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tion (lower left schematic) and its converse, orientation-induced fl ow (lower
right schematic), and with both processes feeding into defects and textures.
While fl ow-induced orientation is well known and characterized in fl exible and
rigid-rod polymers, the full range of effects arising from orientation-induced
fl ow, such as backfl ow, transverse fl ow, and hydrodynamic interactions during
defect-defect annihilation, is less characterized. Furthermore, fl ow - induced
textural transformations can only be understood using defect physics and
rheophysics. The closed loop shown in Figure 2.5 can be achieved at a macro-
scopic level using the Leslie-Ericksen (LE)
n
- vector description (de Andrade
Lima and Rey, 2003a-c, 2004a-e, 2005, 2006a-e; Larson, 1999; Rey 2007, 2009,
2010) or at the mesoscopic level using the
Q
- tensor Landau - de Gennes (LdG)
model (Murugesan and Rey, 2010; Rey, 2007, 2010; Tsuji and Rey, 1998). Only
the latter captures important features such as singular defect nucleation, sin-
gular defect-defect reactions, and singular defect-fl ow interactions. In order
to avoid repetitions (Rey, 2007, 2009, 2010) and concentrate on objectives, we
provide a qualitative brief presentation of nematodynamics; for reviews and
other accounts on this active fi eld see, for example, Larson (1999) and Rey
(2007, 2009, 2010), and references therein.
The Landau-de Gennes model has an external length scale
e
and an inter-
nal length scale
i
as follows (Rey, 2009, 2010; Rey and Denn, 2002; Rey and
Tsuji, 1998 ):
2
L
ckT
3
ckT
LH
*
=
e
(2.10)
=
H
=
=
>>
1
e
i
3
*
/
2
i
where
H
is the system size,
L
(energy/length) is a characteristic orientation
elasticity constant associated with gradients in the directors (
n
,
m
,
l
) and
ckT
*
is the energy per unit volume associated with molecular elasticity (
S
,
P
);
c
is
the concentration per unit volume,
k
is the Boltzmann constant, and
T
* is the
isotropic-nematic transition temperature. The external scale is associated with
micron-scale changes in (
n
,
m
,
l
) and the internal length scale
i
is associated
with nanoscale changes in (
S
,
P
), as in the disclination core shown in Figure
2.5. The ratio of molecular ordering energy to orientation elasticity
R
, or ratio
of square length scales, is of the order of 10
6
- 10
9
. In the LE model,
R
is
assumed to be infi nity, and hence the scalar order parameters (
S
,
P
) are not
taken into account. The external
τ
i
time scales of the LdG
model are ordered as follows (Grecov and Rey, 2003a,b; Rey 2007, 2009,
2010 ):
τ
e
and internal
η
H
L
2
1
i
(2.11)
τ
=
τ
=
τ
>>
τ
e
i
e
3
D
r
where
D
r
is the bare rotational diffusivity and
ckT
* /
D
r
. The external time
scale describes slow orientation variations, and the internal length scale
describes fast order parameter variations. In the LE model
η
=
τ
i
=
0 and no
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