Coefficient of Friction
the ratio of the force required to move one surface over another to the total normal force applied to those surfaces.
Angle of Wall Friction:
Represents the friction between the sliding powder and the wall of the hopper or chute at the onset of flow.
Minimum hopper outlet size needed to insure that the powder will discharge in Mass Flow instead of forming a stable arch across the opening.
Distance between the lid and the bottom of the trough, indicating the depth of the powder.
Maximum internal diameter of the storage vessel. For square or rectangle vessels, the equivalent bin diameter should be used.
The mass of a powder divided by its total volume.
A measure of the strength retained by a powder after if has been compacted to a given Consolidation Level.
The process of applying a Normal and a Shear stress to a bulk solid to move the particles together, in order to observe any increases in its Cohesion, Bulk Density, etc.
A first in-last out discharge pattern where the powder flows from the top of the vessel through a vertical channel above the outlet. Powder that is near the walls of the vessel remains stagnant until the level descends to the point where that powder is at the top surface.
The largest arch span that a given powder can support before collapsing under its self weight.
Critical Consolidation Stress:
The Major Principal Consolidating Stress acting on the powder in the hopper at critical arching dimension during mass flow.
For Rat-Hole: The Major Principal Consolidating Stress acting on the powder in the region of the outlet due to the head of powder in a core flow hopper.
Critical Density: The Bulk Density of the powder forming the Critical Arch or the Critical Rathole. This is determined by taking the Bulk Density at the corresponding Critical Consolidation Stress.
Critical Internal Friction Angle:
The Internal Friction Angle of the powder forming the Critical Arch or the Critical Rathole. This is determined by taking the Internal Friction Angle at the corresponding Critical Consolidation Stress.
The largest Rathole diameter a powder can support before collapsing in a Core Flow regime.
The Unconfined Failure Strength of the powder forming the Critical Arch or the Critical Rathole. This is determined by taking the Unconfined Failure Angle at the corresponding Critical Consolidation Stress.
Critical Wall Friction Angle:
The Wall Friction Angle of the powder forming the Critical Arch or the Critical Rathole. This is determined by taking the Wall Friction Angle at the corresponding Critical Consolidation Stress.
Effective Angle of Internal Friction:
Represents the friction between sliding layers of powder, defines the ratio of the major and minor principal consolidation stresses during steady state flow.
The line of maximum Shear Stress that a powder can support before flow occurs under various over consolidated Normal Stresses. This is dependant on the Consolidation Level.
The Bulk Density of the powder in the trough before any stress is applied.
(Arching) Ratio of the consolidation stress in a powder during Steady State Flow to the stress required to set up a stable arch. This factor depends on both the flow properties of the powder and the shape of the hopper.
Line of a powder’s Unconfined Failure Strength versus the Consolidation stress that is applied to it.
The powder flows reliably through very small outlet dimensions under gravity. Arching and Ratholing does not occur. This is indicated in hopper calculations as “Free Flow” or “0.0”.
Series of values where each value is equal to the previous value times a constant factor. The factor is chosen to space the values over the entire range. In this type of series, there will be more values at the lower end of the range.
Hopper Half Angle:
Maximum angle of the converging hopper wall (from the vertical axis) needed to ensure Mass Flow; Angles greater (shallower) than this will produce Core Flow.
Major Principal Consolidation Stress:
The largest stress acting on the powder during Steady State Flow.
A first in-first out discharge pattern where the powder flows at the vessel walls and all the material is in motion.
(Arching) For the given Flow Factor, the powder always arches. This is indicated in the hopper calculations as “No Flow” or “-----”.
The stress due to the Axial Load. It is stress applied perpendicular (normal) to the powder bed.
After Consolidation, reducing the Normal Stress without shearing so that the Bulk Density is high relative to the new Normal Stress.
Minimum outlet diameter of a Core Flow hopper needed to ensure that the powder will flow instead of forming a stable Rathole.
The stress due to the Torsional Load. It is the stress between parallel layers of powder (Flow Function and Time Consolidated Flow Function tests) or between a layer of powder and the lid (Wall Friction test).
Steady State Flow:
Continuous powder flow where the Normal and Shear Stresses have reached a constant level.
Time Consolidated Test:
Compacts the powder at a given Consolidated Level for an extended period of time (hours, overnight to represent static storage in a hopper) before measuring the Failure Locus.
Distance that the trough has rotated from its starting position at the beginning of the test.
Unconfined Failure Strength:
The stress required to cause a powder to flow at a stress free surface, after it has been compacted to a given Consolidation Level.
A measure of the potential for the powder to stick to a wall surface.
This is dependant on the Consolidation Level.
Wall Friction Test:
The distance the powder travels across the wall surface before the
Failure Locus is measured.