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Shape stability and violent collapse of microbubbles in acoustic traveling waves
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10.1063/1.2716633
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Affiliations:
1 Applied Science and Technology Graduate Group, University of California, Berkeley, California 94720-1708
2 Department of Mechanical Engineering, University of California, Berkeley, California 94720-1740
3 School of Mathematics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
4 Department of Mechanical Engineering, University of California, Berkeley, California 94720-1740 and Applied Science and Technology Graduate Group, University of California, Berkeley, California 94720-1708
a) Present address: School of Mathematics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom.
b) Present address: Research and Breakthrough Innovation, SAP AG, Neurottstrasse 16, 69190 Walldorf, Germany.
c) Author to whom correspondence should be addressed. Electronic mail: aszeri@me.berkeley.edu
Phys. Fluids 19, 047101 (2007)
/content/aip/journal/pof2/19/4/10.1063/1.2716633
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/4/10.1063/1.2716633
View: Figures

## Figures

FIG. 1.

A typical axisymmetric bubble prior to (a) and just after (b) jet impact (, , ). Note that the traveling acoustic wave propagates upward. The vertical line is the axis of cylindrical symmetry. The length is made dimensionless by .

FIG. 2.

Stability and breakup diagram for bubbles with initial radius of driven by a traveling wave of frequency and amplitude . Bubble stability as calculated by the ODE model is shown by the shading of the region (, ) whereas stability results from the BIM model are indicated by individual points (, ). The natural frequency of volume oscillations is .

FIG. 3.

Stability and breakup diagram for bubbles driven by a traveling wave of frequency with varying initial radius and amplitude . Bubble stability and breakup are indicated in the same manner as in Fig. 2.

FIG. 4.

Dimensionless volume vs dimensionless time for a typical spherical bubble collapse (, , ). The dot indicates the transition point from slow to rapid dynamics. Volume and time are made dimensionless by the scales discussed in Sec. ???.

FIG. 5.

Normalized temperature (solid) and volume (dashed) vs dimensionless time for the typical spherical bubble collapse shown in Fig. 4. Both temperature and volume are normalized so that their maximum is unity. Note that temperature is constant at until the bubble switches to rapid dynamics.

FIG. 6.

Normalized pressure (solid) and volume (dashed) vs dimensionless time for the typical spherical bubble collapse shown in Fig. 4. Both pressure and volume are normalized so that their maximum is unity. Note that pressure is not constant during the slow phase but rather the magnitude of change during this phase is small compared to the relatively large pressure increase after the bubble switches to rapid dynamics.

FIG. 7.

Normalized kinetic energy (solid) and volume (dashed) vs dimensionless time for the typical spherical bubble collapse shown in Fig. 4. Both kinetic energy and volume are normalized so that their maximum is unity. Note that the kinetic energy is zero at both the volume maximum and minimum when the bubble motion is instantaneously at rest.

FIG. 8.

SBSL case : Peak temperature vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles. The sum is also shown .

FIG. 9.

SBSL case : Peak pressure vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles. (Note the log scale for the vertical axis.)

FIG. 10.

SBSL case : Minimum volume vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles. (Note the log scale for the vertical axis.)

FIG. 11.

MBSL case : Peak temperature vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles. The sum is also shown .

FIG. 12.

MBSL case : Peak pressure vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles. (Note the log scale for the vertical axis.)

FIG. 13.

MBSL case : Minimum volume vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles. (Note the log scale for the vertical axis.)

FIG. 14.

SBSL case : For a given value of acoustic forcing parameter , the nonspherical bubble shape at minimum volume and (black dot) are shown together. Note that the last three bubbles achieve their volume minimum during the toroidal stage.

FIG. 15.

MBSL case : For a given value of acoustic forcing parameter , the nonspherical bubble shape at minimum volume and (black dot) are shown together. Note that the last two bubbles achieve their volume minimum during the toroidal stage.

FIG. 16.

SBSL case : Peak temperature vs acoustic forcing parameter for spherical () and nonspherical (*) bubbles without chemistry. The sum is also shown .

FIG. 17.

Centroid displacement and velocity vs time for a typical nonspherical bubble collapse (, , ): (a) Centroid displacement (solid) and volume (dashed) normalized to maximum values of unity vs dimensionless time; (b) dimensionless centroid velocity vs dimensionless time near the end of collapse (near minimum volume). Note that the centroid velocity prior to this time is negligible. The time and the centroid velocity in (b) are made dimensionless by the scales discussed in Sec. ???.

FIG. 18.

SBSL case : (a) Net centroid displacement vs acoustic forcing parameter ; (b) maximum centroid velocity vs acoustic forcing parameter . The quantities shown are for a single expansion and collapse cycle as shown in Fig. 17.

FIG. 19.

MBSL case : (a) Net centroid displacement vs acoustic forcing parameter ; (b) maximum centroid velocity vs acoustic forcing parameter . The quantities shown are for a single expansion and collapse cycle as shown in Fig. 17.

/content/aip/journal/pof2/19/4/10.1063/1.2716633
2007-04-13
2014-04-19

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