Convection Instabilities in Nematic Liquid Crystals

Abstract

Pattern formation in hydrodynamic instabilities has been studied intensely over the past few decades (Manneville 1990, Cross & Hohenberg 1993). Rayleigh-Benard convection (RBC) in simple fluids has been the prime example. Our goal in this review is to draw attention to the rich variety of scenarios found in nematic liquid crystals (LCs). Liquid crystals are materials made up of highly anisotropic organic molecules in a phase that reflects this anisotropy. The class of nematic LCs (nematics) is fully liquid without long-range translational, but with long-range uniaxial orienta tiona I ordering of the molecules. Thus in the well-established hydrodynamic description (Ericksen 1 976, Leslie 1 979, de Gennes 1974, Stephen & Straley 1974, Chandrasekhar 1977) the director n characterizing the preferred axis has to be included as an additional variable. One then has six shear viscosities lXI' • . • , 1X6 with 1X6 -1X5 = 1X3 + IXz (1X4/2 corresponds to the isotropic viscosity) in the momentum balance equation (generalized Navier-Stokes equation). In the director equation, which can be associated loosely with a balance of torque, there are two rotational viscosities, YI and Yz, which are expressible in terms of the shear viscosities. For the low-molecular-weight materials discussed here the vis­ cosities relevant in the following are of order 10-1 kg m -I S-I. One needs three orientational elastic modules, kl), k22' k33' to describe the three basic