Electrostatics of conductive particles in contact with a plate electrode affected by a non-uniform electric field

Analytical formulae are available for the estimation of the electric forces on conductive bodies of regular shape (spherical, hemi-spherical, hemi-ell ipsoidal, cylindrical) in contact with a plate electrode affected by a unif orm electric field. The electrode arrangements employed in some electrostat ic processes generate non-uniform electric fields for which no such formula e can be derived. The aim of this paper is to demonstrate the usefulness of numerical techniques for the evaluation of the electric forces that act on conductive particles of any shape in contact with electrodes affected by s uch fields. A computer program based on the boundary element method was emp loyed for analysing the behaviour of conductive cylinders in a two-dimensio nal electrode arrangement that models the actual electric field configurati on of a plate-type electrostatic separator: a cylindrical high-voltage elec trode, parallel to a grounded plate. The numerical results are in good agre ement with the theoretical predictions for a simple case in which the elect ric force can be analytically expressed using the electric image method. Th e computer program enabled the evaluation of the effect of field non-unifor mity on the magnitude of the electric force acting on single particles, in various positions on the surface of the plate electrode. In most of the act ual applications, several particles are simultaneously in contact with the charging electrode. Therefore, the study was extended to the situation of s everal equally spaced cylindrical bodies in contact with the plate electrod e. The output data of the computer program were used for a crude evaluation of the conditions in which conductive particles of different size and spec ific mass detach become detached from an inclined plane under the action of the electric force. In this way, numerical modelling could guide the feasi bility studies and laboratory tests that are needed for the development of any new application of the electrostatic separation method. Several simple experiments on graphite cylinders (radii: 0.25, 0.35 and 0.45 mm) confirmed the numerical simulations. With a program for three-dimensional analysis o f the electric field, the computational procedure presented in this paper c ould be employed for any electrode configuration and any particle shape.