A droplet in a stationary electric field

Water droplets on insulating material influence strongly the aging process of the material. The shape of the droplets signifies the state of the aging material. The present paper discusses a numerical procedure to calculate the droplet shape in an electric field generated by a constant voltage. A combined stationary solution of the droplet shape and the electric field is searched for. This leads to a free boundary value problem which is solved by an iterative method. The typical shapes of the droplets are shown for several voltages. Special care is taken to the singularities of the electric field in the triple points.