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Note on shape oscillations of bubbles. (English) Zbl 0678.76108
Summary: By use of a virial equation introduced in a recent paper [the author, ibid. 181, 349-379 (1987; Zbl 0634.76098)], the main results of a second- order perturbations theory developed by M. S. Longuet-Higgins [ibid. 201, 525-541 (1989)] are recovered in comparatively simple fashion. Asymmetric capillary vibrations of gas bubble in an infinite incompressible liquid are confirmed to generate an increase in the volume of the bubble, a lowering of the mean pressure of the gas and a monopole component in the motion of the liquid. It is shown that the second effect remains when the bubble is incompressible.

MSC:
76T99 Multiphase and multicomponent flows
76M99 Basic methods in fluid mechanics
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References:
[1] Rayleigh, Proc. R. Soc. Lond. 29 pp 71– (1879)
[2] DOI: 10.1146/annurev.fl.09.010177.001045 · doi:10.1146/annurev.fl.09.010177.001045
[3] Longuet-Higgins, J. Fluid Mech. 201 pp 543– (1989)
[4] Longuet-Higgins, J. Fluid Mech. 201 pp 525– (1989)
[5] DOI: 10.1017/S002211208700212X · Zbl 0634.76098 · doi:10.1017/S002211208700212X
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