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Abstract
Results of time-dependent modelling of electrohydrodynamiceffects on the surface of a liquid metallic conductor are reported for aregime where no electron, ion or particle emission occurs. TheNavier-Stokes equations, with free liquid boundaries subject to Maxwellfield stress, surface-tension stress and viscous action, have been solvedby a method that uses transformation of the interfaces into a rectangle;this overcomes a problem of surface oscillations that appeared using themarker-and-cell technique. The situation geometry is a deep unboundedsurface with axial symmetry. With time, an almost flat surface evolves intoa cone-like shape, with the angle of the cone depending on the initialshape of the surface. We describe this structure as a dynamic Taylor cone.The time-dependent profiles of the surface shape are in good agreement withexperimental observations of this process. The calculations have also shownthat, when the protrusion is formed, the time dependences of the surfaceradius of curvature, the electric field value at the protrusion apex andthe axial velocity of the liquid metal, exhibit a run-away behaviour: thephysical values become very large for a short time. As a cusp evolves on asurface, the Maxwell stress acting outwards becomes very large andovertakes the growth of both the surface tension and viscous stress actinginwards. Analysis of the time dependences of physical values can stronglyassist the development of analytical treatments of such phenomena, and giveinsight into the problem of the dynamic description of operating liquidmetal ion source atomisers. The development of numerical methods usingtransformation of the interfaces appears very useful for the treatment ofproblems in which the cathode or the anode significantly change shape. Thissituation occurs, for example, when a liquid surface is covered by a metalplasma and the evolution of the surface occurs in the context of a Langmuirshield.
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