Abstract
The generic behavior of both flow-induced phase separations and rheological responses of complex fluids has been studied. We solve a two-fluid model numerically in a strong-flow regime without using the diffusive equation linearization and adiabatic approximation. Our results show that the formation of the mechanical shear bands and the fluid composition bands can be closely interrelated. We have identified correlations between the microstructure evolution and rheology, and also different mechanisms to reach the steady state. The rheological signature of demixing fluids under shear is that the dependence of the steady-state shear stress on shear rate changes from non-linear to linear. The model selects a steady-state stress in a natural physical way for non-monotonic constitutive equations under strong flow.