Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics

This manuscript is devoted to the nonlinear dynamics of particulate assemblages in metastable liquids, caused by various dynamical laws of crystal growth and nucleation kinetics. First of all, we compare the quasi-steady-state and unsteady-state growth rates of spherical crystals in supercooled and supersaturated liquids. It is demonstrated that the unsteady-state rates transform to the steady-state ones in a limiting case of fine particles. We show that the real crystals evolve slowly in a more actual case of unsteady-state growth laws. Various growth rates of particles are tested against experimental data in metastable liquids. It is demonstrated that the unsteady-state rates describe the nonlinear behaviour of experimental curves with increasing the growth time or supersaturation. Taking this into account, the crystal-size distribution function and metastability degree are analytically found and compared with experimental data on crystallization in inorganic and organic solutions. It is significant that the distribution function is shifted to smaller sizes of particles if we are dealing with the unsteady-state growth rates. In addition, a complete analytical solution constructed in a parametric form is simplified in the case of small fluctuations in particle growth rates. In this case, a desupercooling/desupersaturation law is derived in an explicit form. Special attention is devoted to the biomedical applications for insulin and protein crystallization. This article is part of the theme issue 'Patterns in soft and biological matters'.