(5)
Another close relative is Carr’s Compressibility Index:
      (6)
The percentages provide a means to rank materials:
5-15% free-flowing to excellent flow — granules 
12-16% free-flowing to good flow — powders
18-21% fair to passable powdered granule flow
23-28% easily fluidizable powders — poor flow
28-35% cohesive powders — poor flow
33-38% cohesive powders — very poor flow
>40%  cohesive powders — very very poor flow

These relatively quick and easy measurements can be effective in giving some indication as to how powders will likely behave but are by no means comprehensive; exercise some caution if relying only on this information.

Angle of repose

Another parameter that is used to determine flowability is the angle of repose, which is defined as the angle of the free surface of a heap of particulate material to the horizontal plane. Unfortunately, we are faced with the same problem that we were with bulk density — the angle of repose is not a constant for a given material and depends upon the method of heap formation. There again are two measurements commonly quoted: the poured angle of repose and the drained angle of repose. The poured angle of repose is the angle measured from a heap formed by pouring material on to a flat horizontal surface (Figure 1). The drained angle of repose is the angle measured on the internal conical face that has been formed when material is drained from a orifice on the flat horizontal bottom of a container (Figure 2). A third angle of repose that you may come across is the dynamic angle of repose, which is the angle to the horizontal of the free surface formed in a relatively slowly rotating drum (Figure 3).

Be aware of several things when using angles of repose: First, the angle formed will depend upon the details of the formation process. For example, the fall height for the poured angle or the orifice size for the drained angle will influence the angle. Therefore, the angle measured is not independent of the measuring apparatus. Second, the same material tested using the three techniques will give a different angle for each (Table 2). The measurements only can be reliably made when using powders that are free-flowing to slightly cohesive and are fairly homogenous. Materials that are a mixture of components or that have a wide size distribution will give angles that are difficult to determine and suffer low repeatability. There also are some uncertainties based on the fundamental physics of the problem, relating to stress history and avalanche behavior [2, 3].

Click to enlarge Table 2.

Despite these difficulties, the angle of repose in whatever form can be a useful tool to rank materials. As a rough guide, the relationship between the angle of repose and flowability often follows the structure below:

Angle of repose, degrees  Flowability
25-30     very free-flowing
30-38     free-flowing
38-45     fair flowing
45-55     cohesive
>55     very cohesive

This classification allows us to make some judgement on the likely flow behavior of a material but has very limited value for equipment selection and design. In particular, it is a mistake to use the angle of repose in an estimate of the wall angle required for the converging section of a hopper. However, the angle of repose can serve in some cases to estimate the surcharge (the material at the top of a hopper which forms a “heap”) in a storage vessel or the ground area requirements when forming a stockpile.

Rough guidance

The Compressibility Index and angle of repose both give some indication of flowability under different flow conditions, although the applied stresses in both cases can be considered to be relatively low. There is no obvious benefit in combining both test results into a single index value; both may be usefully applied separately to benchmark or rank materials based on known plant performance. For example, if you have experience that a material with a particular flowability value passes through a chute or indeed an entire process without difficultly, then you may expect that a different material with the same flowability value also will not cause problems. (Most times, you will be correct.) However, a material with a worse flowability value needs be treated with more caution. Plants suffering from poor performance require more detailed testing to establish the cause(s) of the flow difficulties or product hangups.

The material in this article has been extracted and adapted from the author’s recent book “Characterisation of bulk solids” [1].

Dr. Don McGlinchey is a consulting engineer at Glasgow Caledonian University’s Center for Industrial Bulk Solids Handling, Glasgow, Scotland. E-mail him at D.McGlinchey@gcal.ac.uk.

References

1. McGlinchey, D., “Characterisation of bulk solids,” Blackwell Publishing, Oxford, U.K. (2005).
2. Duran, J., “Sands, powders and grains – an introduction to the physics of granular materials,” Springer-Verlag, New York (2000).
3. Nedderman, R.M. “Statics and Kinematics of Granular Materials,” Cambridge University Press, Cambridge, U.K. (1992).