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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.

76T99 Multiphase and multicomponent flows
76M99 Basic methods in fluid mechanics
Full Text: DOI
[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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