Predicting powder flow

Predicting the flow characteristics of powders during manufacture is especially important for the pharmaceutical engineer. Getting the powder flow wrong can be highly disruptive to plant performance and productivity, particularly where equipment has to be taken off-line and stripped down for cleaning out blockages. The flow behaviour of the individual ingredients may be well known, but as these are blended and reacted their flow properties can change.

So how does the pharmaceutical engineer go about predicting powder flow behaviour of particulate solids during manufacture? Typically, this involves making sense of flow behaviour in terms of:

• How the material slides against a contact surface such as a hopper wall or at the blade of a mixer.

• How strong the powder becomes when stored.

• How the bulk density varies under compaction as these features give the material potential to form arches or hinder flow.

Tests that time how long it takes for powder to flow from a funnel, or measure the energy used to stir a paddle in a powder bed are often used because they are relatively easy to perform, but unfortunately the data generated can be difficult to relate to actual plant conditions. Moreover, descriptions, such as 'free flowing' or 'poor flowing' are subjective and only reflect a specific condition in particular circumstances.

A powder can appear to be 'free flowing' when it is loosely poured, but may settle to a very firm and stable condition when de-aerated or subject to compacting stresses. A dry, crystalline product will usually flow through a relatively small orifice, but have extreme reluctance to deform if damp or 'caked' because of the presence of tiny crystal bridges binding particles together.

Powder flow

In most circumstances, the optimum powder flow condition is mass flow, where all the powder moves during discharge. This brings a number of benefits, for example, reducing powder segregation and efficient flow towards the vessel outlet. Achieving mass or near mass flow is dependent upon designing the storage and plant equipment in line with the powder flow behaviour. For example, a high friction material requires a hopper with a flow channel sufficiently large to destabilize any 'rat hole' that may form, and a wall angle steep enough to self-clear if it is to function well.

Rat holes occur when the central region of the hopper immediately above the outlet empties well, but there is a stagnant zone forming a stable rat hole. This zone is where the bulk of the hopper storage capacity is tied up and so only a small proportion of the hopper's contents is readily retrievable. Titanium dioxide has very high friction, even against polished stainless steel, and it is rarely practical to make a conical hopper wall sufficiently steep to generate mass flow to avoid ratholing (Figure 1).

Figure 1

Characterization of powders

Predicting the behaviour of pharmaceutical powders in every case has led some to look for a single number to use as a guide to flow. A variety of techniques are available that use the single number approach to quantify 'flowability'; for example, angle of repose, Hausner ratio, Carr Index and the more scientific Jenike Flow Function.^1–4 This approach however is fraught with problems; for example, there is no obvious reason why a powder that has high friction should also have a strong cohesive tendency or vice versa; so while the situation may worsen for flow when both these features are present, they are not necessarily correlated.

It is the complexity of multiple attributes of a bulk solid and their interaction with many facets of equipment design such as hopper and reactor vessels, screw feeders and conveyors, that defines the actual bulk flow behaviour in practice. Among the many characteristics of a bulk solid, perhaps the most important for flow are how the product slides on a contact surface (wall friction) and the resistance of the bulk solid to deformation (shear or failure strength). Both are influenced by the 'condition' or 'compaction' of the bulk, so bulk density is important, as well as quantifying the bulk 'state' and the driving force for gravity flow.

Consequently, wall friction, shear strength and bulk density are three properties of bulk solids that must be measured to calculate mass flow in a hopper and avoid arching at the outlet. Wall friction can be measured using a linear strain device and a force gauge, and strength by using a vertical shear cell tester.

Improved powder flow predictability

A better approach to predicting flow behaviour is to take the measured characteristics of wall friction (φ_w), shear strength (τ_s) and bulk density (ρ_b) and add three further factors: hopper angle (β_c), outlet size (D_crit) and Hausner ratio (H.R. [The ratio of tapped to loose bulk density; the greater the ratio the more sensitive the powder is to vibration and hence, flowability worsens.]).

Figure 2

Using these factors we can produce a spider diagram comprising a series of three concentric circles that are divided by axes for each of the characteristics. These axes intersect with the smallest diameter circle where that particular characteristic describes 'easy flow' with subsequent bigger diameter circles defining 'modest' and 'poor flow'. Two idealized situations can then be presented for an 'easy flow' material and a 'poor flow' version with the in-filled part of the 'web' detailing the particular characterization attributes (Figures 2 and 3).

