Modelling the role of paper microstructure in electrophotography

We study how paper microstructure heterogeneity affects the electrostatic field acting on toner particles during xerographic printing. We use an efficient multigrid Poisson solver to simulate electrostatic fields. The dielectric distribution of paper is obtained either analytically or input numerically using a recently developed 3D fibre network model of paper. Simulations are used to elucidate the relative importance of paper surface, filler and porosity variations in establishing spatial variations of the electrostatic field. It is found that only long wavelength variations of surface height, bulk filler or porosity variations affect variations in electrostatic transfer forces to any relevant degree. Furthermore, we show that the effect of these long wavelength perturbations can be modelled using a new 1D effective capacitor model. When surface variations and surface filler are mixed together, we found the interesting result that mode mixing can decrease the spatial fluctuations of the electric field. Finally, using simulated 3D paper webs, which mimic the properties of laboratory handsheets, we find that to lowest order surface roughness and not formation is responsible in controlling variations of the electrostatic transfer field, a result of importance in digital printing onto stochastic printing substrates, such as commercial paper.