Population Balance Modeling of Paracetamol Crystal Breakage

Crystals exhibit various shapes including cubes and needles. While cubes have aspect ratios close to one, needle shaped crystals are characterized by larger aspect ratios. It is expected that higher aspect ratio crystals will break into shorter rods. That is, the aspect ratios of the smaller fragments would be lower than the aspect ratios of the parent crystals.

This work presents breakage distribution functions that are developed for modeling needle breakage. This includes functions where the child crystals are shorter rods with the same width as the parent particles. These functions can account for binary breakage and breakage into a greater number of child particles. This two-dimensional model includes the major axis length and the aspect ratio of the crystals. Simulation results are compared to experimental results of paracetamol crystal breakage in a stirred vessel, where the parent crystals have an average aspect ratio of approximately two. Because there are a variety of systems that produce needle-shaped crystals, this breakage model is expected to be applicable to a range of systems in addition to paracetamol.