3rd European-Japanese Two-Phase Flow Group Meeting
Certosa di Pontignano, 21-27 September 2003

LAMINARIZATION OF MICRO-BUBBLE CONTAINING
MILKY BUBBLY FLOW IN A PIPE
Akimi Serizawa1, Tomohiko Inui1, Toshihiko Yahiro2, Zensaku Kawara1
1: Department of Nuclear Engineering, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan
Phone & Fax: +81-75-753-5829, E-mail: E-mail: serizawa@nucleng.kyoto-u.ac.jp,
2: Aura Tec Co., Ltd, 1725-2, Tsubuku-Honmachi, Kurume, Fukuoka 830-0047, Japan
Phone: +81-942-32-2504, Fax: +81-942-38-3806, E-mail: yahiro@kumin.ne.jp
ABSTRACTMicro bubble technology has become to attract people’s concerns due to its wide potential in practicalapplications to a variety of advanced and conventional science and technologies. However, our knowledge of micro
bubbles containing bubbly two-phase flow is almost nothing. We developed a specially designed nozzle which
generates high intensity micro air bubbles (mean diameter~ 40microns, number density more than 2×105/cc). Using
this micro-bubble generator, we carried out, as a first step, a measurement of two-phase frictional pressure drop,
cross-sectional average void fraction and liquid velocity profiles. The measurement of local void fraction isunderway. The range of average void fraction was up to 0.6 % which is enough to realize milky bubbly flow. The
most exciting result we found is that the two-phase flow becomes laminarized by injecting such ultra small bubbles
into the water flow. For 0.3~0.5% void fraction, laminar-turbulent transition occurred at Re=10,000~20,000. The
cross sectional averaged void fraction does not follow a homogeneous flow model, and radial liquid velocity profile
was a little bit flattened. The mechanism of flow laminarization and flow structures are now being pursued.

1. INTRODUCTION
Practical applications of micro bubble technology haverecently become to attract people’s great concerns in wide
variety of areas in advanced and conventional science andtechnologies, such as energy conversion and heat removal
devices, diagnosis by ultrasound echo due to micro bubble
collapse, drug delivery systems, cleaning and sterilization byshock waves due to the collapse of high pressure micro bubbles,
production of ozone water, mining using physical absorption at
gas-liquid interfaces, purification and improvement ofoil-contaminated soil and polluted water by air supply (sea,lake, river etc), absorption of carbon dioxide gas, fish culture,etc. Here, the micro bubbles may be defined as the bubbles
with diameters of the order of less than several tens microns,since these sizes of bubbles exhibit in fact somehow different
behaviors from those observed with ordinary sized bubbles intheir chemical and physical aspects.

Macro scales Λl, Λg (cm)10

Up to now, much attention has been focused merely on theapplication of micro bubble technology and methods of micro
bubble generation. Hydro-dynamic behaviors of micro bubbles
containing two-phase flow unfortunately received much lessattentions. For example, our current understanding of turbulent
structure of bubbly two-phase flow is limited to the flows
where the size of bubbles in the flow generally stands between
the integrated turbulent scale and micro turbulent scale, as
indicated in Figs.1 and 2 (Michiyoshi & Serizawa [1]). The
size of micro bubbles is however smaller than micro turbulent
scale. It is therefore anticipated that the bubbles with diametersmaller than the micro turbulent scale may exhibit different
behaviors from those shown by ordinary sized

0.1<jL>(m/s)

5

0.45
0.61
0.77

1

0.5

Open symbols: longitudinal Λl
Solid symbols: lateral Λg
0.1
0.01

0.05 0.1
Average void fraction α

0.5Micro scales λ l, λ g (cm)Figure 1 Macro Scale of Turbulence [1]Open symbols: longitudinal λl
Solid symbols: lateral λgλl<jL>(m/s)

λg

0.61

0.45

0.77

0.01
0.01

0.1
Average void fraction α

Figure 2 Micro Scale of Turbulence [1]bubbles, specifically in the way of hydrodynamic interactions
with the flow and thus the two-phase flow structures may bechanged, as suggested by Fig.3 (Serizawa & Kataoka [2]).
With this in mind, we aim at clarifying turbulent structures of
air-water milky bubbly flow in a pipe which contains very finebubbles of the order more or less 50 microns.
Liquid & Gas
Flow Rates

