Evolution of a particulate system governed by exchange with its environment

Galenko

2021

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented. The sharp interface model and stability criteria for various crystallization conditions and crystalline symmetries met in actual practice are formulated and discussed. The review is also focused on the determination of the main process parameters—the tip velocity and diameter of dendritic crystals as functions of the melt undercooling, which define the structural states and transitions in materials science (e.g. monocrystalline-polycrystalline structures). Selection criteria of stable dendritic growth mode for conductive and convective heat and mass fluxes at the crystal surface are stitched together into a single criterion valid for an arbitrary undercooling. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Section: The Main Outcomes and Conclusionmentioning

confidence: 99%

A review on the theory of stable dendritic growth

Galenko

2021

“…It is well known that the processes of phase transformations from a metastable liquid state to a solid state are widely spread across various research areas ranging from materials physics, geophysics and chemical industry to biophysics and life sciences [1][2][3][4][5][6][7][8][9][10]. These processes are accompanied by nucleation and growth of crystals at the initial and intermediate stages of phase transformation in supercooled melts and supersaturated solutions, as well as their coagulation, Ostwald ripening and disintegration at the concluding stage.…”

Section: Introductionmentioning

confidence: 99%

The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid

Makoveeva

2021

This manuscript is concerned with the theory of nucleation and evolution of a polydisperse ensemble of crystals in metastable liquids during the intermediate stage of a phase transformation process. A generalized growth rate of individual crystals is obtained with allowance for the effects of their non-stationary evolution in unsteady temperature (solute concentration) field and the phase transition temperature shift appearing due to the particle curvature (the Gibbs–Thomson effect) and atomic kinetics. A complete system of balance and kinetic equations determining the transient behaviour of the metastability degree and the particle-radius distribution function is analytically solved in a parametric form. The coefficient of mutual Brownian diffusion in the Fokker–Planck equation is considered in a generalized form defined by an Einstein relation. It is shown that the effects under consideration substantially change the desupercooling/desupersaturation dynamics and the transient behaviour of the particle-size distribution function. The asymptotic state of the distribution function (its ‘tail’), which determines the relaxation dynamics of the concluding (Ostwald ripening) stage of a phase transformation process, is derived. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

“…The mechanisms of nucleation and crystal growth in metastable liquids (supercooled melts or supersaturated solutions) completely determine the dynamics of a polydisperse ensemble of particles and aggregates, as well as the evolution of the metastability degree (supercooling or supersaturation) [1][2][3][4][5][6][7][8][9][10]. As this takes place, crystal growth rates differ during various stages of the phase transformation processes.…”

Section: Introductionmentioning

confidence: 99%

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

Аlexandrova

2020

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’.