Model of Toner Impaction and Developer Failure

Abstract

High definition digital imaging is enabled in printers by using small micron and nano toner particles. Use of small particles in a housing presents challenges in particle flow as small particles tend to aggregate, clog and impact either on the wall of the housing or on other surfaces. Solids are known to undergo brittle-ductile transition depending on the size of a particle, elastic plastic behavior and strain rates under which they are deformed.In macromolecules, polymer chain flexibility and shear flow of uniformly sized, spherical particles can be analyzed. Inter-particle attractive forces are considered to influence flow of small particles. Simulations performed for different strengths of cohesion, shear rates, particle stiffnesses, particle volume fractions and coefficients of friction show interesting results. From each simulation, the average normal and shear stresses and the average coordination number have been extracted. Generally small particles are externally mixed with nano-sized particles to improve flow. Hard nano-sized particles reduce cohesiveness of toner particles and reduce its aggregation.Particulate flow can some time result in jamming and has been analyzed using Lattice-Boltzmann (LB) or DEM (Discrete Element Methods) involving deformation from collisions resulting from hydrodynamic forces. Consequence of particle impaction on surfaces is a reduction in particle charge with wider distribution causing shortfalls in electro-photographic development and image quality. A rate equation model is developed for impaction in a cylindrical cavity that depends on the impact parameter, rate of volumetric flow, yield stress (modulus) of the elastic-plastic particle, size of the particle and dynamic coefficient of friction. The model predictions are compared with experimental data on the particle (toner) impaction