Effects of Elastic Anisotropy on the Flow and Orientation of
Sheared Nematic
Liquid Crystals
J. Tao and J. J. Feng
J. Rheol. 47, 1051-1070 (2003)
Abstract - We use a finite-difference
algorithm
to
simulate the shear flow of nematic polymers based on the
Leslie-Ericksen
theory, and investigate how unequal elastic constants
affect
the formation, oscillation and breakup of roll cells, the nucleation of
defects and the coarsening of texture upon cessation of flow. With
elastic
anisotropy, the so-called Ericksen number (Er) cascade comprises
the same regimes previously documented for isotropic elasticity: stable
simple shear, steady roll cells, oscillatory roll cells and an
irregular
pattern with thick disclinations. The onset of roll cells is most
sensitive
to K3, the elastic constant for bend. Increasing K3
stabilizes the shear flow against the formation of rolls. For reduced K3,
a second Er cascade may appear for higher Er, with
regularization
and eventual re-appearance of the defect-laden irregular pattern. The
twist
constant K2 is the most important for defect
formation;
a weaker K2 causes roll cells to break up and pairs
of
+-1 defects to nucleate at lower Er. The defects show
distinctive
structures depending on the elastic anisotropy; typically a weaker
elastic
constant gives rise to patterns that incur greater distortion in the
corresponding
mode. After cessation of shear, all textures relax completely to a
monodomain.
The longest-lasting orientational pattern is again attributable to the
weakest of the elastic constants. By analyzing the amount of distortion
in each mode and the associated free energy, we are able to elucidate
the
role of elastic anisotropy in defining the orientational patterns in
sheared
nematics.