(64a) Relative Importance of Cohesion and Internal Friction in Flowability of Pharmaceutical Powder

The flow function, measured by shear cell testers, has become the standard metrics for assessing powder flowability in the development and manufacturing of pharmaceutical solid dosage forms. Commercial shear cell testers calculate flow function by determining a linear yield locus through measurements of yield strengths of materials under different normal stresses. Cohesion and internal friction are two quantities defined in Mohr-Coulomb theory that describe the linear yield locus; hence they also determine flow function. The purpose of our study is to understand the relative contribution of cohesion and internal friction to flow function and to apply the findings to improve powder flowability during formulation development.

Through the analysis of 1130 ring shear tests of various pharmaceutical powders, we found that the flow function is strongly correlated with the ratio of pre-consolidation stress to cohesion. The powders included single-component or multi-component system of excipients and APIs that were prepared by simple blending or granulation. However, flow function had almost no correlation with internal friction angles.

We developed a model based on the Mohr-Coulomb theory to verify the experimental findings. The above observation—flow function strongly correlates with the ratio of pre-consolidation stress to cohesion but not with internal friction—was a mathematical consequence ensued from Mohr-Coulomb failure analysis. The model suggested that if the powders exhibited a small difference between the angle of internal friction at steady-state flow and the angle of internal friction at incipient flow, the correlation remained valid. Most pharmaceutical powders, coincidentally, possess such characteristic. Therefore, in practice, cohesion has a strong correlation with flow function while internal friction has none.

We demonstrated an application by mixing colloidal silicon dioxide with Hypromellose powder to show that substantial increase in flow function was accompanied by large decrease of cohesion while the internal friction angle showed negligible change. In contrast, mixing colloidal silicon dioxide with anhydrous calcium phosphate powder has no effect in flow function when cohesion changed minimally. Practitioners in solid dosage drug development can apply this knowledge and focus on improving powder flowability by reducing powder cohesion instead of internal friction.

¹ This study has been published in Leung et al. 2017. Journal of Pharmaceutical Sciences. 106:1865-1873