Chemistry Reference
In-Depth Information
ξ
= 0
ξ
= 0
0
8
16
24
32
40
Time(s)
Figure 2.25
Flow reversal at six different times for shear startup fl ow
[
)
()
]
[
=→
()
=
]
(
.
H
denotes
the Heaviside unit step function. The corresponding fl ow reversal times are:
t
rv
= 4.94 s
(solid line),
t
rv
= 9.63 s (dot - dash line),
t
rv
= 12.50 s (dash line),
t
rv
= 16.35 s (long dash
line),
t
rv
= 20.11 s (triple dot - dash line),
t
rv
= 27.79 s (dotted line). As the time of the
fl ow reversal is increased, the initial oscillations decrease, which is in agreement with
the experimental observations. [Adapted from Han and Rey (1994a).]
γ
=−
8 1
[
2
Ht t
−
]
s
−
1
,
γ
8
8
s
−
1
,
E
5753
,
temperature
=
35
°
C
v
)
()
(
γ=
81 2
[
−
Ht t
−
]
s
−
1
(2.67)
v
where
H
denotes the Heaviside unit step function. Figure 2.25 shows the shear
stress
as a function of time (s) during fl ow reversal, for six increasing reversal
times
t
rv
τ
4.94 s (solid line), 9.63 s (dot - dash line), 16.35 s (long dash line),
20.11 s (triple dot dash line), and 27.79 s (dotted line). The fi gure shows that
(i) double peaks reappear for earlier reversal times, and (ii) when the fl ow
is reversed at an earlier time, larger amplitude oscillatory behaviors are
predicted.
=
2.5
CONCLUSIONS
A comprehensive review of the theory and computer simulation of lyotropic
nematic phases, including micellar calamitic and discotic phases and wormlike
micellar nematics, was presented based on the classical Leslie-Ericksen and
Landau-de Gennes liquid crystal models. Emphasis was placed on the struc-
ture and dynamics of these systems. Important properties were discussed
such as defects, texturing, and shear rheology using the tools, concepts, scaling
laws, nonequilibrium phase diagrams, instability mechanisms, and pattern for-
mation processes previously reported for calamitic and discotic thermotropic
nematics and lyotropic nematic polymers. Strong similarities and analogous
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