Simulation of the development process in electrophotography

The simulation of the development of the electrostatic latent image using nonmagnetic, nonconducting, monocomponent toner is described. Attention is focussed on the development nip, only a few hundred microns long, the local conditions of which are set by machine elements on a much larger scale. The topics of special interest are electrical relaxation effects in the core of the developer roll and the mass per unit area of toner developed for lines of various widths. The finite-element method is used for the purpose of simulation. To be valid, it relies on careful measurement of material properties. By estimating the relative role of various length scales a local development nip analysis can be justified. Depending on the latent image, the charge distribution along the core/coating interface must arrange itself. This happens on two time scales. One is fast, localized, and based only on the core material; the other is slow and involves the long resistive path of the core and the large capacitance of all layers involved in the development process. For two-dimensional cases a few thousand finite elements and simple algorithms suffice to produce useful time-dependent simulations. Some aspects of solid versus line development can be explained on the basis of a plausible development hypothesis.