Chemistry Reference
In-Depth Information
where
*
/ 6
. According to experimental data on rodlike nematics, the
Miesowicz viscosities are connected as follows (Rey, 2009, 2010; Simoes and
Domiciano, 2003 ):
η=
ckT
D
(
)
ηη η
++ =+
8
CC
ηη
−
(2.40)
1
2
3
1
2
1
2
where
C
1
is a constant and
C
2
is bounded by 2.77
3.84. In the present
model, if we only retain linear terms in
S
in Eq. (2.40) we fi nd that
<
C
2
<
8 6
4
β ν
νβ
2
+
+
*
2
C
2
=
(2.41)
*
2
6
5
) the linearized model is consistent with experiments
For aligning rods (
β>
if
*
. Expressions (2.39) allow to express the reactive parameter
λ
, the
ν
2
>
057
.
shear viscosities (
η
3
), and the normal stress difference
N
l
in terms of the
scalar order parameter
S
. For example, the reactive parameter is (Grecov and
Rey, 2003b )
η
1
,
η
2,
(
)
β
42
6
+−
SS
S
2
(2.42)
λ
=
Rods will always align if
is
interpreted in terms of the geometry of the rheological fl owing unit.
For De
β>
6
5
and disks if
β<−
6
5
. In this model
β
<
1, the predictions are obtained by replacing
S
by its equilibrium
value
S
eq
:
1
4
3
4
8
3
S
(2.43)
=+
1
−
eq
U
For De >> 1 numerical solutions are required. In this regime the Carreau-
Yasuda model becomes (Grecov and Rey, 2003b)
ηη
ηη
−
−
(
na
−
1
)
/
∞
=+
(
)
a
η
=
1
τ
Er
(2.44)
s
al
∞
where
,
a
,
n
refer to the De >> 1 regime. Hence the LdG model predicts a viscosity curve
with three plateaus and two shear thinning regions (Grecov and Rey, 2003b).
As shown in Lhuillier and Rey (2004a,b), the LdG model emerges from the
Doi-Hess molecular model based on the extended Maier-Saupe potential. For
further discussions of the Doi-Hess molecular model, related nematodynamic
models, and rheological applications see Larson and Doi (1991), Larson (1999),
Rey (2007, 2009, 2010), and Rey and Denn (2002).
η
∞
is the plateau viscosity when
S
is close to 1, and the parameters
τ
Search WWH ::
Custom Search