Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 4.2.1 - Dynamics of a Single Bubble Rising in a Gap between Two Parallel Vertical Planes with Magnetic Fluids
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 Material Information
Title: 4.2.1 - Dynamics of a Single Bubble Rising in a Gap between Two Parallel Vertical Planes with Magnetic Fluids Particle Bubble and Drop Dynamics
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: He, Y.Q.
Bi, Q.C.
Shi, D.X.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: magnetic fluids
bubble dynamics
surfactant
 Notes
Abstract: A single bubble rising in magnetic fluids is visualized using a mini-gap between two parallel vertical planes. Water-based Fe3O4 magnetic fluids with particle volume concentration of 6.33 vol% and density 1261.96 kgm-3 are filled in these gaps and a single air bubble is produced through the orifice at the bottom of the gap. The thicknesses of the gaps are 1 and 2 mm, respectively. Diameters of the orifices are 0.64 and 1.02 mm for 1 mm gap, and 0.64, 1.02 and 1.6 mm for 2 mm gap. In addition, four working fluids including deionized water, 25% tetramethylammonium hydroxide (TMAH) aqueous solution and mass concentration 30% and 50% sucrose solution also have been filled in the gaps. The results show that the shape of the bubble in magnetic fluids initially keeps oblate ellipse like that in the water, but after the middle of the journey, it becomes as an oblate elliptical cap like that in the surfactant aqueous solution. A reasonable explanation is obtained considering the diffusion of the surfactants to the interface of the bubble. Rise velocity of the bubble in magnetic fluids increases with the width of the gap, and the rise motion of the bubble become instable in the 2 mm gap, even breakup of a bubble generated by 0.64 mm orifice occurs.
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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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Dynamics of a Single Bubble Rising in a Gap between Two Parallel Vertical Planes with
Magnetic Fluids


Yongqing He, Qincheng Bi and Dongxiao Shi


State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Email: qcbi@amail.xjtu.edu.cn

Keywords: magnetic fluids, bubble dynamics, surfactant

Abstract

A single bubble rising in magnetic fluids is visualized using a mini-gap between two parallel vertical planes. Water-based Fe304 magnetic
fluids with particle volume concentration of 6.33 vol% and density 1261.96 kgm-3 are filled in these gaps and a single air bubble is produced
through the orifice at the bottom of the gap. The thicknesses of the gaps are 1 and 2 mm, respectively. Diameters of the orifices are 0.64 and
1.02 mm for 1 mm gap, and 0.64, 1.02 and 1.6 mm for 2 mm gap. In addition, four working fluids including deionized water, 25%
tetramethylammonium hydroxide (TMAH) aqueous solution and mass concentration 30% and 50% sucrose solution also have been filled in
the gaps. The results show that the shape of the bubble in magnetic fluids initially keeps oblate ellipse like that in the water, but after the
middle of the journey, it becomes as an oblate elliptical cap like that in the surfactant aqueous solution. A reasonable explanation is obtained
considering the diffusion of the surfactants to the interface of the bubble. Rise velocity of the bubble in magnetic fluids increases with the
width of the gap, and the rise motion of the bubble become instable in the 2 mm gap, even breakup of a bubble generated by 0.64 mm orifice
occurs.


Introduction

Magnetic fluids are stable colloidal dispersions containing
single-domain magnetic particles with a size of about 10 nm
in diameter (Rosensweig 1985). These particles are usually
magnetite and are held in suspension by the use of
surfactants which are compatible with both the carrier fluid
and the particles. During the last few decades, researches of
magnetic fluids have been extended to areas of physics,
chemistry, engineering, and even medicine (Berkovski &
Bashtovoy 1996; Berkovsky et al 1993). Some novel
applications have been proposed, such as micro/nano-
electromechanical sensors, actuators, and micro/nanofluidic
devices (Rinaldi et al 2004), and targeted drug-delivery
vectors in biomedical applications (Ganguly et al 2005).
Free interfacial flow of magnetic fluids under external
magnetic fields becomes more complicated, since a jump in
magnetic properties would found at fluid interfaces besides
density and viscosity. Notable cases in point are normal
field instability or Rosensweig instability in which an
initially flat magnetic fluid surface exhibits peaked structure
in a vertical magnetic field (Rosensweig 1985), and
labyrinthine patterns of a magnetic fluid drop formed in a
Hele-Shaw cell (Dickstein et al 1993).
Due to the effect of the magnetic body force, the behavior of
a single air bubble rising in magnetic fluids is quite different
from that in common liquids. Generally, an applied
magnetic field, even if stationary and uniform, can modify
the shape, trajectory and rise velocity of the bubble. The
bubble will be elongated along the direction of magnetic
field, accelerated in the region of negative field gradient,
and decelerated in the region of positive field gradient.
Based these characteristics, Kamiyama et al (1991)
contrived an energy conversion system using bubbly flow
produced by vaporization of the carrier liquid due to heat
addition. A large driving force will be generated in this
system to induce the magnetic fluid flow when a
nonuniform magnetic field was introduced.


