Cavitation bubble dynamics

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SONOCHEMISTRY
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Ultrasonics Sonochemistry 4 (1997) 65-75
Cavitation bubble dynamics
Werner Lauterborn *, Claus-Dieter Ohl
Drittes Physikalisches Institut, Universitiit Gdttingen, D-37073 GOttingen, Germany
Received 7 November 1996
Abstract
The dynamics of cavitation bubbles on water is investigated for bubbles produced optically and acoustically. Single bubble
dynamics is studied with laser produced bubbles and high speed photography with framing rates up to 20.8 million frames
per second. Examples for jet formation and shock wave emission are given. Acoustic cavitation is produced in water in the interior
of piezoelectric cylinders of different sizes (up to 12 cm inner diameter). The filementary structure composed of bubbles is
investigated and their light emission (sonoluminescence) studied for various driving strengths. © 1997 Elsevier Science B.V.
Keywords: Cavitation; Bubble dynamics; Sonoluminescence; Shock waves; High speed photography
I. Introduction
Cavitation is the name given to the phenomenon of
the rupture of liquids and the effects connected with the
motion of the cavities thus generated [1-8]. Cavitation
can be initiated by either setting up a tension in the
liquid or by depositing energy into it (Fig. 1). Tension
appears in fluid flow, such as with ship propellers,
hydrofoils, pipes and pumps. It also occurs in sound
fields in the underpressure cycle of the sound wave, such
as in shock wave lithotripsy and sonochemistry. Local
deposition of energy is brought about by heat transfer
in pipes or by dumping hot bodies into liquids (giving
rise to eventually explosive bubble growth). Not only
sound, but also light can cause cavitation by dielectrically breaking down the liquid or heating up absorbing
impurities fast. This effect is used in eye surgery and for
the study of the dynamics of cavitation bubbles.
Cavitation [
1
I tension I
I energy,ocol
depos t
Fig. 1. Classification scheme for the different types of cavitation.
* Corresponding author. Fax: + 49-551-397720
1350-4177/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved.
PH S 1 3 5 0 - 4 1 7 7 ( 9 7 ) 0 0 0 0 9 - 6
Elementary particles leave energy when crossing liquids
giving rise to bubble formation as seen in the bubble
chamber.
Cavitation is accompanied by a number of effects
having their origin in the dynamics of the bubbles
generated. Cavitation bubbles tend to collapse exceedingly fast, emitting shock waves and even light (sonoluminescence). They erode solid surfaces and induce
chemical reactions.
2. Spherical bubble dynamics
In acoustic cavitation many bubbles usually appear
simultaneously and influence each other. To investigate
the dynamics of a single bubble without interaction
from neighbouring bubbles, the method of optic cavitation, whereby a short pulse of laser light is focussed into
the liquid, has proven useful. Fig. 2 shows an experimental arrangement for photographing laser-produced bubbles at high speed and to record the sound (shock)
waves emitted. The Q-switched pulse of a ruby or
Nd:YAG laser (pulse width, for instance, 8 ns, energy
per pulse around 10 m J) is focussed into a cuvette filled
with water to produce a single bubble by tight focussing
with aberration-minimized lenses. The bubble produced
is photographed with either a high-speed image converter camera to resolve the fast collapse and rebound
phase or with other framing cameras, for instance a
rotating drum or rotating mirror camera for observing
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V~ Lauterborn, C-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65-75
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Fig. 2. Experimentalarrangement for producing single bubbles.
the whole life cycle of the bubble from generation to
the decaying oscillations.
Fig. 3 gives an example of a spherical bubble in
silicone oil and its subsequent oscillations taken at
50 000 frames per second with a rotating drum camera.
Time runs from top to bottom. The series starts with
the bright spot of the laser light from the breakdown
site (and a reflex). A hot plasma is generated that
expands forming a bubble. The bubble is seen as a dark
disk because the illuminating backlight is deflected off
the bubble wall and does not reach the camera.
