The Two-Fluid Theory of Polymer Migration in Slit Flow

The migration phenomenon in polymeric solutions undergoing flow in straight channels is analyzed by using the recent two-fluid theory of Doi and Milner, so far applied to shear flows in rotating devices. Migration is predicted to take place along the transversal direction of the Poiseuille flow (from the walls of the channel toward the center) if a constitutive equation appropriate to the entangled state of polymers is used. More specifically, we considered the behavior of semidilute solutions in good solvents. The detailed formulation of the boundary value problem of the slit flow reveals an unusual boundary condition at the wall. The governing equations are solved in closed form for the steady state and numerically for the transient. It is shown that, although a stationary concentration profile is achieved only after a very long time, effects of the migration phenomenon close to the wall can become significant much sooner. Outlooks for future work are discussed.