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x
F
Same cube of nematic
at time t = 0
x
Unit cube of nematic
at time t = 0
z
y
A
BCDE
Ext
ension Dir
ection
F
Figure 2.4
Different orientations of the nematic disklike phase upon imposing a
strong uniaxial extensional fl ow. [Adapted from Lu et al. (2008).]
Flow kinematics
,
vv
Flow-induced orientation
Defects
and
textures
Orientation-induced flow
Microstructure kinematics
d/dt
Q
Figure 2.5
Schematic of velocity microstrusture kinematics defect and texture cou-
plings that build the nematodynamic cycle. The effect of fl ow on
Q
includes fl ow-
induced orientation of the N phase and fl ow birefringence of the I phase. The effect of
reorientation (d
Q
/dt) on velocity includes hydrodynamic interactions. The bottom left
schematic represents fl ow-induced orientation with defect nucleation (dark circle)
close to a surface due to director tumbling and the top right shows backfl ow (arrows)
generated by
±
1
2
annihilating defects.
x
(left) in the nematic disklike phase reorients the director
n
toward the com-
pression (
y
,
z
) plane (middle and right panel).
2.2.2
Nematodynamics
Flow processes of LCs can be considered in terms of a microstructural reactor,
where orientation, domains, defects, and textures are manipulated by shear
and extension deformation rates and where the fl ow patterns, secondary fl ows,
and hydrodynamic interactions are tightly coupled to liquid crystalline order
(Rey, 2009, 2010).
This LC fl ow analysis paradigm shown in Figure 2.5 is a closed loop that
couples the fl ow velocity and order parameter through fl ow - induced orienta-
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