Dynamics of crystals in metastable liquids with applications to the growth of polypeptide hormones

This study is concerned with the dynamics of a polydisperse ensemble of crystals in a single-component metastable solution/melt. A new theory based on the kinetic and balance equations is developed for the description of initial and intermediate stages of bulk crystallization. Such phenomena as unsteady growth rates of individual crystals with fluctuations, diffusion of the crystal-size distribution function in the space of particle radii, the Gibbs–Thomson and atomic kinetics effects, various crystal nucleation mechanisms are taken into account. The analytical solution is constructed in a parametric form with the modified time being the decision variable. Namely, the metastability degree, particle-radius distribution function, crystallization time, total number of crystals and their mean size are found as the functions of decision variable. The analytical solutions show that the metastability degree decreases with time as a result of liquid desupersaturation/desupercooling. As this takes place, the particle-radius distribution function moves to greater particle radii, becomes wider and lower with increasing the crystallization time. The theory is tested against experiments on the growth of such polypeptide hormones as porcine and bovine insulins. We show that the theory is in good agreement with the experimental data.