Advanced Observation and Modeling of an
Acoustic Cavitation Structure
R. Mettin, P. Koch, D. Krefting, and W. Lauterborn
Drittes Physikalisches Institut, Göttingen University,
Bürgerstraße 42-44, 37073 Göttingen, Germany
E-mail: R.Mettin@physik3.gwdg.de
Abstract. High power input of ultrasound to liquids causes acoustic cavitation. In typical
resonator set-ups cavitation bubbles form dynamic structures that result in an inhomogeneous bubble distribution. The pattern formation processes are still not completely understood, and a detailed observation requires fast recording facilities. With respect to a frequently found double layer bubble structure, this paper presents high-speed images and an
interpretation thereof in terms of the formation mechanism. It is found that bubbles cluster
between pressure node and antinode regions. A simulation by a particle approach based on
nonlinear bubble oscillations can reproduce this feature.
INTRODUCTION
It is well known that acoustic cavitation bubbles form structured patterns in many
cases [1, 2, 3] which results in non-uniform spatial distributions and effects. Main factors
contributing to this phenomenon are standing acoustic waves, acoustic forces on and
between bubbles (Bjerknes forces), and liquid streaming. In spite of the large number of
different applications and set-ups of ultrasound induced cavitation, recent observations
indicate that a number of prototype bubble structures exists. We see classification and
understanding of the patterns as a first step towards a better application and control of
acoustic cavitation. High-speed observations and modeling approaches on a microscopic
level are important tools for this project.
In this paper we report the high-speed observation of a specific double layer pattern
(“jellyfish” structure) that appears in lower frequency (20 50 kHz) standing wave resonators at an elevated sound intensity. The images reveal information about the pattern
and its bubble population, collapse phases, maximum sizes, number densities, and velocities. We give a schematic picture of our understanding of the generation mechanism
of the structure and finally show results from a particle simulation employing nonlinear
Bjerknes forces.
Nonlinear Acoustics at the Beginning of the 21st Century
edited by O.V. Rudenko and O.A. Sapozhnikov (Faculty of Physics, MSU, Moscow, 2002)
vol. 2, pp. 1003-1006
a)
b)
1 cm
FIGURE 1. a) Experimental resonator with transparent walls and transducers at the bottom. b) Side view
of several double layer structures (“jellyfishes”) in reflected light.
THE “JELLYFISH” STRUCTURE
Figure 1(a) shows the cuvette where the bubble figures have been recorded (demineralized water, volume 16.4(w) x 20.2(l) x 14.0(h) cm 3 ). The transducers work at
40 kHz and deliver up to 700 W acoustic power to the liquid. Hydrophone measurements give maximum pressure amplitudes at the antinodes of up to 600 kPa at 150 W. In
reflected light, the bubble structures somehow resemble jellyfishes, see Fig. 1(b). They
are more or less fixed in their vertical position, but can move horizontally (usually outward from the cuvette center). They typically consist of a double layer of filamentary
bubble clusters. Directly under the surface single layers can form. When a double layer
is recorded with short exposure time and at defined phase of the driving, an alternating
(antiphase) oscillation of the layers is revealed, as shown in Fig. 2.
0 us
6.25 us
12.5 us
18.75 us
25 us
31.25 us
37.5 us
43.75 us
FIGURE 2. Eight frame high-speed recording of a “jellyfish” structure with background lighting: antiphase oscillation between top and bottom layer is clearly visible. Frame width: 10 mm, interframe time:
6.25 µs (a quarter driving period), exposure time: 500 ns, acoustical power: 150 W.
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a)
b)
FIGURE 3. Two frames from a high-speed series looking from the top onto the structure (reflected light).
Frame width: 20 mm, interframe time: 12.5 µs (half a driving period), exposure time: 500 ns, acoustical
power: 215 W. First the lower (a), then the upper layer (b) is visible because of the antiphase oscillation.
air
Pa
water
λ
_
2
z
FIGURE 4. Schematic constitution of a “jellyfish” structure (vertical section). Below the
water surface a standing wave develops with
nodal planes (dashed horizontal lines) and
antinode regions (solid horizontal lines; the
pressure amplitude is indicated at the right). A
twin layer of bubbles is formed symmetrically
to a nodal plane. Directly under the surface,
single filaments appear together with a water
bulge. The figures have approximate rotational
symmetry with respect to the dash-dotted vertical line.
The antiphase indicates that the bubble
layers appear symmetrically with respect to a
horizontal nodal plane. The bubbles seem to
originate somewhere near that nodal zone and
move towards the antinodes, but well before
they reach them, they form filamentary clusters. A view from the top exhibits the lateral
structure (see Fig. 3). The regions of maximum
pressure amplitude are void of (visible) bubbles. A schematic plot with respect to the standing pressure wave is given in Fig. 4.
From recordings like Figs. 2 and 3, we
obtained the following (visible) bubble characteristics: number per layer: 200 1000, num
ber density: 1 20 mm 3 , typical maximum
radii: 20 50 µm (a few reach 100 µm), velocities up to 2 m/s, life times: one up to more than
8 observed cycles.
An explanation of the structure is possible if Bjerknes forces of nonlinearly oscillating
bubbles are considered. In contrast to the linear
case [1], pressure antinodes then become repulsive for small bubbles at elevated amplitudes
[4, 2, 3]. An additional assumption necessary
to explain the observed structures is a bubble
generation far from the pressure antinodes and
rather near to the nodal zones (i.e., between two
twin layers).
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A numerical simulation of the tracks of
many single moving bubbles (“particles” [6])
can mimic the “jellyfish” figure to a certain extent. In Fig. 5 we show one simulated layer under consideration of nonlinear primary [4] and
secondary [5] Bjerknes forces. Although parameters and scales are partly different here (as
they are fit to a different experiment), similarities to Figs. 2 and 3 are clearly visible.
z [mm]
-4
-6
-8
-10
4
2
y [mm]
0
-2
-4
CONCLUSION
High-speed observations of bubble structures, as well as suitable simulations, can help
to clarify the at times unexpected dynamics of
cavitation bubbles and their structures in strong
acoustic fields. In the case of the “jellyfish”
pattern, we gained more insight, and we hope
to understand more “species” of bubble structures in the future.
-4
-2
2
0
x [mm]
4
FIGURE 5. Simulation of one “jellyfish” layer
by a particle model (500 bubbles, rest radii at
start 2...7 µm, pressure antinode at (0,0,0), amplitude 150 kPa, frequency 22.5 kHz). All bubbles originate at once on a ring source near the
nodal plane, and all bubble positions are plotted
for a time span of 444 ms.
ACKNOWLEDGEMENTS
This work was supported in part by the European Union (INCO-Copernicus contract No. IC15-CT98-0141), the German ministry of research and technology (BMBF
project “Untersuchung von Kavitationsfeldern”) and Deutsche Forschungsgemeinschaft
(DFG Graduiertenkolleg “Strömungsinstabilitäten und Turbulenz”).
REFERENCES
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dynamics of acoustic cavitation bubble clouds,” Phil. Trans. R. Soc. Lond. A 357, 313-334 (1999).
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by a particle model,” Ultrasonics Sonochemistry 6, 25-29 (1999).
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