Work is done during the expansion of the bubble
against the ambient pressure that stops the expansion
at some maximum radius. From there the bubble starts
to collapse, whereby the bubble contents (gas and
vapour) are compressed. Therefore, the bubble rebounds
to start its next cycle of expansion and collapse. Four
cycles are recorded in Fig. 3. Due to the ever-present
damping, in this case mainly viscosity and sound radiation, decaying oscillations are observed. As can be seen,
the collapse of the bubble is a very fast process. It can
only be resolved at higher framing rates - very high
framing rates. Fig. 4 gives an example of a photographic
series taken at 20.8 million frames per second with an
image converter camera of a nearly spherical collapse
of a laser produced bubble in water. As the maximum
number of frames per shot is only eight, four different
shots have been combined to one series. This is possible
due to the excellent reproducibility of the bubble size.
With this high framing rate the shock wave radiated
upon collapse is easily catched. One single shock wave
is observed. A similar shock wave is radiated during
breakdown and smaller ones are radiated during the
subsequent collapses of the bubble.
3. Jet formation
When a bubble is collapsing in a not spherically
symmetric environment the collapse changes in a
Fig. 3. Dynamics of a spherical, laser produced bubble in silicone oil
taken at 50 000 frames per second. Maximum bubble radius is about
1.5 mm.
W. Lauterborn, C.-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65-75
67
Fig. 4. Collapse of a laser produced spherical bubble in water far from boundaries taken at 20.8 million frames per second (48 ns interframe time).
Picture size is 1.5 x 1.8 mm.
Fig. 5. Bubble dynmaics near a flat solid boundary taken at 75 000 flames per second. Frame size is about 7.2 x 4.6 mm, the maximum bubble
radius is 2.0 mm and the distance of the bubble center at maximum from the boundary is d= 4.9 mm.
r e m a r k a b l e way. A flat solid surface n e a r b y causes the
b u b b l e to involute from the top (surface below the
b u b b l e ) a n d to develop a high-speed liquid jet towards
this solid surface. W h e n the jet hits the opposite b u b b l e
wall from the inside it pushes the b u b b l e wall ahead
causing a funnel shaped p r o t r u s i o n with the jet inside.
Fig. 5 shows a high-speed p h o t o g r a p h i c series of a
b u b b l e collapsing in water near a flat solid wall, t a k e n
at 75 000 frames per second with a r o t a t i n g m i r r o r
camera. The jet is m o s t visible in the first r e b o u n d phase
as the dark line inside the bright central spot of the
b u b b l e where the backlight can pass u n d i s t u r b e d
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W. Lauterborn, C.-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65 75
Fig. 6. Enlargement of a bubble with its jet.
through the smooth surface of the bubble. The funnel
shaped protrusion downwards is the elongated bubble
wall containing the jet that drives the elongation until
its energy is used up. Then the long tube of gas and
vapour becomes unstable and decays into m a n y tiny
bubbles. The main bubble surface snaps back to its
former locally spherical shape. Fig. 6 is an enlargement
of a bubble with a jet and its protrusion pointing to the
solid boundary.
Shock wave radiation is much more involved when
jet formation occurs. There are usually at least three
shock waves radiated, two from the jet and the third
(or more) when the bubble attains its minimum (or near
minimum) shape. This is documented in Fig. 7 where a
sequence of a collapsing bubble with jet formation has
been taken at 20.8 million frames per second with an
image converter camera. The m a x i m u m bubble radius
Rma x is 1.29 m m attained about 90 lam before the first
picture starts. The normalized distance 7 = R,,ax/d to the
boundary is 1' = 2.4, where d is the distance of the bubble
centre at maximum radius to the boundary. The first
shock wave is radiated when the jet hits the (inside
moving) opposite wall of the bubble from its interior.
