Orientational transition in radial flow of a nematic liquid

Abstract

Stationary in-plane and out-of-plane numerical solutions to the Leslie-Ericksen equations are obtained for the creeping, radial, pressure-driven out-flow of a low molar mass nematic liquid crystal between concentric, narrowly spaced, parallel disks with planar director surface orientation. The kinematics are described by the Ericksen number, E. At low E, elastic and shear torques keep the director in-plane for all radial distances. At sufficiently high E, elongation is able to orient the director out of the shear plane. The transition is a supercritical bifurcation: the stable stationary in-plane mode bifurcates into two stationary out-of-plane modes. The critical Ericksen number depends on the radial distance from the entrance hole, since elongation weakens more rapidly than the restoring elastic and shear torques as the edge of the cell is approached. The dissipatively equivalent out-of-plane modes are characterized by a net azimuthal secondary flow.