On the Theory of the Nonstationary Spherical Crystal Growth in Supercooled Melts and Supersaturated Solutions

Alexandrov, Dmitri V.; Аlexandrova, Irina V.; Ivanov, А.А.; Malygin, A. P.; Starodumov, Ilya; Toropova, Liubov V.

doi:10.1134/s0036029519080020

Cited by 19 publications

(19 citation statements)

References 32 publications

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“…The present analytical solutions that describe the intermediate stage in a supercooled melt also describe the phase transformations in a supersaturated solution. In this case, we must replace normalΔT and normalΔT0 by the supersaturation normalΔC and its initial value normalΔC0, and parameters b and qT by b=4πCp/false(3normalΔC0false) and qC=Cpfalse(k0−1false)/Dl [40,58] (here Cp stands for the concentration at saturation, k0 is the partition coefficient, and Dl is the diffusion coefficient).…”

Section: Intermediate Stage Of the Phase Transformation In A Supercooled Meltmentioning

confidence: 99%

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

Makoveeva

Alexandrov

2021

Phil. Trans. R. Soc. A.

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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)’.

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Section: Intermediate Stage Of the Phase Transformation In A Supercooled Meltmentioning

confidence: 99%

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

Makoveeva

Alexandrov

2021

Phil. Trans. R. Soc. A.

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“…It should be especially noted that non-stationary effects in particle evaporation rates [25][26][27]39], the Gibbs-Thomson and attachment kinetic effects [35,40,41], the particle shape effects [42][43][44][45][46], as well as the influence of external sources and sinks [10,11,47,48] may also essentially change the evaporation dynamics by analogy with nucleation and crystal growth processes. For a more complete understanding of the question of the influence of these aspects on evaporation dynamics, further development of the theory is required, taking into account the simultaneous action of the above-mentioned effects.…”

Section: Discussionmentioning

confidence: 99%

Evaporation kinetics of a polydisperse ensemble of drops

Ivanov

Аlexandrova

Alexandrov

2021

Phil. Trans. R. Soc. A.

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A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear ‘diffusion’ term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g. spray drying, cooling, power engineering). The kinetics of heat transfer between phases is theoretically studied. An analytical solution to the integro-differential equations of the process of droplet evaporation is found in a parametric form. Analytical solutions in the presence and absence of the ‘diffusion’ term are compared. It is shown that the fluctuations in particle evaporation rates (‘diffusion’ term in the Fokker–Planck equation) play a decisive role in the evolutionary behaviour of a polydisperse ensemble of vaporizing liquid drops. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

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“…The other regime occurs when the crystals significantly exceed the value of (β * q) −1 , and the growth rate is controlled by heat dissipation velocity. In the case of liquid solutions, Equation ( 9) can be rewritten as [47]…”

Section: The Model Of Nucleation and Crystal Growthmentioning

confidence: 99%

Nucleation and Growth of an Ensemble of Crystals during the Intermediate Stage of a Phase Transition in Metastable Liquids

et al. 2022

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In this paper, an analytical method of solving the integro-differential system of kinetic and balance equations describing the evolution of an ensemble of crystals during the intermediate phase of the bulk crystallization process is described. The theory is developed for kinetic equations of the first- and second order corresponding to the absence and presence of fluctuations in particle growth rates. The crystal-size distribution function as well as the dynamics of metastability reduction in a supercooled melt (supersaturated solution) are analytically found using the saddle-point and the Laplace transform methods. The theory enables us to obtain the crystal-size distribution function that establishes in a supercooled (supersaturated) liquid at the beginning of the final stage of a phase transformation process when Ostwald ripening, coagulation and fragmentation of crystals are able to occur.

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On the Theory of the Nonstationary Spherical Crystal Growth in Supercooled Melts and Supersaturated Solutions

Cited by 19 publications

References 32 publications

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

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

Evaporation kinetics of a polydisperse ensemble of drops

Nucleation and Growth of an Ensemble of Crystals during the Intermediate Stage of a Phase Transition in Metastable Liquids

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