Stability of Electrically Charged Viscous Cylinders

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Abstract
A characteristic equation describing the stability of an electrified fluid cylinder is derived taking into account effects due to the electric field, surface tension, viscosity, and inertia. The electric field causes the cylinder to be unstable subsequent to nonaxisymmetric deformations of the interface. For relatively inviscid fluids electrification can make the growth rates for nonaxisymmetric disturbances almost as large as the rates for axisymmetric forms. It is found that viscous effects tend to damp axisymmetric motions more than motions accompanying a sinuous deformation; thus, the sinuous mode may be the most unstable form of disturbance in many situations. The combined effects of viscosity and the electric field act so that the cylinder manifests the greatest instability at wavelengths about as large as the circumference of the cylinder, when viscous effects are paramount, in contrast to Rayleigh's result for an unelectrified fluid cylinder.

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