The Effect of Heaped and Sloped Powder Layers on Ejection Times and the Residence-Time Distribution of a Conical Mass-Flow Hopper

The flow of a hypothetical Coulomb material flowing under gravity from a conical mass-flow hopper is modelled using stress field theory. The assumptions inherent for a Coulomb material can be combined with the assumption of radial flow within the hopper to determine the velocity profile within the hopper. From the velocity profile, ejection times and residence time distributions may be calculated. Since, in a real granular system, the powder layer interface is generally not flat, but sloped at some angle, (nominally the angle of repose), the residence time distribution and ejection times will be dependent on the initial geometry of the powder layers. Residence time distributions and ejection times are calculated for a given granular material in a conical mass-flow hopper firstly for the case of flat layers, secondly for the case where the powder forms a conical heap at the angle of repose, and thirdly for the case when the powder is sloping against a wall. It is found that the shape of the powder layers greatly changes the residence time distribution and ejection times in the system, and needs to be considered when performing residence time measurements in the industrial setting.