Theory of the nonequilibrium phase transition for nematic liquid crystals under shear flow

We consider the impact of shear flow on the isotropic-nematic transition in crystalline liquids by generalizing Leslie-Ericksen dynamics of nematic systems to include amplitude and biaxial degrees of freedom. Neglecting fluctuations, we find steady-state solutions to the equations of motion for the nematic order parameter and fluid velocity and interpret them in terms of nonequilibrium steady states. We predict a transition temperature increasing with shear rate up to a nonequilibrium critical point, and discuss the singular behavior of the order parameter and external stress near this point.