Acoustic multibubble cavitation in water: A new aspect of the effect of a rare gas atmosphere on bubble temperature and its relevance to sonochemistry

Article abstract of DOI:10.1021/jp064598u

Acoustic cavitation generates transient microbubbles with extremely high temperatures and high pressures, which can provide unique reaction routes. The maximum bubble temperature attained is widely known to be dependent on the polytropic index and thermal conductivity of the dissolved gas. Here, we show for the first time experimental evidence that the bubble temperature induced by a high frequency ultrasound is almost the same among different rare gases and the chemical efficiency is in proportion to the gas solubility of rare gases, which would be closely related to the number of active bubbles.

Full text of DOI:10.1021/jp064598u

2
0081
2006, 110, 20081-20084
Published on Web 09/28/2006
Acoustic Multibubble Cavitation in Water: A New Aspect of the Effect of a Rare Gas
Atmosphere on Bubble Temperature and Its Relevance to Sonochemistry
Kenji Okitsu,* Takeru Suzuki, Norimichi Takenaka, Hiroshi Bandow, Rokuro Nishimura, and
Yasuaki Maeda
Graduate School of Engineering, Osaka Prefecture UniVersity, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan
ReceiVed: July 20, 2006; In Final Form: September 13, 2006
Acoustic cavitation generates transient microbubbles with extremely high temperatures and high pressures,
which can provide unique reaction routes. The maximum bubble temperature attained is widely known to be
dependent on the polytropic index and thermal conductivity of the dissolved gas. Here, we show for the first
time experimental evidence that the bubble temperature induced by a high frequency ultrasound is almost the
same among different rare gases and the chemical efficiency is in proportion to the gas solubility of rare
gases, which would be closely related to the number of active bubbles.
Introduction
Acoustic cavitation has seen diverse application in a number
(MB) cavitation induced by 200 kHz ultrasound in an aqueous
solution under rare gas atmospheres of He, Ne, Ar, Kr, and Xe.
Our report includes a new aspect of the cavitation phenomenon,
which is different from many previous reports.
1
-3
of fields, such as synthesis of nanostructured materials,
4
5
6
processing of biomass, sonofusion, sonodynamic therapy, and
sonochemical degradation of pollutants and hazardous chemi-
cals.7,8 Although new applications of acoustic cavitation continue
Experimental Details
to be developed, the physicochemical properties of the cavitation
bubbles, which are transient and locally formed in the liquid,
are still unclear. A quantitative and systematic analysis of several
Ultrasonic irradiation was performed with a 65 mmφ oscillator
KAIJO 4021 type, 200 kHz, 200 W). The details of the
(
irradiation setup and the characteristics of the reaction vessel
9-13
parameters, including the bubble temperatures
and pres-
3
are described elsewhere. In short, rare-gas-saturated aqueous
1
4
15
sures, number and size distribution of the bubbles, and the
solutions of 2-methyl-2-propanol (t-BuOH) at concentrations
1
6
behavior and dynamics, is required in order to control the
chemical effects of cavitation for application. Active research
has been carried out on estimation of the bubble temperature,
-1
of 1.0, 2.0, 4.0, 6.0, 8.0, and 10.0 mmol L were sonicated in
a water bath maintained at 20 ( 0.3 °C by a cold water
circulation system (TAITEC CL-150R). The bottom of the
vessel was made as flat and thin as possible (1 mm), because
transmission of the ultrasonic waves increases with decreasing
thickness of the bottom. The vessel was mounted at a fixed
position relative to the nodal plane of the sound wave (3.8 mm;
λ/2 from the oscillator). The gas products were measured with
a GC-FID (SHIMADZU). The bubble temperature was esti-
mated by the sonolysis of aqueous t-BuOH in the presence of
different rare gases. The cavitation bubble temperatures can be
estimated from the distribution of the sonolysis products of
C2H2, C2H4, and C2H6. The product ratio (C2H2 + C2H4)/C2H6
9-12,17
18-21
analyses of sonoluminescence,
reaction kinetics,
and
a computer simulation.22 These reports show that the bubble
temperatures are in the range between 4000 and 30 000 K, and
are dependent on a number of parameters, such as the ultrasonic
intensity, frequency, and nature of solvent. It has also been
reported that various physical and thermodynamic properties
of the dissolved gases (such as the polytropic index, thermal
conductivity, and solubility) could influence the bubble tem-
perature and cavitation efficiency.2
3,24
In sonochemical reactions, a rare gas is often used as the
dissolved gas due to its high polytropic index (Cp/Cv ) 1.67)
and chemical inertness; a high Cp/Cv value generates a high
is dependent on the bubble temperature, as previously re-
18-21
ported.
