Hard and refractory particles with various shapes have been added to ceramic materials to enhance creep resistance. Also, many of the particles in food emulsions, magnetic particle suspensions, and other industrial systems may have nonspherical shapes. Hence, it is important to understand the effects of particle shape on the viscosity of suspensions. While the shape of many particles can be approximated as prolate or oblate spheroids, the purpose of the present study is to model the effective viscosity of semidilute suspensions of rigid ellipsoids. Closed-form expressions are obtained; however, their formulations are formidable. For the special cases of rodlike or disklike particles, simple closed-form expressions can be obtained. The present solutions are compared with existing solutions.

1.
J. C.
Chang
,
F. F.
Lange
, and
D. S.
Pearson
,
J. Am. Ceram. Soc.
77
,
19
(
1994
).
2.
A. E.
Larsen
and
D. G.
Grier
,
Phys. Rev. Lett.
76
,
3862
(
1996
).
3.
S. I.
Henderson
and
W.
van Megen
,
Phys. Rev. Lett.
80
,
877
(
1998
).
4.
R.
Lahiri
and
S.
Ramaswamy
,
Phys. Rev. Lett.
79
,
1150
(
1997
).
5.
D. B.
Mei
,
H. G.
Liu
,
B. Y.
Cheng
,
Z. L.
Li
,
D. Z.
Zhang
, and
P.
Dong
,
Phys. Rev. B
58
,
35
(
1998
).
6.
S. S.
Tsao
and
F.
Spaepen
,
Acta Metall.
33
,
881
(
1985
).
7.
R. A.
Buffo
and
G. A.
Reineccius
,
J. Food Eng.
51
,
267
(
2002
).
8.
L.
An
,
R.
Riedel
,
C.
Konetschny
,
H. J.
Kleebe
, and
R.
Raj
,
J. Am. Ceram. Soc.
81
,
1349
(
1998
).
9.
T. M. G.
Chu
and
J. W.
Halloran
,
J. Am. Ceram. Soc.
83
,
2189
(
2000
).
10.
J. A.
Lewis
,
J. Am. Ceram. Soc.
83
,
2341
(
2000
).
11.
12.
V.
Vand
,
J. Phys. Colloid Chem.
52
,
277
(
1948
).
13.
J. M.
Peterson
and
M.
Fixman
,
J. Chem. Phys.
39
,
2516
(
1963
).
14.
G. K.
Batchelor
and
J. T.
Green
,
J. Fluid Mech.
56
,
401
(
1972
).
15.
D.
Bedeaux
,
R.
Kapral
, and
P.
Mazur
,
Physica (Amsterdam)
88A
,
88
(
1977
).
16.
K. F.
Freed
and
M.
Muthukumar
,
J. Chem. Phys.
76
,
6186
(
1982
).
17.
B.
Cichocki
and
B. U.
Felderhof
,
J. Chem. Phys.
93
,
4427
(
1990
).
18.
C. U.
Thomas
and
M.
Muthukumar
,
J. Chem. Phys.
94
,
5180
(
1991
).
19.
I. M.
Krieger
,
Adv. Colloid Interface Sci.
3
,
111
(
1972
).
20.
C. H.
Hsueh
and
P. F.
Becher
,
J. Am. Ceram. Soc.
88
,
1046
(
2005
).
21.
C. W. J.
Beenaker
,
Physica A
128
,
48
(
1984
).
22.
F. L.
Saunders
,
J. Colloid Sci.
16
,
13
(
1961
).
23.
J. C.
van der Werff
,
C. G.
de Kruif
,
C.
Blom
, and
J.
Mellema
,
Phys. Rev. A
39
,
795
(
1989
).
24.
R. J.
Phillips
,
J. F.
Brady
, and
G.
Bossis
,
Phys. Fluids
31
,
3462
(
1988
).
25.
A. J. C.
Ladd
,
J. Chem. Phys.
93
,
3484
(
1990
).
26.
D. G. J.
Thomas
,
Colloid Sci.
20
,
267
(
1965
).
27.
A.
Sierou
and
J. F.
Brady
,
J. Rheol.
46
,
1031
(
2002
).
28.
A. J.
Banchio
and
G.
Nägele
,
J. Chem. Phys.
128
,
104903
(
2008
).
29.
C. H.
Hsueh
and
W. C. J.
Wei
,
J. Phys. D: Appl. Phys.
42
,
075503
(
2009
).
30.
D. S.
Wilkinson
,
J. Am. Ceram. Soc.
81
,
275
(
1998
).
31.
D. J.
McClements
,
Food Emulsions: Principles, Practice, and Techniques
(
CRC
,
Boca Raton, FL
,
1999
).
32.
H. J.
Choi
,
C. A.
Kim
,
T. M.
Kwon
, and
M. S.
Jhon
,
J. Magn. Magn. Mater.
209
,
228
(
2000
).
33.
F. M.
van der Kooij
,
E. S.
Boek
, and
A. P.
Philipse
,
J. Colloid Interface Sci.
235
,
344
(
2001
).
34.
G. K.
Batchelor
,
J. Fluid Mech.
46
,
813
(
1971
).
35.
D.
Barthés-Biesel
and
A.
Acrivos
,
Int. J. Multiphase Flow
1
,
1
(
1973
).
36.
J. G.
Brodnyan
,
Trans. Soc. Rheol.
3
,
61
(
1959
).
37.
S.
Das
,
V. S. R.
Murthy
, and
G. S.
Murty
,
Mater. Sci. Eng., A
241
,
129
(
1998
).
38.
J. D.
Eshelby
,
Proc. R. Soc. London, Ser. A
241
,
376
(
1957
).
39.
T.
Mori
and
K.
Tanaka
,
Acta Metall.
21
,
571
(
1973
).
40.
G. E.
Mase
,
Schaum’s Outline Series: Theory and Problems of Continuum Mechanics
(
McGraw-Hill
,
New York
,
1970
).
41.
G. B.
Arfken
,
Mathematical Methods for Physicists
(
Academic
,
New York
,
1970
).
42.
C. H.
Hsueh
,
A. G.
Evans
,
R. M.
Cannon
, and
R. J.
Brook
,
Acta Metall.
34
,
927
(
1986
).
43.
J.
Bicerano
,
J. F.
Douglas
, and
D. A.
Brune
,
J. Macromol. Sci., Rev. Macromol. Chem. Phys.
C39
,
561
(
1999
).
44.
E. J.
Hinch
and
L. G.
Leal
,
J. Fluid Mech.
52
,
683
(
1972
).
45.
H.
Brenner
,
Int. J. Multiphase Flow
1
,
195
(
1974
).
47.
S.
Kim
and
J. S.
Karilla
,
Microhydrodynamics: Principles and Selected Applications
(
Butterworth-Heinemann
,
Boston, MA
,
1991
).
48.
S.
Lee
,
P. K.
Liaw
,
C. T.
Liu
, and
Y. T.
Chou
,
Mater. Chem. Phys.
61
,
207
(
1999
).
49.
N.
Saitô
,
J. Phys. Soc. Jpn.
5
,
4
(
1950
).
You do not currently have access to this content.