Mechanics of magnetic powders

Abstract

The mechanics of magnetizable powders are strongly influenced by inter-particle, as well as ponderomotive, forces when a non-uniform magnetic field is applied to the medium. These forces are utilized in magnetic brush xerographic copiers. The magnetic tumbling transport and metering of developer materials in such machines is examined using a two-dimensional flow cell. Using 100 μm polymer particles containing up to approximately 50% magnetite by weight in this flow cell, the important features of magnetically driven flow and metering on a magnet roll can be observed. Among various observations is the discovery of a stagnant layer, the thickness of which depends on the overall thickness of the powder layer on the roll and the magnetite content of the particles. It is hypothesized that this stagnant layer phenomenon is a surface effect and that an equilibrium is established between two competing influences: (i) the magnetic gradient force, which tends to compress the powder layer against the sleeve surface, and (ii) the internal magnetic ‘cohesion’, which, according to a continuum electromechanical model based on Maxwell stresses, is negative in planes parallel to the magnetic field and tends to cause spontaneous fracture of the layer. This model is used to obtain a predicting relationship for the thickness of the stagnant layer. This predicting equation shows moderate success when compared with the experimental data. More importantly, the theory predicts that the stagnant layer thickness should be only weakly dependent on the number of magnetic poles on the role and independent of the magnetic pole strength. Furthermore, the model reveals that, for materials with packed powder magnetic permeability greater than approximately 2.0, no stagnant layer phenomenon should be observed. These predictions are consistent with our observations.