This product ratio is equal to the ratio k2/k1, where
2
3
temperature and gives a high reaction yield. In addition, it
has been reported that the temperature of the collapsing bubbles,
the intensity of the sonoluminescence, and the actual chemical
efficiency in every case follow the order He < Ne < Ar < Kr
14 -0.4
3
k1 (rate constant for 2CH3 f C2H6) is 2.4 × 10
T
dm
-1 -1
mol
s
and k2 (rate constant for 2CH3 f C2H4 + H2) is 1.0
1016 exp(-134 kJ/RT) dm mol s . C2H2 is formed via
the thermal reaction of C2H4.
3
-1 -1
×
9
,17,25,26
<
Xe.
To date, the existence of this order has been
thought to be due to the different thermal conductivities of the
rare gases, because these gases have the same Cp/Cv value.
Results and Discussion
Although there are many reports concerning the effects of the
Figure 1 shows the estimated bubble temperatures plotted as
a function of the thermal conductivity of each rare gas. It is
clear that the estimated bubble temperature is almost the same
(ca. 3900 K) among all the rare gases. The temperature estimated
under argon is also in good agreement with the reported values
dissolved gases on the cavitation efficiency,3
,9,17,20,25,26
quantita-
tive studies are still limited.
We describe here conclusive experimental evidence for the
bubble temperature and chemical efficiency of the multibubble
1
0.1021/jp064598u CCC: $33.50 © 2006 American Chemical Society

20082 J. Phys. Chem. B, Vol. 110, No. 41, 2006
Letters
less sensitive in aqueous solution than in organic solvents, which
have a lower vapor pressure.
(3) We note that the bubble temperatures estimated by
sonoluminescence are not comparable with those estimated by
the reaction kinetics, because the principle of each estimation
method is quite different. This opinion is in accord with a recent
2
1
report by Ashokkumar and Grieser. Strictly speaking, the
bubble temperature estimated by the sonoluminescence corre-
sponds to the peak temperature which is formed at the core of
the collapsing bubbles within a scale of picosecond time.27 On
the other hand, the temperatures estimated by the reaction
kinetics, such as the temperature dependent reactions of methyl
18-21
radical recombination,
provide average temperatures of the
bubble, where the reactions proceed over a longer time scale
and a larger volume compared to the sonoluminescence
phenomenon. We propose here that the bubble temperature
estimated by the reaction kinetics would be a more effective
monitor of the chemical efficiency of the cavitation bubbles,
because it should represent the actual temperature at which the
chemical reactions occur.
Figure 1. Cavitation bubble temperatures estimated in the presence
of different rare gases. Each error bar corresponds to the standard
deviation of the measured temperatures (N ) 6, one sigma).
for aqueous t-BuOH (3600 K)18 and aqueous benzene under an
argon atmosphere (4300 K).10 Until now, it has generally been
believed that the bubble temperature and chemical effect of
It is believed that the chemical effects of the cavitation are
dependent on the bubble temperature and follow the order He
cavitation would be strongly affected by the thermal conductivity
of the dissolved gas:9
,17,25,26
the greater the conductivity of the
<
Ne < Ar < Kr < Xe. However, our results clearly suggest
gas, the more heat would be dissipated to the surroundings,
effectively decreasing the bubble temperature. For example, the
temperatures estimated from the MB sonoluminescence at 20
kHz in Cr(CO6)/octanol solution, Xe (5100 K) > Kr (4400 K)
that the bubble temperature is approximately constant among
all of the rare gases.
To provide further support to the above discussion, the
cavitation efficiency was evaluated on the basis of the water
sonolysis. When an aqueous solution is sonicated, the following
reactions occur.
>
Ar (4300 K) > Ne (4100 K) > He (3800 K), were suggested
to be in the same order as the thermal conductivities of the
9
gases. The experimental data presented here have quite dif-
ferent features from the report of ref 9, namely, the thermal
conductivity of the rare gas does not appreciably affect the
bubble temperature, as seen in Figure 1. We can reasonably
explain our results taking into account the following three
factors.
