Elastic actions exchanged by eccentric cylinders in liquid crystals.

Equilibria of a nematic liquid crystal confined between two eccentric cylinders are studied within a purely director approach. A planar equilibrium configuration competes against a three-dimensional one. A stability diagram is obtained in terms of both the ratio between the radii of the bounding cylinders and the distance between their axes. It turns out that the nonplanar minimizer has a structure more complex than that envisaged in the tensorial approach employed by McKay and Virga [Phys. Rev. E 71, 041702 (2005)] and that the planar configuration cannot be the absolute minimizer when the outer cylinder becomes a plane wall. The mechanical actions transmitted by the nematic liquid crystal on both bounding cylinders are computed and compared with other results available in the literature.