  Using Onsager variational principle, we study the dynamic coupling between
the stress and the composition in polymer solution. In the original derivation
of the two-fluid model [Doi and Onuki, J. Phys. II France {\bf 2}, 1631
(1992)], the polymer stress was introduced \emph{a priopri}, therefore a
constitutive equation is required to close the equations. Based on our previous
study of viscoelastic fluids with homogeneous composition [Phys. Rev. Fluids
{\bf 3}, 084004 (2018)], we start with a dumbbell model for the polymer, and
derive all dynamic equations using the Onsager variational principle.
