Electrohydrodynamic stability of a highly viscous jet

Abstract

When a pendant drop of weakly conducting fluid is raised to a high electric potential, it frequently adopts the shape of a Taylor cone from whose apex a thin, charged jet is emitted. Such a jet can display surprising longevity, but eventually breaks up into fine droplets, a fact utilized in electro-spraying devices. This paper examines the linear stability of an incompressible cylindrical jet carrying surface charge q in a tangential electric field E, for various values of the permittivity ratio λ and the finite rate of charge relaxation, τ. The viscosity is assumed to be large. It is shown that all axisymmetric temporal modes can be stabilized for suitable values of (q, E), but sinuous modes with logarithmically large wavelengths are unstable. If these very long waves are excluded, the jet can sometimes be completely stabilized. It is also shown that an uncharged jet with low permittivity is unstable to sinuous waves for large E, contrary to previous belief.