The jet is so broad at its 'tip' that it contacts the lower
bubble wall at a ring above the lowest point, giving rise
to a torus-like shock wave. This 'jet torus shock wave'
W. Lauterborn, C.-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65-75
69
Fig. 7. Collapse of a bubble near a solid boundary (outside below each frame) taken at 20.8 million frames per second. Maximum bubble size is
1.29 ram. Relative distance to the boundary is ? =2.4. Radiation of three shock waves: jet torus shock wave (frames 8, 9, 10), tip bubble shock
wave (frames 10 and onwards), and main bubble shock wave (frames 13 and onwards). Picture size is 2.0 x 1.4 ram.
later combines to a single outgoing shock wave as the
shock torus must close u p o n expansion. The jet torus
shock thereby surrounds the bubble, becomes very weak
and soon ceases to be seen in the frames. The toms-like
shock wave f r o m the jet implies that, in addition to the
bubble becoming a torus by the jet impact, a separate
tiny bubble ('tip bubble') must be created between the
jet °tip' and the curved lower bubble surface. This bubble
will be compressed further by the jet and the ongoing
bubble collapse giving rise to a second shock wave to
be seen in frame 10 o f Fig. 7 and in the subsequent
frames. This 'tip bubble shock wave' definitely emanates
from the lower bubble wall as seen by the asymmetric
propagation in relation to the bubble shape. The collapse
of the tip bubble is m u c h faster than the collapse of the
main bubble and gives rise to the conjecture that it m a y
be the violent compression of this part o f the main
bubble that is responsible for sonoluminescence (see
Section 5). In shock collapsed cylindrical bubbles in
gelatine this indeed has been observed in Ref. [9]. In
frame 13 the bubble is at or near its m i n i m u m volume
and emits a third shock wave seen detaching from the
bubble in the subsequent frames. The collapse o f the
main bubble is thus the latest in this series o f shock
waves. The main bubble collapses in the form o f a torus
whose stability u p o n collapse m a y be questioned. Thus,
several shock waves m a y emanate from the bubble torus.
The b r o a d shock 'front' seen in the last row o f Fig. 7 is
an indication that this in fact m a y have happened. The
protrusion sticking upwards out o f the bubble (see the
last frames o f Fig. 7), formerly called counterjet by us,
is presumably the result o f microcavitation inside the
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hydrophone
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Fig. 8. Cylindrical transducer of piezoelectricmaterial to cavitate a
liquid in its interior.
jet. The jet shock waves not only propagate into the
liquid below the bubble, but also backwards through
the jet. Thereby they are reflected off the jet wall as
tension waves. These waves are assumed to produce
cavitation inside the jet. Therefore, almost no outgoing
shock is seen above the bubble that actually has the
shape of a torus after the jet has hit the bubble from its
interior. This complex series of events is typical for the
asymmetrical collapse of a bubble with jet formation.
4. Acoustic cavitation
Acoustic cavitation can be produced in a variety of
ways, such as with a vibrating 'horn' dipping into a
liquid or by vibrating the walls of a container. We used
a hollow cylinder of piezoelectric material submerged in
the liquid to be cavitated (Fig. 8). The cylinder had a
length and inner diameter of 76 mm and a wall thickness
of 5 mm. The resonance frequency for half a wavelength
across the diameter of the cylinder was about 23 kHz,
slightly dependent on the container and the water height
above the cylinder. When the cylinder was driven at this
frequency (fundamental resonance), the maximum
sound pressure and tension occurred at the centre of
Fig. 9. Filamentary structure of bubbles in sonicallyinduced caviation. (Courtesy of A. Billo).
W. Lauterborn, C.-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65-75
•
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Fig. 10. Forced oscillations of a filamentary structure of cavitation bubbles in water inside a cylindrical piezoelectric transducer dirven at 13 kHz.
Framing rate is 200 000 frames per second.
the cylinder. A second cylinder in use had a length of
45.5 m m and an inner radius of 57 m m and was coated
for cavitation resistence. Besides simply submerging the
transducer into water, it was also used with P M M A
plates closing it at both ends and filled with water. In
the latter configuration, the water could be cavitated
between 8 and 18 kHz.
Beyond a certain threshold of the driving voltage
applied to the cylinder a hissing noise was heard and
bubbles danced around in the liquid. These bubbles
form a branched structure 'streamers') also called
acoustic Lichtenberg figures by us in reminiscence of
the electric Lichtenberg figures. A h o m o g e n e o u s cloud
of bubbles was not observed on any occasion; the
bubbles always organized themselves into filaments.
