Compressibility Effects on the Light Scattered by a Non-Equilibrium   Suspension in a Nematic Solvent
  We calculate the light scattering spectrum of the anisotropic diffusion of impurities (dye) in a compressible nematic solvent. We use a fluctuating hydrodynamic description when the system is in fully thermodynamic equilibrium and in a non-equilibrium steady state ($NESS$) induced by a dye-concentration gradient. We find that the equilibrium spectrum is symmetric (Lorentzian) with respect to the frequency shifts, but anisotropic through its explicit dependence on the ratio of the parallel and normal diffusion coefficients of the dye. The values of these coefficients were taken from experimental measurements of diffusion of methylred and nitrozo di-methyl aniline in a $MBBA$ solvent. We find that the compressibility of the solvent increases the maximum and the width at half height of the Rayleigh peak, with respect to the incompressible case \cite{suspension1}. This increase varies between 12% and 25%, respectively, when the impurities concentrations is the range of 1% - 5%. The $NESS$ induces a coupling between the concentration fluctuations of the dye and the hydrodynamic fluctuations of the solvent. In this case the compressibility effects may increase the maximum and the width of the central peak up to $% 25%$, for values of the concentration gradient four orders of magnitude smaller than those considered in the incompressible case. For the nonequilibrium Brillouin part of the spectrum we find that the intensities of the sound propagation modes are unequal and one of the peaks shrinks in the same amount as the other increases. This asymmetry increases linearly with the magnitude of the solute concentration gradient. The maximum difference between the nonequilibrium and equilibrium contributions to the Brillouin spectrum for various values of the external gradient is also estimated. 
H. H\'ijar and R. F. Rodr\'iguez