Adaptive finite element analysis of electrostatic interactions: a sphere between two charged walls and two isolated spheres

In the process and particle technology-based industries, a number of processing steps involve the separation of a dispersed phase from a continuous phase. The dispersed phase may be in the form of solid and/or liquid particles, for which the use of high electric fields provides a number of electric forces to cause its separation from the continuous phase. Therefore, an analysis of the effect of the applied electric field on the particles is important in order to improve the separation efficiency. In this work, a finite element method, combining an automatic error estimator and an automatic mesh generation algorithm, has been applied to calculate electrical-induced forces in a number of physical systems. These systems include the interaction of a charged sphere between two charged walls, and the interaction between two charged spheres. The finite element formulation, utilising nine-node quadrilateral elements, has been shown to be more accurate than the currently available approximate analytical solutions when the sphere /wall separation distance or sphere /sphere separation distance is smaller than the radius of the sphere. The FE formulation reported here can also produce more accurate results with minimum predetermined error, compared with other numerical solutions. The FE formulation in the present work can be extended to more complicated geometries and structures, including more complex particle shapes and/or drop shapes and non-uniform electric fields. This gives a more complete simulation for real physical systems in the particle technology and separation industries