600) as well as for operating the
couple of fast solenoid valves.
The images were captured using a single-lens-reflex
camera Nikon D70 (maximal resolution 2000x3008 pixels)
with reversely mounted lens Nikkor AF 50mm/1,8D or
with the combination of 12mm, 36mm extension rings with
this lens. The speedlight was used as backlight illumination
with a frosted glass sheet as the light diffuser.
The images were taken during a long-time shutter release
when a PC controlled the speedlight flash and all the
experimental set-up was placed in a black tent. The
shortest possible duration between the two flashes
(controlled by the PC) was 17 ms. This technique was used
because Nikon D70 camera allows only a PC control via
the Nikon Capture program and the accurate time setting
when the image is taken is not possible. An internal
stroboscopic mode of the speedlight was not used because
it had been found that adjusted stroboscope frequency is
not accurate. The stroboscope (Movistrob, BBE) was used
for the verification of detachment frequency of produced
bubble chains.

Ultrapure 96% (wt.)
Liquid Water Ethanol
V [mm'/s] 0,89 1,39

p [kg/m3] 997,0 805,5

o-[mN/m] 72,0 22,1

Mo [-] 1,7.1011 1,7.10-9

log Mo [-] -10,8 -8,8

Figure 3: Characteristics of used liquids.

As the liquid medium, the ethanol of an analytical grade
and ultrapure water was used. This water was prepared
from distilled water by sequential purification with ion
exchange units and a carbon filter (Watrex). The ultrapure
water was poured into the experimental tank with the glass
vessel reserved for this purpose. The experimental tank
was cleaned with chromosulfuric acid to remove any
organic surfactants before the experiments. After this
procedure the tank was rinsed several times with the
ultrapure water. In our case there was water purity
characterized by conductivity. The usual conductivity of
water in the tank was 0.8 pS/cm (at 250C) and this value
did not change significantly during the measurements. A
temperature of the liquid was measured at the end of
experiments to avoid contamination of the tank and their
value was 250C in the experiments with the bubble chain
and 220C in all the experiments with the bubble pairs. The
water level was kept 20 cm above the tip of capillary.
As a gas medium clean air was used. The source air was
supplied from the laboratory air distribution. It was frozen
as to remove water vapours and oil aerosols (Ultrafilter


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

UltraPulse) and filtered through borosilicate glassfibre
filters (Ultrafilter SMF 03/05) to remove solid particles
greater than 10 nanometres.


Experimental setup 2
The second device for controlled bubble production was
used to verify an independence of results on bubble
production method. The experimental tank was a vessel,
made of Plexiglas, with size 0.12 x 0.12 m2 inner
cross-section and height 0.36 m.
5


4


Figure 4: The experimental setup for the experiments with
the bubble generator with an acoustic wave.1-side
high-speed camera, 2-high-resolution camera, 3-front
high-speed camera, 4-experimental tank, 5-flat cold lights.

The bubbles were produced using the bubble generator with
the acoustic wave described in Shirota et al (2008). A
tapered glass capillary glued to a hypodermic needle was
used as the bubble formation segment. The capillary was
prepared by special technique used for manufacturing of
optical (glass fiber) probes developed at Shizuoka
University. The hypodermic needle was connected to the
bubble generator through to the stainless steel tubes and
rigid nylone tube. The stainless steel tubes were held by a
set of positioners, which allowed fixing the capillary
precisely in a vertical position.
A driving signal for the bubble generator was created by a
multifunction synthesizer (WaveFactory WF 1974, NF). The
signal had a rectangular shape with duty ratio 1% (when
duty ratio is defined as ON to OFF period ratio of the
signal). The signal was amplified using a stereo amplifier
(Pioneer VSA-C300).
The high-speed cameras, the additional high-resolution
camera and the bubble generator were triggered using a
digital pulse/delay generator (DG 535, Stenford Research
Systems).
The records of the chain evolution from two sides were
captured using a two high-speed digital camera
Phantom v9.0 (maximal resolution 1632x1200 pixels) with
the lens Nikkor 50mm/1.2 and the lens Micro-Nikkor
105mm/2.8. The small-size high-resolution digital camera
Teli FireDragon Color (CSFU15CC18, maximal resolution
1600x1200 pixels at 15 frame/sec) with zoom-microscopic
and macroscopic lenses (Leica Z16APO and Leica Planapo
lx) was used to get the bubble size more accurately. Two
flat cold lights without flickering (Sakai Glass Sci.;
HF-SL-A48-LCG) were used as backlight illumination.











