Dynamic Taylor cone formation on liquid metal surface: numerical modelling

Results of time-dependent modelling of electrohydrodynamic effects on the s urface of a Liquid metallic conductor are reported for a regime where no el ectron, ion or particle emission occurs. The Navier-Stokes equations, with free liquid boundaries subject to Maxwell field stress, surface-tension str ess and viscous action, have been solved by a method that uses transformati on of the interfaces into a rectangle: this overcomes a problem of surface oscillations that appeared using the marker-and-cell technique. The situati on geometry is a deep unbounded surface with axial symmetry. With time, an almost flat surface evolves into a cone-like shape, with the angle of the c one depending on the initial shape of the surface. We describe this structu re as a dynamic Taylor cone. The time-dependent profiles of the surface sha pe are in good agreement with experimental observations of this process. Th e calculations have also shown that, when the protrusion is formed, the tim e dependences of the surface radius of curvature, the electric field value at the protrusion apex and the axial velocity of the liquid metal, exhibit a run-away behaviour: the physical values become very large for a short tim e. As a cusp evolves on a surface, the Maxwell stress acting outwards becom es very large and overtakes the growth of both the surface tension and visc ous stress acting inwards. Analysis of the time dependences of physical val ues can strongly assist the development of analytical treatments of such ph enomena, and give insight into the problem of the dynamic description of op erating liquid metal ion source atomisers. The development of numerical met hods using transformation of the interfaces appears very useful for thr tre atment of problems in which the cathode or the anode significantly change s hape. This situation occurs, for example, when a liquid surface is covered by a metal plasma and the evolution of the surface occurs in the context of a Langmuir shield.