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

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 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 Doi–Marrucci–Greco ∗Department of Mathematics, University of California, Santa Barbara, California 93106, USA. mailto:[email protected] and mailto:[email protected] †Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA. mailto:[email protected] and mailto:[email protected] See http://anziamj.austms.org.au/V46/CTAC2004/Klei for this article, c © Austral. Mathematical Soc. 2005. Published April 26, 2005. ISSN 1446-8735 ANZIAM J. 46 (E) ppC210–C244, 2005 C211 model show that with increasing shear rate, in accordance with both experimental observations and other theoretical predictions, the model exhibits 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 is accompanied by the formation of ±1 and ±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.