Apparent Slip for an Upper Convected Maxwell Fluid

In this study the flow field of a nonlocal, diffusive upper convected Maxwell (UCM) fluid with a polymer in 3 a solvent undergoing shearing motion is investigated for pressure driven planar channel flow and the free boundary problem 4 of a liquid layer on a solid substrate. For large ratios of the zero shear polymer viscosity to the solvent viscosity, it is shown 5 that channel flows exhibit boundary layers at the channel walls. In addition, for increasing stress diffusion the flow field away 6 from the boundary layers undergoes a transition from a parabolic to a plug flow. Using experimental data for the wormlike 7 micelle solutions CTAB/NaSal and CPyCl/NaSal, it is shown that the analytic solution of the governing equations predicts 8 these signatures of the velocity profiles. Corresponding flow structures and transitions are found for the free boundary problem 9 of a thin layer sheared along a solid substrate. Matched asymptotic expansions are used to first derive sharp-interface models 10 describing the bulk flow with expressions for an apparent slip for the boundary conditions, obtained by matching to the flow in 11 the boundary layers. For a thin film geometry several asymptotic regimes are identified in terms of the order of magnitude of 12 the stress diffusion, and corresponding new thin film models with a slip boundary condition are derived. 13