)))
H O f OH + H (thermolysis)
(1)
(2)
(3)
(4)
2
2
OH f H O
2
2
(1) It is known that the bubble collapse time (as well as the
2H f H2
bubble lifetime) becomes shorter at higher frequencies. Ac-
cording to the report by Neppiras, the bubble lifetime at 200
kHz ultrasound is about 10 times shorter than that at 20 kHz
ultrasound,3 which in turn is dependent on the size of the
cavitation bubble. A relatively high frequency ultrasound is used
here, and thus, the collapse of the bubbles would occur by a
more adiabatic process because of the rapid collapse. Therefore,
it can be suggested that the effect of thermal conductivity on
the bubble temperature is negligible compared to that at lower
frequency ultrasound. In addition, the resonance bubble radius
at 200 kHz ultrasound is about 10 times smaller than that at 20
OH + H f H O
2
,23
where the symbol ))) corresponds to the ultrasonic irradiation.
The thermolysis of water molecules occurs due to the high
temperatures of the collapsing bubbles. OH radicals and H
atoms that are formed rapidly recombine to produce H2O2, H2,
and H2O. The yield of H2O2 can be related to the yield of OH
2
5
3
,28
radicals and hence the cavitation efficiency.
Figure 2a shows the yields of H2O2 under different rare gas
atmospheres, where the yields are plotted as a function of the
thermal conductivity of the rare gases. In the case of each rare
gas atmosphere (He, Ne, Ar, Kr, and Xe), it was observed that
the yield of H2O2 exponentially decreased with increasing
thermal conductivity of the gas. The yields are also plotted for
He/Xe mixed atmospheres, where the thermal conductivity of
3
,23
kHz ultrasound. Since the rate of cooling for larger bubbles
will be different from that for small bubbles, it is also suggested
that the effect of thermal conductivity may become pronounced
in a certain bubble size range.
(2) Suslick et al. reported that the estimated bubble temper-
ature in aqueous solution is lower than those in organic
solvents.10 They suggested that this phenomenon could be
attributed to the number of solvent molecules in the cavitation
bubbles; that is, larger numbers of solvent molecules in the
bubbles result in more endothermic reactions, such as the
decomposition of water molecules. In addition to this, the
presence of more solvent molecules within the bubbles will also
decrease the average polytropic index within the bubbles. Both
of the above-mentioned factors would decrease the bubble
temperature. In other words, a higher temperature cavitation
bubble is generally produced in a solvent with a lower vapor
pressure. Considering this point, we propose that the effects of
the rare gas property on the bubble temperature should become
each mixed gas is calculated on the basis of the solubility and
29,30
established method.
For example, in an 80:20 He/Xe
atmosphere, the ratio of these gases in water corresponds to
23.7:76.3 He/Xe taking into account the solubility of He (mole
-6 31
fraction to water, 7.04 × 10 ) and Xe (mole fraction to water,
-
6 31
90.5 × 10 ) in water. The average thermal conductivity of
-
1
-1
the gas mixture can be estimated to be 23.7 mW m
K
using
-
1
-1 31
-1
values of He (151 mW m K ) and Xe (5.62 mW m
-
1 31
29,30
K ) and eq 5 as given below:
km ) 0.5(ksm + krm)
where km is the thermal conductivity of a mixture and ksm and
(5)

Letters
J. Phys. Chem. B, Vol. 110, No. 41, 2006 20083
TABLE 1: Solubility and Thermal Conductivity of Rare
Gases and Rare Gas Mixtures
solubility
in water/
mole fraction
thermal
atmospheric
gas
gas ratio
in water
cond./mW
-
1
-1
m
K
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6 a
6 a
6 a
6 a
6 a
6 c
6 c
6 c
6 c
6 c
6 c
6 c
6 c
6 c
6 c
151b
49.3
17.9
9.42
5.62
He
7.04 × 10
8.39 × 10
27.5 × 10
50.4 × 10
90.5 × 10
b
Ne
Ar
Kr
Xe
b
b
b
He/Ar ) 10:90 25.5 × 10
He/Ar ) 20:80 23.4 × 10
He/Ar ) 40:60 19.3 × 10
He/Ar ) 50:50 17.3 × 10
He/Ar ) 60:40 15.2 × 10
He/Ar ) 80:20 11.1 × 10
He/Xe ) 20:80 73.8 × 10
He/Xe ) 40:60 57.1 × 10
He/Xe ) 60:40 40.4 × 10
He/Xe ) 80:20 23.7 × 10
He/Ar ) 2.8:97.2c
20.0
d
c
d
d
d
d
d
He/Ar ) 6.0:94.0
22.4
28.9
33.4
39.3
58.8
7.06
9.35
c
c
c
c
He/Ar ) 14.6:85.4
He/Ar ) 20.4:79.6
He/Ar ) 27.8:72.2
He/Ar ) 50.6:49.4
c
d
d
He/Xe ) 1.9: 98.1
c
He/Xe ) 4.9:95.1
c
d
He/Xe ) 10.5:89.5
13.5
23.7
He/Xe ) 23.7:76.3c
d
a
b
Estimated on the basis of ref 31 at 293.15 K and 1 atm. Reference
1 at 300 K and 1 atm. c Estimated with a linear mixing rule.
