RSS feeds
ÐóññêèéEnglish
Issue 3, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2014

 / 

August

←  →

Reviews of topical problems


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.

Fulltext pdf (827 KB)
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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 (111) ↓ Similar articles (20)

  1. Alexandrov D V, Ankudinov V, Toropova L V J. Phys.: Condens. Matter 38 (1) 010202 (2026)
  2. Alexandrov D V, Makoveeva E V et al Eur. Phys. J. Spec. Top. (2025)
  3. Guo Ch, Zha H et al Results In Physics 77 108452 (2025)
  4. Alexandrov D V, Ivanov A A et al Russ. Metall. 2025 (2) 354 (2025)
  5. Zheng 郑 J 建, Zhou 周 X 旋 et al Chinese Phys. B 34 (10) 108102 (2025)
  6. 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)]
  7. Ryzhova T V, Tumarkina D A et al Izv. Vysh. Ucheb 68 (6) 517 (2025)
  8. Garnov S V, Abramov D V et al Phys. Usp. 67 (02) 109 (2024)
  9. Makoveeva E V, Alexandrov D V et al Rasplavy (3) 238 (2024)
  10. Aleshin M P, Tumarkina D D et al Phys. Metals Metallogr. 125 (9) 970 (2024)
  11. Makoveeva E V, Alexandrov D V et al Russ. Metall. 2024 (1) 91 (2024)
  12. Galenko P Phase Field Theory in Materials Physics Chapter 9 (2024) p. 121
  13. Alexandrov D V, Titova E A, Toropova L V Eur. Phys. J. Spec. Top. 233 (23-24) 3239 (2024)
  14. Galenko P K, Alexandrov D V, Toropova L V Physics Reports 1085 1 (2024)
  15. Titova E A, Toropova L V, Alexandrov D V Russ. Metall. 2024 (4) 846 (2024)
  16. 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)]
  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. (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
  20. Titova E A, Alexandrov D V J. Phys.: Condens. Matter 34 (24) 244002 (2022)
  21. Toropova L V, Alexandrov D V et al J. Phys.: Condens. Matter 34 (9) 094002 (2022)
  22. Toropova L V, Alexandrov D V, Galenko P K Russ. Metall. 2022 (2) 69 (2022)
  23. Zhao D, Gao J Crystal Growth & Design 22 (9) 5354 (2022)
  24. Toropova L V Eur. Phys. J. Spec. Top. 231 (6) 1129 (2022)
  25. Alexandrov D V, Galenko P K Math Methods In App Sciences 45 (13) 8060 (2022)
  26. Toropova L V, Galenko P K, Alexandrov D V Crystals 12 (7) 965 (2022)
  27. Chen W, Wu Sh, Wang R Materials 15 (22) 8243 (2022)
  28. (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
  29. Alexandrov D V, Osipov S I et al Crystals 12 (9) 1288 (2022)
  30. Lee Ch, Yoon S et al Computers & Mathematics With Applications 125 25 (2022)
  31. Titova E A, Alexandrov D V J. Phys. A: Math. Theor. 55 (5) 055701 (2022)
  32. Toropova L V, Rettenmayr M et al Math Methods In App Sciences 45 (13) 8069 (2022)
  33. Starodumov I O, Titova E A et al Crystals 12 (11) 1590 (2022)
  34. Alexandrov D V, Toropova L V Sci Rep 12 (1) (2022)
  35. Alexandrov D V, Galenko P K J. Phys.: Conf. Ser. 2114 (1) 012043 (2021)
  36. Baranov M, Velichko E, Greshnevikov K Symmetry 13 (1) 123 (2021)
  37. Alexandrov D V, Titova E A et al J. Phys.: Condens. Matter 33 (44) 443002 (2021)
  38. Luo L, Luo L et al Journal Of Materials Science & Technology 79 1 (2021)
  39. Toropova L V, Alexandrov D V, Galenko P K Math Methods In App Sciences 44 (16) 12139 (2021)
  40. Luo L, Luo L et al Journal Of Materials Science & Technology 61 100 (2021)
  41. Alexandrov D V, Toropova L V et al Phil. Trans. R. Soc. A. 379 (2205) 20200326 (2021)
  42. Alexandrov D V, Galenko P K Phil. Trans. R. Soc. A. 379 (2205) 20200325 (2021)
  43. LUO Lei, XIA Hong-ying et al Transactions Of Nonferrous Metals Society Of China 31 (4) 865 (2021)
  44. Kurz W, Rappaz M, Trivedi R International Materials Reviews 66 (1) 30 (2021)
  45. Toropova L V, Titova E A et al J. Phys.: Condens. Matter 33 (36) 365402 (2021)
  46. Luo L, Luo L et al Journal Of Materials Science & Technology 74 246 (2021)
  47. LIU Shu-cheng, LIU Li-hua et al Transactions Of Nonferrous Metals Society Of China 31 (5) 1518 (2021)
  48. Ruzhitskaya D D, Ryzhikov S B, Ryzhikova Yu V Moscow Univ. Phys. 76 (5) 253 (2021)
  49. Titova E A, Alexandrov D V, Galenko P K Eur. Phys. J. Spec. Top. 229 (19-20) 2891 (2020)
  50. Kao A, Toropova L V et al JOM 72 (9) 3123 (2020)
  51. Gao J TMS 2020 149th Annual Meeting & Exhibition Supplemental Proceedings The Minerals, Metals & Materials Series Chapter 2 (2020) p. 13
  52. Titova E A, Alexandrov D V, Galenko P K Journal Of Crystal Growth 531 125319 (2020)
  53. Toropova L V, Galenko P K et al Eur. Phys. J. Spec. Top. 229 (19-20) 2899 (2020)
  54. Toropova L V, Alexandrov D V et al Journal Of Crystal Growth 535 125540 (2020)
