Electric field detachment of a nonuniformly charged dielectric sphere on a dielectric coated electrode

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 residing surface. Toner particles in electrophotography are often charged by the phenomenon of triboelectricity. Triboelectrically charged particles tend to have nonuniform surface charge distributions which may significantly influence the electrostatic adhesion force and threshold field strength for detachment. In this work, the threshold detachment field strength and the electrostatic adhesion force associated with a nonuniformly charged dielectric sphere are 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. Problems with various complicated geometric configurations can be treated within this computational framework. For illustrative purposes, however, we consider the axisymmetric problem of electric field detachment of a charged sphere on a dielectric coated donor electrode. Our analysis is particularly focused on the effects of a nonuniform charge distribution expressed in terms of Legendre functions on the spherical particle surface. The electrostatic adhesion force appears to vary linearly with the coefficient for each Legendre function. Depending on the orientation of the particle relative to the residing surface, the nonuniformity in the particle surface charge distribution may either enhance or reduce the electrostatic adhesion force.