A bi-directional DEM-PBM coupling to evaluate chipping and abrasion of pharmaceutical tablets

Abstract A bi-directional coupling between the Discrete Element Method (DEM) and Population Balance Modelling (PBM) is suggested to model the failure of pharmaceutical tablets under abrasive conditions such as bulk flow of impact. DEM provides the description of kinetics and permits the extraction of collision energy distributions. Representation of the primary shape of the tablets is achieved by using the multi-sphere approach, a rigid assembly of systematically connected spheres to resemble non-spherical shape. Based on the collision energy distribution and the abrasion characteristics of the tablets by solving the PBM equations, the mass loss of tablets according to their mechanical resistance, as well as the fragment size distribution progeny can be computed. For the description of the abrasive failure characteristics, a multi-stage calibration procedure for the empirical breakage kernels of Vogel and Peukert as well as of Ghadiri and Zhang is also applied. The novelty of the presented approach is the bi-directional coupling: tablet and fragment distribution masses are dynamically updated for subsequent time steps in DEM by the particle replacement method according to the stress history of the system. The outcome of this methodology helps to get a deeper understanding of the process-property relationships, to evaluate the effect of any process or geometry modifications in processing operations, such as drum coating, and to reduce the requirements of experimental investigations.