Shearing the I-N phase transition of liquid crystalline polymers: Long-time memory of defect initial data

Ke Xu; M. Gregory Forest; Xiaofeng Yang

doi:10.3934/dcdsb.2011.15.457

Article Contents

2011, Volume 15, Issue 2: 457-473. Doi: 10.3934/dcdsb.2011.15.457

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Shearing the I-N phase transition of liquid crystalline polymers: Long-time memory of defect initial data

1.
Department of Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7575
2.
Departments of Mathematics and Biomedical Engineering, Institute for Advanced Materials, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250
3.
Department of Mathematics, University of South Carolina, Columbia, SC 29208

Received: November 30, 2009

Revised: February 28, 2010

Published: August 2011

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Abstract

Liquid crystalline polymers have been extensively studied in shear starting from an equilibrium nematic phase. In this study, we explore the transient and long-time behavior as a steady shear cell experiment commences during an isotropic-nematic (I-N) phase transition. We initialize a localized Gaussian nematic droplet within an unstable isotropic phase with nematic, vorticity-aligned equilibrium at the walls. In the absence of flow, the simulation converges to a homogeneous nematic phase, but not before passing through quite intricate defect arrays and patterns due to physical anchoring, the dimensions of the shear cell, and transient backflow generated around the defect arrays during the I-N transition. Snapshots of this numerical experiment are then used as initial data for shear cell experiments at controlled shear rates. For homogeneous stable nematic equilibrium initial data, the Leal group [4, 5, 6] and the authors [12] confirm the Larson-Mead experimental observations [7, 8]: stationary 2-D roll cells and defect-free 2-D orientational structure at low shear rates, followed at higher shear rates by an unstable transition to an unsteady 2-D cellular flow and defect-laden attractor. We show at low shear rates that the memory of defect-laden data lasts forever; 2-D steady attractors of [4, 5, 12] emerge for defect free initial data, whereas 1-D unsteady attractors arise for defect-laden initial data.

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Mathematics Subject Classification: Primary: 76A15, 82D30.

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References

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