In the presence of shear flow, the constitutive equation for the diffusion flux in polymer solutions exhibits two kinds of coupling. One of these couplings comes from the viscous pressure contribution to the chemical potential, and the other one from the divergence of the viscous pressure tensor. The former contribution yields an effective diffusion coefficient depending on the viscous pressure, which may become negative in some circumstances. In such a case, an instability appears and the previously homogeneous system splits into two regions, with different solute concentrations - concentration banding. This separation depends on the polymer molecular mass and therefore it may provide a basis for the chromatographic separation of polymers of different molecular mass. © EDP Sciences/Societé Italiana di Fisica/Springer-Verlag 2007.