Saddle-splay and mechanical instability in nematics confined to a cylindrical annular geometry

The occurrence of a mechanical instability is predicted for a nematic liquid crystal confined to a cylindrical annular geometry. The surfaces impose either a bend distortion (azimuthal configuration) or a splay distortion (radial configuration) in the plane of the cylinders′ cross-section. Remarkably, the instability appears also with strong anchoring, and, when the torsional anchoring is weak, then the saddle-splay elastic constant K24 deeply influences the critical radii.