Morphological population balance for modelling shape evolution of crystals grown from solution

摘要

Crystals are particles structured with multiple facets that often have different surface chemistry and hence varied growth rates during crystallisation. It is possible to manipulate the growth of individual facets e.g. via the introduction of tailor-made additives which via changes in the molecular recognition for the different crystal habit faces effect a reduction in the growth rate of a specific face, providing a means for control of the shape as well the size of the final crystalline product. However the prediction of crystal shape has previously been restricted to single crystals. On the other hand, population balance (PB) modelling of crystallisation has traditionally been mono-dimensional, i.e. based on the assumption that the crystals in a reactor all have a spherical shape. Recently a few researchers have reported two-dimensional (e.g. length and width) PB modelling for rod-like crystals. This paper presents a morphological (or polyhedral) population balance model for modelling the dynamic size evolution in all face directions. The morphological PB approach uses the crystal shape information for a single crystal obtained from morphology prediction or experiment as the initial face locations as well as face growth rates to predict the shape evolution of the crystal population. For every time instant during crystallisation, the shape prediction uses its shape at the last time moment and the growth rate of each face. The methodology is introduced by reference to potash alum (KAl(SO4)2·12H2O) for which literature data is available for comparison and validation.