7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Bubble Dynamics in the Presence of Gold Nanoparticles
Saeid Vafaei and Dongsheng Wen
School of Engineering and Materials Science, Queen Mary University of London, London, UK.
Abstract: This work investigates the dynamics of gas bubble in the presence of gold
nanoparticles and reveals some interesting phenomena. The presence of gold nanoparticle
significantly affects bubble dynamics such as the triple line and the instantaneous contact angle.
It is observed that nanofluids prevent the spreading of the triple line during bubble formation,
consequently the triple line is pinned somewhere in the middle of the tube wall during the rapid
bubble formation stage whereas it spreads to the outer edge of the tube for water. Compared to
the influence on bubble volume and bubble height, the influence of gold nanoparticles lies more
on the triple line area, which suggests a modified gassolidliquid interactions by nanoparticles.
In addition, the static measurement shows that gold nanoparticles modify the gasliquid surface
tension, which would affect bubble departure volume and consequently bubble frequency. A
good agreement between bubble shape inside the gold nanofluid and YoungLaplace prediction
is found for given bubble height and radius of the contact line.
Keywords: Nanofluids, Nanoparticles, Bubble Formation, Boiling, YoungLaplace Equation,
Surface Wettability.
Introduction
Interaction of gasliquidsolid at a triple line is a one of the most complicated physical
matters. The mechanisms of wetting behavior of pure liquid on the solid are still not clearly
revealed. The introduction of nanoparticles into a base liquid, or termed as nanofluids, makes it
more complicated. Many experimental studies have been conducted to understand and identify
the mechanisms of the effects of nanoparticles on contact angles [14], structuring phenomenon
[5], surface tension [67], and boiling heat transfer coefficient and critical heat flux [812].
Wasan and Nikolov [5] observed a particlestructuring phenomenon in the liquid film
meniscus region for latex spherical particles of diameter 1 m at 7% volume fraction, with a
surface charge of 0.8 ,C/cm2, through a reflectedlight digital video microscopy. The Brownian
motion of colloidal latex particles along the solid surface was measured and the period of
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
oscillation was found to be around 2 Hz. In addition, the probability density distribution
functions for disordered and ordered particles were plotted [5]. Theoretically, some analytical
work has shown that particles could spread the triple line to a long distance of 2050 times of the
particle diameter through a structural disjoining pressure as a result of the selfordering of
particles in a confined wedge. However the structural disjoining force only becomes significant
at relative high particle concentrations, i.e. over 20% volume fraction [13], and work best for an
equilibrium system. In spite all of those, no direct evidence of the influence of nanoparticles on
bubble formation has ever been reported. Beside, there are so many discrepancies in literature on
effects of nanoparticles.
The purpose of this study is to investigate the effects of nanoparticles inside the nanofluid on
the evolution and formation of bubble as well as bubble characteristics such as radius of contact
line, contact angle, and etc.
Experimental Setup
The effect of nanoparticles on the formation of bubbles is investigated both experimentally
and theoretically. In the experiment, air is injected through an orifice of 110 micrometer into a
pool of pure liquid and liquid suspensions of gold nanoparticles of 5 nm (see Figure 1) at the
quasisteady state under low gas flow rate conditions. The micro nozzle is submerged into a
square glass container in the size of 20 by 20 mm. The glass container is filled with nanofluid at
a height of 20 mm and open to the atmosphere under ambient temperatures. The air flow is
supplied by a pressurized air cylinder through a pressure reduction valve and flows vertically
into the orifice. The gas flow rate is controlled to be low enough to be able to neglect the shear
stress between the liquid and gas (see Figure 2). A highspeed video camera (1200 Frame/sec) is
employed to visualize the process of bubble formation, which allows one to capture the radius of
contact line and height of bubble (see Figures 34) during the bubble generation and detachment
process.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
20 nm
cv..
4'. .
: : "=
:= . .: i = .
4.
5., .
^... l'l1 i
"' rYl ^~~
1'::< C1^f^RL 
Figure 1. TEM samples of gold nanoparticles.
Cylinder Gas Flow Controller
Figure 2. Schematics of the experimental setup.
I^ :.,.