Liquid KF96 2 KF96 5 KF96 10 KF96 20

V [mm2/s] 2,16 5,41 10,79 21,58

p [kg/m3] 882,6 924,2 941,7 954,3

7 [mN/m] 18,3 19,7 20,1 20,6

Mo [-] 2,4 .10-8 8,7 .10-7 1,4.10-5 2,1 .10-4

log Mo [-] -7,6 -6,1 -4,9 -3,7


Figure 5: Characteristics of used liquids.

As a liquid medium, there were used silicon oils
(dimethylsilicone KF-96, ShinEtsu Silicones). They differ
mainly in their viscosity (2cSt, 5cSt, 10cSt, 20cSt at 250C).
The surface tension and the density change only a little with
the viscosity. The overview of their properties is given in the
table 3.2-2. The temperature was measured at the end of
experiments and it was 21.40C in all the experiments. The
liquids' level was kept 18 cm above the orifice.
As a gas medium, air was used from a pressure gas cylinder.


Data Treatment

Images obtained in the experiments were processed in the
MATLAB (ver. R2007a and previous) using the Image
Processing Toolbox (ver. 5.4 and previous). The movies
were exported into image sequences using a VirtualDub (ver.
1.8 and previous). In all the experimental cases,
characteristic properties of bubbles (e.g. a centroid
coordinate, a bubble size, an initial separation) were
obtained.


Results and Discussion

Two interaction regimes between bubbles in the chain were
found in the ultrapure water and in the ethanol (Fig. 6):

Regime A: Vertical in-line motion of bubbles in the chain
with coalescence
Regime B: Deflection of the bubbles in the chain out of the
vertical line

It was observed that the bubble chains are laterally unstable
at moderate Re. Due to a high detachment frequency, a
"bubble plume" was formed, a funnel-shaped stream of the
bubbles with the origin in a one point. From the snapshots
on Fig. 6 it is visible that the bubbles in the chain are
deflected out of the line after some distance from the source.
They temporarily created a zig-zag pattern. Finally, the
bubbles randomly clustered in the space

Three different interaction scenarios were observed during
experiments with silicon oils (Fig. 7):

Regime A: Vertical in-line motion of bubbles in the chain


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

with coalescence
Regime B: Vertical in-line motion of bubbles in the chain
with bouncing
Regime C: Deflection of the bubbles in the chain out of the
vertical line

It should be noted that the height in the chain where the
bubbles caught up was not constant, it varied in time. In the
case of coalescence, it was observed, that a bubble created
by merging of two smaller bubbles rose by almost at the
same velocity. Only the presence of other bubbles in a small
distance considerably accelerated their rise. The subsequent
coalescence led to the disintegration of the in-line
arrangement. Katz and Menveau (1996) concluded that the
pairing process and the coalescence in the line were a
quasi-steady processes. They did not mention directly that
the height where the bubbles coalesced varied in time.











































A) B)
Figure 6: The bubble chain behaviour in ultrapure water
using two side view (left part of the picture is front view,
right part is side view): A) The laterally stable chain -
coalescence in the line, B) the laterally unstable chain -
deflection out of line.






