Crystals with a large aspect ratio (needle- or platelet-shaped) are a common occurrence in many pharmaceutical and fine chemicals processes. While relatively narrow particle size distribution (PSD) can be obtained in the crystallisation step by precise control of the crystal growth kinetics and hydrodynamic conditions, further fluid-solid separation such as filtration, filter washing, drying, and subsequent solids handling can often lead to uncontrolled changes in PSD due to breakage. In order to understand and eventually predict the effect of these unit operations on breakage patterns, population balance modelling is a useful tool – provided that correct values of input parameters are supplied. In particular, the so-called selection function (which specifies the probability that a particle will undergo a breakage event) and the breakage function (which specifies the size distribution of daughter particles once a breakage event does occur) need to be known. The breakage and selection functions can in principle be evaluated by retro-fitting experimental breakage data, but such procedure is not always reliable and requires considerable experimental effort.

In this contribution we present a new methodology for determining the breakage functions (breakage kernel and daughter distribution function) for a population balance model from Discrete Element (DEM) simulations of needle-shaped particle breakage. The main advantage of this methodology is that individual particles can be traced within a particle assembly during the simulation, and so the frequency of breakage events as well as the size distribution of daughter particles can be evaluated explicitly in a statistically robust way. The methodology consists of two parts: (i) the DEM simulation of needle-shaped particle breakage as described in [1], whereby the influence of parameters such as the aspect ratio, initial length distribution, and the intrinsic mechanical properties of particles and their distribution can be systematically investigated; (ii) post-processing of the DEM simulation outputs (i.e., broken and un-broken particles within a population as function of time and/or compression ratio) and the explicit evaluation of the breakage functions. Convoluted PSD data can be extracted both from DEM simulations and from subsequent population balance models of breakage, and used as an additional verification of the consistency of the two models and their comparison with experimental data.

References:

1. Grof Z., Kohout M., Štěpánek F., Multi-scale simulation of needle-shaped particle breakage under uni-axial compaction, Chem. Eng. Sci. 62, 1418-1429 (2007)