Computational studies of the shear flow behaviour of a
model for nematic liquid crystalline polymers

D.H. Klein, C.J. García-Cervera, H.D. Ceniceros, and L.G. Leal.

Abstract

We present an accurate and efficient numerical method to the solve
the microstructure-flow problem that constitutes the coupling of the
molecular-based Doi-Marrucci-Greco (DMG) model
to the Cauchy equation of motion and
continuity equation. We also provide a general introduction to the
problem of the flow of complex fluids.
Preliminary investigations of the predictive capabilities of the
DMG model show that with increasing shear rate, in
accordance with both experimental observations and other theoretical
predictions, the model was found to exhibit three flow regimes:
steady linear shear flow at low shear rate, steady roll cells at
intermediate shear rates, and irregular flow and orientation patterns
at high shear rates. Given sufficiently high shear rates, the
irregular flow structure was accompanied by the formation of $\pm 1$
and $\pm 1/2$ strength disclinations. Furthermore, at shear rates
large enough to inhibit the tumbling of the average molecular
orientation, the solution no longer contains disclinations or roll
cells, but retains some structure in the flow direction that has the
visual appearance of stripes.