There are some papers have reported on the behavior of
bubbles rising in magnetic fluids under different type of
magnetic fields, experimentally and theoretically. Ishimoto
et al (1995) observed the rising process of a single air
bubble through a Hele-Shaw cell under a nonuniform
magnetic field. They found that the shape of bubble
elongated along the field lines, and the rising velocity
increases in the negative gradient area and decreases in the
opposite case. The vapor bubbles generated in a vertical
pipe also were investigated by using ultrasonic wave echo
technique. Unfortunately, these images are too indistinct to
identify. Subsequently, Ishimoto & Kamiyama (1996)
numerically calculated the growth process and rise motion
of a single bubble in Poiseuille flow taking into account the
effect of magnetic body force made by a nonuniform
magnetic field. The simulation verified their foregoing
experimental results. Bashtovoi et al (2 "'5*11 observed an
interesting phenomenon that a bubble cluster divided into
two clusters in the presence of a uniform magnetic field,
and the disintegration of the clusters enhanced when the
field intensity increases. Then, they made another
experimental investigation on air bubbles separation in
magnetic fluids from the solid surfaces with the presence of
uniform and nonuniform magnetic fields (Bashtovoi et al
2005b). The critical volume of bubbles for separation would
decrease more than 10 times, when the magnetic field
gradient reached 1.5 x 103 kAm2.
Attention in the present work was focused on the effect of
microstructure of magnetic fluids on the rising motion of a
single bubble, and no field effect has been considered. It is
well known that when the water contains surfactant
additives, the velocity of the bubble rising in it is smaller
than that in pure water at the same conditions, and the value
of velocity will decrease to a minimum as the surfactant
concentration increases (Clift et al 1978). The physical
mechanism was first explained by Levich (1962), what the
reason is the surface tension gradient caused by surfactants.
Owing to the effect of diffusive and convective mass






Paper No


transport, the surfactant concentration at the rear of the
bubble is greater than that at the front, and the resulting
Marangoni tension needs a viscous shear stress on the
bubble as compensation, which will decrease the rise
velocity (Fdhila & Duineveld 1996). More detailed
discussions can be found in these literatures (Bush 1997;
Liao & McLaughlin 2000; Zhang & Finch 2001; Hetsroni et
al 2006).
The surfactant additives in magnetic fluids are comprised of
two parts: the molecules absorbed on the nanoparticles and
those which dissociated in the carrier liquid. The previous
researches treated the magnetic fluid as a homogeneous
liquid with a certain magnetization, and no influence of
internal configuration has been taken into account for the
study of bubble behavior in magnetic fluids. As we know,
the influence of suspended magnetic nanoparticles on the
shape and trajectory of the bubble keeps unclear. The
macroscopic effect of the nanoparticles is mainly increasing
the "effective viscosity" of the colloid (Odenbach 2002).
The objective of this work is to understand the behavior of a
single air bubble rising in magnetic fluids, especially to
study the influence of the surfactant additives and the
magnetic nanoparticles on the shape, trajectory and rise
velocity of the bubble. A visualization experiment was
conducted when a bubble formed in the narrow gap between
two parallel vertical glass plates (like a Hele-Shaw cell).
The results were compared with those in pure water,
surfactant aqueous solution, and sucrose solution.

Experimental

Since the magnetic fluid is black and opaque, it is
impossible to observe the bubbles rising through extended
magnetic fluid by naked eye. Therefore, the visualization
was realized using a device which is similar to a vertical
Hele-Shaw cell consisted of two parallel glass plates. The
bubble formed at the bottom rises through the gap, and the
profile of the bubble can be captured under a background
light. Extreme cautions were taken to keep the plates as
clean as possible.
In this experiment, a water-based Fe304 magnetic fluid with
particle volume concentration of 6.33% and density of
1261.96 kgmn3 was used as working fluid, which was
prepared by coprecipitation method using
tetramethylammonium hydroxide (TMAH) aqueous solution
as surfactant. At the same time, pure water, mass
concentration 25% TMAH aqueous solution, and mass
concentration 30% and 50% sucrose aqueous solution also
have been filled in the gaps. The shapes, trajectories and rise
velocities of the bubbles rising in these liquids are compared
with each other.
The schematic diagram of the experimental apparatus is
shown in Fig.1. The narrow gaps are made of two parallel
vertical glass plates with dimensions of 121x120 mm, and
the thicknesses of the gaps are 1 and 2 mm, respectively. A
single air bubble is produced through the orifice at the
bottom of the gap by promoting the syringe which is
connected to the orifice. Diameters of the orifices are 0.64
and 1.02 mm for 1 mm gap, and 0.64, 1.02 and 1.6 mm for 2
mm gap. The height of the fluids in the gaps is nearly 120
mm. Pressure in the syringe was measured by a pressure
transducer with uncertainty of 0.075% (Rosemount 3051 GP
series) so that the state of the air before forming bubble


