A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees–Edwards periodic boundary conditions. The Navier–Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.
REFERENCES
1.
Y.
Nakayama
and R.
Yamamoto
, Phys. Rev. E
71
, 036707
(2005
).2.
Y.
Nakayama
, K.
Kim
, and R.
Yamamoto
, Eur. Phys. J. E
26
, 361
(2008
).3.
T.
Iwashita
, Y.
Nakayama
, and R.
Yamamoto
, J. Phys. Soc. Jpn.
77
, 074007
(2008
).4.
T.
Iwashita
and R.
Yamamoto
, Phys. Rev. E
79
, 031401
(2009
).5.
A. W.
Lees
and S. F.
Edwards
, J. Phys. C
5
, 1921
(1972
).6.
A.
Onuki
, J. Phys. Soc. Jpn.
66
, 1836
(1997
).7.
S.
Toh
, K.
Ohkitani
, and M.
Yamada
, Physica D
51
, 569
(1991
).8.
R. S.
Rogallo
, NASA Tech. Memo.
8135
, 1
(1981
).9.
A.
Onuki
, R.
Yamamoto
, and T.
Taniguchi
, J. Phys. II France
7
, 295
(1997
).10.
Z.
Zhang
, H.
Zhang
, and Y.
Yang
, J. Chem. Phys.
115
, 7783
(2001
).11.
T.
Imaeda
, A.
Furukawa
, and A.
Onuki
, Phys. Rev. E
70
, 051503
(2004
).12.
S.
Nishitsuji
, M.
Takenaka
, and T.
Taniguchi
, Polymer
51
, 1853
(2010
).13.
14.
J. C.
van der Werff
, C. G.
de Kruif
, C.
Blom
, and J.
Mellema
, Phys. Rev. A
39
, 795
(1989
).15.
16.
17.
C. W. J.
Beenakker
, Physica A
128
, 48
(1984
).18.
T.
Iwashita
and R.
Yamamoto
, Phys. Rev. E
80
, 061402
(2009
).19.
K.
Kim
, Y.
Nakayama
, and R.
Yamamoto
, Phys. Rev. Lett.
96
, 208302
(2006
).20.
R.
Yamamoto
, Phys. Rev. Lett.
87
, 075502
(2001
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.