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Linear oscillations of a supported bubble or drop
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10.1063/1.4810959
/content/aip/journal/pof2/25/6/10.1063/1.4810959
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4810959
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Considered configurations and notation; (a) bubble or drop supported by a spherical bowl (constraint of SS), (b) bubble attached to a ring (constraint of BS).

Image of FIG. 2.
FIG. 2.

(a)–(d) Shape of the first four eigenmodes of a pinned bubble for attachment angles θ = 15° (left halves of figures) and 40° (right halves); the attachment positions are indicated by arrows. Solid lines are for the SS constraint, dashed lines are for the BS constraint; when invisible, these lines overlap with the solid line. Darker and lighter gray lines (blue and red online) correspond to positive and negative displacement of the interface at the apex, respectively.

Image of FIG. 3.
FIG. 3.

Dependence of coefficients on attachment angle. The results of the analysis for (a) mode of order = 1, (b) = 2, (c) = 3. Solid lines refer to bubbles with the SS constraint, whereas dotted lines (in some cases overlapping with solid lines) refer to drops with the SS constraint and dashed lines (shown only for and ) refer to bubbles with the BS constraint.

Image of FIG. 4.
FIG. 4.

Predicted eigenfrequencies of (a) bubbles and (b) drops. Solid lines are the prediction for the SS constraint. Dashed and dotted lines are the predictions for the BS constraint considering = 128 and 13 terms, respectively. Circles denote the node positions and eigenmode frequencies for a free bubble or drop. The results are computed for = 0.

Image of FIG. 5.
FIG. 5.

Predicted eigenmode damping rates for (a) bubbles and (b) drops. Solid lines are the prediction for the SS constraint. Dashed and dotted lines are the prediction for the BS constraint considering = 128 and 13 terms, respectively. Circles denote the node positions and damping rates (2) for a free bubble or drop.

Image of FIG. 6.
FIG. 6.

Frequency responses of a bubble with the BS constraint located at (a) θ = 15°, (b) θ = 40°. Black arrows indicate computed eigenfrequencies, whereas white arrows are the eigenfrequencies of a free bubble, Eq. (1) . The results are for = 0.005.

Image of FIG. 7.
FIG. 7.

Dependence of the energy of an oscillating bubble, which is excited by periodic support movement at the frequency of the th eigenmode, on attachment angle. BS constraint, = 0.005.

Image of FIG. 8.
FIG. 8.

Frequency responses of a bubble to support motion (solid lines) and to volume variations (dotted lines – only data for and are shown). The SS constraint with θ = 40°, = 0.005, and = 0 is considered. Black arrows indicate computed eigenfrequencies, whereas white arrows are the eigenfrequencies of a free bubble, Eq. (1) .

Image of FIG. 9.
FIG. 9.

Energy of an oscillating bubble excited at the frequency of the th eigenmode and its dependence on attachment angle. Excitation is by support motion (solid lines) and volume variations (dotted lines). The results are for the SS constraint, = 0.005, = 0.

Image of FIG. 10.
FIG. 10.

Frequency responses of a drop to support motion. The SS constraint with θ = 40°, = 0.005, and = 0 is considered. Black arrows indicate computed eigenfrequencies, whereas white arrows are the eigenfrequencies of a free bubble, Eq. (1) . The first resonance peak reaches a value of 76, which exceeds the plot range.

Image of FIG. 11.
FIG. 11.

Dependency of the energy of an oscillating drop, excited at the th eigenmode frequency, on attachment angle. The results are for = 0.005 and = 0. (a) BS constraint, (b) SS constraint. Excitation is by support motion (solid lines) and by volume variations (dotted lines). Values for the = 1 mode should be read on the right ordinate.

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/content/aip/journal/pof2/25/6/10.1063/1.4810959
2013-06-20
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Linear oscillations of a supported bubble or drop
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4810959
10.1063/1.4810959
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