Phase coexistence of complex fluids in shear flow

We present some results of recent calculations of rigid rod-like particles in shear flow, based on the Doi model. This is an ideal model system for ex hibiting the generic behavior of shear-thinning fluids (polymer solutions, wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We present calculations of phase coexistence under shear among weakly-aligned (paranematic) and strongly-aligned phases, including alignment in the shea r plane and in the vorticity direction (log-rolling). Phase coexistence is possible, in principle, under conditions of both common shear stress and co mmon strain rate, corresponding to different orientations of the interface between phases. We discuss arguments for resolving this degeneracy. Calcula tion of phase coexistence relies on the presence of inhomogeneous terms in the dynamical equations of motion, which select the appropriate pair of coe xisting states. We cast this condition in terms of an equivalent dynamical system, and explore some aspects of how this differs from equilibrium phase coexistence.