Introduction to Acoustics

Fig. 8.21 Distribution of temperature inside an acoustically
driven bubble in dependence on time. Molecular dynamics
calculation with argon and water vapor including chemical
reactions. (after [8.128])
motion and the inner molecular dynamics calculations
are coupled via the gas pressure (at the interface),
which is determined from the molecular dynamics
of the 10 6 particles and inserted into the Rayleigh–
Plesset equation giving the motion of the bubble wall.
A strong focusing of energy inside the bubble is observed
under these conditions. An inward-traveling compression
wave focuses at the center and yields a core
temperature of more than 10 5 K. This temperature is
an overestimate as no energy-consuming effects are
included.
The temperature variation inside the bubble with
time can be visualized for spherical bubbles in a single
picture in the following way (Fig. 8.21). The vertical
axis represents the radial direction from the bubble center,
the horizontal axis represents time and the color gives
the temperature in Kelvin according to the color-coded
scale (bar aside the figure). The upper solid line in the
figure depicts the bubble wall; the blue part is water. In
8.12 Acoustic Chaos
Nonlinearity in acoustics not only leads to shock waves
and, as just demonstrated, to light emission, but to even
deeper questions of nonlinear physics in general [8.4].
In his curiosity, man wants to know the future. Knowledge
of the future may also be of help to master one’s
life by taking proper provisions. The question therefore
arises: how far can we look into the future and where
are the difficulties in doing so? This is the question of
predictability or unpredictability. In the attempt to solve
this question we find deterministic systems, stochas-
Experiment
φ
Measurement
Time series
Fig. 8.22 Visualization of the embedding procedure
φ
t
0.8
0.6
0.4
0.2
Nonlinear Acoustics in Fluids 8.12 Acoustic Chaos 289
r(µm) �10 4K)
0
–190 –95 0
t(ps)
this case an argon bubble with water vapor is taken and
chemical reactions are included. Then the temperature
is lowered significantly by the endothermal processes of
chemical species formation, for instance of OH − radicals.
The temperature drops to about 40 000 K in the
center [8.128].
tic systems and, nowadays, chaotic systems. The latter
are special in that they combine deterministic laws that
nevertheless give unpredictable output. They thus form
a link between deterministic and stochastic systems.
8.12.1 Methods of Chaos Physics
A description of the methods developed to handle
chaotic systems, in particular in acoustics, has been
given in [8.32]. The main question in the context
Embedding
x 4
Trajectory in state space
x 3
x 1
x 2
4
3
2
1
Part B 8.12