...:..r .,f
..,..".."9 '
,. '. % . . = .
...:. .. ,... .. . j ." ... .
i .. NN :,I"I
i ..!" :: .:" ''"' ".
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
1.1E04
1.0E04
9.0E05
8.0E05
7.0E05
6.0E05
5.0E05
0 0.25 0.5
Time (sec)
0.75
Figure 3. Variation of the radius of contact line of bubble in water and gold/water nanofluid with
time and gold concentration (0.254 ml/min).
2.5E03
2.0E03
1.5E03
1.0E03
5.0E04
O.OE+00
0.25 0.5
Time (sec)
0.75
Figure 4. Variation of the height
gold concentration (0.254 ml/min).
of bubble in water and gold/water nanofluid with time and
The captured images of bubble formation are imported into the software of a Drop Shape
Analysis System to measure the surface tension of gold nanofluid and water. The accuracy of
surface tension measurement of device is 0.0lmN/m. The nanofluid and water surface tensions
are measured, using six different bubble images. The surface tension of water and nanofluid
(2.18E4 w) were respectively 0.07238 + 0.002 and 0.06517 + 0.0012 N/m.
** *
*
*
*
Water 2.18E4 w *
* Water o 2.18E4w
Water o 2.18E4 w
*
o
o
o*
*
*
0* *Si *
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Bubble shape prediction
Knowing two parameters of the bubble such as height and radius of the contact line, the
Young Laplace equation is solved to predict the bubble shape and other parameters. The Young
Laplace equation is
dO 2 gz sin0 (
ds Ro cr g r
The YoungLaplace equation can be solved, with the following system of ordinary
differential equations for axisymmetric interfaces, to obtain the bubble shape.
dr
= cos (2)
ds
dz
= sin O (3)
ds
dV
= r2 sin 0 (4)
ds
where dV is the differential bubble volume. This system of ordinary differential equations
avoids the singularity problem at the bubble apex, since
sin 0 1
(5)
r ,=o R
Knowing two parameters of the bubble shape such as the radius of contact line, height of
bubble (see Figures 23), the system of ordinary differential equations (14) is solved to obtain
the axisymmetric bubble shape, using the following boundary conditions [1420].
r(0) = z(0) = 0(0) = V(0) = 0 (6)
The average gas flow rate is calculated by multiplying the bubble frequency and detached
bubble volume, Q,, = V The calculation can be seen in detail in reference 14.
In addition, a differential equation is derived based on a force balance analysis between
gas/liquid hydrostatic pressure, pressure raise due to gas flow rate, surface tension, and buoyancy
force on a slice of a bubble. An analytical expression is obtained by taking integral of the
differential equation over the whole bubble, which relates different bubble parameters such as
the contact angle, radius of contact line, and bubble volume [14]
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
2c 2
R0
Equation (7) gives an analytical expression between parameters of a bubble under low gas
flow rate conditions. This equation also shows that there are various forces acting on the bubble
including the buoyancy force, (p, pg)gV, the force due to the YoungLaplace pressure,
g 72, the hydrostatic force of the gas and liquid phase, (p, pg)gd2 8], and vertical
R0
component of the surface tension force 2cgrd rsin o.
Results and Discussions
For low gas flow rate, the surface tension and buoyancy forces are the dominant downward
and upward forces respectively at the bubble detachment period. Generally as surface tension
force decreases, the buoyancy force and therefore the bubble volume decrease [2123], however
different results are also observed. Some studies reported that as surface tension decreases, the
bubble volume increases as bubbles were allowed to grow further [24] or there is no effect on
bubble volume [2526]. The difficulty is that the effect of surface tension could be modulated by
some other experimental variables such as orifice diameter, gasliquidsolid physical properties
(affects the contact angle) and gas flow rate, whose effect is difficult to be assessed alone. It is
observed as the concentration of gold nanofluid increases, the bubble departure volume
decreases and bubble frequency increases. It is believed that such differences are partly
associated with the modification of gasliquid surface tension due to the presence of gold
nanoparticles.
