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(Gupta and Rey, 2005), (2) stretching and pinching of existing loops in the
bulk, and (3) heterogeneous reorientation upon fl ow start up. Direct numerical
simulation of all these three coexisting nucleation processes for fl ow - aligning
LCs is beyond existing computational power since the ratio of a defect core
to typical shear cell sizes [the energy ratio
in Eq. (2.10)] is at least fi ve or
more orders of magnitude. This critical limitation fuels the motivation of using
simplifi ed models and theoretical frameworks that provide insights to texture
transformations. In a previous work, the loop emission process and its impact
on rheology were investigated (Rey, 1993a,b). Numerical simulations based on
heterogeneous reorientation (Gupta and Rey, 2005; Yan and Rey, 2002, 2003)
indicate that the defect nucleation rate
1 0
4
- 10
6
is well fi tted by a
for
=
power law model (Grecov and Rey, 2003a):
(2.49)
001
.
ϒ
(
Er
−
Er
)
Er
−
Er
ADL
ADL
where
is the Heaviside function and Er
ADL
is the minimum Ericksen number
for defect nucleation processes (Er
ADL
ϒ
1 0
5
). Note that Er
ADL
describes the transition between the antisymmetric processes and defect lattice
mode. The length scale of the texture
=
9
×
1 0
4
for
R
=
t
=
H
/
is given by (Grecov and Rey,
2003b )
H
=
t
(2.50)
c
ϒ
(
Er
−
Er
)
Er
−
Er
ADL
ADL
where
c
is a constant and
H
is the system size. Thus in the absence of coarsen-
ing, the texture length scale predicted by LdG decreases with a
−
1
2
power law
(Grecov and Rey, 2003b ).
2.3.2.2 Texture Coarsening Processes
Defect coarsening processes
occur simultaneously with defect nucleation. Texture refi nement with shear
indicates that the defect nucleation rate is higher that the coarsening rate. The
coarsening process includes (1) defect-defect annihilation, (2) defect-boundary
annihilation, and (3) wall pinching and retraction.
Numerical simulation based on one-dimensional (1D) LdG nematodynam-
ics that take into account the three mechanisms mentioned above predict that
in the presence of nucleation and coarsening the texture length scale
l
t
, given
by the system size divided by the number of defects, follows a decreasing func-
tion of slope close to
−
1
2
, reaches a minimum close to De
=
1, and then diverges
close to De
1 0
6
(Grecov and Rey, 2003a ).
According to LdG nematodynamics (Grecov and Rey, 2003a,b, 2004), defect
nucleation is only a function of the Ericksen number, and hence changing
the temperature
U
will only affect coarsening processes. The transition
dimensionless temperature that indicates the boundary between polydomain
and monodomain textures for
≈
2, as shown in Figure 2.13 for
=
0.18De
0.2
. The
predictions indicate that as the temperature of the LC lowers the De number
needed to attain a monodomain increases.
=
1 0
6
is
T
/
T
*
=
1 /
U
≈
0.4
−
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