Powder Flow Analysis

Powder Flow Analysis Glossary

Coefficient of Friction
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.

Arching Dimension
Minimum hopper outlet size needed to ensure that the powder will discharge in Mass Flow instead of forming a stable arch across the opening.

Axial Distance
Distance between the lid and the bottom of the trough, indicating the depth of the powder.

Bin Diameter
Maximum internal diameter of the storage vessel. For square or rectangular vessels, the equivalent bin diameter should be used.

Bulk Density
Mass of a powder divided by its total volume.

Cohesion
A measure of the strength retained by a powder after it has been compacted to a given Consolidation Level.

Consolidation
Process of applying a Normal and a Shear stress to a bulk solid to move the particles together, to observe any increases in its Cohesion, Bulk Density, etc.

Core-Flow
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 near the vessel walls remains stagnant until the level descends to the point where that powder is at the top surface.

Critical Arch
Largest arch span that a given powder can support before collapsing under its own weight.

Critical Consolidation Stress

For Arching: Major Principal Consolidating Stress acting on the powder in the hopper at critical arching dimension during mass flow.
For Ratholing: 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
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
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.

Critical Rathole
Largest Rathole diameter a powder can support before collapsing in a Core Flow regime.

Critical Stress
Unconfined Failure Strength of the powder forming the Critical Arch or the Critical Rathole. This is determined by taking the Unconfined Failure Strength at the corresponding Critical Consolidation Stress.

Critical Wall Friction Angle
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, defining the ratio of the major and minor principal Consolidation Stresses during steady-state flow.

Failure Locus
Line of maximum Shear Stress that a powder can support before flow occurs under various over-consolidated Normal Stresses. This is dependent on the Consolidation Level.

Fill Density
Bulk Density of the powder in the trough before any stress is applied.

Flow Factor
(Arching) The 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.

Flow Function
Line of a powder’s Unconfined Failure Strength versus the Consolidation Stress that is applied to it.

Free-Flow
Powder flows reliably through very small outlet dimensions under gravity. Arching and Ratholing do not occur. This is indicated in hopper calculations as "Free Flow" or "0.0."

Geometric Spacing
A series of values where each value is equal to the previous value multiplied by a constant factor. The factor is chosen to space the values over the entire range, resulting in 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
Largest stress acting on the powder during Steady State Flow.

Mass-Flow
A first-in, first-out discharge pattern where the powder flows at the vessel walls and all the material is in motion.

No Flow
(Arching) For the given Flow Factor, the powder always arches. This is indicated in the hopper calculations as "No Flow" or "Flow."

Normal Stress
Stress due to the Axial Load, applied perpendicular (normal) to the powder bed.

Over consolidation
After Consolidation, reducing the Normal Stress without shearing so that the Bulk Density is high relative to the new Normal Stress.

Rathole Diameter
Minimum outlet diameter of a Core Flow hopper needed to ensure that the powder will flow instead of forming a stable Rathole.

Shear Stress
Stress due to the Torsional Load, occurring 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 (hours or overnight, to represent static storage in a hopper) before measuring the Failure Locus.

Torsional Distance
Distance that the trough has rotated from its starting position at the beginning of the test.

Unconfined Failure Strength
Stress required to cause a powder to flow at a stress-free surface after it has been compacted to a given Consolidation Level.

Wall Cohesion
A measure of the potential for the powder to stick to a wall surface, dependent on the Consolidation Level.

Wall Friction Test
Measures the distance the powder travels across the wall surface before the Failure Locus is reached.