Acoustic cavitation, bubble dynamics and sonoluminescence.
ABSTRACT Basic facts on the dynamics of bubbles in water are presented. Measurements on the free and forced radial oscillations of single spherical bubbles and their acoustic (shock waves) and optic (luminescence) emissions are given in photographic series and diagrams. Bubble cloud patterns and their dynamics and light emission in standing acoustic fields are discussed.
Conference Proceeding: Sonoluminescence[show abstract] [hide abstract]
ABSTRACT: When an acoustic wave of moderate pressure amplitude is propagated through an aqueous liquid, light emissions can be observed. This conversion of mechanical energy into electromagnetic energy represents an energy amplification per molecule of over eleven orders of magnitude! Recently, we made the discovery that a single, stable gas bubble, acoustically levitated in a liquid, can emit optical emissions each cycle for an unlimited period of time. Presumably, the oscillations of the bubble cause the gas in the interior to be heated to incandescent temperatures during the compression portion of the cycle. We have no current explanation for how this mechanical system sustains itself. Furthermore, recent experimental evidence suggests that the lifetime of the optical pulse is less than 12 picoseconds, and that the temperature in the interior of the bubble can exceed 40,000 K. Since conventional explanations expect the bubble to remained compressed and the temperatures elevated in the interior of the bubble for times on the order of tens of nanoseconds, it is likely that some rather unusual physics is occurring. The recent suggestion that sonoluminescence may be due to quantum vacuum radiation is particularly fascinating. The best guess, however, is that a shock wave is created in the gas which is then elevated to high temperatures by inertial confinement. If shock waves are the mechanism for SL emission, then optimization of the process could lead to extraordinary physics, including thermonuclear fusion, a remote but intriguing possibility. A general review of this engaging phenomenon will be presented as well as the latest explanations for the anomalous behavior. (Work supported by NSF).European Society of SonochemistryEuropean Society of Sonochemistry; 01/1998
Chapter: The Acoustic Bubble01/1994; Academic Press.
ARCHIVES OF ACOUSTICS
33, 4, 609–617 (2008)
ACOUSTIC CAVITATION AND BUBBLE DYNAMICS
Werner LAUTERBORN, Thomas KURZ, Robert METTIN, Philipp KOCH,
Dennis KRÖNINGER, Daniel SCHANZ
Drittes Physikalisches Institut
Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
(received June 15, 2008; accepted October 28, 2008)
Acoustic cavitation is investigated experimentally and theoretically starting with a single
bubble in an acoustic field. The single bubble is trapped in an acoustic resonator and observed
by high-speed imaging and acoustic measurements following its transient dynamics to a possi-
ble steady state after generation by laser light. Numerical calculations are done to explore the
regions of survival for acoustically driven bubbles with respect to dissolution or growth, sur-
face oscillations and positional stability in a standing sound field. The interior gas dynamics
is explored via molecular dynamics simulations. A glance is thrown at the complex dynamics
of multi-bubble systems.
Keywords: acoustic cavitation, bubbles.
Intense sound fields in liquids generate cavities or bubbles that start to oscillate and
move around in the liquid, a phenomenon called acoustic cavitation [2, 11, 13]. The
basic element to start an investigation with is the single, spherical bubble in an infinite
liquid subject to a sinusoidal sound field. The best experimental approximation so far
is realized in the acoustic bubble trap as mainly used for sonoluminescence studies ,
and in bubbles generated by focused laser light . Both cases have been combined to
investigate transient single bubble dynamics and its sonoluminescence in an acoustic
field . Theoretical bubble models have been conceived with different states of so-
phistication to include different influences and phenomena as, for instance, liquid com-
pressibility, heat and mass transfer across the bubble wall or stability of the surface.
Noteworthy is the strong collapse of a bubble at high sound pressure amplitudes leading
to shock wave and light emission and high speed liquid jet formation under appropri-
ate conditions . The interior of a bubble is usually treated as homogeneous with
respect to temperature and pressure. However, this may not be true in the last phase of
W. LAUTERBORN et al.
a strong collapse . This problem is not only tackled by continuum mechanics via
partial differential equations but also in a molecular dynamics approach [10, 15].
The next step in bubble dynamics investigations is given by bubble interaction.
It leads to complicated forms of attraction and repulsion already in the case of two
spherical, interacting bubbles. A survey of bubble structures as they appear in acoustic
cavitation is given in . A particle model has been formulated to address the problem
of multi-bubble systems in an ultrasonic field as a way to cope with acoustic cavitation
bubble ensembles [17, 19]. This paper is a kind of progress report in the field of bubble
dynamics in acoustic fields.
2. Single bubble dynamics
From the many models to describe the oscillation of bubbles in an acoustic field the
model of KELLER and MIKSIS  is adopted:
Here, R is the bubble radius, Clthe sound velocity of the liquid at the bubble wall,
ρlthe density of the liquid, and p the difference between external and internal pressure
terms at the bubble wall, as given in the following equation.
˙R − ps.
The quantities introduced are: pstatthe static ambient pressure, σ the surface tension,
Rnthe radius of the bubble at rest, κ the polytropic exponent of the gas inside the
bubble, and µ the dynamic viscosity. psis an additional external pressure, for instance
the pressure pulse of a lithotripter.
The Keller-Miksis bubble equation has been solved for various parameter configu-
rations with a sinusoidal sound field ps:
ps= ˆ pAsin(2πνt).
Figure 1 gives a typical set of steady-state bubble oscillations with increasing sound
pressure amplitude from ˆ pA= 100 kPa to 200 kPa in steps of 20 kPa at a frequency of
ν = 20 kHz for a bubble with a radius at rest of Rn= 5 µm. After a long expansion
phase a steep collapse occurs with some afterbounces until the cycle repeats. Further-
more, the maximum of the bubble oscillation shifts from the tension phase of the driving
sound field to the pressure phase leading to a shift in the stability position of the bubble
in a standing sound field [1, 14].
For a more thorough desription of the oscillation properties of a bubble condensed
forms of diagrams have been developed to combine special features as in bifurcation
of the oscillation with respect to the forcing sound oscillation for bubbles in the range
ACOUSTIC CAVITATION AND BUBBLE DYNAMICS
Fig. 1. Typical steady-state bubble oscillations with steep collapse and afterbounces. Shift of the relative
phase of the bubble oscillation with respect to the phase of the sound field with increasing sound pressure
amplitude; ˆ pA = 100...200 kPa, ν = 20 kHz, Rn = 5 µm, isothermal.
of 10 µm to 100 µm and for driving pressure amplitudes from 0 to 300 kPa for a sound
field frequency of ν = 20 kHz. It is seen that specific ranges with repeated structures
of interlaced periodicity appear that are similar for other and presumably all bubble
models  and even a larger class of nonlinear oscillators .
0 2040 6080100
Fig. 2. Phase diagram giving the periodicity of the bubble oscillations with respect to the driving sound
oscillation; ν = 20 kHz, isothermal.
The bubble model can be extended to include diffusion processes [3, 4]. Then bub-
bles may dissolve or even grow due to a process called rectified diffusion. Also the
W. LAUTERBORN et al.
bubble may become positional unstable in the sound field due to acoustic radiation
forces (Bjerknes forces). Moreover, when additionally surface oscillation of the bubble
are included  a restricted survival region results in the sound pressure amplitude –
equilibrium bubble radius plane. In Fig. 3 this stability region is shown shaded for bub-
bles with rest radii between 0 and 30 µm and for pressure amplitude between 0 and
300 kPa at a fixed frequency of the sound field of 20 kHz. Below the shaded region
the bubble is diffusion unstable, above the phenomenon of rectified diffusion prevents
the dissolution of the bubble. Above the shaded region the bubble gets unstable due to
surface oscillations that lead to a break-up of the bubble. There is a dotted line running
through the middle of the figure. This dotted line separates the bubbles being attracted
to the pressure antinode in the standing sound field (in a resonator or bubble trap) and
thus can be stably trapped and the bubbles above that are driven away from the pressure
antinode and are sentenced to move to and on a surface of lower pressure in the standing
Fig. 3. Region of stable bubble oscillations in a standing sound field of ν = 20 kHz (shaded area).
This type of diagram can be calculated for other frequencies and for other ranges
of sound pressure and bubble radii. Figure 4 gives an example for ν = 40 kHz in
an extended bubble range normalized to the linear resonance radius Rlin
and for the acoustic pressure range 0 to 500 kPa. It can be noticed that the positionally
stable region (lightly shaded) is a rather small rugged stripe and located below the linear
resonance radius. Generally it can be stated from calculations for higher frequencies
that the survival space shrinks for higher frequencies to a small region in this parameter
When the interior of the bubble is closer looked at, additional phenomena are ob-
served. The interior contents may not be homogeneously distributed, but pile up at the
bubble boundary or in the center, compression waves may run towards the center and
chemical reactions may take place. This problem has been addressed by molecular dy-
= 69 µm
ACOUSTIC CAVITATION AND BUBBLE DYNAMICS
Fig. 4. Region of stable bubble oscillations in a standing sound field of ν = 40 kHz (shaded area).
namics calculations where the interior contents are modelled by a number of particles
that move around in the interior according to the laws of mechanics. They transfer im-
pulse and energy when they hit each other and the bubble wall. The interior dynamics is
calculated when the bubble is subject to a collapse in a sound field . Figure 5 shows
the interior temperature distribution in a bubble for 800 ps around its strong collapse.
In this case with nonreacting particles (Argon) and reacting particles (water molecules)
maximum temperatures of about 18,000 K are reached in the center.
Fig. 5. The distribution of temperature inside a bubble versus time upon collapse. Rest radius of the bubble
Rn = 4.5 µm in a sound field of ν = 26.5 kHz at a pressure amplitude of 1.3 bar. Argon–vapour bubble
including chemical reactions.
To study single bubble dynamics in a controlled way a method to prepare a bub-
ble and insert it in a sound field without negligible disturbance of the field must be