Poiseuille flow of liquid crystals: highly oscillatory regimes

Abstract

In this article we discuss numerical solutions of the boundary value problem of stationary, plane Poiseuille flow of nematic liquid crystals with variable degree of orientation. The role of the Ericksen number in determining the structure of defects and oscillations of the solutions is analyzed. We find that, at the limit of very large Ericksen number, the very large density of defects render the flow effectively isotropic. This follows from the dependence of the Leslie coefficients on the order parameter; it is a property of the model, and it does not depend on the particular sets of data used in the numerical simulations. From physical point of view, this work intends to address flow phenomena of polymeric liquid crystals. One relevant feature of such a polymeric flow is the textured appearance that results from very large defect densities. This article provides a quantitative, one-dimensional model of such defect phenomena. Moreover, it shows that, for large Ericksen number, a flow that satisfies the alignment condition may actually behave as non-aligning.