BubbleInjector

Fluid
Properties

Statistical natureof bubbles at inlet
Geometry
Bubble-bubble interaction
Bubble-flow field interaction
Statistical nature of bubbles
at cross -section of interest

Spatialdistributionof phases
Turbulence
structure

Figure 4 Collision of Two Micro Bubbles (~50microns)
distance L

Interfacial
structure

Bubble 2

Bubble 1
Figure 3 Flow Chart of Bubbly Flow Development
FB

Interaction force

2. WHAT IS A MICRO BUBBLE AND HOW TO MAKE
MICRO BUBBLES
2.1 Bubble behavior
Micro bubbles with diameters smaller than several tens
microns are supposed to have the following features:(1) large interfacial area concentration for given void fraction.
(2) very low rise velocity-long residual time in liquid phase(3)
very low possibility of bubble coalescence-gooddispersion character and mixture homogeneity(4) dissolving character into liquid – bubble life (depending on
the method of micro bubble generation)(5) low electrical potential – good for physiological activation(6) physicochemical properties(7) acoustic properties(8) fluid dynamic properties – reduction in skin friction, etc(9) others
As stated earlier, our concerns are focused on(1) what are bubble-turbulence eddy interactions ?
(2) what are bubble-bubble interactions ?
Based on a visual observation using a microscope, we foundthat micro bubbles behave like solid particles without
significant shape deformation when they collide to each other(Fukami [3]). A series of pictures showing this aredemonstrated in Fig.4. From this finding, we speculated on the
micro bubble motions by numerical experiment, and we cameto a hypothetical bubble-bubble interaction force model which
considers the effects of two major forces acting on two micro
bubbles approaching to each other (Matsumoto et al.[4]).
These forces are working in an opposite direction to each other,in attracting and repulsing directions, respectively, dependingon the distance between the two approaching micro bubbles

Rb

FB

ρ *
C
n
Ps
Rb2− m Lm ρFB =Figure 5 bubble-Bubble Interaction Model [4](see Fig.5), and are given by Esq. (1) and (2).
C1FB ( xs ) =2

LCF ( xs ) =

2

B

n

ρ
ρ

Ps

ρ
n

LRb

ρ

P
s

*

(for L≤ 5R)(1)*(for L> 5R)(2)

where Rｂ, L and xs are radius of micro bubbles, the distance
between two adjacent micro bubbles and surface position,
respectively. C1 and C2 are constants and n(xs) is a normal
vector to the surface at x s . Here,ρ = ∑ Fm ρ m(3)m

ρ = (ρ1 + ρ 2 ) / 2(4)

and Fm and ρm are volume fraction and density of the i-th phase,*respectively. Ps is the surface pressure based on the bubble
radius Rb.
These forces appear in the momentum equation with theCSF (Continuum Surface Force) model [5] in the interface
tracking solver MARS [6] as∂u∂t+ (u ⋅ ∇ ) u = G −where the operator

1ρ( ∇P + ∇ ⋅ τ − F )v , total(5)

2.2 Methods of micro bubble generation

represents a spatial averaging.

The total surface tension force Fv,total at the certain surface
position x s can be expressed as:

Fv ,total = Fv ( xs ) + FB ( xs )(6)

where the nominal surface tension force based CSF model isgiven by
FV ( xs ) = σκ ( xs ) n ( xs )

ρ
ρ

(7)

where the surface curvature at x s , κ ( x s ) , is obtained by unit
normal vector calculated from the F values of surrounding cells
as follows:κ=

1  n ⋅ ∇  n − ( ∇ ⋅ n ) 
n  nvalidated theoretically yet, this bubble interaction force model
predicts well the bubble-bubble interaction as shown in Fig.6.

