Homogeneous instabilities in nematic liquid crystals

Abstract

The effect of a magnetic field on the instability threshold in shear flow and plane Poiseuille flow of nematics has been worked out for the case of unperturbed director orientation normal to the plane of shear. The critical shear rate for the onset of instability has been studied as a function of destabilising field. The dependence of the time constant v on shear and field for time dependent perturbations in shear flow is found to be explained by two solutions which differ from one another to the extent that wave vectors which are real for one solution are imaginary for the other; these solutions exist for different ranges of shear and field but have one common point where they yield the same v value making possible a continuous description of v. In Poiseuille flow even for a destabilising field applied along the primary velocity the occurrence of an instability associated with net secondary flow (flow transverse to the primary velocity) is found to be more favourable than one having no secondary flow. This trend is also observed for low destabilising fields applied along the velocity gradlent but for higher fields the occurrence of an instability without net secondary flow becomes more favourable. Simultaneous application of a stabilising electric field does not change the qualitative nature of the results.