Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 51

where for simplicity the equality 18 η = ζ is used to relate translational ( η ) and

) viscosities [see, e.g., Eq. (2.30) of Rey (2010)]. Figure 2.16a shows
the computed scalar order parameter S and the alignment angle as a function
of De for steady shear of an isotropic solution, for

rotational ( ζ

0.95 and several U
values; the shapes of S curves are consistent with experiments (Gobeaux
et al., 2007; Rey, 2010). Flow-induced birefringence is due to increasing S
and decreasing

β =

θ al as shear rate increases.
From Figure 2.16a it is seen that the limits of a shear rate (Deborah number)
scan then are

1 50

40

0.8

θ @U = 2.6

30

0.6

θ @U = 2

θ @U = 1

S@U = 1
S@U = 2
S@U = 2.6

20

0.4

10

0.2

0

0 0

5
Deborah number, De
(a)

10 16

50

θ @ β = 0.5

S @ β = 0.5

θ @ β = 0.7

S @ β = 0.7

θ @ β = 0.95

S @ β = 0.95

40

30

20

10

0

01 234 5 67 89 0

Deborah number, De

(b)

Figure 2.16 /4) as a function of De of a

sheared isotropic solution of rods: (a) different concentration of rods ( U ) and

Flow - induced birefringence ( S > 0, 0 < θ al < π

β = 0.95;

increasing U increases the initial slope dS / d De. (b) Same but for U = 2 and different β

values; increasing β increases the plateau value of S . [Adapted from Rey (2010) .]