Introduction to Acoustics

288 Part B Physical and Nonlinear Acoustics
Part B 8.11
Bubble radius (µm)
60
50
40
30
20
10
0
0
10
20
30
40 50
Time (µs)
in a small bubble is relatively small, around 10 9 to
10 10 molecules, this approach promises progress for
the question of internal shock waves. At present molecular
dynamics simulations are feasible with several
t = +0 ps, = 389 kg/m3 t = +28 ps, = 519 kg/m3 t = +40 ps, = 584 kg/m3 z/µm
Temperature T/(104K) z/µm
Temperature T/(104K) z/µm
Temperature T/(104K) 0.5
0.0
–0.5
–0.5 0.0 0.5
r/µm
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.5
0.0
–0.5
–0.5 0.0 0.5
r/µm
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.0
–0.5
–0.5 0.0 0.5
r/µm
t = +66 ps, = 753 kg/m3 t = +80 ps, = 844 kg/m3 t = +106 ps, = 998 kg/m3 z/µm
Temperature T/(104K) z/µm
Temperature T/(104K) z/µm
Temperature T/(104K) 0.5
0.0
–0.5
–0.5 0.0 0.5
r/µm
18.0
16.0
0.5
14.0
12.0
10.0
0.0
8.0
6.0
4.0
–0.5
2.0
0.0
–0.5 0.0 0.5
r/µm
Fig. 8.19 Radius-time curve of a trapped bubble in a
water-glycerine mixture derived from photographic observations.
A numerically calculated curve (Gilmore model)
is superimposed on the experimental data points (open
circles). The calculation is based on the following parameters:
driving frequency f0 = 21.4 kHz, ambient pressure
p0 = 100 kPa, driving pressure p0 = 132 kPa, vapor pressure
pv = 0, equilibrium radius Rn = 8.1 µm, density of
the liquid ρ = 1000 kg/m 3 , viscosity µ = 0.0018 Ns/m 2
(measured) and surface tension σ = 0.0725 N/m. The gas
within the bubble is assumed to obey the adiabatic equation
of state for an ideal gas with κ = 1.2. (Measured points
courtesy of R. Geisler)
million particles inside the bubble. Figure 8.20 gives
a graphical view on the internal temperature distribution
inside a collapsing sonoluminescence bubble with
near-adiabatic conditions (reflection of the molecules
at the inner boundary of the bubble) for six different
times around maximum compression. The liquid
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.5
0.0
–0.5
–0.5 0.0 0.5
r/µm
Fig. 8.20 Temperature distribution inside a collapsing sonoluminescence bubble filled with argon, one million particles,
radius of the bubble at rest 4.5 µm, sound pressure amplitude 130 kPa, sound field frequency 26.5 kHz, total time covered
106 ps. (Courtesy of B. Metten [8.126])
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0