Chemistry Reference
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the surfactant N
d
solution is different because of the different sign in the
magnetic susceptibility
χ
a
[see Eq. (2.57) ].
2.4.1.5 Flow Alignment
As mentioned earlier (Section 2.2), the ability
of the director
n
to orient in a shear fl ow fi eld is a dominant rheological
property for oscillatory, steady, startup, and cessation of shear fl ow. Replica-
tion of 8CB (thermotropic N
c
) experimental steady and transient shear rheol-
ogy using the LE model in the aligning and tumbling modes has been
presented elsewhere (Kundu et al., 2009). The N
c
and N
d
phases of SDS/
decanol/water were investigated in a Couette fl ow cell for both steady fl ow
0 02
(
)
(
)
.
s
−
1
<<
γ
300
s
−
1
, step change
01
.s
−
1
<<
γ
10
s
−
1
, and fl ow reversal. The
study indicates that under steady shear, the alignment angles for N
d
and N
c
are 105° and 12° with respect to the fl ow direction, respectively. The wall
orientation appears to be planar for N
c
and face-on for N
d
. In order to under-
stand the theory explained in Section 2.2.3, we can analyze the data for the
N
c
and N
d
phases of SDS solutions with the LdG and LE model predictions
(Grecov and Rey, 2006). (i) From the reported alignment angles (N
c
: 12 ° ; N
d
:
105°) and Eq. (2.51), it is found that:
C
D
λ
=
1/cos(2
×
12)
=
1.09, and
λ
=
C
1/cos(2
1.02
(MBBA at 25°C), 1.01 (PAA at 122°C), 1.1 (5CB at 25°C). For thermotropic
N
d
such as polydispersed carbonaceous mesophases,
×
105)
=
−
1.15. For thermotropic N
c
the following is found:
λ
=
D
values as low as
1.45
were estimated. (ii) The steady-state viscosity as a function of shear rate for
N
c
and N
d
phases has a low shear rate plateau up to
λ
−
γ<
10
s
−
1
and a power
η
∼
()
−
m
law shear thinning region of
055 04 05
, where the fi rst two
values are for two N
c
phases and the latter for the N
d
phase. Using the LdG
model, the predicted shear thinning viscosity of a thermotropic N
d
was shown
to be consistent with experiments. For this case the shear thinning was con-
sistent with texturing under shear, where the texture length scale decreases
with a power law of
,
≈
. ,.,.
1
2
.
Figure 2.21 shows the predictions for the shear viscosity (in the power law
region), texture length scale, and visualization of the director fi eld across the
shear cell gap as functions of strain (Kundu et al., 2009). In general the
Carreau-Yasuda LC model [Eq. (2.16)] includes several viscosity reduction
mechanisms, such as the viscous anisotropy and texturing that arise in the LE
and LdG models. These mechanisms affect the three parameters
−
,
a
, and
n
so
that specifi c fl ow, wall-anchoring, and material conditions need to be specifi ed,
as shown elsewhere (Grecov and Rey, 2003a-c). Under fl ow reversal condi-
tions the stress exhibits oscillations followed by a long relaxation. For shear
step-down the stress relaxes quickly with no oscillations. In addition to the
particular stress relaxation, the signals superpose by plotting the shear stress
as a function of strain scaled with the steady-state value:
τ
() ()
/
ss
.
Simulations based on the LE and LdG models for fl ow aligning N
d
and N
c
phases with and without defects predict stress overshoots and undershoots as
well as scaling behavior under certain orientation kinematics. Stress over-
shoots and undershoots under transient shear are due to a nonmonotonic
τγ τ γ
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