Mathematical modeling of the growth of ellipsoidal crystals in metastable melts and solutions

被引：9
|
作者：
Nikishina, Margarita A. [1 ]
Alexandrov, Dmitri V. [1 ]
机构：
[1] Ural Fed Univ, Dept Theoret & Math Phys, Lab Multiscale Math Modeling, Lab Math Modeling Phys & Chem Proc Multiphase Med, Ekaterinburg, Russia
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 16期
基金：
俄罗斯科学基金会;
关键词：
crystal growth; ellipsoidal particles; mathematical modeling; nucleation; phase transformations; NUCLEATION; EVOLUTION; KINETICS; SUBSTANCES; PARTICLES; MECHANISM; DYNAMICS;
D O I：
10.1002/mma.6987
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The evolution of individual crystals of ellipsoidal shape in supercooled one-component and binary melts as well as in supersaturated solutions is studied theoretically. The crystal volume growth rate is derived using the prolate ellipsoidal coordinates. We show that this rate is a function of the current crystal volume and supercooling/supersaturation of the ambient liquid. Also, we demonstrate that the particle growth rate increases with increasing the volume of ellipsoidal crystals and supercooling.
引用
收藏
页码：12252 / 12259
页数：8
相关论文
共 50 条
  • [1] Mathematical Modeling of Nucleation and Growth Processes of Ellipsoidal Crystals in Binary Melts
    Nikishina, Margarita A.
    Alexandrov, Dmitri, V
    [J]. CRYSTALS, 2022, 12 (10)
  • [2] Desupersaturation dynamics in metastable solutions with ellipsoidal crystals
    Nikishina, Margarita A.
    Alexandrov, Dmitri, V
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2022, 231 (06): : 1107 - 1113
  • [3] Desupersaturation dynamics in metastable solutions with ellipsoidal crystals
    Margarita A. Nikishina
    Dmitri V. Alexandrov
    [J]. The European Physical Journal Special Topics, 2022, 231 : 1107 - 1113
  • [4] Growth of spherical and ellipsoidal crystals in a metastable liquid
    Alexandrova, Irina, V
    Ivanov, Alexander A.
    Malygin, Alexey P.
    Alexandrov, Dmitri, V
    Nikishina, Margarita A.
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2022, 231 (06): : 1089 - 1100
  • [5] Growth of spherical and ellipsoidal crystals in a metastable liquid
    Irina V. Alexandrova
    Alexander A. Ivanov
    Alexey P. Malygin
    Dmitri V. Alexandrov
    Margarita A. Nikishina
    [J]. The European Physical Journal Special Topics, 2022, 231 : 1089 - 1100
  • [6] Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids
    Nikishina, Margarita A.
    Alexandrov, Dmitri V.
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2021, 379 (2205):
  • [7] MATHEMATICAL MODELLING OF AVASCULAR ELLIPSOIDAL TUMOUR GROWTH
    Dassios, G.
    Kariotou, F.
    Tsampas, M. N.
    Sleeman, B. D.
    [J]. QUARTERLY OF APPLIED MATHEMATICS, 2012, 70 (01) : 1 - 24
  • [8] Uniformly Parameterized Mathematical Modeling of the Ellipsoidal Helical Surfaces
    Gu, Lizhi
    Zhou, Longfei
    Zhao, Can
    Xiao, Leilei
    [J]. 2015 INTERNATIONAL CONFERENCE ON INFORMATION SCIENCE AND INTELLIGENT CONTROL (ISIC 2015), 2015, : 356 - 361
  • [9] The growth of ellipsoidal crystals in supercooled and supersaturated liquids
    Margarita A. Nikishina
    Dmitri V. Alexandrov
    [J]. The European Physical Journal Special Topics, 2023, 232 : 1189 - 1198
  • [10] The growth of ellipsoidal crystals in supercooled and supersaturated liquids
    Nikishina, Margarita A.
    Alexandrov, Dmitri V.
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2023, 232 (08): : 1189 - 1198
12345