Kinetic Theory of a Dilute Polymer Solution in a Small Channel: Equilibrium Results

The problem of a bead-spring model macromolecule in the presence of two parallel impenetrable walls is studied. General phase-space kinetic theory expressions for the polymer concentration and the bulk stress are utilized. The conservation equation for the spatial distribution function together with the relevant boundary conditions is obtained. Explicit results are reported for equilibrium conditions. Our most important finding is that in equilibrium the stress tensor is transversely isotropic. The corresponding first normal stress difference is strictly non-negative and has a maximum value of about one third the value the normal components of the particle stress assumes outside the boundary layer. The boundary layer thickness is estimated.