IRROTATIONAL FLOW DUE TO FORCED OSCILLATIONS OF A BUBBLE

• Published in: The ANZIAM journal Vol. 66; no. 3; pp. 152 - 180
• Main Authors: COCKERILL, MADELEINE C., FORBES, LAWRENCE K., BASSOM, ANDREW P.
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 01.07.2024
• Subjects: Acoustics; Axisymmetric flow; Behavior; Bubbles; Damping; Forced vibration; Formability; Oscillations; Potential flow; Resonance; Shape effects; Singularities; Spectral methods; Surface tension; Velocity; Viscosity
• ISSN: 1446-1811; 1446-8735
• DOI: 10.1017/S144618112400021X

The behaviour of an axisymmetric bubble in a pure liquid forced by an acoustic pressure field is analysed. The bubble is assumed to have a sharp deformable interface, which is subject both to surface tension and to Rayleigh viscosity damping. Two modelling regimes are considered. The first is a linearized solution, based on the assumption of small axisymmetric deformations to an otherwise spherical bubble. The second involves a semi-numerical solution of the fully nonlinear problem, using a novel spectral method of high accuracy. For large-amplitude nonspherical bubble oscillations, the fully nonlinear solutions show that a complicated resonance structure is possible and that curvature singularities may occur at the interface, even in the presence of surface tension. Rayleigh viscosity at the interface prevents singularity formation, but eventually causes the bubble to become purely spherical unless shape-mode resonances occur. An extended analysis is also presented for purely spherical bubbles, which allows for a more detailed study of the effects of resonance and the Rayleigh viscosity at the bubble surface.