**Understanding the nip angle by Barbara Fretter and Michael Schupp.**

The Thin Layer Model allows for understanding of some general aspects of powder densification between the rolls in dry granulation and especially the nip angle. Part 1[1] describes the model and how the nip angle can be estimated easily. It also outlines that a stronger densification results inevitably in larger nip angles. Part 2 focuses on the interaction of nip angle and gap and the practical meaning in R&D and Scale-Up.

## The thin layer model

Based on the geometric considerations of the Thin Layer Model it is possible to plot the nip angle versus the densification factor of the powder for different gaps (Figure 1). And an important relation can be derived: to achieve the same densification factor at a larger gap requires a larger nip angle - see Figure 1.

For example, a densification factor of two requires a nip angle of 5o at a gap of 1mm and a nip angle of 10o at a gap of 4mm. This has some practical consequences for R&D and Scale-Up. Let’s assume that in R&D you have found the right granule properties for your product at certain roller compactor settings. Often small gaps like 2mm or less are chosen in R&D because the available amount of Active Pharmaceutical Ingredient (API) is limited. Additionally, the specific roll force (or a range of it) is defined. Although force and gap are specified for this product, the actual parameter determining the granule properties is the ribbon or at-gap density and they coincide with a certain densification factor. For reproducing the granule properties the at-gap density must be reproduced. This is also valid when the gap is increased. Because the powder density when being drawn-in is mainly independent of the gap, a general strategy for changing the gap is to keep the densification factor constant. And as shown in Figure 1, increasing the gap at the same densification factor means that the densification must start at larger nip angles. Otherwise, the granule properties will change.

## Mistakes made in dry granulation

Realising this correlation has some serious consequence for the specific roll force and ignoring it is one of the most made mistakes in Scale-Up. When increasing the gap at the same specific roll force, the resulting at-gap density cannot stay the same. Figures 2 and 3 give the explanation. By using the Thin Layer Model and simple geometric considerations (Figure 2) the solid fraction in each layer can be calculated for different gaps. Assuming that an at-gap solid fraction of 0.7 is the target value which should not be changed if the gap is increased.

Figure 3 shows the progression of the solid fractions for two gaps, 2mm and 4mm, towards the assumed at-gap solid fraction of 0.7. It gets obvious, that for each distance the solid fraction for the 4mm gap is larger than for the 2mm gap. Transferring this to the Thin Layer Model (Figure 2) means each horizontal layer must have a larger solid fraction for the 4mm gap than for the 2mm gap. But a larger solid fraction implicates a stronger densification and therefore a higher force which acts onto the rolls. The sum of all forces which act simultaneously onto the rolls must be higher. This is the reason changing the gap without adapting the specific roll force never results in the same granule properties.

Unfortunately, this is one of the most made mistakes in roller compaction especially in development and scale-up when increasing the throughput by increasing the gap. [Several examples for the influence of gap on ribbon or at-gap density can be found in literature, however, unfortunately, not always with the right explanation. Allesø [2] examined ribbons porosities for microcrystalline cellulose at two gaps and three different specific roll forces. His findings (Figure 4) prove the above made considerations: at the same specific roll force and a lager gap the resulting solid fraction of the ribbon is lower. The extend of this effect is caused by the densification properties of the material and substance specific.

## Larger gaps require larger nip angles

Based on the Thin Layer Model and geometric calculations an explanation can be given why larger gaps require larger nip angles to achieve the same at-gap density. As consequence, changing the gap without adapting the specific roll force result in granules with different properties. This is an often made mistake in Scale-Up. To achieve the same granule properties upon increasing the gap an increase of specific roll force is mandatory but in its extent substance

specific.

**References: **

*[1] Barbara Fretter, Michael Schupp, Understanding the Nip Angle, Eurolab (Dec 2023), https://content.yudu.com/web/15ex3/0A2nilh/EurolabDec2023/html/index.html?page=52&origin=reader*

*[2]] Allesø,M., et al., Roller compaction scale-up using roll width as scale factor and laser-based determined ribbon porosity as critical material attribute, European Journal of Pharmaceutical Sciences (2015), http://dx.doi.org/10.1016/j.ejps.2015.11.001*

Barbara Fretter is Managing Partner at the **Solids Development Consult GmbH****, **Michael Schupp ias Head of Process Engineering at **Gerteis Maschinen + Processengineering AG**

*What is dry granulation?*

*Granulation is a process in which powder particles are made to adhere to each other, resulting in larger, multi-particle entities, so called granules. If such a process is performed without adding liquids, this is called dry granulation.*

*In dry granulation, the powder blend is compacted by applying a force onto the powder, which in general causes a considerable size enlargement.*

*The compacts obtained are called ribbons, flakes or briquettes.*

*In order to obtain the desired granules, the compaction process is followed by a milling step.*