Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 17.5.3 - Study on Bubble Nucleaion and Growth Behavior in High Viscous Fluid duirng Rapid Decompression
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00428
 Material Information
Title: 17.5.3 - Study on Bubble Nucleaion and Growth Behavior in High Viscous Fluid duirng Rapid Decompression Environmental and Geophysical Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Asai, H.
Kaneko, A.
Abe, Y.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: bubble nucleation
high viscous fluid
rapid decompression
 Notes
Abstract: In volcanic eruption, bubble nucleation and growth process in magma which is high viscous fluid have an important role. The occurrence of fragmentation of bubbles in expansion process determines whether the eruption is explosive or effusive. Since the volcanic eruption contains several complex factors, conditions on which explosive eruption occurs are not cleared. In the present study, the experiments with rapid decompression experiments are conducted in order to investigate the factors affecting bubble nucleation and growth in high viscous fluid under rapid decompression conditions. Furthermore, the influence on bubble nucleation of viscosity of the fluid, decompression rate and concentration of dissolved air is investigated. As results, it is found that the decompression rate have an effect on the number of nucleated bubbles. In addition, being supposed that minute bubble expands and grows up to visible bubble, time variation of bubble radius is numerically simulated. The possibility of the influence of minute bubble on bubble nucleation is discussed with comparison of the calculation results and the experimental results.
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: VID00428
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1753-Asai-ICMF2010.pdf

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


Study on Bubble Nucleation and Growth Behavior in High Viscous Fluid
during Rapid Decompression


Hideaki ASAI*1, Akiko KANEKO*1 and Yutaka ABE*1

*Department of Engineering Mechanics and Energy, University of Tsukuba,
1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan
hasai@ edu.esys.tsukuba.ac.jp


Keywords: Bubble nucleation, High viscous fluid, Rapid decompression



Abstract

In volcanic eruption, bubble nucleation and growth process in magma which is high viscous fluid have an important role.
The occurrence of fragmentation of bubbles in expansion process determines whether the eruption is explosive or effusive.
Since the volcanic eruption contains several complex factors, conditions on which explosive eruption occurs are not cleared.
In the present study, the experiments with rapid decompression experiments are conducted in order to investigate the factors
affecting bubble nucleation and growth in high viscous fluid under rapid decompression conditions. Furthermore, the influence
on bubble nucleation of viscosity of the fluid, decompression rate and concentration of dissolved air is investigated. As results,
it is found that the decompression rate have an effect on the number of nucleated bubbles. In addition, being supposed that
minute bubble expands and grows up to visible bubble, time variation of bubble radius is numerically simulated. The
possibility of the influence of minute bubble on bubble nucleation is discussed with comparison of the calculation results and
the experimental results.


Introduction

In volcanic eruption, bubble nucleation and growth
process in magma which is high viscous fluid have an
important role. Rapid decompression caused by breaking a
cap of conduit or ascent of magma trigger a bubble
nucleation and growth. It is thought that bubble nucleation
significantly controls magma flow dynamics (Yamada et al.,
2005). The occurrence of magma fragmentation in
expansion process determines whether the eruption is
explosive or effusive (Massol et al., 2005). The volcanic
eruption contains several complex factors, such as the effect
of volatile substance, viscosity of magma and
decompression rate. Therefore, the conditions on which the
explosive eruption occurs are not cleared. In the previous
study, in order to simulate volcanic eruption the rapid
decompression experiments with two-phase fluid of silicone
oil as high viscous fluid and acetone as volatile substance
have been conducted (Fujii et al. (2008)). However, it is not
clear whether bubbles are generated by the phase-change of
acetone or cavitations.
In the present study, the objective is to clarify the factor
affecting bubble nucleation and growth in high viscous fluid
under rapid decompression conditions, and two kinds of
experiments and numerical calculation are conducted. As
the first, the experiment with one-phase fluid of silicone oil
under rapid decompression conditions is conducted. The
influence on bubble nucleation of volatile substance is
discussed with comparison of the results by Fujii et al. As
the second, the experiment with saturated water and


degassed water is conducted to investigate the effect of
concentration of dissolved air. The numerical calculation for
the time variation of bubble radius is conducted. It is
supposed that minute bubble expands and grows up to
visible bubble. In the calculation, the pressure data obtained
from experiments are input to the Rayleigh-Plessset
equation (Toramaru, 1995) as surrounding pressure
condition. The possibility of the influence on bubble
nucleation of bubble nucleus is discussed to compare the
calculation results and the experimental results.

