The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining the nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.

A systematic methodology is presented for the selective crystallization of the metastable form of a monotropic dimorph, l-glutamic acid, for batch cooling crystallization. Attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy coupled with chemometrics was used to determine the solute concentration and solubility curves of both α- and β-forms of l-glutamic acid in aqueous solution. The metastable limit associated with secondary nucleation for a seeded system was determined using laser backscattering (focused beam reflectance measurement, FBRM). Batch crystallizations seeded with the metastable α-form crystals following various preset supersaturation profiles were implemented using concentration feedback control which regulated the cooling rate based on the in situ measurement of solute concentration. Batch crystallizations operated at constant relative supersaturation in an appropriate temperature range prevented secondary nucleation of both polymorph types and were successful in selectively growing large metastable crystals with uniform size.

in Wiley InterScience (www.interscience.wiley.com).Polymorphism, in which there exist different crystal forms for the same chemical compound, is an important phenomenon in pharmaceutical manufacturing. In this article, a kinetic model for the crystallization of L-glutamic acid polymorphs is developed from experimental data. This model appears to be the first to include all of the transformation kinetic parameters including dependence on the temperature. The kinetic parameters are estimated by Bayesian inference from batch data collected from two in situ measurements: ATR-FTIR spectroscopy is used to infer the solute concentration, and FBRM that provides crystal size information. Probability distributions of the estimated parameters in addition to their point estimates are obtained by Markov Chain Monte Carlo simulation. The kinetic model can be used to better understand the effects of operating conditions on crystal quality, and the probability distributions can be used to assess the accuracy of model predictions and incorporated into robust control strategies for polymorphic crystallization.