Shear flow in nematic liquid crystals: Fréedericksz transition as a bifurcation

Arup Mukherjee, Bagisa Mukherjee

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We numerically investigate the Fréedericksz transition for steady state plane shear flow of nematic liquid crystals between two parallel plates in the presence of external magnetic fields. Three typical configurations with the external field in the plane of the flow and perpendicular to it, in the plane and along the flow, and where it is perpendicular to the plane of the flow are considered. In each case, the Fréedericksz transition is studied as a bifurcation problem. Beginning with a steady state shear flow, solutions corresponding to slowly increasing magnetic fields and those corresponding to fields which are suddenly turned on at a given intensity are studied. For a typical idealized nematic, we show that the symmetric pitchfork bifurcation in the absence of shear becomes a transcritical bifurcation from the trivial solution in one configuration while in another it resembles a disconnected pitchfork where the turning point of the disconnected branch is a generic singularity in the absence of symmetry or a trivial solution.

Original languageEnglish
Article number021703
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume71
Issue number2
DOIs
StatePublished - 1 Feb 2005

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