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Ask an Expert
Angle of repose versus angle of internal friction
Q: Can you explain angle of repose versus angle of internal friction and how they may influence bulk solids handling equipment?
Many times people get confused between the terms angle of repose and angle of internal friction. Both of these material properties are used by researchers to identify the flow properties of bulk solids. Generally, the higher the angle of repose or angle of internal friction, the more difficult the material flows. The opposite is also true; the lower the angle of repose or angle of internal friction, the easier the material flows. Regarding bulk handling equipment design, the angle of repose measurement is widely used when designing belt conveyors and transfer chutes whereas the angle of internal friction is considered when designing bins and hoppers.
A material's angle of repose is defined as the angle of heap formed when an unconsolidated material is poured freely onto a horizontal surface. This is called the static angle of repose. The angle of repose changes when the pour height changes. Similarly, the angle of repose for a material can change when a material is poured onto a moving surface because of the agitation caused by the movement. That angle is called the dynamic angle of repose. This measurement can be important when designing a belt conveyor for your material.
When designing a belt conveyor, the material's dynamic angle of repose determines how much material the belt conveyor can hold in terms of heap height, which determines the belt conveyor's capacity. If the incorrect angle of repose is used to determine the material feedrate, this will lead to material over-feeding onto the belt conveyor, spillage, and the potential for a dust explosion.
rihfOther factors that influence the angle of repose are particle size and shape, density, surface area, cohesion, moisture content, and the material's coefficient of friction. When the material's overall particle size decreases, each particle's surface area increases, which will increase the material's cohesive tendencies. The higher the cohesive forces, the higher the angle of repose values. For example, granular sugar (0.53- to 0.67-millimeter particle size) forms a low angle of repose with a regular conical shape, as shown in Figure 1, whereas powdered sugar (80- to 100-micron particle size) forms a higher angle of repose with an irregular shape, as shown in Figure 2.
rihfThe powdered sugar's surface area is greater than that of the granular sugar. A material's angle of repose is influenced by other factors such as cohesive forces, friction forces, and steric repulsions. Additionally, liquid bridge formation, electric static charge generation, van der Waals forces, and magnetic forces can also influence the material's cohesiveness. See Figure 3 for more information about angle of repose with respect to particle size.
The following table offers the angles of repose for some common materials:
Type of Material Angle of Repose
Caffeine 25
Hydroxypropyl cellulose 28
Sodium carboxymethyl cellulose 29
Gypsum 30
α-Lactose monohydrate 31
Cement 35
Carbon black 35
Magnesium chloride 40
Chalk 45
Barium carbonate 45
rihfA material's angle of internal friction is defined as the angle between the material's shear stress and normal stress (Mohr's circle) at which material failure occurs. This value is determined by a direct or ring shear tester. In this test, the material won't flow until it loses its shear strength following the Mohr-Coulomb failure criterion, which is the linear envelope obtained between the shear strength of a material and normal applied stress. See Figure 4. This shear strength depends on the material's cohesion and frictional properties. The greater the cohesion and frictional values, the greater the shear strength or angle of internal friction will be and the more difficult the material flows.
In a loose material state, the angle of repose equals the angle of internal friction. When the material gets compacted, the angle of internal friction changes. The angle of internal friction also increases with an increase in moisture content. For example, zinc ore's angle of internal friction is 32 degrees at 18 percent moisture and 56 degrees at 23 percent moisture. The material's angle of internal friction is used when designing a hopper to determine the material hopper's vessel angles for mass and funnel flow.
John Lawrence is the research director at the KSU Bulk Solids Innovation Center.
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