Stress boundary layers for the Giesekus fluid at the static contact line in extrudate swell

We used the method of matched asymptotic expansions to examine the behavior of the Giesekus fluid near to the static contact line singularity in extrudate swell. This shear-thinning viscoelastic fluid had a solution structure in which the solvent stresses dominated the polymer stresses near to the singularity. As such, the stress singularity was Newtonian dominated, but required viscoelastic stress boundary layers to fully resolve the solution at both the die wall and free surface. The sizes and mechanism of the boundary layers at the two surfaces were different. We gave a similarity solution for the boundary layer at the die wall and derived the exact solution for the boundary layer at the free-surface. The local behavior for the shape of the free-surface was also derived, which we showed was primarily determined by the solvent stress. However, the angle of separation of the free surface was determined by the the global flow geometry. It was this which determined the stress singularity and then in turn the free-surface shape.