Unsteady translation and repetitive jetting of acoustic cavitation bubbles

Till Nowak and Robert Mettin

Phys. Rev. E 90, 033016 – Published 30 September 2014

Abstract

High-speed recordings reveal peculiar details of the oscillation and translation behavior of cavitation bubbles in the vicinity of an ultrasonic horn tip driven at 20 kHz. In particular, a forward jump during collapse that is due to the rapid reduction of virtual mass is observed. Furthermore, frequently a jetting in the translation direction during the collapse phase is resolved. In spite of strong aspherical deformations and frequent splitting, these bubbles survive the jetting collapse, and they rebound recollecting fragments. Because of incomplete restoration of the spherical shape within the following driving period, higher periodic volume oscillations can occur. This is recognized as a yet unknown source of subharmonic acoustic emission by cavitation bubbles. Numerical modeling can capture the essentials of the unsteady translation.

Received 25 June 2014
Revised 1 September 2014

DOI:https://doi.org/10.1103/PhysRevE.90.033016

Authors & Affiliations

Till Nowak and Robert Mettin

Christian Doppler Laboratory for Cavitation and Micro-Erosion, Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

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Issue

Vol. 90, Iss. 3 — September 2014

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Images

Figure 1
Cavitating zone below the horn tip at comparable conditions to those in the rest of the figures (tip visible on the top, bubbles appear dark and are close to maximum expansion phase; exposure time 2 $μ s$ ; marked areas: see text).
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Figure 2
Sequence of vertical stripe frames (“pseudostreak”) from the dotted region in Fig. 1 (driving voltage here is 200 V $p p$ ). Shown is a time span of 69 frames recorded at 10 000 fps (scale indicated, exposure time 2 $μ s$ ). A beat oscillation of the bubbles can be perceived as the acoustic frequency of 20 610 Hz was slightly higher than twice the frame recording rate. For a full movie and an enlarged figure, see [18].
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Figure 3
Sequence of vertical stripe frames from the small (continuous) rectangle in Fig. 1. High-speed recording at 250 000 fps (sonotrode tip on top; time from left to right, upper row first; exposure time 1 $μ s$ ; resolution enhanced); one full acoustic period corresponds to one black or white segment of the line on top of the frames (phase arbitrary). For a full movie, see [18].
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Figure 4
Enlargement of detail A of Fig. 3. Collapse and upward jetting took place between frames 1 and 2. The bubble shape in the rebound phase still shows the characteristic indentation on the downward side and a bulge from the hitting jet flow on the upward side (frames 3 and 4). After a pronounced afterbounce collapse after frame 4, the bubble develops irregular surface motion and is splitting into several parts. Therefore, the next collapse shows a quite distorted geometry and appears earlier than one acoustic period after the first (already around frame 11). Again, a pronounced afterbounce collapse happens (after frame 13). Only then is the spherical shape restored, and the fragments are recollected during the next rebound (compare Fig. 3). One full acoustic period is indicated by the white line on top (similar in Fig. 5).
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Figure 5
Enlargement of detail B of Fig. 3. The collapse between frames 2 and 3 leads to a splitting of the bubble, as a small satellite is ejected on the bottom, similar to the well-known counter-jet phenomenon [20]. An afterbounce collapse is observed (frame 5), and the irregularly shaped rebound phase ends in the next nonspherical collapse with further splitting. The lower fragment is not recollected in this case, but it forms a separate bubble (compare Fig. 3).
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Figure 6
(a) Equivalent bubble radius $R$ (dashed line, right labels) and vertical position coordinate $z$ (continuous line, left labels; horn tip at $z$ = 0) vs time (in driving periods) as evaluated from Fig. 3 (error bars given at the right). The instants of main collapse (from maximum expansion during one acoustic cycle) are approximately marked by arrows to highlight the alternation of intervals (a thicker arrow after the longer interval). (b) Simulation of radius $R$ (dashed, right labels) and vertical position $z$ (continuous line, left labels) vs acoustic driving periods for a spherical bubble ( $R_{0}$ = 15 $μ m$ ) in the field of a circular piston (1 cm diam, 0.4 m/s velocity amplitude, 20 610 Hz; standard water parameters at room temperature [18, 27]). Acoustic pressure at the bubble position shown by the dotted curve (labels at the right).
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