Numerical study of the oscillations of a non-spherical bubble in an inviscid, incompressible liquid. Part II: the response to an impulsive decrease in pressure

• Published in: International journal of multiphase flow Vol. 25; no. 5; pp. 921 - 941
• Main Authors: McDougald, Neil K, Leal, L.Gary
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.1999; Elsevier
• Subjects: Drops and bubbles; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Nonhomogeneous flows; Oscillations; Physics; Pressure; Resonance; Spheres; Gas liquid interface; Pressure fluctuation; Geometrical shape; Bubbles; Non viscous fluid; Pulse response; Digital simulation; Oscillations; Non spherical particle; Incompressible fluid
• ISSN: 0301-9322; 1879-3533
• DOI: 10.1016/S0301-9322(98)00074-3

We consider the response of a gas bubble in an inviscid, incompressible fluid, to a rapid, impulsive change of the ambient pressure, from some initial value down to a minimum and then back up to the initial value. The most important result is the sharp decrease in the amplitude of volume oscillations which results from finite amplitude coupling between the purely radial and shape modes. When the bubble has a steady shape that is non-spherical, there can be resonance between radial mode oscillations and one of the shape modes. This contributes to growth of the resonant shape mode from an initial spherical shape, and produces a ‘phase-lock’ with the two modes either in-phase or π radians out-of-phase. For in-phase conditions, this leads ultimately to a geometric amplification of higher-order shape modes and a sharp decrease in the amplitude of the volume oscillations. The same geometric amplification mechanism also appears in the absence of mean shape deformation (and thus 1:1 resonance), but only if there is another mechanism for the appearance of shape modes. There is also no phase-locking when there is no mean deformation, and so the importance of the geometric amplification effect is greatest whenever the phase difference between P 0 and P 2 is small.