(8)There are so many methods of micro bubble generation so far
proposed. In general, all of the existing or proposed methods
use a combination of either two or three among depressurizeation of air-saturated water, bubble break-up by shear force
and cavitation. Some of the typical examples are shown in
Fig.7. We tested all of these devices and others bycomputer-aided visual observation of micro bubble diameter
distributions (Serizawa et al.[7]). We eventually came to aconclusion that our developed device “cavitation nozzle”
showed the best operational performance in terms of the mean
bubble diameter, standard deviation in bubble size distribution
and bubble number density (Fig.8).
A question is raised as to the maximum void fraction
attained with various methods of bubble generation. Small
bubble number density of micro bubbles results in low void

Here, n is the norm of n .
It is thus assumed in this model that the interaction forces
act on the bubbles in two different ranges: the long range( L > 5 Rb ) (attracting force) and the short range ( L ≤ 5 Rb )(repulsion force). In the short range, the interaction force
works like a Coulomb force resulting from a dipole moment at
surfaces, proportional to L-2. Whereas in the longer range, thisforce is interpreted as a non-local force like a force originatingfrom pressure propagation caused by rapid change of the
bubble shape, i.e., resulting from the effect of liquidcompressibility due to pressure waves caused by interface
deformation of neighboring bubbles. This force is supposed tobe related to thermodynamic processes for the surface excessenergy at the interface and thus proportional to surface
curvature of the bubbles (~1/Rb). Although these forces are not(a) Swirl Flow Type(c) Cavitation Nozzle
air
water

(d) Venturi Type(b) Aura-Jet(e) OHR Mixer

Figure 7 Various Designs of Micro Bubble Generation

PDF (arbitrary unit)

mean diameter= 37.2 µ m

0

0

50

100

mean diameter= 72.2 µm

0
150 0

50

Bubble diameter (µm)

Cavitation Nozzle

Venturi

50

100

150

mean diameter= 79.6 µm

mean diameter= 48.8 µm

0100

Bubble diameter (µm)

150 0

50

100

Bubble diameter (µm)

Bubble diameter (µm)

Swirl Flow Nozzle

OHR

150

Figure 8 Bubble Size Distribution with Different Devices
Figure 6 Comparison between Prediction and Observation

fraction, and thus we cannot realize milky bubbly flow in a
flowing system. Figure 9 shows a diagram of bubble diameter(µm) versus bubble number density (bubbles/cm3) obtained byconventional bubble generation methods [8]. Figure 10 shows
the maximum void fraction estimated from the envelop shownin Fig.9 [9].

Bubble number density (bubbles/cc)

After a long struggle with high density micro bubble
generation methods, we found that our developed cavitation
nozzle successfully satisfies the requirements for beautiful
milky bubbly flow in a pipe, giving up to 0.6% void fraction
for a wide range of liquid velocity condition (Fig.11).

Depressur-ization

GALF(depressurization)envelop
Mixingvane

EjectorPorousBubble diameter (µm)

the water flow through a ventury-type nozzle equipped at adowncomer just before a high-pressure pump. The air
dissolves partially into the water flow and is depressurized by amicro bubble generator nozzle to form micro bubbles
containing milky bubbly flow along with cavitation bubbles.
The mean diameter of micro bubbles is roughly 40 µm
throughout measurements with a negligible change of bubble
size along the flow direction. The water flow in the test section
was adjusted mainly by a bypath flow to keep the void fraction
at a constant value irrespective of liquid flow rates. The micro
air bubbles are separated from the water at the top of the test
section by using three-stage swirl flow-type separator which is
our original design (Fig.13).
The test section is a 4m long transparent acrylic circular pipewith 20 mm in inner diameter. We measured two-phase
frictional pressure drop by using a monometer over a 1m long
distance starting at roughly 2m downstream of the micro
bubble generation nozzle. The cross-sectional average void
fraction was precisely measured by two-phase mixture mass
which was sampled in a 500 cc bottle submerged in a samplingtank equipped at the exit of the test section. The sampled
mixture mass is measured by a high-precision electronicbalance. The accuracy of void fraction measurement (∆α/α)
was within about ± 5%. The local liquid velocity profile inradial direction was measured at a 3m elevation from the micro
bubble generation nozzle with a calibrated Pitot tube based ona continuous squeeze model given by the following equation.

Figure 9 Bubble Diameter versus Bubble Number Density [8]Average void fraction (%)

∆pk

u=k

100

(9)

ρ (1 − α 2 )where u, k, ∆pk, α and ρ are liquid velocity, calibration
10

separator
1

sampling tankstorage tank
1

10

100
Bubble diameter (µm)

1000

Figure 10 Maximum Void Fraction versus Bubble Diameterpressure drop
measurement

1000mm0.1

bypath line
test section
flow meter

Figure11 Cavitation Nozzle and Micro Bubble Generation

micro-bubble
generatorpressuregauge

single-phaseflow linepump
air suction

3.

