Non-equilibrium chemical potential and stress-induced migration of polymers in tubes

A non-equilibrium chemical potential depending on the viscous pressure tensor is used to describe shear-induced diffusion in polymer solutions flowing along cylindrical tubes. Our results generalize previous ones in three main aspects: a Flory–Huggins expression for the equilibrium contribution to the chemical potential is used instead of the ideal-gas like expression, the full expression for the steady-state compliance of the solution is taken into account instead of only the polymer contribution, and the influence of the solute molecular mass is explicitly considered. As a qualitatively new result of considerable practical interest, it stands the prediction that in some circumstances, a dynamical instability may appear, which accelerates and enhances the separation process.