On the instability of conical protrusions of liquid surface in electric field

Electric field is analyzed at the tip of the conical protrusion of a conductive liquid surface that forms as the field strength approaches certain threshold values. When the field exceeds the threshold, the cone tip generally becomes unstable and emits a slender jet. The field strength at the sharp tip of a conducting liquid cone tends to infinity. Even though the field has a singularity, the cone tip becomes unstable only if the semi-cone angle decreases below the Taylor angle, which is the same for all conducting liquids. It is shown that similar conical protrusions can form if the liquid is a dielectric and its permittivity is sufficiently high. In this case, the equilibrium cone angle depends on the permittivity. When the permittivity is lower than approximately 17.60, cones cannot form, and the ensuing phenomena do not occur.