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Roller Compaction Scale-Up Made Simple: An Approximate Analytical Solution to Johanson's Rolling Theory

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We derive an approximate analytical solution to Johanson's rolling theory, demonstrating that the solution produces a single dimensionless parameter that remains invariant during process scale-up or equipment transfer. This parameter establishes a relationship between the densification factor and various factors, including process parameters (roll force and gap), geometric parameters (roll diameter and width), and material properties. Importantly, the model prediction, to a first approximation, does not rely on the nip angle, eliminating the necessity for powder rheometry measurements like wall friction and internal shear angle. The model's accuracy is validated against data obtained from pilot-scale roller compactors of different manufacturers and literature data from Nesarikar. Notably, the model provides reliable predictions of ribbon density even when calibrating material properties using uniaxial die compression.
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