Re-entrant corner behaviour of the Giesekus fluid with a solvent viscosity

The local asymptotic behaviour is described for planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. Similar to the PTT model, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PTT, a weaker polymer stress singularity is obtained O(r−((1−λ0)(3−λ0)/4)) with slightly thinner stress boundary layers of thickness O(r(3−λ0)/2), where λ0 is the Newtonian flow field eigenvalue and r the radial distance from the corner. In the benchmark case of a 270° corner, we thus have polymer stress singularities of O(r−2/3) for Oldroyd-B, O(r−0.3286) for PTT and O(r−0.2796) for Giesekus. The wall boundary layer thicknesses are O(r4/3) for Oldroyd-B, O(r1.2278) for Giesekus and O(r1.1518) for PTT. Similar to the PTT model, these results for the Giesekus model breakdown in both the limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit).