THE STAGNATION FLOW BEHIND A SPHERE

The flow of a viscoelastic liquid past a rigid sphere held on the centreline of a circular cylinder is examined both experimentally (laser Doppler velocimetry) and theoretically (finite elements). The study focuses on the stagnation flow along the centreline behind the sphere. In this region elastic properties provide an enhanced decelerating force on the fluid far from the sphere, leading to the well documented downstream shift in the streamlines relative to the flow of a Newtonian fluid. It has been less widely reported, however, that a corresponding acceleration effect close to the sphere may be sufficient to cause a localized upstream shift in the streamlines. Here the acceleration of the fluid exceeds that of the Newtonian fluid. This effect is quite separate from any similar behaviour produced by the presence of shear-thinning properties. Such a phenomenon has already been predicted for the case of unbounded flow past a cylinder or a sphere. In the current study we observe this effect experimentally and then use finite element simulations to show that it depends strongly on the fluid properties and the flow geometry. The conditions prevailing in most previous studies of this problem do not favour the observation of this enhanced acceleration.