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

could be confirmed. Three T-type thermocouples were
disposed to measure the temperatures of working fluids,
environment and the air in the connecting pipe. These data
were collected by a data acquisition system (IMP 3595
series), and the analog were converted to digital data for
storing in computer. Experiments were carried out under
conditions of atmospheric pressure (0.097MPa) and room
temperature of 25 C.

Background
'l4ight

SThermocouple

o Air Data
tn e b ubblc acquisition
system
CCD camera



Pressure
transducer




syringe Computer

Figure 1: Schematic diagram of the experimental
apparatus

A CCD camera was employed to visualize bubble behavior
in the gaps. For a typical experimental run, the rise motion
of air bubble released at the bottom of the cell were
recorded at a speed of 25 pictures per second, and the time
between two consecutive pictures was 40 ms. The bubbles
were simplified as two-dimensional, and no 3D effects were
considered. The image contained 350 x 280 pixels and
typically covered an area of 120 mm x 91 mm. During the
image analysis, the centroid and outline of the bubbles were
captured by the software of SigmaScan, so that the rise
velocity could be calculated by dividing the time interval at
a given experimental condition.

Results and Discussion

Shapes and trajectories

Figure 2 and Fig. 3 show the superimposed frames of a
single bubble from the detachment from the orifice to the
annihilation at the free surface of the liquids. The bubbles
are generated by 0.64 mm and 1.02 mm orifices in a 1 mm
gap. In these figures, the MF denotes magnetic fluids,
TMAH denotes mass concentration 25% tetramethyl-
ammonium hydroxide aqueous solution, and Sucrose 30%
and Sucrose 50% denote mass concentration 30% and 50%
sucrose aqueous solution, respectively. The time in the
bracket indicates the time interval of the adjacent bubbles.
When air was continuously injected into the gap at the lower
central orifice by promoting the syringe a bubble began to
form and grow. As it did so, it detached from the bottom,
and rose as a self-contained entity under the action of the
buoyancy force acting upon it.
The diameters d of bubbles rising in the 1 mm gap are in





Paper No


range of 5-10 mm, which are much larger than the gap
thickness b (d/b>>l ), so a two-dimensional description is
receivable. All bubbles in five working fluids followed a
straight line except pure water, in which the breakup of the
bubble generated by 0.64 mm occurred. The trajectory of
the bubble in water produced by 1.02 mm slightly deviated
from the axis line when it approached the free surface, the
reason may be the lower viscosity of water.


watei
(80 ms)
Figure 2:


MF TMAH Sucrose 30% Sucrose 509
(80 ms) (120 ms) (120 ms) (160 ms)
Trajectories of the bubbles generated by 0.64
mm orifice rising in 1 mm gap


Water MF TMAH Sucrose 30% Sucrose 50%
(40 ms) (80 ms) (160 ms) (80 ms) (240 ms)
Figure 3: Trajectories of the bubbles generated by 1.02
mm orifice rising in 1 mm gap

The shape of the bubble rising in magnetic fluids initially
kept oblate elliptical like that in the water and 30% sucrose
solution, but after middle of the journey, it became as an
oblate elliptical cap like that in the surfactant aqueous
solution. The curvature at the nose of bubble was obviously
larger than that at the rear, while the bubble in water always
kept same shape in the whole process. The case in the
surfactant solution was completely different from that in the
water, where the bubble exhibits approximately spherical
cap with its symmetry axis parallel to the bubble-centre
velocity, and the bubble shape remains constant and slightly
elongated along the vertical axis after the initial acceleration
stage. This phenomenon could be explained as the existence
of surfactant additives. As the bubble rose in the liquid,
surfactants tend to adhere to the bubble interface, which will
result in a lower, non-uniform surface tension along the
interface and introduce the Marangoni force. Further, there
may be exchange (adsorption/desorption) of surfactants
between the interface and the bulk. As a result, the
concentration of surfactant additives on the bubble interface
is nonuniform. Since the velocity of bubble is larger than the
surrounding liquid, surfactants will be accumulated at the
trailing end of the bubble, and a surfactant concentration
difference between the front and back of bubble will be
produced. Then, the deformation of lower half of the bubble


