Coexistence and Phase Separation in Sheared Complex Fluids

We demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken-symmetry order parameter (nematic, smectic, crystalline, etc.) are coupled to shear rate. Our construction relies on a selection criterion, the existence of a steady interface connecting two stable homogeneous states. We use the (generalized) Doi model of lyotropic nematic liquid crystals as a model system, but the method can be easily applied to other systems, provided non-local effects are included.