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Instability of compressible drops and jets

Abstract We revisit the classic problem of the stability of drops and jets held by surface tension, while regarding the compressibility of bulk fluids and spatial dimensions as free parameters. By mode analysis, it is shown that there exists a critical compressibility above which the drops (and discs) become unstable for a spherical perturbation. For a given value of compressibility (and of the surface tension and the density at equilibrium), this instability criterion provides a minimal radius below which the drop cannot be in stable equilibrium. According to the existence of the above unstable mode of the drop, which corresponds to a homogeneous perturbation of a cylindrical jet, the dispersion relation of Rayleigh–Plateau instability for cylinders drastically changes. In particular, we identify another critical compressibility above which the homogeneous unstable mode is predominant. The analysis is carried out for non-relativistic and relativistic perfect fluids, the self-gravity of which is ignored.