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Dendrite growth under forced convection: analysis methods and experimental tests

 a,  b, c
a Department of Mathematical Physics, Ural Federal University named after the First President of Russia B. N. Yeltsin, prosp. Lenina 51, Ekaterinburg, 620083, Russian Federation
b Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, Löbdergraben Strasse 32, Jena, 07743, Germany
c Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Köln, Germany

An analysis is given of the nonisothermal growth of a dendrite under forced fluid flow in a binary system. The theoretical model used employs a free moving crystal—liquid interface and makes use of the Oseen approximation for the equation of motion of the liquid. A criterion for the stable growth of a two-dimensional and a three-dimensional parabolic dendrite is derived under the assumption of an anisotropic surface tension at the crystal—liquid interface, which generalizes the previous known results for the stable growth of a dendrite with convection in a one-component liquid and for the growth of a dendrite in a two-component system at rest. The criterion obtained within the Oseen hydrodynamic approximation is extended to arbitrary Peclet numbers and dendrite growth with convection in a nonisothermal multicomponent system. Model predictions are compared with experimental data on crystal growth kinetics in droplets processed in electromagnetic and electrostatic levitation facilities. Theoretical and simulation methods currently being developed are applied to crystallization processes under Earth and reduced gravity conditions.

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Fulltext is also available at DOI: 10.3367/UFNe.0184.201408b.0833
PACS: 05.70.Fh, 05.70.Ln, 68.70.+w (all)
DOI: 10.3367/UFNe.0184.201408b.0833
URL: https://ufn.ru/en/articles/2014/8/b/
000345112400002
2-s2.0-84911489822
2014PhyU...57..771A
Citation: Alexandrov D V, Galenko P K "Dendrite growth under forced convection: analysis methods and experimental tests" Phys. Usp. 57 771–786 (2014)
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Received: 7th, December 2013, revised: 18th, March 2014, 26th, March 2014

Îðèãèíàë: Àëåêñàíäðîâ Ä Â, Ãàëåíêî Ï Ê «Äåíäðèòíûé ðîñò ñ âûíóæäåííîé êîíâåêöèåé: ìåòîäû àíàëèçà è ýêñïåðèìåíòàëüíûå òåñòû» ÓÔÍ 184 833–850 (2014); DOI: 10.3367/UFNr.0184.201408b.0833

References (94) Cited by (110) ↓ Similar articles (20)

  1. Alexandrov D V, Ivanov A A et al Russ. Metall. 2025 (2) 354 (2025)
  2. Alexandrov D V, Makoveeva E V et al Eur. Phys. J. Spec. Top. (2025)
  3. Kolesnikov S V, Syromyatnikov A G et al Uspekhi Fizicheskikh Nauk 195 (04) 377 (2025) [Kolesnikov S V, Syromyatnikov A G et al Phys. Usp. 68 (04) 357 (2025)]
  4. Ryzhova T V, Tumarkina D A et al Izv. Vysh. Ucheb 68 (6) 517 (2025)
  5. Guo Ch, Zha H et al Results In Physics 77 108452 (2025)
  6. Zheng 郑 J 建, Zhou 周 X 旋 et al Chinese Phys. B 34 (10) 108102 (2025)
  7. Makoveeva E V, Alexandrov D V et al Russ. Metall. 2024 (1) 91 (2024)
  8. Galenko P Phase Field Theory in Materials Physics Chapter 9 (2024) p. 121
  9. Alexandrov D V, Titova E A, Toropova L V Eur. Phys. J. Spec. Top. 233 (23-24) 3239 (2024)
  10. Aleshin M P, Tumarkina D D et al Phys. Metals Metallogr. 125 (9) 970 (2024)
  11. Titova E A, Toropova L V, Alexandrov D V Russ. Metall. 2024 (4) 846 (2024)
