Paper: Flow of particulates, toners and carriers in a housing cavity

Abstract

Flow of small particles micron in size is important in several industrial applications such as digital imaging, polymer processing, powder coating and in dispersing fertilizers to name a few. In digital imaging toner particles surrounded by silica or titanium are triboelectrically mixed with carrier particles to form developer particles. The toner particles are then separated from carrier particles by electric field and conveyed to photoreceptor for development. Optimum flow rates of both toner particles and of developer particles are essential for development process. Interparticle forces, bulk properties (compressibility and cohesion) and stresses (frictional, cohesive and viscous stresses) are used to analyze powder flow. In inter-particle forces, the presence of humidity can result in capillary forces (surface tension) being important along with both electrostatic and van der Waal forces in affecting toner and developer flow. Several models can be put forth to explain the mechanisms of charges on toner and developer particles and their effect on flow. Correspondingly, hardness and modulus of a particle or particles are important material variables in van der Waal forces. Flow of toner particles and developers in a housing is analyzed by considering driving force from applied shear energy (rotating augers) against constraints of extrinsic constraints (consolidation, boundary) and intrinsic constraints (cohesion, compressibility and inter-particle forces). Both Discrete Element Method (DEM) and Continuum Models have been used to analyze powder flow with DEM uses models at particle level and is therefore requires costly computation where as Continuum Models are less accurate for complicated geometries and free surfaces. Empirical correlations are costly to obtain for predicting developer flow from frequent bench experiments (Freeman tester, Jenike shear cell and Seville tester) and tests in fixtures and housings.