Angle of Repose
The ‘angle of repose’ of a bulk material is often quoted as a specific value and sometimes cited as a measure of the materials flow prospects. In practice, the inclination adopted by an unconfined surface of a bulk material depends to a greater or lesser extent on the manner of its formation and its relevance to the way in which the bulk material flows is limited to unconfined behaviour. The ‘loose poured’ angle of repose normally forms a conical pile from a single point fill with the loose material sliding down a diverging surface. This separation of the particles on a moving layer of reducing thickness allows the finer fractions to be deposited, whilst the larger components roll further down the slope. This is the most common form a segregation in bulk products that has a wide particle size distribution. The main value of this angle of repose it that it determines the ‘Ullage’ of a hopper, that is, the space above the surface of the material that cannot be filled by gravity flow.
A ‘drained angle of repose’ forms when a funnel flow hopper discharges by drawing down material from a narrow channel above the outlet. This generates a conical surface where flow converges in an increasing depth, allowing finer fractions to sift through the moving bed. These fines tend to accumulate with progressive reduction of the surface level, leading to a terminal flush of fines when the hopper finally empties. The drained angle of repose tends to be steeper than the poured repose angle for three reasons.
1. The particle interference on the converging, deepening surface restricts the freedom of movement of the flowing media, whereas the diverging bed of reducing thickness is more dilate and allows much greater freedom of particle movement.
2. The poured repose condition has a dynamic momentum and significant inertia, usually from a free fall situation, whereas the drained repose has to initiate motion from rest and accelerate the material against the resistance of internal friction of the bed.
3. The stored material may well have been at rest for some time and layers below the initial surface subjected to consolidating pressures from the overlaying contents. This will tend to have introduced closer particle packing and strengthen the bulk due to ‘time consolidation’.
A further ‘repose’ condition is developed when material is extracted from the edge of a stockpile or a ‘rathole’ is formed in a funnel flow hopper. The surface inclination may vary from a loose drained state to an overhang, depending on how the strength of the bulk material has been affected. The term ‘angle of repose’ is virtually meaningless for cohesive materials and fine powders that are prone to retain excess air and attain a fluid-like condition when aerated. Such materials tend to settle to an impervious mass that resists the permeation of air into the expanding void space caused by shear expansion as the bulk deforms to flow. This creates a partial vacuum in the voids, the differential pressure to ambient imposing a compacting force on the bulk to oppose flow.
The angle of repose is not applicable to elongated and dendretic shaped particles, those that sinter, ‘cake’, or plastically deform under pressure. It should only be used when repeatable under given conditions and to reflect its slope forming characteristics.