Estimated on the basis of refs 29 and 30, where the formation of
3
d
cavitation bubbles with the estimated gas ratio was assumed.
krm are the mean conductivities based on simple mixing and
reciprocal mixing, respectively:
ksm ) x k +x k
2 2
(6)
1
1
and
1
/krm ) x /k + x /k
1 1 2 2
(7)
where x1 and x2 are the mole fractions and k1 and k2 are the
thermal conductivities of each rare gas. The thermal conductivi-
ties estimated by eq 5 are summarized in Table 1. In the case
of the He/Xe mixture, the same tendency is observed for the
two curves in Figure 2a. To get more quantitative information,
a He/Ar mixture was used for the atmospheric gas (Figure 2b).
Although the yield gradually decreased as the thermal conduc-
tivity increased, there appears to be no direct correlation between
the thermal conductivity and the H2O2 yields. For example, at
-
1
-1
a thermal conductivity of 40-50 mW m K , the Ne
-1
atmosphere provides a yield of about 60 µmol L , whereas
-
1
the He/Ar atmosphere provides a yield of about 80 µmol L .
Figure 2c and d shows the H2O2 yields plotted as a function
of the solubility of the rare gases. A linear dependence between
the gas solubility and the H2O2 yields can be clearly observed
in both pure and mixed rare gases. This result would suggest
that the number of cavitation bubbles can be related to the gas
solubility. Figure 2c and d also shows that the H2O2 yield
follows the order He < Ne < Ar < Kr < Xe. A similar trend
has been reported in a previous study for the yield of spin-
trapped hydroxyl radicals. However, as described above, it
should be noted that the bubble temperature is the same among
all of the rare gases. Therefore, it is clear that the cavitation
efficiency is significantly affected by the amount of dissolved
gas in water.
2
5
The relationship between the gas solubility and the cavitation
efficiency presented here is also applicable to the discussion
given in previous reports. For example, Suslick et al. reported
the chemical efficiency of hydrodynamic cavitation under
32
-
Ar/He mixtures, where the rate of I oxidation decreased expo-
nentially as the thermal conductivity of the dissolved gas in-
creased. If the gas solubility were to be plotted along the x-axis
instead of the thermal conductivity, a clear relationship could
2 2
Figure 2. Concentrations of H O formed from the sonolysis of pure
water as functions of thermal conductivity of rare gases (a and b) and
solubility in water (c and d) under various rare gas atmospheres.
Conditions: temperature of bulk solution, 20 ( 0.3 °C; irradiation time,
-
3
0 min; (blue [), He; (green 9), Ne; (green 2), Ar; (green b), Kr;
also be observed between the rate of I oxidation and gas
(green [), Xe; (orange 1), He/Xe mixture; (red 1), He/Ar mixture.
solubility.

20084 J. Phys. Chem. B, Vol. 110, No. 41, 2006
Letters
We propose that, to determine the effects of thermal
(5) Taleyarkhan, R. P.; Cho, J. S.; West, C. D.; Lahey, R. T., Jr.;
Nigmatulin, R. I.; Block, R. C. Phys. ReV. E 2004, 69, 036109.
conductivity and solubility on the cavitation efficiency, both
parameters should be plotted, as shown in Figure 2. To our
knowledge, no reports have quantitatively measured the effect
of the gas solubility on the cavitation efficiency among different
rare gases. This may be due to the following reasons: (1) it
has been strongly believed that the thermal conductivity would
affect the bubble temperature, (2) the actual cavitation efficiency
was not investigated quantitatively, and (3) the relationship
between the gas solubility and the number of active bubbles
has not yet been understood correctly. This paper shows for
the first time conclusive experimental evidence that the bubble
temperature induced by a high frequency ultrasound is almost
the same among different rare gases and the cavitation efficiency
is in proportion to the gas solubility of rare gases, which would
be closely related to the number of active bubbles.
(6) Rosenthal, I.; Sostaric, J. Z.; Riesz, P. Ultrason. Sonochem. 2004,
1
1, 349.
7) Okitsu, K.; Iwasaki, K.; Yobiko, Y.; Bandow, H.; Nishimura, R.;
Maeda, Y. Ultrason. Sonochem. 2005, 12, 255.
(
(
(
8) Hung, H.-M.; Hoffmann, M. R. J. Phys. Chem. A 1999, 103, 2734.
