Intermediate conductivities-the crossover function for insulative and conductive two-component magnetic brush development in electrophotography

A derivation is presented using a macroscopic three-slab charge flow model of xerographic magnetic brush development which results in an analytic exponential crossover function connecting the expressions for the solid-area developed mass/area between the insulative and conductive material regimes. The crossover function is dependent on a lumped parameter called the charge flow, which is the sum of the developer conductivity, connectivity, etc. All of the model parameters can be explicitly measured. Charge flow, developability, and line/solid ratio measurements made with several materials are found to agree very well with the model. Charge-flow measurements of some supposedly insulative materials show currents which, together with the model, appear to account for their higher than expected developabilities.<>