  55. (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
  56. Alexandrov D V, Zubarev A Yu Eur. Phys. J. Spec. Top. 229 (19-20) 2881 (2020)
  57. Kao A, Toropova L V et al J. Phys.: Condens. Matter 32 (19) 194002 (2020)
  58. Nabavizadeh S A, Eshraghi M et al Heat Mass Transfer 56 (4) 1329 (2020)
  59. Zhao D, Gao J, Kao A International Journal Of Heat And Mass Transfer 159 120113 (2020)
  60. Cai X, Wang H P, Wei B International Journal Of Heat And Mass Transfer 151 119386 (2020)
  61. Alexandrov D V, Galenko P K Phil. Trans. R. Soc. A. 378 (2171) 20190243 (2020)
  62. (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
  63. Ferreira e Pereira André, Planas G Journal Of Mathematical Analysis And Applications 482 (1) 123494 (2020)
  64. Kazak O V, Alexandrov D V, Galenko P K Eur. Phys. J. Spec. Top. 229 (2-3) 239 (2020)
  65. Toropova L V, Galenko P K et al Eur. Phys. J. Spec. Top. 229 (2-3) 275 (2020)
  66. Alexandrov D V, Toropova L V, Galenko P K 1790-5044 15 29 (2020)
  67. Titova E A, Galenko P K, Alexandrov D V Journal Of Physics And Chemistry Of Solids 134 176 (2019)
  68. 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
  69. Wang T, Semenov S et al Metall Mater Trans B 50 (6) 3039 (2019)
  70. Reuther K, Seyring M et al Materialia 8 100457 (2019)
  71. (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
  72. (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
  73. Semyonov V I, Yu Ch A IOP Conf. Ser.: Mater. Sci. Eng. 643 (1) 012129 (2019)
  74. Nabavizadeh S A, Eshraghi M et al International Journal Of Multiphase Flow 116 137 (2019)
  75. Alexandrov D V, Alexandrova I V Phil. Trans. R. Soc. A. 377 (2143) 20180209 (2019)
  76. Toropova L V, Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1997 (2018) p. 020030
  77. Alexandrov D V, Galenko P K J. Phys.: Condens. Matter 30 (10) 105702 (2018)
  78. Ruzhitskaya D D, Ryzhikov S B, Ryzhikova Yu V Moscow Univ. Phys. 73 (3) 306 (2018)
  79. Alexandrov D V, Alexandrova I V, Ivanov A A (AIP Conference Proceedings) Vol. 1978 (2018) p. 470066
  80. Toropova L V, Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1953 (2018) p. 040005
  81. Alexandrov D V, Galenko P K, Toropova L V Phil. Trans. R. Soc. A. 376 (2113) 20170215 (2018)
  82. Galenko P K, Alexandrov D V, Titova E A Phil. Trans. R. Soc. A. 376 (2113) 20170218 (2018)
  83. Alexandrov D V, Toropova L V, Galenko P K (AIP Conference Proceedings) Vol. 1978 (2018) p. 470065
  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. Gao J Phil. Trans. R. Soc. A. 376 (2113) 20170209 (2018)
  87. Buchbinder G L, Galenko P K Physica A: Statistical Mechanics And Its Applications 489 149 (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. Titova E A, Alexandrov D V, Galenko P K Russ. Metall. 2018 (8) 737 (2018)
  91. Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1906 (2017) p. 200004
  92. Alexandrov D V, Galenko P K Physica A: Statistical Mechanics And Its Applications 469 420 (2017)
  93. Alexandrov D V, Galenko P K Acta Materialia 137 64 (2017)
  94. Alexandrov D V, Galenko P K Journal Of Physics And Chemistry Of Solids 108 98 (2017)
  95. Alexandrov D V, Galenko P K (AIP Conference Proceedings) Vol. 1906 (2017) p. 200003
  96. Toropova L V, Dubovoi G Yu, Alexandrov D V IOP Conf. Ser.: Mater. Sci. Eng. 192 012007 (2017)
  97. Galenko P K, Danilov D A et al Journal Of Crystal Growth 457 349 (2017)
  98. Titova E A, Alexandrov D V, Galenko P K IOP Conf. Ser.: Mater. Sci. Eng. 192 012025 (2017)
  99. Alexandrov D V, Dubovoi G Yu et al Russ. Metall. 2017 (2) 127 (2017)
  100. Titova E A, Alexandrov D V, Galenko P K IOP Conf. Ser.: Mater. Sci. Eng. 192 012002 (2017)
  101. Rodriguez Ju E, Matson D M Acta Materialia 129 408 (2017)
  102. Alexandrov D V, Alexandrova I V (AIP Conference Proceedings) Vol. 1863 (2017) p. 560012
  103. Zhao R, Gao J et al Journal Of Crystal Growth 475 354 (2017)
  104. Alexandrov D V, Galenko P K EPL 119 (1) 16001 (2017)
  105. Gao J, Kao A et al Journal Of Crystal Growth 471 66 (2017)
  106. Gu Ch, Wei Ya et al Metall Mater Trans B 48 (6) 3388 (2017)
  107. Buyevich Yu A, Alexandrov D V IOP Conf. Ser.: Mater. Sci. Eng. 192 012001 (2017)
  108. Gao J, Han M et al Acta Materialia 103 184 (2016)
  109. Alexandrov D V, Danilov D A, Galenko P K International Journal Of Heat And Mass Transfer 101 789 (2016)
  110. Galenko P K, Danilov D A, Alexandrov D V International Journal Of Heat And Mass Transfer 89 1054 (2015)
  111. Alexandrov D V, Galenko P K Phys. Chem. Chem. Phys. 17 (29) 19149 (2015)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions