The process of solidification of ternary systems in the presence of moving phase transition regions has been investigated theoretically in terms of the nonlinear equation of the liquidus surface. A...

This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found. In the case of unsteady-state crystallization with polymerization, the particle-size distribution function is determined analytically for different space–time regions by means of the Laplace transform. Two functional integro-differential equations governing the dimensionless temperature and polymerization degree are deduced. These equations are solved by means of the saddle-point technique for the evaluation of a Laplace-type integral. The time-dependent distribution function, temperature and polymerization degree at different polymerization rates and nucleation kinetics are derived with allowance for the main contribution to the Laplace-type integral. In addition, the general analytical solution by means of the saddle-point technique and an example showing how to construct the analytical solutions in particular cases are given in the appendices. The analytical method developed in the present paper can be used to describe the similar phase transition phenomena in the presence of chemical reactions. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z ₁ ( t )= βt ^7/2 and Z ₁ ( t )= βt ² in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α , β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Evolution of crystal ensembles in supersaturated solutions is studied at the initial and intermediate stages of bulk crystallization. An integro-differential model includes fluctuations in crystal growth rates, initial crystal-size distribution and arbitrary nucleation and growth kinetics of crystals. Two methods based on variables separation and saddle-point technique for constructing a complete analytical solution to this model are considered. Exact parametric solutions based on these methods are derived. Desupersaturation dynamics is in good agreement with the experimental data for bovine and porcine insulin. The method based on variables separation has a strong physical limitation on exponentially decaying initial distribution and leads to the distribution function increasing with time. The method based on saddle-point technique leads to a dome-shaped crystal-size distribution function decreasing with time and has no strong physical limitations. The latter circumstance makes this method more reasonable for describing the kinetics of bulk crystallization in solutions and melts.