Re-entrant corner flow for PTT fluids in the natural stress basis

We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles π/απ/α where 1/2≤α<11/2≤α<1. The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with stress singularities of O(r−2(1−α))O(r−2(1−α)) and stream function behaviour O(rα(1+α))O(rα(1+α)) (r   being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using natural stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of α∈(2/3,1)α∈(2/3,1) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180°180° and 270°270°.