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(a)
(b)
(c)
(d)
Figure 2.14
Computed Schlieren textures for different orientations of the cross polars
indicated by the cross. The charge of the wedge disclinations enumerated on the left
panel are: (1)
−
1
2
, (4)
+
1
2
, (6)
−
1
2
.
−
1, (2)
+
1, (3)
−
1, (5)
Figure 2.15
Computed visualization based on the LdG model of texture generation
by the Kibble mechanism and coarsening through defect annihilation. The top is the
polarized light intensity and the bottom the
+
1
2
and
−
1
2
disclinations. [Adapted from
Tsuji and Rey (1998) .]
potassium laurate/decanol/water has been characterized experimentally for
conditions close to the I/lamellar transition. The fl ow birefringence due to
transient shear fl ow was detected using optical transmittance, which is propor-
tional to the square of the order parameter
S
produced by the shear fl ow. By
fi tting experimental data with the LdG, the orientational diffusivity and the
intermicellar characteristic length scale can be estimated. Here, the LdG
model for fl ow birefringence under steady fl ow is used to illustrate the estima-
tion of rheological parameters from the experimental signal. Using a planar
director fi eld, simple shear, and steady uniaxial nematodynamics [Eq. (2.33)],
the following relation between fl ow alignment
θ
al
and
S
is predicted (Rey,
2010 ):
2
(
)
1
6
42
S
SS
3
−
U S
−+
US
2
2
US
3
−
cos 2
θ
==
1
+
1
λ
2
=
0
(
)
al
λβ
+−
2
D
e
(2.51)
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