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

surface was restricted, and the bending of the upper half
became relatively easy. The content of the surfactant
additives is small, and most of them are coated on the
magnetic nanoparticles, only a few loitered in the carried
fluid. There is a relaxation when the accumulation of
dissociative surfactants on the rear of bubble achieved to the
extent which can make influence on the appearance of the
bubble, so the behavior of bubble in magnetic fluids only
takes the shape of that in TMAH aqueous solution at the
remaining half of journey.
From these pictures, we can also conclude that the behavior
of bubble in magnetic fluids is similar to that in the mass
concentration 30% sucrose aqueous solution at the initial
stage. The viscosity of magnetic fluids is larger than pure
water due to the influence of nanoparticles. The viscosity
will increase to 1.45 mPa-s for magnetic fluids with particle
volume concentration of 6.33%, which can be calculated
from the Rosensweig's formula (Rosensweig 1985) in no
magnetic field case:


Where q is the dynamic viscosity of magnetic fluids, rlo is
the viscosity of carrier liquid, q9 the volume concentration of
particles including their surfactant, pc, the critical volume
concentration, usually be 0.74. And the viscosity of 30%
sucrose solution is 2.78 mPa-s (Mathlouthi & Gotelle 1995),
twice as the magnetic fluids, and with the same value of the
surfactant solution (about 2.8 mPa-s). The deformation of
the bubbles in the 50% sucrose solution is not significant.
They remain spherical and their trajectory is rectilinear.
They have effective diameters less than 6 mm, nearly half of
the magnetic fluids, which may be caused by their higher
density of 1227.37 kg/m3 (Bubnik et al 1995) and viscosity
of 12.6 mPa-s (Mathlouthi & Gotelle 1995). The larger
density difference between the working fluids and air would
result in the reduction of the bubble departure diameter.
Further, the smaller the size of the bubble was, the
deformation of the bubble was less obvious, and the bubble
kept sphere easier. In addition, the viscous drag force also
resisted the expansion of the bubble surface.
Figure 4 to Fig. 6 show the rise motion of bubbles through
the 2 mm gap, where the bubbles were produced by 0.64,
1.02 and 1.6 mm orifices. From the pictures, the shapes of
the bubbles varied obviously from each other as the
diameter of the orifice increases, even breakups of bubbles
in magnetic fluids and 30% sucrose solution occurred when
the diameters of the orifices are 0.64 and 1.02 mm. The
bubble diameters increase substantially compared to the 1
mm gaps at the same condition, especially which of the 50%
sucrose solution increases almost double. And the diameter
of the bubble generated by the 1.02 mm orifice in magnetic
fluids even reached 12 mm.
A plane zigzag trajectory can be found in water, magnetic
fluids and even 30% sucrose solution, while the trajectories
of bubbles in surfactant and 50% sucrose solution still keep
rectilinear. The onset of the path instability was delayed
when bubbles generated through small orifices and these
bubbles have bigger diameters. But the oscillation deviated
from the centerline started as song as the bubble detached
from the orifice for the case of 1.6 mm orifice, and the
diameter was smaller than the previous examples. Kelley &


5oi5 52
77 77 P 2 P


(PI






Paper No


Wu's experimental results (1997) indicated that the path
instability in a Hele-Shaw cell was caused by the vortex
shedding in the wake of the bubble.


water
(40 ms)
Figure 4:


VVactl
(40 ms)
Figure 5:


MF TMAH Sucrose 30% Sucrose 50%
(40 ms) (80 ms) (40 ms) (80 ms)
Trajectories of the bubbles generated by 0.64
mm orifice rising in 2 mm gap


MF TMAH Sucrose 30% Sucrose 50%
(40 ms) (80 ms) (40 ms) (40 ms)
Trajectories of the bubbles generated by 1.02
mm orifice rising in 2 mm gap


Water MF TMAH Sucrose 30% Sucrose 50%
(40 ms) (40 ms) (80 ms) (40 ms) (160 ms)
Figure 6: Trajectories of the bubbles generated by 1.6 mm
orifice rising in 2 mm gap

