Abstract
The effect of radial pulsations on the stability of a compressible cylindrical gas column surrounded by an ambient liquid is discussed. In the absence of pulsations, the stationary interface is susceptible to the Rayleigh capillary instability, which promotes the growth of longitudinal waves whose wave length is larger than 2π times the column radius, irrespective of the Reynolds number. A Floquet stability analysis for potential flow shows that the pulsations further destabilize the interface by extending the range of unstable wave numbers to a sequence of islands. A similar stability analysis for Stokes flow shows that the pulsations also have a destabilizing influence, though the presence of an insoluble surfactant has a competing stabilizing influence that may cause an overall reduction in the range of unstable wave numbers.
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