Figure 5 shows the prediction of bubble shape with the YoungLaplace equation and
compares against of experimental data inside the 5nm gold nanofluid for a gas flow rate of 0.254
ml/min. An excellent agreement is observed between prediction of the YoungLaplace equation
and experimental data inside nanofluid except for a time period of t=400470 ms where the
contact angle reaches to minimum and start being increased again. There is a perfect match
between the YoungLaplace prediction and bubble shape inside water.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
o t498.28 ms o t=685.76 ms
2.0E03
1.5E03
1.OE03
N
5.0E04
O.OE+00
0.E+00 5.E04 1.E03
r(m)
Figure 5. Comparison between experimental bubble shape and prediction of YoungLaplace
equation at a flow rate of 0.254 ml/min (Exp: Dotted points, Prediction: solid lines). The
concentration of nanofluid is 2.18E4 w.
Figures 3 and 4 compare the variation of radius of contact line and bubble height inside the
water and 5 nm gold nanofluid. Reduction of bubble height might be related to decrease of
bubble volume as results of reduction of gasliquid surface tension due to existence of 5nm gold
nanoparticles in nanofluid. Promotion of the pinning behavior of bubble triple line is the one of
most significant phenomenon happens due to presence of 5nm gold nanoparticles inside base
liquid. This phenomenon can be seen in general inside Figure 6 and in detail in Figures 3 and 7.
Since the nanoparticles are well suspended inside nanofluid and there is no heating involved on
substrate, the modification of solid surface is negligible due to deposition of nanoparticles. The
low concentrations of nanoparticles exclude the possible contribution from structural disjoining
pressure as proposed by Wasan and Nikolov [5]. It is likely that the observed dynamics of the
triple line is related to the variation of the solid surface tensions due to the presence of
nanoparticles and consequently, promotion of the pinning behavior of triple lines. Further
mechanistic investigation is on going. Figure 8 illustrates the variation of the radius of contact
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
line with gas flow rate between water and 5nm gold nanoparticle concentration (1E4 w), which
shows that the existence of nanoparticles inside the nanofluid would affect the radius of contact
line of bubble more than the effect of gas flow rate.
Stainless Steel Tube
Figure 6. Comparison of the radius of contact lines of gas bubbles on top of a stainless steel tube
(outside radius 105 /w) between water (left) and 1E4 w gold/water nanofluid (right) at bubble
volume of 2.73 /l. Gag flow rate is 0.48 ml/min.
1.1E04
1.0E04
9.0E05
E 8.0E05
7.0E05 
6.0E05
Water o2.18E4 w
5.0E05
O.E+00 2.E09 4.E09
Volume (m3)
Figure 7. Variation of the radius of contact line of bubble in water and gold/water nanofluid with
bubble volume and gold concentrations (0.254 ml/min).
In general, bubble departs with a lower height when forming in a nanofluid. There is a weak
dependence of bubble departure height on the particle concentration, i.e. the bubble departure
height decreases slightly with the increase of nanoparticle concentrations. The decrease of
bubble height might be related to reduction of bubble volume departure as results of presence of
gold nanoparticles.
Figures 8, 9 and 10 show the variation of bubble contact angle with time, volume and gas
flow rate inside the water and gold nanofluid. It is clear that the existence of nanoparticles inside
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
the nanofluid has more effects than gas flow rate on contact angle. In general, the bubble contact
angle of all cases experiences a decrease and then increase period (see Figures 810). The
decrease period is not monotonic but a stepwise, i.e. an initial sharp decrease at the very
beginning when the bubble starts forming, then a nearly constant value period as the radius of
contact line is pinned, which followed by another sharp decrease period as the radius of contact
line start moving rapidly outward. Afterwards, the value of the contact angle starts increasing as
the effect of buoyancy becomes dominant, when the bubble being stretched until to the necking
and departure period. Though a similar trend is observed, the minimum contact angle is slightly
smaller inside nanofluids due to the presence of gold nanoparticles.
160
SWater o 2.18E4w
120
9o 80 8
40
40 
0
0 0.25 0.5 0.75 1
Time (sec)
Figure 8. Variation of the contact angle of bubble in water and gold/water nanofluid with time
and gold concentration (0.254 ml/min).
