On the flow of a non-Newtonian fluid between rotating,coaxial discs

In recent times, workers in numerical methods for non-Newtonian flows have been concerned with the high Weissenberg number problem. This problem which may be caused by a number of different things, manifests itself in the failure of numerical methods at some finite and often small Weissenberg number.This paper is concerned with the torsional flow of an Oldroyd-B fluid. The kinematics is restricted to that commonly referred to as Von Kármán kinematics. These restrictions allow the reduction of the problem to a set of ordinary differential equations. The problem is then solved with finite differences using well-known branch following and jumping techniques.The solution of this set of equations is discussed, and it is found that the solutions either lose stability at subcritical bifurcation points, or fold back on themselves at limit points. Either of these will cause a high Weissenberg number problem.Comparisons are also made with the known solutions to the Newtonian problem by considering small values of the Weissenberg number.