Abstract
A theoretical model has been developed to investigate the effects of fluid flow on the dendrite coarsening. The accelerated convective solute transport due to convection is considered by incorporating the new apparent diffusivity parameter into the classical coarsening model for stagnant melts. The model predicted that the dendrite arm coarsening followed the
and
relationships under laminar and turbulent fluid flow conditions respectively. The model predictions are found to be in good quantitative agreement with experimental data in literature.
Get full access to this article
View all access options for this article.
References
1.
Langer
JS
:
Rev. Mod. Phys.
, 1980 , 52 , 1 –28 .
2.
Huang
SC
,
Glicksman
ME
:
Acta Metall.
, 1981 , 29 , 717 –734 .
3.
Ratke
L
,
Voorhees
PW
: ‘Growth and coarsening: Ostwald ripening in materials processing’ ; 2002 , Munich , Springer-Verlag .
4.
Flemings
MC
:
Mater. Trans.
, 2005 , 46 , 895 –900 .
5.
Flemings
MC
:
Metall. Trans. A
, 1991 , 22A , 957 –981 .
6.
Fan
Z
:
Int. Mater. Rev.
, 2002 , 47 , 49 –85 .
7.
Ichikawa
K
,
Kinoshita
Y
,
Shimamura
S
:
Trans. Jpn Inst. Met.
, 1985 , 26 , 513 –522 .
8.
Molenaar
JMM
,
Salemans
FWHC
,
Katgerman
L
:
J. Mater. Sci.
, 1985 , 20 , 4335 –4344 .
9.
Martinez
RA
,
Flemings
MC
:
Metall. Mater. Trans. A
, 2005 , 36A , 2205 –2210 .
10.
Reisi
M
,
Niroumand
B
:
J. Alloys Compd
, 2009 , 475 , 643 –647 .
11.
Reisi
M
,
Niroumand
B
:
J. Alloys Compd
, 2009 , 470 , 413 –419 .
12.
Modigell
M
,
Pola
A
:
Trans. Nonfer. Met. Soc. China
, 2010 , 20 , 1696 –1701 .
13.
Lifshitz
IM
,
Slyozov
VV
:
J. Phys. Chem. Solids
, 1961 , 19 , 35 –50 .
14.
Wagner
C
:
Z. Elektrochem.
, 1961 , 65 , 581 –591 .
15.
Wan
G
,
Sahm
PR
:
Acta Metall. Mater.
, 1990 , 38 , 2367 –2372 .
16.
Wan
G
,
Sahm
PR
:
Acta Metall. Mater.
, 1990 , 38 , 967 –972 .
17.
Akaiwa
N
,
Hardy
SC
,
Voorhees
PW
:
Acta Metall. Mater.
, 1991 , 39 , 2931 –2942 .
18.
Baldan
A
:
J. Mater. Sci
., 2002 , 37 , 2171 –2202 .
19.
Ji
S
,
Roberts
K
,
Fan
Z
:
Scr. Mater.
, 2006 , 55 , 971 –974 .
20.
Kattamis
TZ
,
Coughlin
JC
,
Flemings
MC
:
Trans. Met. Soc. AIME
, 1967 , 239 , 1504 –1511 .
21.
Flemings
MC
: ‘Solidification processing’ ; 1974 , New York , McGraw-Hill .
22.
Vogel
A
,
Cantor
B
:
J. Cryst. Growth
, 1977 , 37 , 309 –316 .
23.
Schlichting
H
: ‘Boundary-layer theory’ , 500 –520 ; 1968 , New York , McGraw-Hill .
24.
Knudsen
JG
,
Hottle
HC
,
Sarofim
AF
,
Wankat
FC
,
Knaebel
KS
: in ‘Perry's chemical engineers’ handbook’ , (ed. ,
Perry
R H
, ed), 7th edn, Section 5 ; 1997 , New York , McGraw-Hill .
25.
Levich
VG
: ‘Physicochemical hydrodynamics’ , 80 ; 1962 , Englewood Cliffs, NJ , Prentice-Hall .
26.
Sherwood
TK
,
Pigford
RL
,
Wilke
CR
: ‘Mass transfer’ , 214 ; 1975 , New York , McGraw-Hill .
27.
Hines
AL
,
Maddox
RN
: ‘Mass transfer: fundamentals and applications’ , 194 ; 1985 , Englewood Cliffs, NJ , Prentice-Hall .
28.
Steinberger
RL
,
Treybal
RE
:
AIChE J.
, 1960 , 6 , 227 –232 .
29.
Mullin
JW
: in ‘Crystal growth’ , (ed. ,
Pamplin
B R
, ed), 289 –325 ; 1975 , London , Pergamon Press .
30.
Szekely
J
,
Themelis
NJ
: ‘Rate phenomena in process metallurgy’ ; 1971 , New York , Wiley .
31.
Vand
V
:
J. Phys. Colloid Chem.
, 1948 , 52 , 277 –299 .
32.
Falak
P
,
Niroumand
B
:
Scr. Mater.
, 2005 , 53 , 53 –57 .
33.
Kirkwood
DH
:
Int. Mater. Rev.
, 1994 , 39 , 173 –189 .
34.
Iida
T
,
Guthrie
IL
: ‘The physical properties of liquid metals’ ; 1988 , Oxford , Clarendon Press .
35.
Smeulders
RJ
,
Mischgofsky
FH
,
Frankena
HJ
:
J. Crys. Growth
, 1986 , 76 , 151 –169 .
36.
Jackson
KA
,
Hunt
JD
:
Acta Metall.
, 1965 , 13 , 1212 –1215 .
37.
dam
JCVan
:
J. Mater. Sci. Lett.
, 1986 , 5 , 812 –814 .
38.
Glicksman
ME
,
Schaefer
RJ
,
Ayers
JD
:
Metall. Trans. A
, 1976 , 7A , 1747 –1759 .
39.
Witzke
S
,
Riquet
JP
,
Durand
F
:
Acta Metall.
, 1981 , 29 , 365 –374 .
40.
Burden
MH
,
Hunt
JD
:
J. Cryst. Growth
, 1974 , 22 , 99 –108 .
41.
Ramati
SDE
,
Abbaschian
GJ
,
Mehrabian
R
:
Metall. Mater. Trans. B
, 1978 , 9B , 241 –245 .
