Growth of spherical and ellipsoidal crystals in a metastable liquid

Аlexandrova, Irina V.; Ivanov, А.А.; Malygin, A. P.; Alexandrov, Dmitri V.; Nikishina, Margarita A.

doi:10.1140/epjs/s11734-022-00513-w

Cited by 14 publications

(8 citation statements)

References 63 publications

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“…Note that every constant value of the parameter σ 0 > 1 defines the isothermal surface of an ellipsoidal particle evolving in ellipsoidal coordinates (see, for details, [40]). Let us especially emphasize that the growth rate of ellipsoidal particles has been compared with experimental data in a recently published paper [42]. Here a comparison of growth rates of ellipsoidal and spherical crystals has been made as well.…”

Section: Growth Of a Polydisperse Ensemble Of Ellipsoidal Particlesmentioning

confidence: 99%

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Nucleation and growth of ellipsoidal crystals in a supercooled binary melt

Nikishina¹,

Alexandrov²

2022

J. Phys. A: Math. Theor.

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When considering the evolution of particulate assemblages in supercooled and supersaturated liquids, the shape of crystals often differs from spherical. Existing experiments show that evolved crystals often are ellipsoidal. Motivated by important applications in materials physics, chemistry, and biophysics, we develop here a growth theory of a polydisperse ensemble of ellipsoidal crystals in a binary supercooled melt. An integro-differential model of kinetic and balance equations supplemented by initial and boundary conditions that describe desupercooling dynamics and particle-volume distribution function with allowance for the ellipsoidal shape of growing crystals is formulated and solved analytically using the saddle-point technique for a Laplace-type integral. The distribution function increases up to the maximal volume of particles and shifts to larger crystal volumes with time. The solute concentration substantially changes the evolution of a particulate assemblage. The melt supercooling decays faster and the particle-volume distribution function is lower with increasing the initial solute concentration. The theory under consideration generalizes previously developed growth theories for spherical crystals in a binary melt (Alexandrov 2014 {\it J. Phys. A: Math. Theor.} {\bf 47} 125102) and ellipsoidal crystals in a single-component melt (Nikishina and Alexandrov 2021 {\it Phil. Trans. R. Soc. A} {\bf 379} 20200306).

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Section: Growth Of a Polydisperse Ensemble Of Ellipsoidal Particlesmentioning

confidence: 99%

“…Here a comparison of growth rates of ellipsoidal and spherical crystals has been made as well. We refer the interesting reader to reference [42] for more detailed information on this subject.…”

Section: Growth Of a Polydisperse Ensemble Of Ellipsoidal Particlesmentioning

confidence: 99%

Nucleation and growth of ellipsoidal crystals in a supercooled binary melt

Nikishina¹,

Alexandrov²

2022

J. Phys. A: Math. Theor.

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“…The growth of single spherical and ellipsoidal crystals in metastable liquids (supercooled melts and supersaturated solutions) is considered in Ref. [1]. The next papers [2,3] continue this study.…”

Section: Introductionmentioning

confidence: 99%

“…1. Metastable liquids [1][2][3][4][5][6][7][8][9]; 2. External impacts [10][11][12][13][14][15][16][17].…”

Section: Introductionunclassified

Transport phenomena and phase transitions in soft and disordered systems

Alexandrov

Zubarev

2022

Eur. Phys. J. Spec. Top.

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The present special issue is devoted to the experimental, theoretical and computational studies of fundamental features in transport phenomena, structural and phase transitions in various soft and disordered systems (polymers, colloids, glasses, amorphous, crystalline, and composite materials) involved in macroscopically non-equilibrium processes (hydrodynamic flows; non-stationary deformations, heat and mass transfer and so on). Special attention is focused on a detailed microscopical study of the effects of internal structural and phase transformations on macroscopic physical properties and phenomena in the systems under study.

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“…This theory was then generalized to account for fluctuations in crystal growth rates in [24,25] when the initial crystal-size distribution is zero. Note that this theory has been generalized to account for non-spherical shape of crystals and non-stationarity in their growth rates in [26,27]. A fundamentally different approach, based on the separation of variables for a first-order kinetic equation, was proposed in [28,29].…”

Section: Introductionmentioning

confidence: 99%

Desupersaturation dynamics in solutions with applications to bovine and porcine insulin crystallization

Makoveeva,

Alexandrov,

Ivanov

et al. 2023

J. Phys. A: Math. Theor.

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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.

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Growth of spherical and ellipsoidal crystals in a metastable liquid

Cited by 14 publications

References 63 publications

Nucleation and growth of ellipsoidal crystals in a supercooled binary melt

Nucleation and growth of ellipsoidal crystals in a supercooled binary melt

Transport phenomena and phase transitions in soft and disordered systems

Desupersaturation dynamics in solutions with applications to bovine and porcine insulin crystallization

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