Formation of the Taylor cone on the surface of liquid metal in the presence of an electric field

The hydrodynamic evolution of the surface of a liquid metal in the presence of an electric field is investigated using both analytical and numerical techniques. It is established that a free liquid surface with axial symmetry evolves with time into a cone-like shape, with the cone angle equal to Taylor's static value of 98.6°. The mechanism behind such interesting flow behaviour is that the system of electrohydrodynamic (EHD) equations has a self-similar asymptotic solution that generalizes Taylor's static result. The asymptotic solutions are found and the time-dependent behaviours of basic physical quantities (electric field strength, fluid velocity and surface curvature) near the singularity are established. The results and the analytical and numerical techniques used are thought to be useful in the development of time-dependent models of operating liquid metal ion sources and EHD sprayers.