Transient periodic dissipative structures in nematics confined between coaxial cylinders

Abstract

The onset of transient periodic dissipative structures (TPDS) is studied using the linear perturbation approximation when a sufficiently strong magnetic field (B) is impressed on the uniformly aligned director (no) of a nematic confined to the annular space between two coaxial cylinders of radii R2 and RI (Rz > RI). Only TPDS with axial or azimuthal periodicity is considered. An approximate expression for the magnetic body force density is employed. The solutions mainly concern rigid anchoring. When no is along the common axis, a radial field or an azimuthal field causes TPDS with periodicity along the axis when the calamitic nematic has positive diamagnetic anisotropy (χA >O); an axial field has a similar effect when χA < 0. The dependence of the rise time as well as the periodicity wavevector are studied as functions of the applied field strength and the ratio of the radii (R2, = R2/RI). A weakening of director anchoring has a deleterious effect on the formation of TPDS. When no is azi- muthal and χA > 0, a radial or an axial field may induce TPDS having an azimuthal periodicity wavevector which is an integer and related to the number of domains; continuous changes in control variables cause discontinuous changes in the wavevector. Using hypothetical material parameters, it is shown that an axial (or an azimuthal) field may induce TPDS with a continuously varying (or discontinuously varying) wavevector in a radially aligned discotic nematic having χA > 0. If χA < 0, a radial field may induce TPDS with modulation along both the axial and the azimuthal directions in a discotic nematic. When R21 is close to unity, the results of this work go over to those obtained for a flat sample.