Nomenclature

u bubble growth rate (ms-1)
L length of major axis (mm)
P pressure (MPa)
R bubble radius (mm)
NB number of molecule of gas
k Boltzmann constant (m2kgs-2K 1)
T temperature
Greek letters
p density (kgm-3)
u viscosity (Pas)
y surface tension (mNm')
Subscripts
i the condition of ith
0 initial condition
g gas phase
I liquid phase





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


Figure 1: Schematic diagram of the experimental
apparatus.


Table 1: Experimental conditions for effect of fluid
viscosity and decompression rate.

Experimental Diaphragm
SViscosity [Pa-s]
number _____thickness [mm]
Exp. 1 1.0 0.05
Exp. 2 1.0 0.10
Exp. 3 1.0 0.15
Exp. 4 10 0.05
Exp. 5 10 0.10
Exp. 6 10 0.15
Exp. 7 100 0.05
Exp. 8 100 0.10
Exp. 9 100 0.15


Experimental Apparatus and Methods

Experimental apparatus
A schematic diagram of the present experimental
apparatus is shown in Fig. 1. This apparatus is mainly
consisted of a plunger pump, test section, a diaphragm and a
vacuum tank. The plunger pump injects working fluid and
compresses it. The test section is consisted of 6 visible
acrylic blocks as shown in Fig. 2 to observe bubble behavior.
Size of the block is 100 mmx100 mmxl40 mm and inner
diameter is 40 mm. Height of the test section is 1065 mm. A
sample of diaphragm is shown in Fig. 3. The diaphragm
made of stainless-steel divides a high-pressure region from
a low-pressure region. The high-pressure region is
decompressed rapidly when the diaphragm is ruptured. The
rupture pressure is controlled by changing the thickness of
diaphragm. The pressure transition is measured with 7
pressure transducers (PT1-7) which are placed at the joint of
blocks.

Experimental methods
First, the plunger pump injects the test fluid into the
high-pressure section which is divided by the diaphragm.
Additionally the high-pressure region is compressed by


Figure 2: Avisible block
constructing test section.


Figure 3: The diaphragm
before and after rupture.


Table 2: Experimental conditions for the effect of
dissolved air.

Experimental Dissolved air Diaphragm
number [mg/L] thickness [mm]
Exp. 10 38.7 0.05
Exp. 11 25.6 0.05
Exp. 12 24.8 0.05
Exp. 13 34.4 0.10
Exp. 14 25.3 0.10
Exp. 15 24.8 0.10
Exp. 16 34.4 0.15
Exp. 17 26.0 0.15
Exp. 18 25.2 0.15
Exp. 19 3.9 0.05
Exp. 20 3.5 0.10
Exp. 21 3.5 0.15

injecting the working fluid. The diaphragm is ruptured when
the pressure exceeds its critical pressure corresponding to a
diaphragm thickness. The high-pressure region is
decompressed rapidly when the diaphragm is ruptured. The
flow behavior in the test section is observed with high-speed
camera, and the pressure transition is measured with the
pressure transducers simultaneously.

Experimental Conditions

Effect of fluid viscosity and decompression rate
Experimental conditions are shown in Table 1. Nine
kinds of experiments were conducted. Three varieties of
silicone oil (Shin-Etsu Chemical Co., Ltd., KF96-1000cs,
KF96H-10000cs, KF96H-100000cs) which are different
viscosity of 1.0, 10, 100 Pas is used as working fluid. They
contain volumetric 19 % of air at saturation of 20 C
(Shin-Etsu Chemical Co., Ltd., 2003). And three different
diaphragms of the thickness (0.05 mm, 0.10 mm, 0.15 mm)
are employed for variety of decompression rate.

Effect of dissolved air
Experimental conditions are shown in Table 2. Saturated
water and degassed water are used as working fluids to


Paper No






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


4.

