Sheared nematic liquid crystal polymer monolayers

Abstract

We provide a comprehensive study on the planar (2D) orientational distributions of nematic polymers under an imposed shear flow arbitrary strength. We extend previous analysis of persistence of equilibria in steady shear and for transitions to unsteady limit cycles, from closure models to the Doi-Hess 2D kinetic equation. A variation on the Boltzmann distribution analysis of Constantin et al. and others 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.