Non-Equilibrium Phase Transitions in Nematic Liquid Crystals under Shear Flow†

Abstract

We discuss the impact of shear flow on the isotropic-nematic transition in crystalline liquids, paying particular attention to the notion of a non-equilibrium coexistence line. We establish a non-equilibrium phase diagram spanned by temperature and externally applied shear stress, by interpreting thc locally stable solutions to the equations of motion for the entire nematic order parameter and fluid velocity, in the case of planar Couette flow. This system displays several characteristics reminiscent of homogeneous equilibrium phenomena: a region in the phase diagram in which two states are locally stable; a critical point at which this two-state region vanishes; and singularities associated with this non- equilibrium critical point. By analyzing inhomogeneous solutions of the equations of motion we address the issue of whether a particular state is selected within the two state region. We find state selection throughout the two-state region, except on a coexistence line interpolating between the equilibrium transition point and the non-equilibrium critical point. We mention the singular nature of the interface width and the order parameter discontinuity in the neighborhood of the critical point.