A Model for Magnetic Brush Development in Xerographic Machines

A physical model for magnetic brush development of toner in xerographic machines is described. Deposition and scavenging rates are derived from electrostatic and adhesive force balances on toner particles. Ordinary differential equations (ODE) are derived for toner number densities as a function of toner charge, toner diameter, and position in the development nip. A numerical technique is described for solving these ODE´s based on the method of moments. Model predictions of developed mass per unit area, average developed charge per unit mass, and average developed size as a function of development potential for solid areas are compared with experimental data.