Hydrodynamic coupled modes of a nematic under a temperature gradient and   a uniform gravitational field
  Fluctuating hydrodynamics (FH) describes the dynamics of the fluctuations for fluids at mesoscopic scales. Here we use this approach to study the fluctuations of the hydrodynamic variables of a thermotropic nematic liquid crystal (NLC) in a nonequilibrium steady state (NESS). This state is induced by an externally imposed temperature gradient and a uniform gravity field. We calculate analytically both, the equilibrium and nonequilibrium hydrodynamic modes. We find that in this NESS the nonequilibrium effects produced by the external gradients only affect the longitudinal variables. This gives rise to a pair of sound modes, one orientation mode of the director and two visco-heat modes formed by the coupling of the shear and thermal modes. We also find that the last three modes exhibit the largest changes. The analytical expressions that we have found for the visco-heat modes imply that the heat and shear modes of the NLC are coupled, that they reduce to those of simple fluid in the isotropic limit and that these modes may become propagative, a feature that also occurs in the simple fluid. In the isotropic limit of the nematic our results also reduce to the hydrodynamic modes of a simple fluid in the presence of the same temperature gradient and the pressure gradient produced by the gravity field. 
J. F. Camacho and R. F. Rodriguez
cond-mat.soft