values are expressed as a wall friction angle or coefficient of sliding friction. The lower the coefficient of sliding friction, the less steep the hopper walls need to be to ensure mass flow. You can measure the coefficient of sliding friction by determining the force it takes to slide a solid sample across a stationary wall surface. The friction that develops between the wall surface and the bulk solid resists this force.

For a given bulk material and wall surface, the wall friction angle is not necessarily a constant, but often varies with normal pressure, usually decreasing as normal pressure increases. Once you have measured wall friction angles, you can determine hopper angles for mass flow. Jenike provided a means to determine the required angles for mass flow from the wall friction angle in his Bulletin 123.3

Compressibility

is a range of material bulk densities that vary as a function of consolidating pressure. A solid's bulk density is an essential value used in the analysis of its flow properties. Bulk solids do not just have loose and/or packed densities. They exhibit a range of bulk densities that depends on the consolidation pressure applied by the material in the bin. Compressibility values are useful for calculating hopper angles and opening sizes, as well as bin and feeder loads.

Material permeability

is the material's ability to interact with air. You can determine a material's permeability by passing air or other gas through a representative column of bulk solid. The gas flow rate is measured while the pressure across the bed is regulated. This approach allows the bulk solid's permeability to be determined as a function of its bulk density.

Permeability values can help you calculate critical, steady-state discharge rates through various size outlets in mass flow bins. You then can modify the bin geometry to increase discharge rate.

Flow and equipment performance

Flow problems can cause flow stoppages, equipment failure, downtime and degraded product quality. No-flow conditions such as arching or ratholing, erratic flow, flooding, limited discharge and segregation are typical flow problems. See Fig. 3 and Fig. 4. These problems can result in limited live capacity, caking or agglomeration, vibrations and structural failure. They also can increase feeder power requirements.

Figure 3. Arch Figure 4. Rathole

These two examples of no-flow conditions can result in limited live capacity, caking or agglomeration, vibrations and structural failure.

Bins and silos are intended to discharge product to a process, truck, railcar, package or other destination. When a poorly designed bin creates flow stoppages, it also affects efficiency. If a plant is dependent on a product it produces instead of purchases, the entire plant stops production when a flow problem occurs.

A gravity flow approach to ensuring flow from a bin is better than an approach requiring flow aid devices, which are noisy, require constant maintenance and do not always work well. Gravity-powered discharge is efficient, cost-effective and reliable.

Do not accept 70 degrees as a "magic angle" for mass flow. The hopper angle for mass flow depends on the smoothness and steepness of the hopper wall, as well as the properties of the bulk solid.

Feeders are intended to discharge material reliably and at a particular rate. If the feeder is not designed to withdraw material from the bin properly, it will cause one of the previously mentioned flow stoppages. Feeders meter solids at a controlled rate from a bin to a process, truck or other destination and must be designed to:

Maintain uniform flow across the entire outlet cross-sectional area to ensure mass flow.

Minimize solids loading to reduce feeder torque and motor requirements.

Control discharge rate accurately.

You can meet these requirements by learning about your bulk solids flow properties and proper feeder design techniques.

Often, it is necessary to transfer solids from the bin outlet to a process, truck or another bin. Equipment designed to mechanically convey or transfer solids works quite well. However, for short distances, this approach can be expensive.

Chutes can be used in place of expensive conveyors to transfer solids short distances. A chute is simply a pipe or trough that is sized properly and at the correct slope angle to ensure sliding of the material to be transferred. A chute must be steep enough and smooth enough to ensure sliding along its entire length.

Conclusion

To avoid flow problems, you must ensure the correct flow pattern, which ," in most cases ," is mass flow. To do so, you must measure your material flow properties and remember that the feeder design is as important as the bin design. You can go to great lengths to modify your bin for reliable flow and destroy your efforts by using an improperly designed feeder.

Marinelli is president of Solids Handling Technologies Inc. in Fort Mill, S.C. Since 1972, he has been active in testing bulk solids and consulting on materials handling systems design. He lectures frequently, teaching courses on solids flow principles and flow property testing, and has authored several papers and an encyclopedia section on the subject. He can be reached at joe@solidshandlingtech.com or (803) 802-5527.

References 1. American Society for Testing and Materials, Standard D 6128,"97. 2. Marinelli, J. A. and J. W. Carson. "Cha-racterize Bulk Solids to Ensure Smooth Flow," Chemical Engineering, April 1994. 3. Jenike, A. W. "Storage and Flow of Solids," Bulletin No. 123, University of Utah Engineering Experiment Station, Salt Lake City, November 1964.