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

Abstract

We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles π / α where 1 / 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 ) ) and stream function behaviour O ( r α ( 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 ) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180 ° and 270 ° .