A finite-element analysis of the electrostatic force on a uniformly charged dielectric sphere resting on a dielectric-coated electrode in a detaching electric field

In the electrophotographic process, charged toner particles are transferred from one surface to another with an electric field. To enable electric field transfer of toner, the externally applied field strength must be greater than a threshold value, so that the Coulomb force can overcome the toner adhesion force at the supporting surface. In this paper, the threshold field strength to detach a charged dielectric particle is determined efficiently by using the Galerkin finite-element method to simultaneously solve the Laplace equation for the field distribution and an overall constraint equation for the force balance. This computational method also enables calculation of the electrostatic adhesion force and is applicable to various particle-electrode configurations. For illustrative purposes, however, we consider the axisymmetric problem of electric field detachment of a dielectric sphere with uniform surface charge resting on a planar dielectric-coated electrode. The analysis is particularly focused on the dependence of the electrostatic force upon the dielectric overcoating thickness and spacing between parallel plate electrodes. The electrostatic force on a uniformly charged particle in contact with a surface is found to be influenced significantly by the thickness of dielectric overcoating and the spacing between electrodes when either becomes less than five times the particle radius.