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The earliest of these was developed around the Carr indices Carr, (1965). The Hosokawa Powder Characteristics rheometers® Ilari, (2001) and measures the angle of repose, the angle of spatula, the compressibility of the material and its cohesiveness. It produces a flowability index in a scale of 1 – 100 (see Figure 2.21). Figure 2.19: Spider diagrams based on the flow facets in Table 2.3. Note all these parameters may not be correct for crushed limestone, shear strength and bulk density may need to be adjusted to better reflect limestone properties.

The Carr indices are a combination of parameters which provide an indication of the flow properties of a bulk solid.

The angle of repose is the angle that forms between the horizontal and a static pile of bulk solid that has been dropped from a height. However, there is also a poured angle of repose which is the angle the material forms when a container is emptied through an orifice smaller than the container’s diameter. These angles are often not the same, the poured is generally steeper than the dropped, the steeper the angle of repose the less free flowing a bulk solid usually is. Materials with an angle of repose less than 35º are usually easy flowing.

The angle of spatula is the angle formed by a bulk solid on a flat blade when it is lifted vertically through the bulk solid. Materials with angle of spatula less than 40º are generally easy flow materials.

Compressibility of a material is another indicator of powder flow properties. The more compressible a bulk solid or powder is the more likely there will be flow problems. The standard measure of compressibility is obtained by dividing the tap density by the loose poured or aerated bulk density. The tap density is found by either tapping a sample in a tap tester until the volume stops reducing, or by manually tapping a sample in a container vertically for at least 100 times from a height of about 2.5 cm until the volume ceases to reduce. A loose poured density is found by filling a container from above gently usually by means of a hopper and screening off, the over fill, the mass is then divided by the volume. This ratio tap density/ loose bulk density is known as the Hausner ratio (Table 2.4).

Table 2.4: The Hausner ratio and corresponding flow properties

Hausner Ratio Flow-ability

> 1.4 Very difficult

1.25 - 1.4 Difficult

1.1 -1.25 Medium flowing

1.0 - 1.1 Free flowing

The Hosokawa Powder Characteristics tester uses a uni-axial shear test to measure the cohesiveness of the powder based upon an idea by Carr, (1965). A column of powder

is supported on all sides and consolidated by a normal stress. The supporting walls are removed and the column is sheared by a normal stress. The stress required to shear the unsupported column is the unconfined yield stress UYS σc. If this stress is greater

than 0.25 of the consolidation normal stress σ1 then the material is considered to be

cohesive. This coincides with the Jenike flow index in Table 2.2, which is the inverse of the flow function. Hence the 4 rating which is the cohesive measure of the Jenike

index coincides with _

     1

σ

σ

> 0.25 which is the measure of cohesiveness provided by

the Carr index.

Similarly the Johanson Indicizer® uses an automated patented uni-axial cell to measure 8 indices using three machines (Figure 2.22). Table 2.5 below summarises the indices taken from Johanson, (1995). Cohesion is measured in this instrument with a hang up cell. The cell is used to consolidate the load, the bottom withdraws and the powder sheared by a normal stress on the cell, the sheared powder falls through the cell bottom of the shear cell.

Table 2.5: Johanson Indices and their applications (Johanson, 1995)

Index

(length) Repose segregation potential and capsule fill weight variations

Rat-hole Index

RI (length)

Predicts: rat-holing hang-ups, lump formation and flushing potential

Hopper Index HI (degrees)

Predicts: hopper slope angles required to cause flow at the walls, chute segregation potential and hopper wall angles for clean out

Flow Rate Index

FRI (wt/time)

Predicts: limiting feed rates from hopper outlets, fluidization and air current segregation potential, flushing potential, de-aeration time in containers, pre rate limits and capsule till rate limits

Bin Density Index

BDI (wt/vol.)

Predicts: bin gravimetric capacity and loads on bin walls

Feeder Density Index

FDI (wt/vol.)

Predicts: feeder gravimetric rates and, when compared with BDI, gives the range of densities possible at tableting presses.

Chute Index CI (degrees)

Predicts: build-up in chutes, feeders, conveyors and press feed shoes.

Springback Index

SBI (percent)

Predicts: special hang-up problems with elastic wind-up.

There are at least two companies producing automated rotational shear cells, Freeman’s apparatus (Freeman et al, 2007) has produced automated powder flow data within a few minutes over a wide range of materials (Figure 2.21). These shear cells have a helical blade and have an aerating conditioning phase that claims to remove the product history of the material being tested. They then measure the force required to move the blade through the material and have computer algorithms that relate these measurements to flow characteristics from the torque measured. A similar device is available from Stable Micro Systems, a ‘Powder Flow Analyser’, and is operated as

an attachment to their Texture Analyser, (Figure 2.23). This device measures the work done by plotting the area under a Force / Distance graph. In both cases the indices measure an increase in cohesion and caking by a larger number which is the opposite of the Jenike Flow Index, Table 2.6.

All the automatic rheometers claim to be able to produce replicable results with important flow/ no flow information on bulk solids in a matter of minutes rather than weeks which makes them a practical, commercial necessity in assessing material flow properties in industry.

Table 2.6: A Table comparing Stable Micro Systems Powder Flow Analyser Cohesive

Cohesive Index (CI) Flow Behaviour >19 Hardened/Extremely Cohesive 19 – 16 Very cohesive 16 – 14 Cohesive 14 – 11 Easy flowing <11 Free flowing

Figure 2.21: The Freeman FT4 Powder Rheometer

The automated rheometers are all supplied with proprietary software which enables them to produce a test result independent of operator influence. However, except for the Shulze and the Peschl automated shear cells, which are unlimited displacement direct shear cells based on the principles of Jenike (1964) and Carr and Walker (1967), the others can not be used for bulk solid study from first principles.

Figure 2.22: The 3 Johanson Indicizers Figure 2.23: The SMS Powder Flow Analyser