Early stage kinetics in a unified model of shear-induced demixing and mechanical shear banding instabilities.

We present a unified model of shear-induced demixing and "mechanical" shear banding instabilities in polymeric and surfactant solutions, by combining a simple flow instability with a two-fluid approach to concentration fluctuations. Within this model, we calculate the "spinodal" limit of stability of initially homogeneous shear states to demixing/banding, and predict the selected length and time scales at which inhomogeneity first emerges after a shear start-up "quench" into the unstable region, finding qualitative agreement with experiment. Our analysis is the counterpart, for this driven phase transition, of the Cahn-Hilliard calculation for unsheared fluid-fluid demixing.