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η
η
η
al
η
η
η
al
η
η
η
η
(a)
(b)
Figure 2.6
Orientation reduction mechanism predicted by the LE nematodyanmics
for (a) disks and (b) rods.
η
2
) (de Gennes and Prost,
1993; Grecov and Rey, 2003a-c, 2004, 2005, 2006; Rey, 2007, 2009, 2010; Rey
and Denn, 2002). The shear viscosity under fl ow alignment, defi ned by
For disks (rods), it is found that
η
1
>
η
3
>
η
2
(
η
1
<
η
3
<
η
al
, is
2
1
2
1
4
1
−
(
)
+
(2.22)
η
=
η
+
η
−
γ
α
1
al
1
2
1
1
λ
and it is slightly larger than
1, as
the shear rate increases, the LE nematodynamics describes an orientation vis-
cosity reduction mechanism (OVR), as shown in Figure 2.6 (Grecov and Rey,
2003a-c, 2004, 2005, 2006; Rey, 2007, 2009, 2010). For example, if a CM sample
is sheared with a random director orientation distribution, the increasing effect
of shear is to narrow the distribution with a peak that is parallel to the fl ow
alignment angle (close to the shear gradient direction), and hence the apparent
viscosity will decrease with increasing shear since the fl ow alignment angle is
close to the minimum possible viscosity, which in the case for disks is
η
2
for disks and
η
1
for rods. Hence when |
λ
|
>
η
2
.
Steady shear fl ow simulations indicate that for any arbitrary Er, the LE
nematodynamics can be fi tted with the Carreau-Yasuda LC model (Grecov
and Rey 2003b; Rey, 2009):
ηη
ηη
−
−
(
na
−
1
)
/
al
=+
(
)
a
η
=
1
τ
Er
(2.23)
s
0
al
s
is the scaled shear viscosity,
n
is the “ power - law exponent, ”
a
is a
dimensionless parameter that describes the transition region between the zero
shear rate region and the power law region,
where
η
τ
is a dimensionless time constant,
and
η
0
is the zero shear rate viscosity. The fi rst transition region in the Carreau-
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