  12. Makoveeva E V, Alexandrov D V et al Rasplavy (3) 238 (2024)
  13. Garnov S V, Abramov D V et al Phys. Usp. 67 (02) 109 (2024)
  14. Galenko P K, Alexandrov D V, Toropova L V Physics Reports 1085 1 (2024)
  15. Toropova L V, Alexandrov D V et al Uspekhi Fizicheskikh Nauk 193 (07) 770 (2023) [Toropova L V, Alexandrov D V et al Phys. Usp. 66 (07) 722 (2023)]
  16. (PROCEEDINGS OF THE 11TH INTERNATIONAL ADVANCES IN APPLIED PHYSICS AND MATERIALS SCIENCE CONGRESS & EXHIBITION) Vol. PROCEEDINGS OF THE 11TH INTERNATIONAL ADVANCES IN APPLIED PHYSICS AND MATERIALS SCIENCE CONGRESS & EXHIBITIONThe boundary integral equation for the growth of a 2D dendrite in the presence of convectionE. A.Titova2803 (2023) p. 040003
  17. Makoveeva E V, Alexandrov D V et al Eur. Phys. J. Spec. Top. 232 (8) 1153 (2023)
  18. Gruzd S A, Mosin A I, Krivilyov M D Comp. Contin. Mech. 16 (2) 179 (2023)
  19. Chen W, Wu Sh, Wang R Materials 15 (22) 8243 (2022)
  20. Toropova L V, Alexandrov D V et al J. Phys.: Condens. Matter 34 (9) 094002 (2022)
  21. Lee Ch, Yoon S et al Computers & Mathematics With Applications 125 25 (2022)
  22. Toropova L V, Galenko P K, Alexandrov D V Crystals 12 (7) 965 (2022)
  23. Alexandrov D V, Toropova L V Sci Rep 12 (1) (2022)
  24. Titova E A, Alexandrov D V J. Phys.: Condens. Matter 34 (24) 244002 (2022)
  25. Toropova L V Eur. Phys. J. Spec. Top. 231 (6) 1129 (2022)
  26. Titova E A, Alexandrov D V J. Phys. A: Math. Theor. 55 (5) 055701 (2022)
  27. Toropova L V, Alexandrov D V, Galenko P K Russ. Metall. 2022 (2) 69 (2022)
  28. Starodumov I O, Titova E A et al Crystals 12 (11) 1590 (2022)
  29. Toropova L V, Rettenmayr M et al Math Methods In App Sciences 45 (13) 8069 (2022)
  30. (EIGHTH INTERNATIONAL CONFERENCE NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES2021)) Vol. EIGHTH INTERNATIONAL CONFERENCE NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES2021)Boundary integral method with convection for the needle dendrite growthEkaterina A.Titova2459 (2022) p. 030037
  31. Alexandrov D V, Galenko P K Math Methods In App Sciences 45 (13) 8060 (2022)
  32. Zhao D, Gao J Crystal Growth & Design 22 (9) 5354 (2022)
  33. Alexandrov D V, Osipov S I et al Crystals 12 (9) 1288 (2022)
  34. Luo L, Luo L et al Journal Of Materials Science & Technology 61 100 (2021)
  35. Alexandrov D V, Galenko P K J. Phys.: Conf. Ser. 2114 (1) 012043 (2021)
  36. Toropova L V, Alexandrov D V, Galenko P K Math Methods In App Sciences 44 (16) 12139 (2021)
  37. Kurz W, Rappaz M, Trivedi R International Materials Reviews 66 (1) 30 (2021)
  38. Luo L, Luo L et al Journal Of Materials Science & Technology 74 246 (2021)
  39. Ruzhitskaya D D, Ryzhikov S B, Ryzhikova Yu V Moscow Univ. Phys. 76 (5) 253 (2021)
  40. Baranov M, Velichko E, Greshnevikov K Symmetry 13 (1) 123 (2021)
  41. Luo L, Luo L et al Journal Of Materials Science & Technology 79 1 (2021)
  42. Alexandrov D V, Titova E A et al J. Phys.: Condens. Matter 33 (44) 443002 (2021)
  43. LIU Shu-cheng, LIU Li-hua et al Transactions Of Nonferrous Metals Society Of China 31 (5) 1518 (2021)
  44. Toropova L V, Titova E A et al J. Phys.: Condens. Matter 33 (36) 365402 (2021)
  45. Alexandrov D V, Toropova L V et al Phil. Trans. R. Soc. A. 379 (2205) 20200326 (2021)
  46. LUO Lei, XIA Hong-ying et al Transactions Of Nonferrous Metals Society Of China 31 (4) 865 (2021)
