ON THE MOTION OF A SPHERE FALLING THROUGH AN ELASTIC LIQUID CONTAINEDIN A TIGHTLY-FITTING CYLINDRICAL CONTAINER

We give further consideration to the fall of a sphere through highly e lastic liquids. Earlier work is extended to include the case of a tigh tly-fitting cylindrical container (beta approximate to 0.9). For all t hree elastic liquids investigated (two Boger fluids and the Internatio nal Test Fluid S1), there is a decrease in drag as the Weissenberg num ber W-e increases. In the case of the Boger fluids, the drag reduction is the order of 17% before plateauing out, with virtually constant va lues of the normalized drag for a range of Weissenberg numbers. Owing to the obvious and unavoidable limit on the weight of the sphere, it w as not possible to search for the anticipated drag enhancement due to extensional viscosity effects at high W-e. To overcome this frustratio n, we considered the related problem of pressure-driven flow past a lo ne stationary sphere in a tightly fitting cylindrical container. In th is case it was possible to observe the full range of phenomena, i.e, a Newtonian plateau response at very small W-e, followed by a drag decr ease to a second plateau region and then a significant drag enhancemen t at high W-e.