Oscillations, Waves, and Interactions - GWDG

Acoustic cavitation 173
strated in Fig. 1 by two photographs of long and short exposure time, respectively.
This clearly motivates the description of the cavitating zone via many single bubbles
and their respective behavior. For the consideration of spatial bubble distributions,
we can treat them as individual point-like particles: each bubble has a well defined
position and velocity, and it is reacting to forces acting upon its centre of mass.
Following this approximation, the dynamics of the two-phase liquid transfers to a
many-body problem, in a way similar to stars moving in a galaxy, or electrons and
ions moving in a plasma. 2 Indeed, notable parallels exist as compared to gravitation
or electromagnetism, but the acoustic origin of the forces and the presence of a liquid
bear also specific differences, which renders the many-body problem a rather peculiar
one.
The following Sections 2 and 3 will briefly discuss the origin of bubbles and their
oscillation dynamics under the presence of a driving sound field. The treatment is
limited to spherical bubbles, and the loss of spherical stability as well as rectified
gas diffusion are addressed. Section 4 deals with acoustic forces on the bubbles
and aspects of their translational motion like added mass and viscous drag. A brief
discussion of bubble life cycles follows in Sect. 5. The extension to a multibubble
particle model is proposed in Sect. 6, and some examples of spatial bubble structure
formations together with their numerical simulation are presented. A conlusion and
outlook is given in Sect. 7.
2 Cavitation inception and bubble nucleation
If a continuous (cw) acoustic field of gradually increased intensity is applied to a
liquid, sooner or later the cavitation inception threshold will be reached, and bubbles
are created. Because the sound is permanently irradiated into the now cavitating
liquid, generated bubbles will have a subsequent (possibly complicated) destiny, and
further new bubbles can appear all the time. Reserving the term “inception” for the
global transition from quiet to cavitating liquid, here the notion of “bubble creation”
will be preferred for the local origin of a bubble. Indeed, one can observe several
differerent ways of bubble creation in cw fields. Some bubbles appear suddenly “out
of nothing” in the bulk liquid, others seem to occur from an invisible continuous
source in the bulk, or from continuous sources at walls. Sometimes the source is
a larger bubble that emits smaller ones. The nature of bubble creation or source
can be very important for the spatial cavitation patterns that appear, and some are
illustrated in the following.
Figure 2 shows the process of a spontaneous nucleation near a high acoustic pressure
zone in bulk water. A small object suddenly appears isolated and without any
precursor in the liquid (first frame) and develops into a cluster. It travels at relatively
high speed towards a lower acoustic pressure region. Crum and Nordling
2 Another point of view is taken by continuous models of cavitation, where the gas void
fraction or the density of bubbles is understood as a quantity continuously varying in space
and time. Such models do not resolve individual bubbles, and they are usually formulated
by partial differential equations. A particle approach results in a set of ordinary differential
equations.