Mathematics and Computers in Simulation 63 (2003) 529–539
A droplet in a stationary electric field
Department of Mathematics, University of Rostock, D-18051 Rostock, Germany
Received 23 August 2002; received in revised form 30 May 2003; accepted 11 June 2003
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.
© 2003 IMACS. Published by Elsevier B.V. All rights reserved.
Keywords: Stationary electric field; Insulators; Droplets; Free boundary value problem; Corner points; Numerical analysis
This investigation is initiated by the observation that water droplets on the surface of insulating material
influence strongly the process of its aging. While aging the material looses its hydrophobic and insulating
characteristics and hence its proper purpose .
The present paper considers a simple droplet in an electric field. The droplet lays on a solid support
made of resin, and the electric field is generated by a voltage between two electrodes inside the resin. The
acting forces and the droplet shape are determined. Note that the droplet shape feeds back to the electric
In [12,14] the problem was numerically handled by finite integration techniques, , on a three-
dimensional equidistant grid in a quasi-stationary formulation. In the present paper, we concentrate on
the variable shapes of the droplets and their behaviour under the influence of different voltages. Thus, finite
elements on a triangulat