Prediction of ice crystal size distribution after freezing of pharmaceutical solutions

In the pharmaceutical industry, much attention has been given to the problem of predicting the average size of solvent crystals formed during freezing of pharmaceutical solutions. All the methods proposed in the literature to respond to this request are based on empirical laws, while the present work focuses on the development of a mechanistic model. This model was found to give physical theoretical background on the relationship between solvent crystal size, velocity of the freezing front, and temperature gradients within the product being frozen, which was postulated by the empirical laws previously proposed. Model simulations were validated upon experimental observations obtained by scanning electron microscopy. More specifically, the average size of solvent crystals was determined from that of pores formed after lyophilization of the frozen solutions, provided that no matrix collapse occurred. The developed model was demonstrated to be valid over a wide range of freezing conditions, and for solutions containing both amorphous and crystalline solutes. As a further step, a simplified model for dilute solutions has also been developed and experimentally validated.