Anisotropic relaxation in liquid crystals

We describe phenomenologically the sound propagation at ultrasonic and hypersonic frequencies in nematic and smectic liquid crystals and corresponding isotropic liquid phases. To account for the experimentally well-established effects the standard hydrodynamic equations should be completed by two nonhydrodynamic relaxation mechanisms. More specifically, we prove that by a single nonhydrodynamic relaxation mechanism it is impossible to explain simultaneously both the anisotropy of the sound propagation in the hypersonic regime and the increase of the elastic constants compared to their values in the ultrasonic range. The possible origins of these two nonhydrodynamic relaxation mechanisms are briefly discussed.