Figure 3

The spider diagrams can be more than qualitative if the data from the tests on a large number of materials are used to define the 'easy', 'modest' and 'poor' flow circles (Table 1).⁵ Note that the bulk density axis is the reverse of the others as decreasing bulk density usually means poorer flow. A practical example is that most milling operations lower bulk density and worsen flowability of powders when they are stored. This tabulated data indicates that the 'easy flow' and 'poor' materials had the following characteristics:

Table 1 Parameters suggested by the tests reported in McGee Thesis (2005).

'Easy flow' material. This would be a low friction material (<20°), which would mass flow in a conical hopper with a wall angle of 65° to the horizontal. It would have a high bulk density (around 1200 kg/m³ ), but not be affected much by compaction or vibration and would, therefore, have a low Hausner ratio (up to 1.1). Its low shear strength (maximum 300 N/m² ) coupled with the high bulk density would guarantee flow through a small outlet (<15 cm diameter). A practical example would be a free flowing grade of lactose with a wall friction angle of 17° against stainless steel, shear strength 197 N/m² , Hausner ratio of 1.1, rat hole diameter of 9 cm and requiring a 64° wall angle for mass flow in a conical hopper. With a bulk density of 867 kg/m³ this particular example would have a small spike on the density axis of the spider diagram indicating a slight deviation from the ideal flow material.

Key points

'Poor flow' material. This would be a high friction material (>30°), which would barely mass flow in even the steepest conical hopper (>80°); in fact, it would probably require a V-shaped hopper. It would have a low bulk density (about 400 kg/m³ ), which would be significantly affected by compaction indicated by a high Hausner ratio (about 1.5). Its high shear strength (2000 N/m² ) coupled with the low bulk density would mean very large outlets (>100 cm) would be needed to ensure flow. A practical example would be a grade of titanium dioxide with a wall friction of 33.8° against stainless steel, bulk density of 664 kg/m³ , shear strength 2690/m² , Hausner ratio of 1.33, rat hole diameter 165 cm and requiring a wall angle for mass flow in a conical hopper of almost 80° to the horizontal.

This technique, when applied to two other examples, highlights particular aspects of the 'profile' that merit special attention. Figure 4 shows the resultant diagram for a chemical intermediate 1; all aspects for flow are good except the shear strength and outlet size. To overcome potential flow problems for batch handling of this material, invertible IBC bins are used with a large outlet that upsets the consolidation of the material to ensure reliable flow to process.

Figure 4

The pharmaceutical powder in Figure 5 has high wall fiction, but low shear strength. Had this material been stored and transferred without thought to its flow characteristics, difficulties with chute work featuring an insufficiently steep slope and sharp corners would have occurred. The spider diagram in this case directs attention towards examining the effects of surface finish and using generous radiused corners as practical solutions to providing trouble free powder flow.

Figure 5

Conclusion

In conclusion, a spider diagram approach to integrating the three measured parameters (wall friction, shear strength and bulk density), and three calculated parameters (hopper wall angle, outlet size [shear strength/bulk density ratio] and Hausner ratio) offers a more rounded and informative picture of flow characteristics.

The technique was developed for general flowability with bounds based on the data from the large number of tests conducted for this work. A development of the technique can be used for individual materials (e.g., different grades, batches, suppliers and seasonal variations) to set acceptable boundaries that could be modified by plant performance or indicate processing strategies for optimum performance.

Refinement of this approach to include other factors such as internal friction, lateral stress ratio and increased definition in scale can only improve the engineer's ability to match plant performance/design to bulk solids characteristics for reliable handling.

Dr Eddie McGee

is technical director at Ajax Equipment. His first degree was a BSc Physics from University of Strathclyde then an MSc in Bulk Solids Handling Technology from Glasgow Caledonian University (1992). Since 1992, Eddie has worked at Ajax, he has accumulated extensive industrial experience in the technical review and engineering of working solutions for a large number of solids handling projects in chemical, pharmaceutical, nuclear, waste handling, food, confectionery and other industries.

References

1. E. Tenou, J. Vasseur and M. Krawcyk, Powder Handling and Processing, 7(3), 219–227 (1995).

2. R.O. Grey and J.K. Beddow, Pow. Technol., 2, 323–326 (1969).

3. R.L. Carr, Chemical Engineering, 72, 69–72 and 163–168 (1965).

4. A.W. Jenike, Bulletin 123, 3(26), 56, Utah Engineering Experiment Station (University of Utah, UT, USA, 1964).

5. E. McGee, "An investigation into characterisation of bulk solids and flow in hoppers", Ph.D. Thesis, Glasgow Caledonian University, UK (2005).