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
150
100
50
u !
O.E+00 2.E09 4.E09
Volume (m3)
Figure 9. Variation of the contact angle of bubble in water and gold/water nanofluid with volume
and gold concentrations (0.254 ml/min).
Water, 0.254 ml/min 1 E4w, 0.254 ml/min
A Water, 0.83 ml/min 1 E4w, 0.83 ml/min
150
120
90
6O
60 A A
A 0
30 0 0
0 I
O.E+0 0 2.E09 4.E09
0.E+00 2.E09 4.E09
Volume (m3)
Figure 10. Variation of the contact angle of bubble in water and gold/water nanofluid (1E4 w)
with volume and gas flow rate
Figure 11 shows variation of buoyancy force, (p, pg)gV, the force due to the Young
R0
with tiLaplace pressure, water and 5 nm govertical cona ponen t of the surface ension force r that as the
with time inside water and 5 nm gold nanofluid (1E4w). It can be seen in Figure 11 that as the
Water o 2.18E4 w
i *
r o
1
U
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
effect of buoyancy force increasing, the force due to Laplace pressure decreases and
consequently the dominant forces are vertical component of the surface tension and buoyancy.
For constant volume the buoyancy force is the same therefore as nanofluid concentration
increases, the radius of contact line and surface tension decreases and as results the bubble
contact angle has to increase. Figure 9 explains that the contact angle of same bubble volume
inside nanofluid is higher than that inside water as the effect of buoyancy force rising.
Vertical Componenet of Surface Tension Force
o Laplace Pressure Force
A Buoyancy Force
4.E05
S3.E05 *
2 2.E05 A
0 . *
U
1.E05 o o o
06m o
o A oo
O.E+00 , 6 
0 0.2 0.4 0.6 0.8 1
Time (sec)
Figure 11. Variation of force due to Laplace pressure, vertical component of surface tension, and
buoyancy with time and particle concentration for 0.254 ml/min gas flow rate. The black belong
to water and red to 1E4 w gold nanofluid.
Figure 12 compares the analytical prediction of bubble volume (see equation (7)) with the
predictions from YoungLaplace (see equations (14)) for 0.48 ml/min gas flow rate inside
nanofluid (1E4 w) and water, using bubble height and radius of the contact line as two inputs.
An excellent agreement is observed both inside water and nanofluid. The variation of bubble
departure volume and bubble frequency with nanofluid concentration can be seen in Figure 13.
The bubble departure volume decreases as nanofluid concentration increases and consequently
the bubble frequency increases.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
* Analytical Volume, 1E4w, 0.48 ml/min
Numerical Volume, 1 E4w, 0.48 ml/min
x Analytical Volume, Water, 0.48 ml/min
o Numerical Volume, Water, 0.48 ml/min
5.E09
E 4.E09
E 3.E09
5
2.E09
1.E09
^ 1.E09
OQ
O.E+00
0 0.1
0.2 0.3
Time (sec)
Figure 12 Comparison between bubble volume determined by Numerical solution of the Laplace
equation and analytical expression (equation 7), inside water and 1E4 w nanofluid concentration
(0.48 ml/min).
Volume o Frequency
4.5E09
4.0E09
3.5E09
3.0E09
2.5E09
O.E
+00
1.4
N
1r
I
1.3 >
C)
1.2
LP
U
a)
1.1
1
1.E04 2.E04
Gold Nanoparticle Concentration (w)
Figure 13 Variation of bubble departure volume and bubble frequency with nanofluid
concentration.
aa
0
*a<
o
0
1 0
0
o
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Conclusions
This work reports an ongoing study of bubble dynamics in the presence of gold nanoparticles,
and many interesting phenomena are revealed in this work, which includes
A unique pinning behavior of the triple line is identified by the presence of gold
nanoparticles
The instantaneous contact angle is found to be slight larger for gold nanofluids for a given
bubble volume
The combination of the above two contribute to an improved wettability by the presence of
gold nanoparticles.
The YoungLaplace equation can predict bubble shape well for given two experimentally
determined inputs.
The mechanisms investigation is ongoing with a focus on the modified solidliquidgas
interaction at the triple line area.
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