The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution
The evolution of a polydisperse ensemble of prolate and oblate ellipsoidal crystals in a supercooled one-component melt is theoretically studied. The volume growth rates for prolate and oblate ellipsoids are analytically found and compared at the same melt supercooling. We show that prolate crystals...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724001761 |
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| author | Dmitri V. Alexandrov Margarita A. Nikishina Eugenya V. Makoveeva Irina V. Alexandrova Liubov V. Toropova |
| author_facet | Dmitri V. Alexandrov Margarita A. Nikishina Eugenya V. Makoveeva Irina V. Alexandrova Liubov V. Toropova |
| author_sort | Dmitri V. Alexandrov |
| collection | DOAJ |
| description | The evolution of a polydisperse ensemble of prolate and oblate ellipsoidal crystals in a supercooled one-component melt is theoretically studied. The volume growth rates for prolate and oblate ellipsoids are analytically found and compared at the same melt supercooling. We show that prolate crystals evolve faster than the oblate ones and the difference between their growth rates increases with increasing the melt supercooling. Then taking these volume growth rates into account, we formulate the model describing the evolution of an ensemble of prolate/oblate ellipsoidal particles. The analytical solution to this integrodifferential model is found for two nucleation mechanisms in cases of prolate and oblate ellipsoids using the saddle-point method. Our solution demonstrates that an ensemble of prolate particles grows and removes the melt supercooling faster than an ensemble of oblate particles. As a result, the particle-volume distribution function for prolate crystals is shifted to larger crystal volumes than the same distribution for oblate crystals. Keeping this behavior in mind, we conclude that the shape of crystals plays a decisive role in the melt supercooling dynamics and their volume distribution. |
| first_indexed | 2024-03-07T23:06:17Z |
| format | Article |
| id | doaj.art-99beec0e99394ea99bd5c5ff95815213 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-24T23:18:07Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-99beec0e99394ea99bd5c5ff958152132024-03-17T07:53:41ZengElsevierResults in Physics2211-37972024-03-0158107494The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolutionDmitri V. Alexandrov0Margarita A. Nikishina1Eugenya V. Makoveeva2Irina V. Alexandrova3Liubov V. Toropova4Laboratory of Multi-Scale Mathematical Modeling, Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg, 620000, Russian FederationLaboratory of Multi-Scale Mathematical Modeling, Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg, 620000, Russian FederationLaboratory of Multi-Scale Mathematical Modeling, Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg, 620000, Russian FederationLaboratory of Multi-Scale Mathematical Modeling, Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg, 620000, Russian FederationLaboratory of Multi-Scale Mathematical Modeling, Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg, 620000, Russian Federation; Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, 07743, Germany; Corresponding author at: Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, 07743, Germany.The evolution of a polydisperse ensemble of prolate and oblate ellipsoidal crystals in a supercooled one-component melt is theoretically studied. The volume growth rates for prolate and oblate ellipsoids are analytically found and compared at the same melt supercooling. We show that prolate crystals evolve faster than the oblate ones and the difference between their growth rates increases with increasing the melt supercooling. Then taking these volume growth rates into account, we formulate the model describing the evolution of an ensemble of prolate/oblate ellipsoidal particles. The analytical solution to this integrodifferential model is found for two nucleation mechanisms in cases of prolate and oblate ellipsoids using the saddle-point method. Our solution demonstrates that an ensemble of prolate particles grows and removes the melt supercooling faster than an ensemble of oblate particles. As a result, the particle-volume distribution function for prolate crystals is shifted to larger crystal volumes than the same distribution for oblate crystals. Keeping this behavior in mind, we conclude that the shape of crystals plays a decisive role in the melt supercooling dynamics and their volume distribution.http://www.sciencedirect.com/science/article/pii/S2211379724001761Bulk crystallizationPopulation balance equationParticulate ensemblesEllipsoidal crystalsMetastable liquids |
| spellingShingle | Dmitri V. Alexandrov Margarita A. Nikishina Eugenya V. Makoveeva Irina V. Alexandrova Liubov V. Toropova The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution Results in Physics Bulk crystallization Population balance equation Particulate ensembles Ellipsoidal crystals Metastable liquids |
| title | The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution |
| title_full | The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution |
| title_fullStr | The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution |
| title_full_unstemmed | The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution |
| title_short | The evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution |
| title_sort | evolution of a polydisperse ensemble of ellipsoidal particles in the form of prolate and oblate ellipsoids of revolution |
| topic | Bulk crystallization Population balance equation Particulate ensembles Ellipsoidal crystals Metastable liquids |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724001761 |
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