Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 59

stress surface as a function of the in-plane tilt angle and out-of-plane twist
angle.
Figure 2.22 shows a gray-scale plot dimensionless shear stress surface

as
a function of twist and tilt angles. In this plot, white corresponds to the local
maximum shear stress (

τ

τ = τ max = 2.6) and black corresponds to the local

minima ( 0.85). A good characterization of shear stress response

during shear startup is to consider the evolution from the three Miesowicz
director orientations toward the steady state (Han and Rey, 1994a-c). By

τ = τ max =

3

1

1 2

S U S

U

0

-1

-3 -2 -1 0 1 2 3

Tilt angle, θ

(a)

1

Er = 500
Er = 800
Er = 1000

0

-1

-2

-3

-4

-5

0 5 10

Strain

15 20

(b)

Figure 2.22 (a) Gray-scale visualization of the shear stress surface as a function of
the twist and tilt angles for N d . Light corresponds to local stress maxima and dark to
minima. U and S denote the unstable and stable orientation, respectively. Path 1: evolu-
tion from velocity direction to fl ow alignment produces 1 overshoot; path 2: from
velocity gradient to fl ow alignment produces monotonic change; path 3: from vorticity
direction to fl ow alignment produces 1 undershoot. (b) Scaled dimensionless shear
stress during fl ow-start up for three Ericksen numbers, with initial alignment at 60° to
fl ow direction. Overshoots, undershoots, and scaling are predicted. [Adapted from
Grecov and Rey (2003c) .]