Ericksen number and Deborah number cascade predictions of a model for liquid crystalline polymers for simple shear flow

We consider the behavior of the Doi-Marrucci-Greco (DMG) model for nematic liquid crystalline polymers in planar shear flow. We found the DMG model to exhibit dynamics in both qualitative and quantitative agreement with experimental observations reported by Larson and Mead [Liquid Crystals, 15 (1993), pp. 151–169] for the Ericksen number and Deborah number cascades. For increasing shear rates within the Ericksen number cascade, the DMG model displays four distinct regimes: stable simple shear, stable roll cells, irregular structure followed by large-strain disclination formation, and irregular structure preceded by disclination formation. In accordance with experimental observations, the model also predicts both ±1 and ±1/2 disclinations. Although ±1 defects form via the ridge-splitting mechanism first identified by Feng, Tao, and Leal [J. Fluid Mech., 449 (2001), pp. 179–200], a new mechanism is identified for the formation of ±1/2 defects. Within the Deborah number cascade, with increasing Deborah number, the DMG model exhibits a stream-wise banded texture, in the absence of disclinations and roll cells, followed by a monodomain wherein the mean orientation lies within the shear plane throughout the domain.