Electrocapillary instability of a conducting liquid cylinder

The electrocapillary instability of a conducting liquid cylinder is analyzed. Exact solutions to the linearized Navier-Stokes equations are examined. Growth rates are found for several unstable modes, including both axisymmetric and nonaxisymmetric ones. Special attention is given to the electric field effects on the temporal growth and length scales of unstable modes. It is shown that, whereas capillary instability is axisymmetric in the absence of electric field, nonaxisymmetric surface modes also become unstable in a nonzero electric field, growing with time. With increasing electric field strength, azimuthal modes are “switched on” (begin to grow with time) sequentially and the highest temporal growth rate monotonically increases.