  We study the dynamics of shear-band formation and evolution using a simple
rheological model. The description couples the local structure and viscosity to
the applied shear stress. We consider in detail the Couette geometry, where the
model is solved iteratively with the Navier-Stokes equation to obtain the
time-evolution of the local velocity and viscosity fields. It is found that the
underlying reason for dynamic effects is the non-homogeneous shear
distribution, which is amplified due to a positive feedback between the flow
field and the viscosity response of the shear thinning fluid. This offers a
simple explanation for the recent observations of Transient Shear Banding in
time-dependent fluids. Extensions to more complicated rheological systems are
considered.
