ON THE STAGNATION FLOW BEHIND A SPHERE IN A SHEAR-THINNING VISCOELASTIC LIQUID

The flow of a viscoelastic liquid past a rigid sphere held on the centerline of a circular cylinder is examined experimentally by laser Doppler velocimetry and numerically by finite elements. The study deals with elastic fluids that exhibit shear-thinning behaviour, and focuses on the stagnation flow along the centerline behind the sphere. The experimental Weissenberg number is varied up to approximately 3.5. The speed of the sphere relative to the cylinder is fixed and the Weissenberg number is changed by adjusting the fluid properties. In this way a wide range of behaviour is produced, varying from the upstream shift of streamlines and velocity overshoot ('negative wake') seen in some previous experimental investigations to the downstream shift of streamlines characteristic of elastic fluids having shear-constant viscosity. The simulations indicate that the net response is strongly influenced by the elongational properties of the fluid, and this is used to rationalise the observed behaviour. In particular, it is shown that the Weissenberg number alone is not a sufficient basis for characterisation of the flow.