EXPERIMENTAL APPARATUS

Figure 12 shows a schematic of air-water test loop used in
the present work. The working fluids are deionized water andthe air supplied from a gas bottle. The air flow was adjusted at
the desired values by a flow control valve, and was sucked intopump

two-phase flow line

Figure 12 A Schematic of Two-Phase Flow Test Loop

G:gas), radial position and tube radius, respectively. The
suffixes c and w represent the values at tube center and at thewall, respectively. The exponents m and n are experimentally
determined constants. Then, we have the following equation
for the distribution parameter C0 .

String-like air flow (core) +water flow (outer region)

Micro bubblewater mixture
flow

Figure 13 Micro Bubble-Water Separation
coefficient of the Pitot tube, measured dynamic pressure, local
void fraction and liquid density, respectively. The local void
fraction measurement within good accuracy is a very difficult
job, since the order of magnitude of void fraction is more orless 0.1~0.6%. We are now trying to carry out local void
fraction measurement by using a sampling probe method.
4. EXPERIMENTAL RESULTS AND DISCUSSIONS
4.1 Cross-sectional average void fraction
Figure 14 shows the measured void fraction 〈α〉 against
volumetric air flow ratio β. Contradictorily to our intuition,
the experimental evidence suggests that the cross-sectional
average void fraction follows a slip flow model with slip ratio
S = 1.4, that is,

α = 0.702 β

j
jc

( R)

α − αw(11)( R)= 1− rn(12)

In view of the negligibly small quality (gas content) of micro
bubbles containing milky bubbly flow, we may well define thetwo-phase friction factor fm and the two-phase Reynolds
number Re in the same way for single-phase flow:∆Pf<jL> (m/s)
2 .0 6

1 .3 5

1 .7 0

1 .0 2<α>= 0.702 β

1 .4 6

0.4
0.2
0

l

0

0.2

= fm

Re =

ρ jL

2

(15)

2D

ρ jL D(16)µ

where ∆Pf , l and µ are frictional pressure drop over the lengthl , the distance between the two pressure taps and liquid
viscosity, respectively.
Figure 15 represents the measured two-phase friction factor
versus the two-phase Reynolds number diagram. Here thefriction factors in laminar and turbulent flows given by thefollowing equations are referred to.
0.1<α> = 0.833 β (Armand’s correlation)

0.6

(14)

4.2 Two-phase frictional pressure drop<α> = β (homogeneous flow)

0.8

(13)

Eq. (14) can be of course obtained straightforward from thedefinition of Co as well. From this argument, theexperimentally observed value of C0 = 1.42 is never consistent
with uniform void distribution whatever the liquid velocity
distribution is. To make clear the reason, we have to measure
the phase distribution profiles.

0.4
0.6
0.8
1.0
Volumetric air flow ratio β（％）

Figure 14 Void Fraction Measurement

Two-phase friction factor f m

Measured void fraction < α> （％）αc − αwmj αw 
1 − α 
m+n+2
2

C0 = 1(10)= 1− rα= 1+

For uniform void fraction distributions, we have <α>= αw and
n=0, irrespective of the value of the void fraction. Then,
Eq.(13) yields toThis equation is equivalent to a drift flux model equation withthe distribution parameter C0 = 1.42 and negligible voidweighted area-averaged drift velocity. Let us assume thefollowing exponential laws for local void fraction and total
flux distributions, where α, j, r and R are local void fraction,
local total volumetric flux (= jL + jG) (the suffix L: liquid ,

1.0

αj

C0 =

Re=12000
0.05
turbulent flow

laminar flow<α> (%)
0
0.2
0.3
0.5

0.01

0.005
500

1000

Re=22000

5000 10000
50000 100000
Two-phase Reynolds number Re

Figure 15 Measured Single- and Two-Phase Friction Factors

Laminar flow:

f m = 64

(17)

Re

Turbulent flow: f m = 0.3164 Re

−0.25

(18)

