Chaotic orientational behavior of a nematic liquid crystal subjected to a steady shear flow

Based on a relaxation equation for the second rank alignment tensor characterizing the molecular orientation in liquid crystals, we report on a number of symmetry-breaking transient states and simple periodic and irregular, chaotic out-of-plane orbits under steady flow. Both an intermittency route and a period-doubling route to chaos are found for this five-dimensional dynamic system in a certain range of parameters (shear rate, tumbling parameter at isotropic-nematic coexistence, and reduced temperature). A link to the corresponding rheochaotic states, present in complex fluids, is made.