3.

3.

2.

2.

1.

1.

0.

0.


0 2


4 6 8 10
Time [ms]


Figure 4: Time variation of pressure
during rapid decompression.


0 2 4 6 8 10
Time [ms]
Figure: The relation between diaphragm
thickness and pressure change.

compare the effect of quantity of dissolved air. Tap water is
degassed through a deaerator to obtain degassed water.
Quantity of dissolved oxygen is measured with the
dissolved oxygen meter (HORIBA, Ltd., OM-51) and
quantity of dissolved air expected as non-condensable gas is
estimated from the quantity of oxygen. In fact, the
concentration of non-condensable gas of saturated water and
degassed water are 24.8-38.8 mg/L and 3.5-3.9 mg/L,
respectively.



Experimental Results and Discussions

Effect of fluid viscosity and decompression rate
Rapid decompression behavior
Time variation of pressure decreasing induced by
breaking the diaphragm in Exp. 1 is shown in Fig. 4. The
vertical axis in the figure indicates absolute pressure and the
horizontal axis indicates time variation. The time when the
decompression starts is defined at 0 ms. The lines of PT1, 2
and 3 are the pressure in high-pressure region. The other
lines are the pressure in low-pressure region. The pressure in
high-pressure region rapidly decreases when the diaphragm
is broken. Then, the pressure becomes 0 MPa at 3 ms and


0
5- PT-1
5 l-- PT-2
0 PT-3
-- PT-4
5 \ PT-5
-) PT-6
0 PT-7
5

0

5




2 4 6 8
Time [ms]


Figure 7: Time variation of bubble growth rate and
length of major axis (Exp. 4).

converges to 0.01 MPa which is as same as the initial
pressure in low-pressure region after 6 ms. The pressure
when the diaphragm is broken is 3.82 MPa, and the
minimum pressure is -0.16 MPa in this case. The
decompression rate is 1.20 GPa/s under this condition.
Decompression rate is defined that the rate of the pressure
decreasing to 0 MPa. On the other hand, the pressure of
low-pressure region hardly changes from the initial
pressure.
The relation between diaphragm thickness and pressure
change is shown in Fig. 5. The lines indicate the pressure of
PT1. The diaphragm thickness of Exp. 1, Exp. 2 and Exp. 3,
is 0.05 mm, 0.10 mm and 0.15 mm, respectively. The
rapture pressure of each diaphragm is 3.82 MPa, 7.67 MPa
and 13.0 MPa, respectively. As the diaphragm thicken, the
pressure increases. However, the time when the pressure
become 0 MPa did not change in each case. The result
shows that the decompression rate increases corresponding
to the diaphragm thickness. The decompression rate is 1.20
GPa/s, 2.35 GPa/s and 4.02 GPa/s, respectively. The rapid
decompression behavior shows similar behavior when the
working fluid is saturated water or degassed water.

Bubble nucleation and growth behavior
One of the typical snapshots of bubble nucleation and
growth behavior is shown in Fig. 6. In this experiment,
viscosity and decompression rate are 10 Pas and 1.06 GPa/s,
respectively. Observation of the behavior and pressure
measurement were conducted simultaneously. The bubbles


Paper No


Figure 6: Bubble nucleation and growth behavior
during rapid decompression (Exp. 4).

5.0
4.5 - Growth rate
Length of major axis
4.05- .
3.5 .


I I-T






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


are appeared due to rapid decompression at 3.0 ms despite
volatile substance is not contained in the working fluid from
these images. Similarly, the bubble nucleation behavior have
been observed when the experiments with silicone oil
contained acetone as volatile substance were conducted in
the previous study (Fujii et al. (2008)). In the present study,
it is found that the number of bubbles does not change in 3.0
ms and 6.0 ms. Bubble nucleation is concluded by very
short time and the bubbles grow after nucleation without the
number of the bubbles changing in Fig. 6.
Time variation of bubble growth rate and length of
major axis of the bubbles which are surrounded with red
circles in Fig. 6 is shown in Fig. 7. Bubble growth rate ug is
defined as following,
L1,, L
u = (1)

