Converging flow of tumbling nematic liquid crystals

Abstract

A similarity solution of the Leslie-Ericksen equations is obtained for flow between converging planes for nematic liquid crystals which experience a tumbling instability (α₃ > 0). The relative intensities of the stabilizing extensional flow near the centre plane, the destabilizing shear flow near the bounding plane, and the stabilizing Frank elasticity near both the boundary and the centre planes admit a variety of director distributions, depending on the rheological parameters; all distributions become unstable at critical values of the Ericksen number, leading to splay-bend walls for α₃ close to zero. A radial inhomogeneous magnetic field can suppress the instability. Closed-form analytical solutions are obtained for the transitions and the characteristic dimensions of splay-bend walls and boundary layers.