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


37 i coalescence in line, Ethanol
drift from line, Ethanol
2 O coalescence in line, Water
32 drift from line, Water
A coalescene in line, Silicon oil
27 A bouncing in line, Silicon oil
A drift from line, Silicon oil
o coalescence (Katz et al., 1994)
22 ---


















i scenarios in the bubblee cha i
17 ing t eri


Il I I--o
46 i i


I 0 20 40 60 80 100
~~ ,; '_... nr: Re

' : '. Figure 8: The stability map of bubble chains. Red marks-drift





SThree different interaction scenarios in the bubble chain
. were observed in the experiments. Their behaviour can be
depicted in a parametric map of the lateral stability Re-S,.
A-V (see Fig. 8). First, laterally stable chain where the bubbles in
L the vertical line were attracted and coalesced (blue marks).
Second, the laterally stable chain, when the lateral stability
Swas broken on close approach of the attracting bubbles by
.bouncing land sideway deflection (green marks). Third, the
I il laterally .unstable chain, when bubbles drift out of line
during their rise without direct contact (red marks).
The change between stable (blue and green marks) and
i unstable (red marks) region occurred at Re 18, at small
S. vertical separation of bubbles. The critical value of Re
increased with growing vertical separation.
F igeTo our7 knowledge, the lateral instability of the bubble chain
has not been experimentally observed so far. These results
Confirm the Harper's (1970) result, that the bubble chain is
inr le unstable to any perturbation of bubble position in lateral
ap p- C direction at moderate Re.

3 Acknowledgements

This work was supported by the Grant Agency of Academy
-of Sciences of CR under grant KJB 200720901. The support
of Grant Agency of the Czech Republic (grant No.
"m 104/07/1110) for some experimental equipment used in this
J .:,.' work is gratefully acknowledged.

References

Harper J.F., On bubbles rising in line at large Reynolds
numbers, J. Fluid Mech., Vol. 41, pp. 751-758 (1970).

Harper, J.F. Axisymmetric Stokes flow images in spherical
A) B) C) free surfaces with application to rising bubbles. Journal of
Australian Mathematical Society Series B, Vol. 25, pp.
Figure 7: The interaction regimes in the bubble chain 217-231 (1983)
rising in silicon oils. A coalescence in line, B bouncing
in line, C deflection out of line. Harper, J.F. Bubbles rising in line: why is the first
approximation so bad?. Journal of Fluid Mechanics, Vol.
351, pp. 289-300 (1997)






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


Katz J., Meneveau C., Wake-induced relative motion of
bubbles rising in line, Int. J. of Multiphase Flow, Vol. 22,
pp. 239-258 (1996)

Martin, W.W., Chandler, G.M. The local measurements of
the size and velocity of bubbles rising in liquids. Applied
Scientific Research, Vol. 38, pp. 239-246 (1982)

Morisson, F.A. Breakup of a bubble chain. Chemical
Engineering Science, vol. 28, pp. 1115-1116 (1973)

Omran, N.M., Foster, PJ. The terminal velocity of a chain of
drops or bubbles in a liquid. Transactions of the Institution
of Chemical Engineers, Vol. 55, pp 171-177 (1977)

Ruzicka M.C., On bubbles rising in line. International
Journal of Multiphase Flow, Vol. 26, no. 7, pp. 1141-1181
(2000)

Ruzicka M.C., Vertical stability of bubble chain: Multiscale
approach, Int. J. Multiphase Flow, Vol. 31, pp. 1063-1096
(2005)

Shirota, M., Sanada, T, Sato, A., Watanabe, M. Formation
of a submillimeter bubble from an orifice using pulsed
acoustic pressure waves in gas phase. Physics of Fluids, Vol.
20, Art. 043301, pp. 1-11 (2008)

Vejrazka, J., Fujasovi, M., Stanovsky, P., Ruzicka M.C.,
DrahoS, J. Bubbling controlled by needle movement. Fluid
Dynamics Research, Vol. 40, pp. 521-533 (2008)

Yuan, H. Prosperetti, A. On the in-line motion of two
spherical bubbles in a viscous fluid. Journal of Fluid
Mechanics, Vol. 278, pp. 325-349 (1994)




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