Identification of nucleation rates in droplet-based microfluidic systems

Characterization of the rate of nucleation of crystals from solution continues to be of interest, both for investigations into fundamental molecular phenomena as well as for applications in the pharmaceuticals, biotechnology, and fine chemicals industries. Substantial experimental evidence indicates that nucleation in some solute-solvent systems does not agree with classical theory, especially at high supersaturations. An approach is proposed for computing bounds on the nucleation rate as a function of supersaturation that does not require an assumed analytical expression for the nucleation kinetics. The approach involves (1) a high-throughput microfluidic platform that measures crystal nuclei formation in droplets, (2) the analytical solution of the Chemical Master equation for nucleation that takes finite-volume effects into account, and (3) a numerical algorithm that employs linear splines to construct upper and lower bounds on the nucleation rate from the experimental data produced by the microfluidic platform. The approach is demonstrated for mean induction times measured for the nucleation of paracetamol and glycine crystals in aqueous solution, as examples in which the measured nucleation kinetics are consistent or inconsistent with classical nucleation theory, respectively. The approach can be used to suggest dependencies for the development of new nucleation expressions and for providing kinetic information needed for the simulation of crystallizers that operate at high supersaturations, such as dual-impinging-jet and vortex-mixer crystallizers.