Resonance oscillations of a drop (bubble) in a vibrating fluid

The paper deals with the resonance oscillations of a drop (bubble) surrounded by a fluid of different density in a container subjected to small amplitude vibrations in zero gravity conditions. The drop size is considered to be large in comparison with both the vibration amplitude and the thickness of viscous Stokes layers. The calculations for parametrically excited oscillations of the drop are carried out in the linear approximation, for inviscid and low viscous media, neglecting compressibility effects. The resonant oscillation is a doublet of neighbouring modes of eigen-oscillations of the drop, for which the sum of frequencies coincides with the frequency of the forced vibrations. This means that the basic state becomes unstable against quasi-periodic oscillations. The finite viscosity implies a finite threshold for the excitation of resonance. On the other hand, the viscosity plays a destabilizing role; at non-zero (even infinitesimal) viscosity the width of the instability frequency range turns out to be greater than in the case of inviscid fluids.