Pre- and Post-Transitional Behavior of the Flow Alignment and Flow-Induced Phase Transition in Liquid Crystals

The flow alignment in the isotropic and nematic phases of a liquid crystal is studied theoretically with special emphasis on temperatures close to the transition temperature. The point of departure is a nonlinear, inhomogeneous relaxation equation for the alignment tensor which is applicable to both phases. The stationary solutions of this equation are analysed. In addition to some well-known results which are recovered as limiting cases for small velocity gradients, it is found that a sufficiently large velocity gradient can induce a transition into an ordered phase if the temperature is between the transition temperature for equilibrium conditions and a somewhat larger critical temperature. In the nematic phase, a weak dependence of the flow alignment angle on the magnitude of the velocity gradient is obtained. The relaxation towards a steady state is also considered.