Re-entrant Corner Singularity of the Giesekus Fluid.

The local asymptotic behaviour is described for steady planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. The re-entrant corner angle is denoted by π/α where 1/2<=α<1. Similar to another shear thinning model, namely the Phan-Thien-Tanner (PTT) fluid, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PTT, a weaker polymer stress singularity is obtained O(r-<FRACTION><NUM>(1-λ0)(3-λ0)</NUM><DEN>4</DEN></FRACTION>) with slightly thinner polymer stress boundary layers of thickness O(r<FRACTION><NUM>(3-λ0)</NUM><DEN>2</DEN></FRACTION>), where λ0 is the Newtonian flow field eigenvalue and r the radial distance to the corner. For comparison purposes in the benchmark case of a 270° corner, we thus have polymer stress singularities of O(r-<FRACTION><NUM>2</NUM><DEN>3</DEN></FRACTION>) for Oldroybd-B, O(r-0.3286) PTT and O(r-0.2796) for Giesekus. The wall boundary layer thicknesses are O(r<FRACTION><NUM>4</NUM><DEN>3</DEN></FRACTION>) for Oldroyd-B, O(r1.2278) for Giesekus and O(r1.1518) for PTT. As for the PTT model, these results for the Giesekus model breakdown in both limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit). It is also implicitly assumed that there are no regions of recirculation at the upstream wall i.e. we consider flow in the absence of a lip vortex. [ABSTRACT FROM AUTHOR]