It has been confirmed that the single phase flow changed
from laminar flow to turbulent flow at the Reynolds number Re= 2,300 ~ 2,500 as usually observed.
The most exciting and important finding in this work isevidence that the two-phase flow becomes laminarized byinjecting micro bubbles into the water flow. For 0.3 ~ 0.5 %void fractions, the laminar-to-turbulent transition initiated at
the Reynolds number Re = 10,000 ~ 12,000, as clearly
indicated in Fig.15. It is also noted that the flow laminarization takes place even at such low void fraction as 0.2%. A
similar flow laminarization has been reported to occur by anaddition of either surfactant or polymer solution or fiber. The
mechanism of flow laminarization which has been observed in
the present work has not yet been clarified. However, we canfind some statements as below which might be useful to pursue
the mechanisms involved.
Marie [10] proposed an analytical model to explain the
reduction of skin friction caused by small bubbles in the wallboundary layer. His conclusion is that micro bubbles are sosmall that they can penetrate into the buffer layer, affecting the
turbulence in the buffer layer, and thus causing a change of
certain physical properties of this layer. In practice, the dragreduction by bubble injection has been a topic for shipbuilders.
Usually this type of researches has been conducted by using
normal sized air bubbles instead of “real micro bubbles”. A
significant drag reduction has been reported so far. But themechanism has not been clarified yet. We carried out a similar
experiment for drag reduction using a model ship (2400mm
long, 400mm wide acrylic boat) and “real micro bubble”
injection with a cavitation nozzle similar to that used in thepresent experiment (Fig.16). Results indicated no reduction indrag coefficient caused by micro bubble injection, but up toroughly 5% reduction in drag coefficient was brought about by
much larger air bubbles (approximately a few mm ~ 10 mm indiameter) at ship velocities even lower than 1.4 m/s (Serizawa
et al.[11]).

Another statement comes from the work by Rashidi etal.[12]. It is well known that when the shear rate is increased ina boundary layer near the wall, high speed and low speed
regions alternately appear near the boundary.
This
low-speed/high-speed flow pattern results from counterrotating streamwise vortex pairs that are broken up
periodically near the wall, thus initiating bursting process. Thisbursting process is a randomly occurring event consisting of a
gradual local liftup of low-speed streaks, sudden oscillationand ejection of low-momentum fluid from the wall region intomain stream. This is then followed by a sweep ofhigh-momentum fluid into the wall region. This bursting
phenomenon was shown to be responsible for most of
turbulence energy production and to be the major contribution
to the transport of Reynolds stresses. Their particle-laden fluid
experiments and visual observation showed that the particles
can penetrate into the viscous sublayer because of their small
size and large momentum, and they tend to accumulate in the
low-speed streaks of the wall structures, as shown in Fig.17.
These particles are then lift up (depending on their size anddensity) by the inclined vortex-loops of the wall region and areejected into the bulk flow. Therefore, the frequency of the wall
ejection and the streak velocities are influenced by particle
loading. Rashidi et al. observed that the large particles (1100µm polystyrene particles) caused an increase of the number ofwall ejections and enhanced turbulence intensities andReynolds stresses. On the other hand, the smaller polystyrene
particles (~120 µm) caused a decrease in the frequency of wall
ejection, giving lower turbulence intensities and Reynolds
stresses. This effect is reported to have been enhanced as
particle loading was increased. Although the micro air bubbles
have much smaller momentum compared to the solid particles,
micro bubbles injection into the water flow may affect theprocesses of sweep and ejections.

x

Accelerationof flowu ( y, t )“breakdown”

lo w

-s p

ejections
ee

ds

t re

ak

y+
60
40

formation of
low-speed streaks

20

oxygen-bubble
marker lines

Mirror image (upper half)
airdirection of ship motion
water surface∆ x + ∼ 1000 Counter-rotating
vortices∆ z + ∼ 50z
Fig.17 Mechanism of Ejection and Particle Transport
near the Wall (Rashidi et.al.[12])ship model
Cloud of micro bubbles
water
Figure 16 Drag Reduction Experiment using a Model Ship in
Water Pool [11]4.3 Liquid velocity
Laser Doppler anemometry and hot film anemometry are
typical and powerful tools to measure local liquid velocity in
gas-liquid two-phase bubbly flow. However both of thesetechniques are not available for micro bubbles containing
milky bubbly flow. Firstly, the micro bubbles containing milky

Figures 18 and 19 show liquid velocity profiles in radial
direction for single-phase and two-phase milky bubbly flows at
the Reynolds number = 12,000 and 22,000, respectively. These
values of the Reynolds number are indicated with solid lines in
Fig.15 just for reference. By recalling that, in milky bubbly
two-phase flow cases, the laminar-to-turbulent transition
occurred roughly at Re ≈ 11,000 for α = 0.3% and α = 0.5%,
Re = 12,000 corresponds to nearly laminar flow condition and
Re = 22,000 corresponds to almost turbulent. As can be noticed
from these figures, the single–phase water flow follows the 1/7
power law at both Reynolds numbers. On the other hand, inmilky bubbly two-phase flow cases, i.e., α = 0.3% and α =0.5%, there is a slightly different trend observed between the
two Reynolds number cases. At Re = 12,000, the liquid
velocity profiles become slightly flattened with being
decelerated in the center portion of the tube and being
accelerated in the wall region. This trend agrees with theexperimental tendency observed in air-water bubbly flow
consisting of ordinary sized bubbles (2 ~ 5 mm in diameter)(Serizawa et al. [13, 14]). On the other hand at Re = 22,000, theliquid velocity profile does not change for different void
fraction <α> but follows the 1/7-power law.
These observed trends in liquid velocity profiles are notinconsistent with the arguments about the <α> versus βdiagram described in section 4.1. This speculation leads to ahypothesis that micro bubbles may collect to the center portionof the flow passage where the liquid velocity is high. This

Liquid velocity u (m/s)

1.0

1.5

Liquid velocity u (m/s)

bubbly flow is not optically transparent because of very highbubble number density (105 ~ a few mega bubbles/cc).
Secondly, the two-phase mixture contains so small bubbles
that the hot film sensor is easy to be covered by such bubbles
attached onto the sensor, yielding to an unstable and fabulous
operation. We therefore decided to use a very classical method,that is, a Pitot tube based on a continuous squeeze model
expressed by Eq.(9)1.0

Re = 22,000
<α> =

0 (%)

<α> = 0.3 (%)

0.5<α> = 0.5 (%)

0
-10

0

+10

Radial position r (mm)Figure 19 Liquid Velocity Profiles at Re = 22,000
4.

CONCLUSIONS

We successfully realized a vertically upward micro bubbles
containing milky bubbly two-phase flow in a 4m long, 20 mm
ID transparent acrylic tube. This air-water two-phase test loop
is equipped with a high performance micro bubble generating
nozzle specially designed and developed in collaboration with
Aura Jet Co. Ltd. This device generates micro bubbles withmean bubble diameter~ 40 µm and bubble number density
higher than 2×105 bubbles/ cm3. The maximum crosssectional average void fraction attained was about 0.6 %,which is large enough to realize milky bubbly two-phase flow.
In view of small bubble sizes compared with micro
turbulence scales in two-phase bubbly flow, we anticipate
different bubble-bubble interactions and bubble-turbulence
eddies interaction from those reported in earlier works aboutnormal sized bubbles, i.e., bubbles with 1 ~ 5 mm in diameter,
and hence different flow structures.
We measured cross-sectional average void fraction,
two-phase frictional pressure drop and local liquid velocity
profiles. The following conclusions have been drawn from thepresent work.
(1) The measured cross-sectional void fraction was correlatedby the following empirical equation:

Re = 12,0000.5

α = 0.702 β<α> = 0 (%)<α> = 0.3 (%)<α> = 0.5 (%)
0
-10

0

Radial position r (mm)+10Figure 18 Liquid Velocity Profiles at Re = 12,000
hypothesis meets the requirement for high slip ratio S = 1.4. In
order to confirm the validity of this hypothesis, the local void
fraction measurement should be preferably conducted.
However, this measurement is not an easy job at the moment
due to a lack of precise measurement techniques. We are now
trying to develop a method using a sampling tube, but we have
not reliable data yet.

This result is not necessarily consistent with our intuition
that the flow is rather homogeneous with negligibly small
slip in macroscopic character between the two phases. The
reason for this result has been discussed based on a drift
flux model and measured local liquid velocity profiles.
This speculation suggests non-uniform local void fraction
distribution in the flow channel. However this should be
confirmed and verified by experiment.
(2) Two-phase frictional pressure drop measurement clearly
exhibits the flow laminarization by injecting micro
bubbles into the water flow. This laminarization occurredat cross sectional void fractions larger than 0.2%.
Although the mechanisms for this phenomenon have notbeen made clear yet, we think this is a very exciting andimportant finding with respect to the enhancement of ourcurrent understanding of physics in bubble-turbulenceinteractions in bubbly two-phase flow. This finding shouldbe expected to be extended to new applications in micro
bubble technology as a functional or smart fluid.
(3) The local liquid velocity in milky bubbly flow follows
nearly a 1/7-power law at high Reynolds numbers inturbulent flow, and a little bit flattened profile in radial
direction at lower Reynolds numbers in near laminar flow.
However, neither parabolic nor near-parabolic profiles
have been observed under the flow conditioned covered in
the present

REFERENCES
1.
2.

3.
NOMENCLATURES
distribution parameter
constants
tube diameter
bubble-bubble interaction force
volume fraction of m-th phase
friction factor
nominal surface tension force
total surface tension force
volumetric flux
distance between two adjacent bubbles
ldistance between pressure taps
m, nconstants
nunit vector normal to surface
Ppressure∆Ppressure difference∆Pffrictional pressure dropR
tube radiusrradial coordinate
bubble diameter
Rb
Re
Reynolds number (= ρjLD/µ)uvelocity(x,y,z) coordinate systemsurface position
xs

Co
C1, C2
D
FB
Fm
fm
Fv
Fv,totalj
L

Greeks and operators
local void fraction
αvolumetric gas flow ratio (= jG/(jL+jG))βκsurface curvature
macro scale of turbulenceΛ
λmicro scale of turbulenceµviscosityρ
densitysurface tensionστ
shear stress<>area-averaging
SuffixL, G
liquid and gas phasesl, glongitudinal and lateral direction, respectivelyc, w
tube center and tube wall

4.

5.
6.
7.
8
9

10
11

12
13
14

Michiyoshi, I, and Serizawa, A., 1986, Turbulence in
two-phase bubbly flow, Nuclear Engineering and Design,
Vol.95, pp.253-267.
Serizawa, A, and Kataoka, I., 1987, Phase distribution in
two-phase flow, in Transient phenomena in Multiphase
Flow, edited by N.H. Afgan, Hemisphere Pub.Co., N.Y.,
pp.179-224.
Fukami, T., 2002, A study of hydro-dynamic characteristics of multiphase flow with micro bubbles, Masterthesis, Kyoto University (in Japanese)
Matsumoto, Y.,Fukami, T., Kunugi, T. and Serizawa, A.,
2001, Fluid-Dynamic Structure of Air-Water Bubbly
Flow with Micro-Bubbles, Proc. Of the 4th International
Conference on Multiphase Flow(ICMF-2001), New
Orleans, LA, USA, Paper No.332 (in CD-ROM).
Brackbill, J.U., Kothe, D.B. and Zemach, C., 1992, J.
Comput. Phys., Vol.100, pp.335-344.
Kunugi, T., 1997, Direct numerical algorithm for
multiphase flows with free surfaces and interfaces, Trans.
JSME, Ser.B., No.63, pp.1576-1584.
Serizawa, A. and Yahiro, T., 2001, Micro bubble nozzles
and their operation, Proc. of the Annual Meeting of theJapanese Society for Multiphase Flow.
Machiya, K., et al., 1994, Production of bubbly water andits applications, IDEC REVIEW, Izumi Electric Co. Ltd.,(in Japanese)
Serizawa, A., 2003, New aspect of two-phase flow –Application of Micro bubbles and its physics, Orally
presented at the 5th UK-Japan Seminar on Multiphase
Flow, April, 2003, Surrey University, Surrey, UK.
Marie, J.L., 1987, Modeling of skin friction and heattransfer in turbulent two-component bubbly flow in pipes,
Int. J. Multiphase Flow, Vol.13, No.3, pp.309-325.
Serizawa, A., 2003, A study on drag reduction with micro
bubble injection nozzle for application to ships, Report of
the Activities from Joint Research Projects, ResearchInstitute of Applied Mechanics, Kyushu University (inJapanese).
Rashidi, M., Hetsroni, G. and Banerjee, S., 1990,
Particle-turbulence interaction in a boundary layer, Int. J.
Multiphase Flow, Vol.16, No.6, pp.935-949.
A. Serizawa, 1974, Fluid Dynamic Characteristics of
Two-Phase Flow, Dissertation, Kyoto University.
Serizawa, A., Kataoka, I. and Michiyoshi, I., 1975,
Turbulence structure of air-water bubbly flow – II. Local
properties, Int. J. Multiphase Flow, Vol.2, pp.235-246.