Re-entrant corner flows of PTT fluids

We consider the local asymptotic behaviour for planar flow of Phan-Thien-Tanner (PTT) fluids around re-entrant corners, i.e. corners of angle π/α, where 1/2≤α<1. We assume the situation of complete flow around the corner with lip vortices implicitly assumed to be absent and consider the PTT model parameter regime κ=O(1) with no solvent viscosity. A class of solutions was identified in previous work [3] and identified a three region asymptotic structure comprising an outer core flow region in which the upper convected stress derivative dominates together with narrow boundary layer regions at upstream and downstream walls where viscometric behaviour is recovered. An outer solution with stress singularity of O(r ^-2(1-α)) and streamfunction behaviour O(r ^α(1+α)) was identified, where r is the distance from the corner. Here we complete this analysis be providing a solution for the downstream layer. Surprisingly, we now find a restriction on the validity of this solution being limited to the corner angles between 180° and 270° i.e. for 2/3<α<1. This follows from the solution in the natural stress variables, the details of which will be presented in the poster.