Simiple Shear Flow of a Non-Aligning Nematic

Abstract

AbstractThis paper presents a nonlinear numerical analysis of the orientational instabilites, textures, and flow patterns of a characteristic rod-like nematic liquid crystal in steady simple shear flow. The parameter vector V=(λ,E) is given by the reactive parameter (λ) and the Ericksen number (E). There are two stationary solutions: in-plane(IP) and out-of-shear-plane(OP), according to whether the average orientation lies in or out of the plane of shear. For a given λ the in-plane stationary solutions may undergo a continuous transition (second order) to two dissipatively equivalent OP solutions when E=Eo or a discontinuous transition (first order) to a highly distorted IP solution when E=Ei. The continuous transition at E=Eo is a supercritical (pitchfork) bifurcation and the discontinuous transition at E=Ei is a limit point instability. Nonlinear numerical analysis shows that for the studied liquid crystal Eo < Ei. The orientation phase diagram for stable stationary solutions therefore consist of a region of OP solutions separated from a region of IP solutions by the curve Vo = (λ,Eo), describing a set of continuous supercritical bifurcations. These stable OP solutions are characterzied by the absence of sharp splay and bend deformations and by the presence of complex secondary flows arising from the three dimensional orientation. Presented results also include the dependence of the three dimensional texture, primary and secondary velocity fields on E.