Fig. 9 shows an example of this filamentary structure.
Obviously, a homogeneous distribution of bubbles in
the presence of a strong sound field is unstable. This
can also be shown theoretically. The pattern formed
seems to be unstable as it is steadily rearranging on a
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l~ Lauterborn, C-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65 75
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Fig. 11. Nonlinear bubble oscillation in the sound field in a cavltating liquid (water).
human time scale, although it is stable over at least
hundreds of cycles of the driving sound field. The
processes in the bubble cloud are very complex due to
competing influences made up of attracting and repelling
forces and due to the thousands of tiny interacting
bubbles.
The filamentary structure oscillates with the driving
sound field, i.e. the bubbles collapse every cycle. This
can be seen in Fig. 10, which has been taken at 200 000
frames per second with a rotating mirror camera. The
frequency of the driving sound field is 13 kHz and
slightly more than one cycle of the driving is covered
by these twenty frames. The disappearance and reappearance of the complex filamentary structure is remarkable pointing to a tightly coupled bubble system.
The bubbles in acoustic cavitation oscillate non-linearly as photographs reveal. Fig. 11 shows a sequence
of the bubble cluster in the centre where the streamers
converge, taken at 100 000 frames per second. A good
fit to the oscillation can be obtained with a bubble
having a radius, at rest, of Rn=248 ~tm driven at a
sound pressure amplitude Ofpa = 0.323 bar at the experimentally given driving frequency of v = 1 2 . 9 6 k H z .
Fig. 12 shows the result of a calculation with the
Rayleigh Plesset model where the diamonds are from
the experiment.
5. Sonoluminescence
When the cavitation bubble field is observed in total
darkness with a dark-adapted eye (after 15-20min),
light can be seen emanating from the liquid, often in
the form of filaments. As the primary input is sound,
V~ Lauterborn, C-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65 75
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Fig. 12. Nonlinear bubble oscillation in a sound field in a cavitating
liquid (water). Upper diagram: driving sound pressure,pa =0.323 bar.
Lower diagram: comparison of experiment (diamonds) with theory
(solid line). Different bubble than given in the previous figure.
73
the phenomenon is called sonoluminescence. The faint
light emitted can be photographed with a CCD-camera
equipped with a micro-channel plate as 'light intensifier'
(ICCD=intensified CCD). Fig. 13 shows an image of
the interior of a piezoelectric cylinder (this time of
diameter 6.5 cm, length 13 cm) driven at 20 kHz as it
appears in its own emitted light. Again, a filamentary
structure is seen. Moreover, it has been found that light
is only emitted in a small window of the driving phase
comprising 1/12 the period of the driving. This confirms
the highly concerted action of all bubbles as seen in
Fig. 10. It has already been established (long ago) that
the light is emitted from the bubbles in their collapsed
state and that it must come from bubbles in the approximate radius size range 0.8-2 gm.
A certain minimum sound pressure amplitude is
needed for the filamentary structure to appear. However,
it has been found that there is also an upper threshold
where the filaments cease to exist and light is emitted
from just one centre. Fig. 14 shows this bifurcation or
phase change in the bubble structure in a sequence of
luminescence images that appear at different voltages
applied to the cylinder, the light being integrated over
many seconds. The luminescence starts localized (here
at 180V). Soon filaments form at higher voltages
(190 V, 195 V) and a large area of the liquid is involved
Fig. 13. The light output of a liquid insonified at 20 kHz taken with an ICCD camera: a luminescence image.
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W. Lauterborn, C-D. Ohl / UltrasonicsSonochemistry 4 (1997) 65 75
17 SV
lgOV
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Fig. 14. Integrated luminescenceimages at differentdriving voltages. Frame size is 3.4 x 3.7 cm.
in the light emission. At still higher driving, the emission
shrinks to a single stable emission centre (200 V). This
centre starts to move around in the liquid (210 V) giving
the integrated appearance of a large quite-unstructured
emission region. Below, in Fig. 15, time-resolved measurements are given to underpin this interpretation. At
still higher driving, the emission centre splits up into
two and again a richer structure appears (220 V, 230 V).
