In this work, using currently developing model of convective transport and dendrite growth, results on theoretical modeling are presented. A stable relation for the dendrite tip velocity V and its tip diameter ρ via the selection theory and undercooling balance ΔT is discussed. It is shown that convective transport plays essential role in quantitative description of dendrite growth kinetics.
REFERENCES
1.
W.
Kurz
and D.
Fisher
, Fundamentals of Solidification
3rd ed. (Trans Tech Publ.
, Aedermannsdorf
, 1989
).2.
D.
Alexandrov
and P.
Galenko
, Phys.–Usp.
57
, 771
–786
(2014
).3.
4.
J.
Langer
, Rev. Mod. Phys.
52
, 1
–28
(1980
).5.
D.
Alexandrov
, P.
Galenko
and D. M.
Herlach
, J. Cryst. Growth
312
, 2122
–2127
(2010
).6.
P.
Pelcé
and D.
Bensimon
, Nucl. Phys. B
2
, 259
–270
(1987
).7.
E.
Brener
and V.I.
Melnikov
, Adv. Phys.
40
, 53
(1991
).8.
D.A.
Kessler
, J.
Koplik
and H.
Levine
, Adv. Phys.
37
, 255
(1988
).9.
Ph.
Bouissou
and P.
Pelcé
, Phys. Rev. A
40
, 6673
–6680
(1989
).10.
M.
Ben Amar
and P.
Pelcé
, Phys. Rev. A
39
, 4263
–4269
(1989
).11.
H.
Müller-Krumbhaar
, T.
Abel
, E.
Brener
, M.
Hartmann
, N.
Eissfeldt
and D.
Temkin
, JSME Int. J. Ser. B
45
, 129
(2002
).12.
D.V.
Alexandrov
and P.K.
Galenko
, Phys. Rev. E
87
, 062403
(2013
).13.
D.V.
Alexandrov
and P.K.
Galenko
, Phys. Chem. Chem. Phys.
17
, 19149
–19161
(2015
).14.
D.V.
Alexandrov
and P.K.
Galenko
, Acta Mater.
137
, 64
–70
(2017
).15.
P.K.
Galenko
, D.A.
Danilov
, K.
Reuther
, D.V.
Alexandrov
, M.
Rettenmayr
, D.M.
Herlach
, J. Crystal Growth
457
, 349
–355
(2017
).16.
D.V.
Alexandrov
, D.A.
Danilov
, P.K.
Galenko
, Int. J. Heat Mass Trans.
101
, 789
–799
(2016
).17.
D.V.
Alexandrov
and P.K.
Galenko
, J. Phys. Chem. Solids
108
, 98
–103
(2017
).18.
19.
K.
Libbrecht
, Am. Sci.
95
, 52
(2007
).20.
Y.
Teraoka
, A.
Saito
, S.
Okawa
, Int. J. Refriger.
25
, 218
(2002
).21.
D.V.
Alexandrov
and P.K.
Galenko
, EPL
119
, Iss. 1
, 16001
(2017
).22.
D.V.
Alexandrov
and P.K.
Galenko
, IUTAM Bookseries
34
, 203
–215
(2019
).23.
D.V.
Alexandrov
, P.K.
Galenko
and L.V.
Toropova
, Phil. Trans. R. Soc. A
376
, 2113
, 20170215
(2018
).24.
P.K.
Galenko
, D.V.
Alexandrov
and E.A.
Titova
, Phil. Trans. R. Soc. A
376
, 2113
, 20170218
(2018
).25.
H.
Hartmann
, P.K.
Galenko
, D.
Holland-Moritz
, M.
Kolbe
, D.M.
Herlach
and O.
Shuleshova
, J. Appl. Phys.
103
, 073509
(2008
).26.
D.V.
Alexandrov
and A.P.
Malygin
, Phys. Earth Planet. Inter.
189
, 134
–141
(2011
).27.
M.G.
Worster
, J. Fluid Mech.
167
, 481
–501
(1986
).28.
V.V.
Mansurov
, Math. Comput. Modelling
14
, 819
–821
(1990
).29.
D.V.
Alexandrov
, A.A.
Ivanov
and I.V.
Alexandrova
, Phil. Trans. R. Soc. A
376
, 2113
, 20170217
(2018
).30.
D.V.
Alexandrov
, I.A.
Bashkirtseva
and L.B.
Ryashko
, Phil. Trans. R. Soc. A
376
, 2113
, 20170216
(2018
).31.
A.A.
Ivanov
, I.V.
Alexandrova
and D.V.
Alexandrov
, Phil. Trans. R. Soc. A
377
, 2143
, 20180215
(2019
).32.
H.
Huppert
, J. Fluid Mech.
212
, 209
–240
(1990
).33.
R.N.
Hills
, D.E.
Loper
and P.H.
Roberts
, Q. J. Appl. Math.
36
, 505
–539
(1983
).34.
E.V.
Makoveeva
and D.V.
Alexandrov
, Phil. Trans. R. Soc. A
377
, 2143
, 20180210
(2019
).
This content is only available via PDF.
© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.
