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

An approximate analytical solution to Johanson's rolling theory is derived. It is shown that the solution yields a single dimensionless parameter invariant in process scale-up or equipment transfer, which relates the densification factor with process parameters (roll force and gap), geometric parameters (roll diameter and width) and material properties. It is shown that, to a first approximation, the model prediction does not depend on the nip angle evading the need to powder rheometry measurements such as wall friction and internal shear angle. The model is benchmarked against data obtained from pilot-scale roller compactors from different manufacturers as well as literature data from Nesarikar. The model yields good ribbon density predictions even when calibrating material properties from uniaxial die compression.