This sequence has been obtained reproducibly, whereby
changes in the actual values of the voltages may occur.
Noteworthy is the appearance of a single stable emission centre and its motion at higher driving. Fig. 15
shows time-resolved images of the dancing emission
centre. A possible explanation relates to the strong nonlinearity of the bubble oscillation. It has been found
that a small bubble can be kept stable in the pressure
antinode only in the case of not too large non-linearity
in the oscillation of the bubble, otherwise the attracting
primary Bjerknes force becomes repelling and the bubble
becomes positionally unstable. Thus, the bubble has to
leave the high pressure region. When it does so, it
experiences a lower amplitude of the driving and also
lowers its oscillation amplitude. The repelling force then
ceases. In a rotationally symmetric system, the bubble
would settle somewhere away from the maximum sound
pressure on some surface, being free to move along it
upon slight additional disturbances. That way, the seemingly irregular motion observed in Fig. 15 may be
explained.
6. Summary
The dynamics of bubbles in liquids has been investigated. Violent processes take place in the collapse of
bubbles manifesting themselves in the emission of shock
W. Lauterborn, C.-D. Ohl / Ultrasonics Sonochemistry 4 (1997) 65-75
75
Fig. 15. Luminesenceimages in the course of time in the dancing bubble regime.
waves and light. Single bubble dynamics has been
studied with laser produced bubbles and high-speed
photography. Detailed results on bubble collapse and
shock wave emission could be obtained. Asymmetric
bubble collapse results in the emission of (normally)
three shock waves: two which are jet induced and one
induced by bubble compression. The two jet-induced
shock waves combine into one in the case where the
curvature of the jet tip is higher than the curvature of
the bubble wall that is hit. This happens for ~ smaller
than about two and larger than about 1.2. Bubbles
appearing in the process of acoustic cavitation assemble
themselves into filamentary structures that breeze in the
rhythm of the driving (Fig. 10) and radiate light
(Fig. 13). From the single bubble studies it can be
conjectured that also in the case of acoustic cavitation
with many bubbles the individual bubble collapse will
be similarly fast and often resemble that shown in Fig. 5,
as a bubble nearby another one corresponds to an
induced asymmetry similar to that of a solid boundary.
Thus, highly involved processes can be expected to occur
in a bubble cloud as given in Fig. 9. It is conjectured
that these processes will play a role in sonochemistry.
Acknowledgement
We thank the Nonlinear Dynamics and Cavitation
groups at G6ttingen and Darmstadt that in a combined
effort over a long time collected most of the results
reported here. Special thanks go to R. Blatt for loan of
the I C C D camera to photograph the light emitted by
the bubbles. The work has been sponsored by the
Fraunhofer Gesellschaft, Mtinchen, and the Deutsche
Forschungsgemeinschaft, Bonn.
References
[ 1] C.E. Brennen, Cavitation and Bubble Dynamics, Oxford University Press, Oxford, 1995.
[2] T.G. Leighton, The Acoustic Bubble, Academic Press, London,
1994.
[3] J.R. Blake, J.M. Boulton-Stone, N.H. Thomas (Eds.), Bubble
Dynamics and Interface Phenomena, Kluwer, Dordrecht, 1994.
[4] F.R. Young, Cavitation, McGraw-Hill, London, 1989.
[5] K.S. Suslick (Ed.), Ultrasound: Its Chemical, Physicaland Biological Effects, VCH, New York, 1988.
[6] L. van Wijngaarden (Ed.), Mechanics and Physics of Bubbles in
Liquids, Martinus Nijhoff, The Hague, 1982.
[7] W. Lauterborn (Ed.), Cavitation and Inhomogeneities in Underwater Acoustics, Springer, Berlin, 1980.
[8] L.A. Crum, Phys. Today 47 (1994) 22.
[9] N.K. Bourne, J.E. Field, J. Fluid Mech. 244 (1992) 225.