Two-fluid model for the breakdown of flow alignment in nematic liquid crystals.

We present a macroscopic two-fluid model to explain the breakdown of flow alignment in nematic liquid crystals under shear flow due to smectic clusters. We find that the velocity difference of the two fluids plays a key role to mediate the time-dependent behavior as soon as a large enough amount of smectic order is induced by flow. For the minimal model it is sufficient to keep the nematic degrees of freedom, the mass density of the smectic clusters and the degree of smectic order, the density, and two velocities as macroscopic variables. While frequently a smectic A or C phase arises at lower temperatures, this is not required for the applicability of the present model. Indeed, as pointed out before by Gähwiller, there are compounds showing a breakdown of flow alignment over a large temperature range and no smectic phase, but a solid phase at lower temperatures. We also demonstrate that, using a one velocity model, there is no coupling under shear flow between induced smectic order and the director orientation in stationary situations thus rendering such a model to be unsuitable to describe the breakdown of flow alignment. In a two-fluid description, flow alignment breaks down and becomes unstable with regard to a space- and time-dependent state due to an induced finite velocity difference. In an Appendix we outline a mesoscopic model to account for the sign change in the anisotropy of the electric conductivity observed in nematics with smectic clusters.