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.
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