**Barbara Fretter & Michael Schupp discuss estimation of the nip angle.**

Roller compaction has evolved to a common and well-established agglomeration method. Due to its benefits such as being continuous, having a relatively large throughput, requiring small floor space and the absence of granulation liquid, roller compaction is considered to be the most economic granulation method.

In Fig. 1 the densification of powder with a roller compactor is shown schematically. Loosely packed powder is conveyed by the feed unit into the area between the two counter rotating rolls. The densification of the powder starts at the nip angle α, at which the powder is drawn-in by the rolls, and is continued until the smallest distance between the rolls is achieved: the gap g. This region is called the nip area. Within the gliding area upstream the powder flow, the powder is not conveyed by the rolls and in general, only slightly densified, if at all.

The Thin Layer Model divides the powder which is densified within the nip area into thin layers with equal height and width. Only the distance between the rolls decreases – starting from “b” at the nip angle α to the gap “g” – and therefore the volume of each layer. Assuming that the mass within each layer stays constant, the density of each layer increases until the maximum density is achieved at the gap “g”. This density is also called the at-gap density. It is a density under pressure and higher than the final ribbon density, because after the gap the densified powder recovers elastically. Nevertheless, ribbon and at-gap density correlate so that the at-gap density can be used as key quality parameter in roller compaction. The at-gap (or ribbon) density is directly related to important granule properties as recompactability and flowability, and is influenced by two major parameters: the specific roll force and the gap. An even better parameter is the solid fraction which divides the at-gap density by the particle density and therefore gives a better idea of the densification of the material.

## Understanding densification

With the Thin Layer Model some general understanding of the densification between the rolls can be achieved. First of all, an estimation of the nip angle α is possible. The powder densification starts at the nip angle α and ends at the gap g and can be defined as densification factor DF which is the quotient of b over g.

Simple geometric considerations correlate the densification factor DF to the nip angle α, the gap g and the diameter of the rolls d.

For estimating the magnitude of the densification factor, it can be assumed that the material is compacted from bulk to at-gap density. A lot of pharmaceutical powders have solid fractions between 0.2 – 0.5 and ribbons between 0.6 – 0.7. A good estimation for densification factors in pharmaceutical roller compaction is 1.5 – 3. For the Pactor line having rolls of 250mm diameter and for a 4mm gap, this would correspond to nip angles between 7.2° and 14.5°. Experimentally, nip angles have been determined between 4° and 14°. This shows that nip angles can be well estimated with the above equations.

By replacing the densification factor in the equation above by the ratio of at-gap solid fraction to bulk solid fraction, Fig. 2 can be drawn. A loosely packed powder needs a larger nip angle when being compressed to the same at-gap solid fraction than a powder with a higher bulk density. It gets obvious that the nip angle α depends on the powder and its densification properties and is therefore no constant value.

A full picture of the correlation between the densification factor and the nip angle for a 250 mm roll and a gap of 3mm is given in Fig. 3: a larger densification factors results in a larger nip angle. This is only possible with higher at-gap densities. Arithmetical, also a lower powder density at the nip angle would result in larger densification factors. But this would also mean that the powder is fluidised within the roller compactor, and this is more than unlikely. Therefore, the only reasonable explanation is: a larger densification factor at the same gap result in higher at-gap densities. The higher at-gap density implies also a higher specific roll force because the powder must be densified stronger. How much the roll force must be increased depends on the densification properties of the compressed powder. Powders which can be densified easily without applying high forces will need a smaller increase as stiff powders with a high resistance against their densification. Nevertheless, general predictions about nip angle and necessary specific roll force are not possible without characterising the densification behaviour of the compressed powder.

## Summary

By geometric considerations of the Thin Layer Model, the nip angle can easily be estimated from the at gap density of the ribbons and the assumption that the density of the powder when being drawn-in is bulk or tap density. If a material is densified strongly a large nip angle is the consequence. This means in general, that low bulk densities require larger nip angles.

Michael Schupp is with **Gerteis Maschinen + Processengineering** & Barbara Fretter is with **Solids Development Consult**.