Summary: Ericksen number and Deborah number cascade predictions of a model for
liquid crystalline polymers for simple shear flow
D. Harley Klein
and L. Gary Leal
Department of Chemical Engineering,
University of California Santa Barbara
Santa Barbara, California 93106 USA
Carlos J. Garc´ia-Cervera and Hector D. Ceniceros
Department of Mathematics, University of California Santa Barbara
Santa Barbara, California 93106 USA
(Dated: January 5, 2006)
1
Abstract
We consider the behavior of the Doi-Marrucci-Greco (DMG) model for nematic liquid crystalline poly-
mers 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.
151­169] 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

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics