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Volume oscillations of a constrained bubble
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View: Figures


Image of FIG. 1.
FIG. 1.

Gas bubble tethered to a wire loop (a) and cross section view (b) illustrating wetting conditions. The center of the bubble is located at the point O. The diameter of the wire ring AB is denoted by . The center of the wire constraint is located at ϑ. Location of the bubble surface relative to the wire loop for the non wetting, partial wetting, and full wetting condition are shown by dashed-dotted line, solid line, and dotted line, respectively. The case of the partial wetting corresponds to the wetting angle equal to 90°.

Image of FIG. 2.
FIG. 2.

Illustration of toroidal coordinates. The toroidal coordinates of any point are given by the intersection of a sphere, a torus, and an azimuthal plane (a). Surfaces of constant ϑ correspond to spheres of different radii that all pass through the focal ring but are not concentric. The surfaces of constant ξ are non-intersecting tori of different radii. The centers of the constant-ϑ spheres lie along the -axis, whereas the constant-ξ tori are centered in the plane. The coordinate α is the azimuthal angle about the axis. Circles of constant ξ and ϑ in the (ρ, ) plane of cylindrical polar coordinates (ρ = + ) are shown in (b).

Image of FIG. 3.
FIG. 3.

Streamlines (solid lines) near the wire loop marked by the values of the dimensionless stream function: 1, 0.5, 0.1, –0.1, –0.5, –1. The dashed lines and the dashed-dotted line represent cross section of the bubble surface and the wire.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Volume oscillations of a constrained bubble