Convection Instabilities in Nematic Liquid Crystals

Pattern formation in hydrodynamic instabilities has been studied intensely over the last decades [1, 2], Although Rayleigh-Benard convection (RBC) in simple fluids has been the prime example [3], the rich variety of scenarios found in nematic hquid crystals (LCs) has attracted increased attention. 

1 We will concentrate here on the planar case. Some remarks about other alignments are made in Section 13.5. 

260 Macromolecular Systems Microscopic Interactions and Macroscopic Properties Deutsche Forschungsgemeinschaft (DFG) 

Copyright 2000 WILEY-VCH Verlag GmbH, Weinheim. ISBN 978-3-527-27726-1 

Further highlights were the identification of thermal noise shghtly below threshold by Rehberg et al. [38-40] and finally the clear identification of a Hopf bifurcation leading to travelling rolls or waves in sufficiently thin layers, below about 50 pm and clean material (low conductivity) by Refs. [18, 41-43]. It is not possible to explain the Hopf bifurcation within the conventional theoretical framework the standard model (SM), see Section 13.2, where the LC is treated as an anisotropic ohmic conductor. Indeed some of the theoretical effort, in particular the inclusion of the rather complicated flexoelectric terms [14, 44 46], was aimed primarily at resolving this problem. The situation is fiirther complicated by the fact that the bifurcation is often observed to be slightly subcritical, i.e. with a very small hysteresis [38-40, 47], whereas the theory predicts a supercritical bifurcation. 

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R. Ribotta, A. Joets Defects and interactions with the structure in ehd convection in nematic liquid crystals, in J. E. Wesfreid, S. Zaleski (eds) Cellular Structure in Instabilities, Springer, Berlin, p. 249 (1984)... 

Various other instances of hydrodynamic and electrohydrodynamic instabilities in nematic and, to a lesser extent, smectic liquid crystals have been investigated. No attempt is made here to review this work. For the present discussion, it is sufficient to note that (a) most of the work has dealt with oriented layers having anisotropic properties, and (b) some interesting instabilities arise in oriented layers which do not occur for isotropic materials. An example of the latter is cellular convection in a fluid layer confined between horizontal plates maintained at different temperatures. With an isotropic fluid, convection can arise only if the lower plate is hotter than the upper plate. Then, fluid near the lower plate is less dense and tends to rise while fluid near the upper plate is denser and tends to sink. With an oriented layer, however, convection can arise even when the upper plate is hotter if the anisotropy of thermal conduction properties is of a particular type (8). 

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