Oscillations, Waves, and Interactions - GWDG

Acoustic cavitation 193
(a) (b)
(c)
1 cm
Figure 16. Double layer (“jellyfish”) structure of bubbles in a standing wave. Photographs
from the side (a) and from the top (b) in a 25 kHz resonator (water). Simulated bubble
tracks are given in (c) and (d) (from Ref. [53]).
6.3 Cone bubble structure
As a final example we briefly discuss a conical bubble arrangement that appears at
larger emitting surfaces at high intensities (Fig. 17, left). It was first reported to
appear below a sonotrode (horn transducer) of larger surface area at 20 kHz [58,59],
but similar bubble structures are seen, for instance, at extended submerged surface
transducers [53]. Bubbles are generated directly at the emitter, and they travel rather
fast away from it, in direction of the radiated wave. On their way, they form a cone,
i. e., the bubble tracks meet close to a distinct point (the tip of the cone). There the
bubbles stop and partly merge to form larger bubbles. Those, in turn, move further
away from the sonotrode.
The pressure field forms a decaying progressive wave with a local maximum some
centimetres in front of the surface, lying inside the bubbly cone and not at the cone
tip [59]. The bubbles are driven to the tip point by primary Bjerknes forces, and in
this case both terms on the right hand side of Eq. (3) contribute. Indeed, the tip
point is for smaller bubbles a stagnation point in the sense that there both terms
just cancel, i. e., the pressure amplitude gradient term and the phase gradient term
are equal but of opposite sign [39]. This is not true for larger bubbles, and if smaller
ones grow by rectified diffusion and merging, they sooner or later are driven again
away from the tip in the forward wave direction.
(d)