  47. Alexandrov D V, Galenko P K Phil. Trans. R. Soc. A. 379 (2205) 20200325 (2021)
  48. (THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019) Vol. THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019Dendrite growth with arbitrary symmetry in the presence of convective heat and mass transfer boundary conditionsL. V.ToropovaD. V.AlexandrovP. K.Galenko2314 (2020) p. 030068
  49. Toropova L V, Alexandrov D V et al Journal Of Crystal Growth 535 125540 (2020)
  50. Alexandrov D V, Zubarev A Yu Eur. Phys. J. Spec. Top. 229 (19-20) 2881 (2020)
  51. Titova E A, Alexandrov D V, Galenko P K Eur. Phys. J. Spec. Top. 229 (19-20) 2891 (2020)
  52. Kao A, Toropova L V et al J. Phys.: Condens. Matter 32 (19) 194002 (2020)
  53. Kao A, Toropova L V et al JOM 72 (9) 3123 (2020)
  54. Titova E A, Alexandrov D V, Galenko P K Journal Of Crystal Growth 531 125319 (2020)
  55. Gao J TMS 2020 149th Annual Meeting & Exhibition Supplemental Proceedings The Minerals, Metals & Materials Series Chapter 2 (2020) p. 13
  56. Toropova L V, Galenko P K et al Eur. Phys. J. Spec. Top. 229 (19-20) 2899 (2020)
  57. Nabavizadeh S A, Eshraghi M et al Heat Mass Transfer 56 (4) 1329 (2020)
  58. Zhao D, Gao J, Kao A International Journal Of Heat And Mass Transfer 159 120113 (2020)
  59. Alexandrov D V, Toropova L V, Galenko P K 1790-5044 15 29 (2020)
  60. (THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019) Vol. THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019Modeling of a mushy zone during quasi-stationary solidification of TiAl alloyOlga M.ZhukovaIrina G.NizovtsevaEugeny V.PavlyukIlya O.StarodumovAlexander A.Ivanov2314 (2020) p. 060042
  61. Toropova L V, Galenko P K et al Eur. Phys. J. Spec. Top. 229 (2-3) 275 (2020)
  62. Ferreira e Pereira André, Planas G Journal Of Mathematical Analysis And Applications 482 (1) 123494 (2020)
  63. Cai X, Wang H P, Wei B International Journal Of Heat And Mass Transfer 151 119386 (2020)
  64. Kazak O V, Alexandrov D V, Galenko P K Eur. Phys. J. Spec. Top. 229 (2-3) 239 (2020)
  65. Alexandrov D V, Galenko P K Phil. Trans. R. Soc. A. 378 (2171) 20190243 (2020)
  66. Alexandrov D V, Alexandrova I V Phil. Trans. R. Soc. A. 377 (2143) 20180209 (2019)
  67. (PHYSICS, TECHNOLOGIES AND INNOVATION (PTI-2019): Proceedings of the VI International Young Researchers’ Conference) Vol. PHYSICS, TECHNOLOGIES AND INNOVATION (PTI-2019): Proceedings of the VI International Young Researchers’ ConferenceEffect of forced convection on dendrite growth kineticsL. V.Toropova2174 (2019) p. 020177
  68. Semyonov V I, Yu Ch A IOP Conf. Ser.: Mater. Sci. Eng. 643 (1) 012129 (2019)
  69. Reuther K, Seyring M et al Materialia 8 100457 (2019)
  70. Wang T, Semenov S et al Metall Mater Trans B 50 (6) 3039 (2019)
  71. Alexandrov D V, Galenko P K IUTAM Bookseries Vol. IUTAM Symposium on Recent Advances in Moving Boundary Problems in MechanicsSelection Criterion of Stable Mode of Dendritic Growth with n-Fold Symmetry at Arbitrary Péclet Numbers with a Forced Convection34 Chapter 17 (2019) p. 203
  72. Titova E A, Galenko P K, Alexandrov D V Journal Of Physics And Chemistry Of Solids 134 176 (2019)
  73. (PHYSICS, TECHNOLOGIES AND INNOVATION (PTI-2019): Proceedings of the VI International Young Researchers’ Conference) Vol. PHYSICS, TECHNOLOGIES AND INNOVATION (PTI-2019): Proceedings of the VI International Young Researchers’ Conference3D dendrite shape in the large chemical Péclet number limit in the case of rotational symmetryE. A.Titova2174 (2019) p. 020176
