An Experimental and Theoretical Study of the Flow of Xerographic Developer Powders from Small Hoppers

An experimental and theoretical study is presented which characterizes the flow of xerographic developer powders out of small hoppers. A small hopper in this reference is defined as one having a maximum height of 12 in. Two walls of the hopper converge at the gate and the remaining two walls are parallel to each other. The flow is studied as a function of the gate opening, hopper angle, particle size, the total height of the particulate material in the hopper, and the angle of repose. Experimental results are presented for particle diameters between 100 ? and 600 ?. A theory is presented to predict flow rates. The predicted functional dependence agrees very well with the observations. The predicted flow rates are about 3.75 times higher than the observed ones. It is suggested that this is due to a resistive force originating in particle interactions. Inclusion of this correction factor in the theory results in very good agreement between theoretical predictions and experimental observations.     

Encapsulated Toners in Xerography and their Shell Fracture Mechanics

The effect of various elastic and physical parameters on the strength of the shell in encapsulated toner is examined. The contact problem of a toner particle and a pressure roller is discussed, and the mechanism of shell fracture from the viewpoint of Hertz's impact theory is reviewed. The magnitudes of the impact force, the fracturing force, and the paper damaging stress are estimated. Within the framework of linear elasticity theory, general expressions for the stresses induced in the shell and core have been derived for both solid and liquid cores. Particular cases have been computed and presented in normalized graphical form on a unit loading basis. The shell strength depends strongly on the geometrical and elastic properties of the core and shell materials, specifically on the shell thickness, the ratio of the core and shell shear moduli, and the tensile strength of the shell material. The modes of toner fracture and the significant effects of the elastic properties of the paper on the crushing force of the particles is discussed. It is shown that the breaking of the particles is facilitated by a harder surfaced paper.     

Measurement of Carrier Bead Velocity Distribution in Cascade Flow

A miniature piezoelectric impact probe is described for measuring the impact velocity of carrier beads in a cascade flow. The probe can sense a force of a few dynes. It has a response time of about 1 ?s and a total settling time of less than 40 ?s. The impacts of a few microgram particles due to a free-fall under gravity of a distance of about 50 ?m and at a count rate in excess of 20 000/s have been measured. The probe has been used in measuring the impact velocity distribution of carrier beads in a cascade flow. The impact velocity distributions have been measured at different flow conditions and compared with theoretical predictions. The characteristics of the cascade flow are briefly discussed in terms of the two parameters: the number density of the carrier beads in the flow and the diffusion constant of the flow.     

A Theoretical Study of the Mechanics of a Xerographic Cleaning Blade

The use of a polymeric blade is common in removing the residual toner from the imaging surface in xerography. The cleaning action of such a blade is influenced by its local deformation in the contacting region. A nonlinear beam theory approach is presented for studying the deformation of a xerographic cleaning blade. Both the straight and tip regions of the blade are examined. The parameters studied include the normal load, the ratio of tangential and normal forces (the coefficient of friction , ?), the blade tip angle, blade inclination angle, Young's modulus, Poisson's ratio, blade length, and thickness. The effect of these parameters on the size of the contacting region is presented. The critical ratio ?c and the critical inclination angle which determine blade curl-under and curl-up are discussed. The maximum blade inclination angle which governs the tip stability is predicted. Cleaning performance criteria for planning and local curl-unders are developed in terms of the pressure in the contacting region. Agreement of the analytical findings with the available experimental data is good.