Dirk Langemann
Department of mathematics
Rostock university
email: dirk.langemann@mathematik.uni-rostock.de
Rain water droplets on the surface of insulators in high-voltage equipment influence negatively the insulating and hydrophobic properties of the insulating material. The shape of the droplets signifies the state of the aging material. Therefore studying the behaviour of droplets in strong electric fields is of economical interest.
Mathematically, the problem of determining the droplet shape is a free boundary value problem with the free surface of the water droplet. The free surface of the droplet, i. e. the droplet shape influences the electric field in the neighbourhood of the droplet, and the electric field feeds back to the droplet shape, because the dipoles of the water concentrate on the surface. Thus the electric field generates a normal force density which is acting on the droplet surface.
The paper presents the fundamental ideas of solving the free boundary value problem, gives an effective numerical algorithm for the determination of the droplet shape and compares the results for two- and three-dimensional models of dielectric and conductive droplets in differently strong electric fields.
Furthermore, it will be shown that a droplet even without any additional electric charge may suffer a non-vanishing resulting force from an electric field and is initiated to move as a whole. The moving droplets moisten the insulator and leaves behind a water film.