Stress boundary layers for the Phan-Thien–Tanner fluid at the static contact line in extrudate swell

The method of matched asymptotic expansions is used to examine the behaviour of the Phan-Thien–Tanner (PTT) fluid in the neighbourhood of the contact line singularity in extrudate swell. The solution structure for this shear-thinning viscoelastic fluid model has solvent stresses that dominate the polymer stresses, but requires stress boundary layers to fully resolve the solution at the die wall and free surface. The sizes and mechanism of the boundary layers at the two surfaces are different. We derive and present a similarity solution for the boundary layer at the die wall and an exact solution for the boundary layer at the free surface. An expression for the local behaviour of the free surface is also derived. The results for the boundary layers completes the preliminary asymptotic results for the PTT model presented in previous work.