  74. Nabavizadeh S A, Eshraghi M et al International Journal Of Multiphase Flow 116 137 (2019)
  75. Toropova L V, Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1997 (2018) p. 020030
  76. Alexandrov D V, Galenko P K J. Phys.: Condens. Matter 30 (10) 105702 (2018)
  77. Ruzhitskaya D D, Ryzhikov S B, Ryzhikova Yu V Moscow Univ. Phys. 73 (3) 306 (2018)
  78. Alexandrov D V, Alexandrova I V, Ivanov A A (AIP Conference Proceedings) Vol. 1978 (2018) p. 470066
  79. Toropova L V, Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1953 (2018) p. 040005
  80. Titova E A, Alexandrov D V, Galenko P K Russ. Metall. 2018 (8) 737 (2018)
  81. Galenko P K, Alexandrov D V, Titova E A Phil. Trans. R. Soc. A. 376 (2113) 20170218 (2018)
  82. Alexandrov D V, Toropova L V, Galenko P K (AIP Conference Proceedings) Vol. 1978 (2018) p. 470065
  83. Alexandrov D V, Galenko P K, Toropova L V Phil. Trans. R. Soc. A. 376 (2113) 20170215 (2018)
  84. Makoveeva E V, Alexandrov D V Phil. Trans. R. Soc. A. 376 (2113) 20170327 (2018)
  85. Toropova L V, Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 2034 (2018) p. 020003
  86. Buchbinder G L, Galenko P K Physica A: Statistical Mechanics And Its Applications 489 149 (2018)
  87. Gao J Phil. Trans. R. Soc. A. 376 (2113) 20170209 (2018)
  88. Kao A, Gao J, Pericleous K Phil. Trans. R. Soc. A. 376 (2113) 20170206 (2018)
  89. Toropova L V (AIP Conference Proceedings) Vol. 2015 (2018) p. 020103
  90. Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1906 (2017) p. 200004
  91. Alexandrov D V, Galenko P K Acta Materialia 137 64 (2017)
  92. Alexandrov D V, Galenko P K Journal Of Physics And Chemistry Of Solids 108 98 (2017)
  93. Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1906 (2017) p. 200003
  94. Alexandrov D V, Galenko P K Physica A: Statistical Mechanics And Its Applications 469 420 (2017)
  95. Titova E A, Alexandrov D V, Galenko P K IOP Conf. Ser.: Mater. Sci. Eng. 192 012002 (2017)
  96. Galenko P K, Danilov D A et al Journal Of Crystal Growth 457 349 (2017)
  97. Titova E A, Alexandrov D V, Galenko P K IOP Conf. Ser.: Mater. Sci. Eng. 192 012025 (2017)
  98. Alexandrov D V, Dubovoi G Yu et al Russ. Metall. 2017 (2) 127 (2017)
  99. Rodriguez Ju E, Matson D M Acta Materialia 129 408 (2017)
  100. Toropova L V, Dubovoi G Yu, Alexandrov D V IOP Conf. Ser.: Mater. Sci. Eng. 192 012007 (2017)
  101. Alexandrov D V, Alexandrova I V (AIP Conference Proceedings) Vol. 1863 (2017) p. 560012
  102. Zhao R, Gao J et al Journal Of Crystal Growth 475 354 (2017)
  103. Alexandrov D V, Galenko P K EPL 119 (1) 16001 (2017)
  104. Gao J, Kao A et al Journal Of Crystal Growth 471 66 (2017)
  105. Gu Ch, Wei Ya et al Metall Mater Trans B 48 (6) 3388 (2017)
  106. Buyevich Yu A, Alexandrov D V IOP Conf. Ser.: Mater. Sci. Eng. 192 012001 (2017)
  107. Gao J, Han M et al Acta Materialia 103 184 (2016)
  108. Alexandrov D V, Danilov D A, Galenko P K International Journal Of Heat And Mass Transfer 101 789 (2016)
  109. Galenko P K, Danilov D A, Alexandrov D V International Journal Of Heat And Mass Transfer 89 1054 (2015)
  110. Alexandrov D V, Galenko P K Phys. Chem. Chem. Phys. 17 (29) 19149 (2015)
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