Development of the solid–liquid interface, distribution of the particle concentration field, as well as the development of thermosolutal convection during solidification of colloidal suspensions in a differentially heated cavity are investigated. The numerical model is based on the one-fluid mixture approach combined with the single-domain enthalpy porosity model for phase change, and it is implemented in fluent software package. The linear dependence of the liquidus and solidus temperatures with the concentration of the nanoparticles was assumed. A colloidal suspension consisting of water and copper or alumina nanoparticles were considered. In the current investigation, the nanoparticle size selected was 5 and 2 nm. The suspension was solidified unidirectionally inside a square differentially heated cavity that was cooled from the left side. It was found that the solid–liquid interface changed its morphology from a planar shape to a dendritic one as the solidification process proceeds in time, due to the constitutional supercooling that resulted from the increased concentration of particles at the solid–liquid interface rejected from the crystalline phase. Initially, the flow consisted of two vortices rotating in opposite directions. However, at later times, only one counter clockwise rotating cell survived. Changing the material of the particle to alumina resulted in crystallized phase with a higher concentration of particles. If it is compared to that of the solid phase resulted from freezing the copper–water colloidal suspension. Decreasing the segregation coefficient destabilizes the solid–liquid interface and increases the intensity of the convection cell with respect to that of the case of no particle rejection. At slow freezing rates, the resulting crystal phase consisted of lower particle content compared to the case of higher freezing rate.

References

References
1.
Boden
,
S.
,
Eckert
,
S.
,
Willers
,
B.
, and
Gerbeth
,
G.
,
2008
, “
X-Ray Radioscopic Visualization of the Solutal Convection During Solidification of a Ga-30%wt Pct in Alloy
,”
Metall. Mater. Trans. A
,
39
(
3
), pp.
613
623
.
2.
Han
,
H.
, and
Kuehn
,
T. H.
,
1991
, “
Double Diffusive Natural Convection in a Vertical Rectangular Enclosure—II. Numerical Study
,”
Int. J. Heat Mass Transfer
,
34
(
2
), pp.
461
471
.
3.
Chakraborty
,
S.
, and
Dutta
,
P.
,
2003
, “
Three-Dimensional Double-Diffusive Convection and Macrosegregation During Non-Equilibrium Solidification of Binary Mixtures
,”
Int. J. Heat Mass Transfer
,
46
(
12
), pp.
2115
2134
.
4.
Turner
,
J. S.
,
1974
, “
Double-Diffusive Phenomena
,”
Annu. Rev. Fluid Mech.
,
6
(
1
), pp.
37
54
.
5.
Selva
,
B.
,
Daubersies
,
L.
, and
Salmon
,
J.-B.
,
2012
, “
Solutal Convection in Confined Geometries: Enhancement of Colloidal Transport
,”
Phys. Rev. Lett.
,
108
(
19
), p.
198303
.
6.
Kuzenetsov
,
A. V.
, and
Nield
,
D. A.
,
2011
, “
Double-Diffusive Natural Convective Boundary-Layer Flow of Nanofluid Past a Vertical Plate
,”
Int. J. Therm. Sci.
,
50
(
5
), pp.
712
717
.
7.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
The Onset of Double-Diffusive Nanofluid Convective in a Layer of a Saturated Porous Medium
,”
Transp. Porous Media
,
85
(
3
), pp.
941
951
.
8.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2011
, “
The Cheng–Minkowycz Problem for the Double-Diffusive Natural Convection Boundary Layer Flow in Porous Medium Saturated by Nanofluid
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
374
378
.
9.
Turner
,
J. S.
,
1985
, “
Multicomponent Convection
,”
Annu. Rev. Fluid Mech.
,
17
(
1
), pp.
11
44
.
10.
Beckermann
,
C.
, and
Viskanta
,
R.
,
1988
, “
Double-Diffusive Convection During Dendritic Solidification of Binary Mixture
,”
Physicochem. Hydrodyn.
