Oscillations, Waves, and Interactions - GWDG

seeding phase [deg]
0
50
100
150
200
250
300
The single bubble – a hot microlaboratory 159
350
0 5 10
time [ µ s]
15 20
Figure 23. Numerical simulation of the transient dynamics of a laser generated bubble as
a function of seeding phase and time. The bubble radius has been calculated by the Gilmore
model and is shown colour-coded, the initial conditions and sound field parameters are taken
from the experiment as described in the text. For the phase interval where luminescence
of transient bubbles can be observed in the experiment this calculation gives a peak radius
that is larger than that of the steady oscillation.
Because of the small laser pulse energy used in this experiment the non-driven bubble
remains small and collapses shortly after its inception. Due to nonlinear optical
effects it attains a cylindrical shape (see Sect. 3.1). Such a bubble does not emit any
detectable luminescence light. The driven bubble is generated at the beginning of
the negative-pressure phase. In the presence of sound the bubble grows significantly
larger and becomes more spherical. The maximum radius that can be obtained for a
given driving level depends, of course, on the instant of bubble inception relative to
the pressure cycle, the seeding phase ϕs 1 . Figure 23 shows a numerical simulation of
the first transient oscillation cycle of a laser-generated bubble as a function of seeding
phase based on the Gilmore model. The bubble’s initial conditions have been
taken from the corresponding experiment and are the same for all phase values [27].
Around ϕs ≈ 220 ◦ the simulation yields a particularly large maximum radius as the
bubble is optimally expanded by the sound field and the laser pulse energy is utilized
as well.
For seeding phases of ϕs < 180 the bubble behaviour is different. Because of
the overpressure now acting on the bubble just generated, it collapses quickly and
stays small until the sound field creates tension to expand it again. For ϕ → 0
1 The seeding phase is defined to be zero at the beginning of the positive-pressure phase
of the sound field.
radius [10 µ m]