ON CORNER FLOWS OF OLDROYD-B FLUIDS

Exact series solutions for planar creeping flows of Oldroyd-B fluids in the neighbourhood of sharp corners are presented and discussed. Both reentrant and non-reentrant sectors are considered. For reentrant sectors it is shown that more than one type of series solution can exist formally, one type exhibiting Newtonian-like asymptotic behaviour at the corner, away from walls, and another type exhibiting the same kind of asymptotics as an Upper Convected Maxwell (UCM) fluid. The solutions which are Newtonian-like away from walls are shown to develop non-integrable stress singularities at the walls when the no-slip velocity boundary condition is imposed. These mathematical solutions are therefore inadmissible from the physical viewpoint under no-slip conditions. An inadmissible solution, with stress singularities which are not everywhere integrable, is identified among the solutions of UCM-type. For a 270-degrees reentrant sector the radial behaviour of the normal stress is everywhere r-0.613. In the viscometric region near a wall, the radial normal stress sigma(rr) behaves like (repsilon)-0/613, where epsilon is the angle made with the wall. In addition sigma(rtheta) is infinite (not integrable) at the wall even when r is non-zero. Another UCM-type solution has a normal stress behaviour away from walls which is r-0.985 for a 270-degrees sector. Again, this solution has a non-integrable stress singularity and is therefore inadmissible. Finally, for non-reentrant sectors it is shown that the flow is always Newtonian-like away from walls.