On the theory of the unsteady-state growth of spherical crystals in metastable liquids

2021

Self Cite

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)’.

Section: Transient Dynamics Of Individual Crystals In a Metastable Liquid: The Gibbs–thomson And Atomic Kinetics Effectsmentioning

confidence: 99%

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

Makoveeva

2021

Self Cite

“…To answer this question, we solve the corresponding boundary-value problem using the coordinate system of a prolate ellipsoid of revolution. In the limiting case, this theory transforms into the previously developed expressions for spherical crystals [34][35][36]. Using this growth law, we develop in §3 the nucleation theory without fluctuations in particle growth rates.…”

Section: Introductionmentioning

confidence: 99%

Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids

Nikishina

2021

Self Cite

When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered. The nonlinear transport (diffusivity) of ellipsoidal crystals in the space of their volumes is taken into account in the Fokker–Planck equation allowing for fluctuating growth rates. The complete analytical solutions of integro-differential models of kinetic and balance equations are found and analysed. Our solutions show that the desupercooling dynamics is several times faster for ellipsoidal crystals as compared to spherical particles. In addition, the crystal-volume distribution function is lower and shifted to larger particle volumes when considering the growth of ellipsoidal crystals. What is more, this function is monotonically increasing to the maximum crystal size in the absence of fluctuations and is a bell-shaped curve when such fluctuations are taken into account. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

“…This paper, which is directly connected with experiments and simulations presented in papers [11,12], opens a new perspective on the theory of phase transformations at the intermediate stage, which is presented in the next paper by Eugenya Makoveeva & Dmitri Alexandrov [15]. In this paper, a new theory describing the evolution of a phase transformation process in supersaturated and supercooled liquids is considered with allowance for the fluctuation corrections in particle's growth rates [14]. Note that some important applications of this theory in the life sciences and biophysics are considered in the last subsection of this issue.…”

Section: (B) Metastable and Non-ergodic Systems Governed By Macroscopmentioning

confidence: 79%

“…Namely, the paper presented by Dmitri Alexandrov & Irina Nizovtseva [18] is devoted to the theoretical development of the nucleation processes and connects the theory and experimental data on protein and insulin crystallization. Specifically, this paper develops the previous papers [14,15] to describe the effect of the 'diffusion' of the particle-size distribution function in the space of particle radii. In addition, the obtained and generalized dynamical laws are used here to describe and explain existing experiments for biomedical applications.…”

Section: (C) Biomedical Applications Of Heterogeneous Materialsmentioning

confidence: 99%

Heterogeneous materials: metastable and non-ergodic internal structures

Zubarev

2019

Self Cite

This issue is concerned with structural and phase transitions in heterogeneous and composite materials, the effects of external magnetic fields on these phenomena and the macroscopic properties and behaviour of materials with isotropic and anisotropic internal structures. Using experimental, theoretical and computer methods, these transitions are studied at the atomic and mesoscopic levels. The fundamental specific feature of structural transitions in many heterogeneous media consists of the fact that these transitions are stacked for a long time in non-equilibrium states that appear due to either macroscopic dissipative processes (an alternating magnetic field or hydrodynamic flow, for instance) or system lifetime in a metastable state. It is important to explain and describe these transitional states using the general approach of non-equilibrium physical mechanics. The review and research articles in the issue will cover the whole spectrum of scales (from nano to macro) and materials (from metastable liquids to biological polymers) in order to exhibit recently developed trends in the field of heterogeneous materials. Atomistic modelling, structuring induced by external magnetic fields and hydrodynamic flows, metastable and non-ergodic states, mechanical properties and phenomena in heterogeneous materials—all these are covered. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.