where L, is the length of major axis measured from the
snapshot shown in Fig. 6 at certain time, L,+1 is the length of
major axis at the next moment and At is time interval of
those snapshots. In this figure, the length of major axis is
increase by 15 ms as time passing. The growth rate shows
the maximum value between 2.0 ms and 3.0 ms, and then
the value decrease. This graph indicates that the bubbles
expand rapidly when the bubbles are nucleated. As time
passing, the bubbles grow slowly.
Behavior of bubbles just after nucleation at 3.0 ms with
variation of viscosity and decompression rate are shown in
Fig. 8. The viscosity and decompression rate are 1.0 Pas, 10
Pas, 100 Pas and 1.2 GPa/s, 2.4 GPa/s, 4.0 GPa/s,
respectively. When the decompression rate is 1 GPa/s, the
bubble number density is the value between 1x105 m3 and
10x105 m 3. Whereas, when the decompression rate is 4
GPa/s, the number density is the value between 10x05 mM3
and 100x105 m 3. It is found that there is a tendency to
increase the number of bubbles as the decompression rate
increases.
Relation between decompression rate and bubble
number density N are shown in Fig. 9 with the results of
Fujii et al. Bubble number density defined as the number of
bubbles per unit volume. The experiments with silicon oil as
working fluid containing acetone as volatile substance have
been conducted by Fujii et al. (2008). The bubble number
density increases when the decompression rate increases for
both results. Since both results show similar distribution, it
is suggested that the number of nucleated bubbles is not
affected with acetone.
Bubble nucleation and growth behavior under the
condition of Exp. 7 is shown in Fig. 10. Bubbles nucleate
between 2.0 ms and 4.0ms. After the nucleation, the bubbles
grow and shrink rapidly. The bubble number density is
13.7x 105 m3 in these images. The time variation of pressure
at PT1 and the value of the bubble radius which are
measured from the images are shown in Fig. 11. The
decompression rate is 1.20 GPa/s. It is indicated that
bubbles are nucleated at 2.5 ms when the pressure is
decompressed to about 0.5 MPa. After that moment, the
bubbles grow up as decrease of the pressure. And then, the
bubbles shrink steadily with increase of the pressure, and
shrink steeply at 7.0 ms when the pressure recovers to 0.2
MPa. The maximal value of the bubble radius is 1.48 mm at
3.5 ms. Bubble radius change is depending on pressure
change dominantly.
Bubble nucleation and growth behavior under the


100







L1o

U)
0
)
.U)


.


1 3 5
Decompression rate [GPa/s]
Figure 8: Bubble nucleation behavior at 3.0 ms
after rupture of a diaphragm.


100
E
C)
x
: 10

c
-n
I 1


-n
-n


Decompression rate [GPa/s]


Figure 9: Relation between decompression rate and
bubble number density.


Figure 10: Bubble nucleation and growth behavior
(Exp. 7).


Paper No


* 1.0Pa-s
* 10Pa-s
100 Pa-s 00
MODO



00

0
0 0.7 Pa-s (Fujii(2008))
S8 6.0 Pas (Fujii(2008))
0 80 Pas (Fujii(2008))






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


2.4

2.0

1.6 c-

1.2

0.8

0.4

0.0


0 1 2 3 4 5 6 7 8 9 10
Time [ms]
Figure 11: Time variation of pressure and bubble
radius (Exp. 7).

condition of Exp. 8 is shown in Fig. 12. The decompression
rate is 2.60 GPa/s. Bubbles are nucleated between 2.0 ms
and 4.0ms, and then the bubbles grow and shrink as well as
those in Fig. 10. It is found that the number of bubbles is
larger than that in Fig. 10. The bubble number density is
13.7 x 105 m in these images. The time variation of pressure
at PT1 and the value of the bubble radius which are
measured from the images under the same condition are
shown in Fig. 13. In this figure, it is found that bubbles
nucleate at 2.5 ms when the pressure is decompressed to
about 1.2 MPa. After that time, the bubbles grow up as
decrease of surrounding pressure, and shrink steadily as
increase of the pressure and shrink steeply at 8.5 ms. The
maximal value of the bubble radius is 1.65 mm at 4.7 ms. In
these figures, it is found that the number of bubbles
increases as decompression rate increasing but the radius of
one bubble does not increase.