Similar to the behavior of the bubble in 1 mm gap, the shape
of the bubble in magnetic fluids transformed form an oblate
ellipse to an oblate elliptical cap after the middle of the
journey. Small orifice may produce big bubble, even the
bubble produced by the 0.64 mm orifice burst after a
distance from the bottom. The trajectory of the bubble
produced by the 1.6 mm orifice initially kept rising in a
straight line, but the path became instable at the late stage of
the rise motion. The bubbles in magnetic fluids and 30%
sucrose solution have almost the same trajectories.
Compared to the 1 mm gap, the wall effect is not so
significant for the 2 mm gap. When the departure diameter
reduced to the order of the gap thickness, such as the
situation in the Fig. 6, the motion of bubbles became
instable considerably like the situations in the bulk liquid.


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

Rise Velocities

The rise motion of the bubbles is determined by buoyancy,
surface tension, viscous drag force and so on. Therefore, the
rise velocities of the bubbles are strongly influenced by the
properties of the fluids. Fig.7 and Fig.8 show the typical
velocity of a single bubble as a function of y coordinate,
where the bubbles in Fig.7 were generated by 1.02 mm
orifice rising in 1 mm gap and in Fig.8 were generated by
1.6 mm orifice rising in 2 mm gap, respectively. The
transient velocities were given by the distance between the
centroid of two adjacent bubbles dividing by the time
interval, which is a constant of 40 ms. The initial data point
was set as the centroid of the bubble which completely
detached the orifice. The whole process of the rise motion
could be divided into three stages: acceleration process with
positive velocity gradient, free rise with constant velocity,
and annihilation stage where the bubble dramatically
decelerated and finally burst at the surface of the liquid. In
general speaking, the terminal velocity is the velocity in free
rise period.

16 .


0 20 40 60 80 100 120 140
y/mm
Figure 7: Velocities of the bubbles generated by 1.02 mm
rising in 2 mm gap

18I


0 20 40 60 80 100 120 14C
y /mm
Figure 8: Velocities of the bubbles generated by 1.6 mm
orifice rising in 1 mm gap orifice

According to the values of the viscosities of the working
fluids, the largest one was 50% sucrose solution followed in
descending order by surfactant solution, 30% sucrose
solution, magnetic fluids, and water. The terminal velocities






Paper No


of the bubbles rising in water and magnetic fluids have
larger values, and the 50% sucrose solution has the smallest
value, which are inversely proportional to their viscosities.
The viscous drag force plays an important role on the
bubble rising in a narrow gap. The abnormal phenomenon
happened on the surfactant solution, the rise velocity of it
was smaller than that in 30% sucrose solution although they
have nearly same values of viscosities, even smaller slightly
than the situation in 50% sucrose at the later period. It
seemed that the surfactant additives decreased the velocity
as described in the paper of Fdhila & Duineveld (1996). The
surfactants induced additional shear stress which resisted the
rise motion of the bubble.
Moreover, when the gaps were filled with other fluids
except 50% sucrose solution, the velocities of the bubbles in
2 mm gap were larger than those in 1 mm gap. It can be
concluded that the wall effect has an obvious influence on
the lower viscous fluids. Compared with the bubble in water,
the fluctuation of the velocity of the bubble in 50% sucrose
solution was negligible, and the bubble in it kept a uniform
speed. The velocity of the bubble rising in magnetic fluids
was smaller than that in water in 1 mm gap, but they were
almost the same when the bubbles rose in 2 mm gap.
Figure 9 shows the velocities of the bubbles rising in
magnetic fluids. It was observed that the velocities of the
bubbles in 2 mm gap were much larger than those in 1 mm


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

nanoparticles, the viscosity of the magnetic fluid was larger
than that of the carried liquid, and the larger viscous drag
force was induced. Additionally, the rise motion of the
bubble also was affected by the dissociative surfactants. As
a result, the behavior of the bubble rising in magnetic fluid
becomes more complicated. Under the influence of
surfactants, the shape of the bubble rising in magnetic fluids
will transform from an oblate ellipse to an oblate elliptical
cap after the initial acceleration stage. Furthermore, the rise
velocity was smaller than that in water in 1 mm gap due to
the larger viscous drag force, and the bubbles rose along the
vertical axis with a uniform speed. But in the 2 mm gap case,
the shapes and paths became irregular, even breakup and
zigzag trajectory appeared. The path of bubble in magnetic
fluids still kept rectilinear at the initial stage due to its
bigger viscosity, meanwhile the bubble immediately swung
in water after the detachment from the orifice.

Acknowledgements

This work is supported by National High-Tech Research and
Development Plan in China, project number is
2008AA05Z417.

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ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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