A thermodynamic model for shear-induced concentration banding and macromolecular separation

We present a simple thermodynamic model for shear-induced concentration banding in polymer solutions, based on a nonequilibrium chemical potential depending on the shear rate. This dependence provides a coupling between diffusion and shear, besides the more classical coupling provided by the divergence of the viscous pressure tensor. When both couplings are taken into account, shear-induced concentration banding appears in a natural way. If the initial homogeneous concentration is higher than a threshold value, shear banding appears for sufficiently high value of the shear rate γ̇; if the initial concentration is lower, the steady-state concentration profile under shear is smooth. The banding profile depends on the polymer molecular mass and therefore it provides a basis for the chromatographic separation of polymers of different molecular mass.