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-ellipsoidal, cylindrical) in contact with a plate electrode affected by a uniform electric field. The electrode arrangements employed in some electrostatic processes generate non-uniform electric fields for which no such formulae 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 such fields. A computer program based on the boundary element method was employed for analysing the behaviour of conductive cylinders in a two-dimensional electrode arrangement that models the actual electric field configuration of a plate-type electrostatic separator: a cylindrical high-voltage electrode, parallel to a grounded plate. The numerical results are in good agreement with the theoretical predictions for a simple case in which the electric force can be analytically expressed using the electric image method. The computer program enabled the evaluation of the effect of field non-uniformity 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 actual applications, several particles are simultaneously in contact with the charging electrode. Therefore, the study was extended to the situation of several equally spaced cylindrical bodies in contact with the plate electrode. The output data of the computer program were used for a crude evaluation of the conditions in which conductive particles of different size and specific mass detach become detached from an inclined plane under the action of the electric force. In this way, numerical modelling could guide the feasibility 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 of the electric field, the computational procedure presented in this paper could be employed for any electrode configuration and any particle shape.