Effect of the concentration of dissolved air

The observation results of saturated water during rapid
decompression under the condition of Exp. 11 are shown in
Fig. 14. The amount in dissolved air is 25.6 mg/L in this
condition. The snap shots are indicated every 2.0 ms from
the rapture of a diaphragm. It is noted that bubble is hardly
nucleated in the test section but only at the joint of blocks as
shown in the images from 6.0 ms to 10 ms. The observation
result in degassed water during rapid decompression under
the condition of Exp. 19 is shown in Fig. 15. The amount of
dissolved air is 3.9 mg/L. Here, a few bubbles are generated
at 4.0 ms. Bubbles are hardly nucleated in the experiment
with saturated water which contains more dissolved air than
degassed water in the test section. In addition, it is found
that few bubbles are generated when water as low-viscous
fluid is decompressed rapidly.
The relation between bubble number density and
decompression rate with saturated water, degassed water
and silicone oil is shown in Fig. 16. The bubble number
density in any silicone oil is increase when the
decompression rate increases. On the other hand, the
number density in saturated water and degassed water
remained 0.5x105 m3 as increasing of the decompression
rate. It is suggested that the silicone oil have a lot of minute
bubble as nucleus even if it is placed for a long time,


Figure 12: Bubble nucleation and growth behavior
(Exp. 8).

S Pressure (PT-1) 2.4
8 Bubble radius (Exp. 8)
77 \ 2.0

5 --


6 34 0.8 1
2
0.4

0.0
0 1 2 3 4 5 6 7 8 9 10
Time [ms]
Figure 13: Time variation of pressure and bubble
radius (Exp. 8).















Figure 14: Observation result in saturated water
during rapid decompression (Exp. 11).















Figure 15: Observation result in degassed water
during rapid decompression (Exp. 19).


Paper No






Paper No


E8
-7
x
6
5
4
"o

E
2

0-
m


1.0 1.5 2.0 2.5 3.0 3.5 4.0
Decompression rate [GPa/s]
Figure 16: Bubble number density of saturated
water, degassed water and silicone oil.


because it is high viscous fluid and small bubbles are hardly
to be released. On the other hand, it is possible that saturated
water and degassed water have few bubble nuclei because of
low viscous fluid. It is suggested that the existing bubble
nuclei have an effect on bubble nucleation.

Numerical calculation to investigate the influence
of existing minute bubble

The following calculations are conducted to indicate that
existing bubble nuclei expand and reach to visible bubbles.
The pressure difference between inside and outside of
bubble is balanced on the inertia force, the viscous force,
and surface tension force, described by the following
equation (Toramaru, 1995):

P(t)- P (t)=

d2R(t) 3 dR(t) 4u dR(t) 2y
) Rt +- dt )+ (2)
dt 2 dt R(t) dt R(t)
where Pg is inside pressure of bubble, Pi is pressure of fluid,
pi is density of fluid, p is viscosity of fluid and y is surface
tension coefficient. The inside pressure of bubble is
calculated by the state equation of ideal gas:


Pg t) 2R (t)3'j N~kT
(3b7


(3)


where NB is number of molecule of gas, k is Boltzmann
constant and T is temperature. When it is presupposed that
there is no phase change and temperature is constant, the
following equation is described:
NBkT = const. (4)
The pressure difference across the fluid interface is
described by the following Young-Laplace equation:

P,(t) P(t) + 2(5)
R(t) (5)
The following equation is obtained to input initial bubble
radius, Ro and initial pressure of fluid, Pro into equation (3),
equation (4) and equation (5):

t) RP + 2R (6)
R(t) (6)


* Slicone oil (1.0Pa-s)
* Slicone oil (10Pa-s)
Slicone oil (100Pa-s)
* Saturated water
0 Degassed water

*


0 5 10 15
Time [ms]
Figure 18: The comparison of the experimental
result and the calculation result (Exp. 7).
0.