9) McNamara, W. B., III; Didenko, Y. T.; Suslick, K. S. Nature
(
London) 1999, 401, 772.
10) Didenko, Y. T.; McNamara III, W. B.; Suslick, K. S. J. Am. Chem.
Soc. 1999, 121, 5817.
(11) Hilgenfeldt, S.; Grossmann, S.; Lohse, D. Nature (London) 1999,
(
3
98, 402.
(
(
12) Flannigan, D. J.; Suslick, K. S. Nature (London) 2005, 434, 52.
13) Camara, C.; Putterman, S.; Kirilov, E. Phys. ReV. Lett. 2004, 92,
24301.
(14) McNamara, W. B., III; Didenko, Y. T.; Suslick, K. S. J. Phys. Chem.
B 2003, 107, 7303.
15) Tuziuti, T.; Yasui, K.; Iida, Y. Ultrason. Sonochem. 2005, 12, 73.
16) Lauterborn, W.; Kurz, T.; Mettin, R.; Ohl, C. D. AdV. Chem. Phys..
999, 110, 295.
17) Young, F. R. J. Acoust. Soc. Am. 1976, 60, 100.
(18) Tauber, A.; Mark, G.; Schuchmann, H.-P.; von Sonntag, C. J. Chem.
Soc., Perkin Trans. 1999, 2, 1129.
19) Hart, E. J.; Fischer, C.-H.; Henglein, A. Radiat. Phys. Chem. 1990,
6, 511.
20) Nagata, Y.; Okuno, H.; Mizukoshi, Y.; Maeda, Y. Chem. Lett. 2001,
142.
(21) Ashokkumar, M.; Grieser, F. J. Am. Chem. Soc. 2005, 127, 5326.
1
(
(
It is suggested that the chemical effects of MB cavitation in
1
8,28,33
water are the highest in the frequency range 200-500 kHz.
(
Hence, the use of high frequency ultrasound should be of
significant interest in various research fields and industries.
Depending on the irradiation conditions, it is clear that various
types of cavitation dynamics need to be considered to explain
sonochemical reactions. For example, the gas solubilities in
(
3
(
3
1
water are much lower than those in organic solvents, sug-
gesting that the different cavitation dynamics should occur
between water and organic solvents.
(
(
(
(
22) Yasui, K. Phys. ReV. E 2001, 63, 035301.
23) Neppiras, E. A. Phys. Rep. 1980, 61, 159.
24) Henglein, A. Ultrasonics 1987, 25, 6.
25) Kondo, T.; Gamson, J.; Mitchell, J. B.; Riesz, P. Int. J. Radiat.
Acknowledgment. We acknowledge the support from 21st
century COE program of JSPS in Japan. We also acknowledge
Dr. Y. Nagata and Dr. M. Ashokkumar for their fruitful
discussion.
Biol. 1988, 54, 955.
(26) Didenko, Y. T.; Pugach, S. P. Ultrason. Sonochem. 1994, 1, S9.
(27) Bradley, B. P.; Putterman, S. J. Nature (London) 1991, 352, 318.
28) Koda, S.; Kimura, T.; Kondo, T.; Mitome, H. Ultrason. Sonochem.
003, 10, 149.
29) Reid, C. R.; Sherwood, K. T. The properties of gases and liquids;
McGraw-Hill Book Company, Inc.: New York, 1958.
(
2
(
References and Notes
(
30) Brokaw, R. S. Ind. Eng. Chem. 1955, 47, 2398.
(
(
1) Suslick, K. S.; Price, G. J. Annu. ReV. Mater. Sci. 1999, 29, 295.
2) Bradley, M.; Ashokkumar, M.; Grieser, F. J. Am. Chem. Soc. 2003,
(31) Kagaku Binran, II-66, II-156 (1993), Ed by The Chemical Society
of Japan, Maruzen, Japan.
(32) Suslick, K. S.; Mdleleni, M. M.; Ries, J. T. J. Am. Chem. Soc.
1997, 119, 9303.
(33) Okitsu, K.; Ashokkumar, M.; Grieser, F. J. Phys. Chem. B 2005,
109, 20673.
1
25, 525.
3) Okitsu, K.; Yue, A.; Tanabe, S.; Matsumoto, H.; Yobiko, Y.; Yoo,
Y. Bull. Chem. Soc. Jpn. 2002, 75, 2289.
4) Stavarachea, C.; Vinatoru, M.; Nishimura, R.; Maeda, Y. Ultrason.
Sonochem. 2005, 12, 367.
(
(