Sheared nematic liquid crystal polymer monolayers

M. Gregory Forest; Hongyun Wang; Hong Zhou

doi:10.3934/dcdsb.2009.11.497

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2009, Volume 11, Issue 2: 497-517. Doi: 10.3934/dcdsb.2009.11.497

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Sheared nematic liquid crystal polymer monolayers

1.
Department of Mathematics & Institute for Advanced Materials, University of North Carolina, Chapel Hill, NC 27599-3250
2.
Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064
3.
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216

Received: November 30, 2007

Revised: March 31, 2008

Published: August 2009

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Abstract

We provide a comprehensive study on the planar (2D) orientational distributions of nematic polymers under an imposed shear flow of arbitrary strength. We extend previous analysis for persistence of equilibria in steady shear and for transitions to unsteady limit cycles, from closure models [21] to the Doi-Hess 2D kinetic equation. A variation on the Boltzmann distribution analysis of Constantin et al. [3, 4, 5] and others [8, 22, 23] for potential flow is developed to solve for all persistent steady equilibria, and characterize parameter boundaries where steady states cease to exist, which predicts the transition to tumbling limit cycles.

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Mathematics Subject Classification: Primary: 82D60, 76A15; Secondary: 65Z05, 35Q99.

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