,
10
(
2
), pp.
195
213
.
11.
Jarvise
,
R. A.
, and
Huppert
,
H. E.
,
1995
, “
Solidification of a Binary Alloy of Variable Viscosity From Vertical Boundary
,”
J. Fluid Mech.
,
303
(
1
), pp.
103
132
.
12.
Wroster
,
M. G.
,
1986
, “
Solidification of an Alloy From a Cooled Boundary
,”
J. Fluid Mech.
,
167
(
1
), pp.
481
501
.
13.
Kerr
,
R. C.
,
Wood
,
A. W.
,
Worster
,
M. G.
, and
Huppert
,
H. E.
,
1990
, “
Solidification of an Alloy Cooled From Above Part 1. Equilibrium Growth
,”
J. Fluid Mech.
,
216
(
1
), pp.
323
342
.
14.
Wettlaufer
,
J. S.
,
Wroster
,
M. G.
, and
Huppert
,
H. E.
,
1997
, “
Natural Convection During Solidification of an Alloy From Above With Application to the Evolution of Sea Ice
,”
J. Fluid Mech.
,
344
(
2
), pp.
291
316
.
15.
Peppin
,
S. S. L.
,
Aussillous
,
P.
,
Hupport
,
H. E.
, and
Wroster
,
M. G.
,
2007
, “
Steady-State Mushy Layers: Experiments and Theory
,”
J. Fluid Mech.
,
570
(
5
), pp.
69
78
.
16.
Peppin
,
S. S. L.
,
Huppert
,
H. E.
, and
Wroster
,
M. G.
,
2008
, “
Steady-State Solidification of Aqueous Ammonium Chloride
,”
J. Fluid Mech.
,
599
(
6
), pp.
465
476
.
17.
Mashl
,
S. J.
,
Flores
,
R. A.
, and
Trivedi
,
R.
,
1996
, “
Dynamics of Solidification in 2% Corn Starch–Water Mixtures: Effect of Variation in Freezing Rate on Product Homogeneity
,”
J. Food Sci.
,
61
(
4
), pp.
760
765
.
18.
Halde
,
R.
,
1980
, “
Concentration of Impurities by Progressive Freezing
,”
Water Res.
,
14
(
6
), pp.
575
580
.
19.
Chang
,
A.
,
Dantzig
,
J.
,
Derr
,
B. T.
, and
Hubel
,
A.
,
2007
, “
Modeling the Interaction of Biological Cells With Solidifying Interface
,”
J. Comput. Phys.
,
226
(
2
), pp.
1808
1829
.
20.
Deville
,
S.
,
2008
, “
Freeze-Casting of Porous Ceramics: A Review of Current Achievement and Issues
,”
Adv. Eng. Mater.
,
10
(
3
), pp.
155
169
.
21.
Deville
,
S.
,
Maire
,
E.
,
Bernard-Granger
,
G.
,
Lasalle
,
A.
,
Bogner
,
A.
,
Gauthier
,
C.
,
Leloup
,
J.
, and
Guizard
,
C.
,
2009
, “
Metastable and Unstable Cellular Solidification of Colloidal Suspensions
,”
Nat. Mater.
,
8
(
12
), pp.
966
972
.
22.
Khodadadi
,
J. M.
, and
Hosseinizadeh
,
S. F.
,
2007
, “
Nanoparticle-Enhanced Phase Change Materials (NEPCM) With Great Potential for Improved Thermal Storage
,”
Int. Commun. Heat Mass Transfer
,
34
(
5
), pp.
534
543
.
23.
Waschkies
,
T.
,
Oberacker
,
R.
, and
Hoffmann
,
M.
,
2011
, “
Investigation of Structure Formation During Freeze–Casting From Very Slow to Very Fast Solidification Velocities
,”
Acta Mater.
,
59
(
13
), pp.
5135
5145
.
24.
Deville
,
S.
