Understanding the properties of the powder is the 1st step to a good design, or efficient troubleshooting, of an industrial installation. Unfortunately, all interesting data are not always available to the Engineer. This section is focusing on the most important data. They are listed and described in the following table.
Table 1 : Powder Properties
|Bulk density||kg/l||Sizing of vessels, mixers, bags, feeders... all items that hold powder or dose powder
Note : the bulk density can be referred as tapped or untapped. Untapped should be considered as long as the powder is aerated (in a receiver after a pneumatic transport for example)
|Particle density||kg/l||Particle density will be relevant when the movement of the solid must not anymore be considered as a mass, but as individual. It is the case for pneumatic transport.|
|Cohesive strength||Cohesive strength will be used in silo / hopper design in order to calculate the proper outlet size|
|Wall friction||Degrees||The wall friction is used to calculate the angle of hopper cones, as well as the internal friction parameter|
|Permeability||Permeability will give an indication of the capacity of the solids to retain air. It is a parameter used in calculating discharge rates and settling times|
|Segregation tendency||Will give interesting information on the risks of segregation that can happen when handling a powder (segregation at discharge, difficulty to mix...)|
|Sliding at impact points||Will help to determine the angle of piping after a hopper, to let the powder slide (to a mixer, a bag filler...)|
|Particle friability||Is the particle fragile, can we anticipate particular measures to transport it, mix it|
The performance of an industrial process will be judged, among other parameters, according to its capacity to reach a nominal speed (expressed in terms of throughput, cycle time or number of batches / h. If a hopper which is supposed to deliver powder at a given rate cannot do it, be it placed at the beginning, middle, or end of the process, the whole installation "speed" will be affected
The following notions, important to design properly hoppers and to promote solids flow, will be explained in this page
The Shear Tester or Shear Cell will allow to estimate very important powder properties like the Cohesive strength and the wall friction which can in return be used to calculate hopper outlet diameters and angle of discharge
2 shear tests need to be done in order to determine the properties. 1 test is to measure the angle of internal friction ; for getting this property, the test cell will measure the strength necessary to make the powder slide on ITSELF. On the other hand, the wall friction angle will be determine thanks to a cell that is measuring the strength necessary to make a sample of powder slide on a MATERIAL plate, the material being commonly the metal in which the silo will be built.
Figure 1 : Jenicke cells
2 forces are a applied to a sample of powder. 1 normal, which is set, and that is being gradually increased. And the second to the side (shear force). This 2nd force is measured and corresponds to the force to slide the sample of material.
Each couple (Normal stress ; Shear Stress) is recorded and then plotted. From this curve, different characteristics can be calculated. The graph obtained, called wall yield locus is shown below (example - not an actual powder)
The following powder properties can be determined from the graph obtained (called "Yield Locus")
Table 2 : Shear cells output
|Shear Tester||Direct determination||Calculated|
|Shear cell measuring material / powder interaction||Wall friction angle Phi's||Flow factor*|
|Shear cell measuring powder / powder interaction||Static Angle of Internal friction Phi
Effective Angle of internal friction delta
Major consolidation stress sigma1
Cohesive strength fc
Draw the yield locus from the data obtained from the cell testing the interactions powder / powder
Figure 2 : data obtained from yield locus of powder - powder shear cell
Draw the yield locus from the data obtained from the cell testing the interactions powder / material
Figure 3 : data obtained from yield locus of powder - material shear cell
The yield locus is performed according to an initial consolidation state. It is possible to vary the initial consolidation state. Drawing the different yield locus, at different initial consolidation, will give the basis to determine the flow function of the powder. An illustrative example, with 3 yield locus is given below.
Figure 4 : Graphical determination of powder flow function
From the 3 different yield locus, 3 couples (Major consolidation stress sigma1 ; Cohesive strength fc) can be calculated. A graph showing fc=f(sigma1) can then be drawn. This is the flow function of the powder being tested. The flow function brings key information on the behaviour of the powder, in a more reliable way than shortcut methods like the angle of repose or some indexes. In the example, only 3 couples are considered, but more will be used to draw the actual flow function. The graph can be divided in different areas by straight lines passing by the origin and with the slope i=(sigma1)/fc. The different values of i are giving information on the flowability, depending on the position of the flow function on the graph, its flowability can be determined.
Figure 5 : powder flow function and flowability of powder
Some experimental methods have been developped to approximate the results obtained with the Jenicke's method which is quite time consumming if specific equipment are not available. A series of tests has been developped by Johanson. It allows to determine different indexes that can be linked to the key design parameters defined above.
Table 3 : list of simplified methods for flowability evaluation
|Hang-up Indicizer||Arching Index AI (=critical outlet diameter)
Rathole Index RI (=rathole diameter)
|Hopper Indicizer||Hopper Index HI (=cone angle)
Chute Index (=sliding at impact)
|Flow Rate Indicizer||Flow Rate Index FRI (=max discharge throughput by gravity - without discharging aid but with a totally NON aerated powder)
Unpacked density FDI and Packed density BDI (=loose and tapped density)
To get these particular data, it is necessary to buy or have access to machine built by companies active in the field of Powder analysis.
A shear tester may not be available in factory day to day life, when a new bin needs to be calculated or the process needs to be troubleshooted. Other methods have been developped, quicker, to have an idea of the behaviour of powder. The use of such shortcut method should be done with care, always considering that they will give an indication of the behaviour of powder, but cannot be used for direct calculation
Table 4 : Calculated Index for assessment of flowability
|Carr Index||I=(tapped density - loose density)/(tapped density)*100||I less than 15% : good flow
I more than 25% : bad flow
|Hausner Index||Hr=(tapped density)/(loose density)||Hr more than 1.4 : cohesive powder
Hr less than 1.2 : free flow
In between : intermediary behaviour
|Angle of repose||Poured angle of repose||angle less than 30 : good flow
angle from 30 to 50 : difficult flow
angle more than 30 : almost impossible flow
A potential use for these shortcut methods is to perform comparison between powders. If a hopper is designed for a powder A and has a fairly satisafctory design, then checking Carr Index and angle of repose of powder B can give an idea if such a design could also fit for powder B. If the values of Carr Index and angle of Repose are very far, then it can be an indication that deeper work should be done to assess the characterisctics of powder B and use rigorous methods for the design.
One phenomena often overlooked in the analysis of powder flow is the influence of static electricity. This particularly true for very fine particles, for which the electrical forces become significant compared to other forces (gravity for example).
The parameters that will influence static electricity are the following :
- Intensity of friction
- Size and nature of particles
- Surface characteristics
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