E
E
- 6

4~
3


0 5 10 15 20
Time [ms]
Figure 19: The comparison of the experimental
result and the calculation result (Exp. 8).


where subscript, 0 means the condition just before the fluid
is decompressed. The pressure data of Exp. 7 and Exp.8
shown in Fig. 17 which is measured at PT-1 is input to P1. In
addition, the value of initial bubble radius, Ro as 0.1
utm-0.01 utm is input to equation (2) and (6), and the time
variations of bubble radius are calculated.
The result of calculation when the pressure data of Exp.
7 is input and the bubble radius measured from the


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



8 1.20 GPa/s (Exp. 7)
7 2.60 GPa/s (Exp. 8)
6
5
4
3
2




0 5 10 15 20
Time [ms]
Figure 17: Time variation of pressure which is
inputted into PI (Exp. 7 Exp. 8).


*- ,


- 0.1 Ltm
- 0.09 Ltm
0.08 Ltm
- 0.07 Ltm
0.06 Ltm
- 0.05 Ltm
0.04 Ltm
0.03 Ltm
- 0.02 Ltm
- 0.01 Ltm
1 Experimental
result 2.60 GPa/s






Paper No


observation result are shown in Fig. 18. The decompression
rate is 1.20 GPa/s in this condition. Fig. 18 shows that the
bubble radius can increase when the size of initial bubble
radius, Ro is more than 0.05 gim. On the other hand, the
bubble does not expand when Ro is less than 0.04 gim. In the
result, the bubble radius begins to increase at about 3.5 ms
and turn to decrease at about 7 ms and shrink at 10 ms. The
maximal value of calculated result is between about 1.4 mm
and 2.2 mm. These tendencies are similar to experimental
result. The result of calculation when the pressure data of
Exp. 8 is input and the bubble radius measured by the
observation result are shown in Fig. 19. The decompression
rate is 2.60 GPa/s in this condition. Fig. 19 shows that the
bubble radius can increase when the size of Ro is more than
0.03 gm. On the other hand, the bubble does not expand
when Ro is less than 0.02 gim. The maximal value of
calculated result is about 8 mm. The value is smaller than
experimental result, although the order of the value is
almost same. The difference between the experimental and
the numerical results are appeared because the calculation
considers one bubble in the fluid, whereas several bubbles
are generated in the experiment. It is found that smaller
initial bubble can expound in Fig. 19 to compare Fig. 18.
This means that smaller bubble can expand as
decompression rate increases. The effect of the
decompression rate on the bubble number density is
supposed to be the intensity of the tensile force induced by
the decompression rate. It is suggested that the bubble
nucleation in the experiments is caused by expansion of
existing minute bubbles.

Conclusions

In order to investigate the factor which effect on bubble
nucleation and growth in high viscous fluid under rapid
decompression conditions, the experiments are conducted.
And, numerical calculations to investigate the influence of
existing minute bubble are conducted.

Conclusions are as follows.

1) The bubble nucleation is observed despite volatile
substance is not contained in the test fluid.
2) It is suggested that volatile substance does not
influence bubble nucleation comparison with the
results by Fujii et al. (2008) and the present
experimental result.
3) It is suggested that existing minute bubbles may effect
bubble nucleation in comparison with the numerical
and the experimental result.
4) It is suggested that the bubble growth is depending on
surrounding pressure change dominantly.

References

Fujii, H., Fujiwara, A., Wakabayashi, N. and Abe, Y.
"Bubble forming behavior of high viscous fluid under rapid
decompression,"Transactions of the visualization society of
Japan, 28-5 (2008), pp.27-32. (in Japanese)

Massole, H. and Koyaguchi, T "The effect of magma flow
on nucleation of gas bubble in volcanic conduit," Journal of
volcanology and geothermal research, 143 (2005), pp.


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

69-88.

Shin-Etsu Chemical Co., Ltd. "Silicone oil KF96
performance test result," (2003).

Toramaru, A. "Numerical study of nucleation and growth of
bubbles in viscous magmas," Journal of geophysical
research, 100 (1995), pp.1913-1931.

Yamada, K., Tanaka, H., Nakazawa, K. and Emori, H. "A
new theory of bubble formation in magma," Journal of
geophysical research, 110 (2005), B02203.




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