,
Maire
,
E.
,
Lasalle
,
A.
,
Bogner
,
A.
,
Gauthier
,
C.
,
Leloup
,
J.
, and
Guizard
,
C.
,
2009
, “
In Situ X-Ray Radiography and Tomography Observations of the Solidification of Aqueous Alumina Particle Suspensions Part I: Initial Instants
,”
J. Am. Ceram. Soc.
,
92
(
11
), pp.
2489
2496
.
25.
Deville
,
S.
,
Maire
,
E.
,
Lasalle
,
A.
,
Bogner
,
A.
,
Gauthier
,
C.
,
Leloup
,
J.
, and
Guizard
,
C.
,
2009
, “
In Situ X-Ray Radiography and Tomography Observations of the Solidification of Aqueous Alumina Particle Suspensions. Part II: Steady State
,”
J. Am. Ceram. Soc.
,
92
(
11
), pp.
2497
2503
.
26.
Peppin
,
S. S.
,
Elliott
,
J. A.
, and
Wroster
,
M. G.
,
2006
, “
Solidification of Colloidal Suspensions
,”
J. Fluid Mech.
,
554
(
1
), pp.
147
166
.
27.
Peppin
,
S. S.
,
Wroster
,
M. G.
, and
Wettlaufer
,
J. S.
,
2007
, “
Morphological Instability in Freezing Colloidal Suspensions
,”
Proc. R. Soc.
,
463
(
2079
), pp.
723
733
.
28.
Peppin
,
S. S. L.
,
Wettlaufer
,
J. S.
, and
Worster
,
M. G.
,
2008
, “
Experimental Verification of Morphological Instability in Freezing Aqueous Colloidal Suspensions
,”
Phys. Rev. Lett.
,
100
(
23
), p.
238301
.
29.
Elliot
,
J. A. W.
, and
Peppin
,
S. S.
,
2011
, “
Particle Trapping and Banding in Rapid Colloidal Solidification
,”
Phys. Rev. Lett.
,
107
(
24
), p.
168301
.
30.
El Hasadi
,
Y. M. F.
, and
Khodadadi
,
J. M.
,
2013
, “
Numerical Simulation of the Effect of the Size of Suspensions on the Solidification Process of Nanoparticle Enhanced Phase Change Material
,”
ASME J. Heat Transfer
,
135
(
5
), p.
052901
.
31.
Voller
,
V. R.
,
Brent
,
A. D.
, and
Prakash
,
C.
,
1989
, “
The Modeling of Heat, Mass and Solute Transport in Solidification Systems
,”
Int. J. Heat Mass Transfer
,
32
(
9
), pp.
1719
1731
.
32.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
251
.
33.
Chellaiah
,
S.
, and
R.
Viskanta
,
1989
, “
Freezing of Water-Saturated Porous Media in the Presence of Natural Convection: Experiments and Analysis
,”
ASME J. Heat Transfer
,
111
(
2
), pp.
425
432
.
34.
ansys fluent,
2006
, “fluent User Guide.”
35.
Wakao
,
N.
, and
Kaguei
,
S.
,
1982
,
Heat and Mass Transfer in Packed Beds
,
Gordon and Breach
,
New York
, pp.
175
205
.
36.
Voller
,
V. R.
, and
Prakash
,
C.
,
1987
, “
Fixed Grid Numerical Modeling Methodology for Convection–Diffusion Mushy Region Phase Change Problems
,”
Int. J. Heat Mass Transfer
,
30
(
8
), pp.
1709
1719
.
37.
Patankar
,
S.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
CRC Press
,
Boca Raton, FL
.
38.
Hannoun
,
N.
,
Alexiades
,
V.
, and
Mai
,
T. Z.
,
2005
, “
A Reference Solution for Phase Change With Convection
,”
Int. J. Numer. Methods Fluids
,
48
(
11
), pp.
1283
1308
.
You do not currently have access to this content.