Wall Effects on a Sphere Falling in Quiescent Power Law Fluids in Cylindrical Tubes

The effect of finite boundaries on the drag experienced by a sphere settling in quiescent power law fluids in cylindrical vessels has been investigated numerically. In particular, the momentum equations have been solved numerically over the following ranges of conditions: sphere Reynolds number, 1-100; power law index, 0.2-1; and sphere-to-tube diameter ratio, 0-0.5. Due to the backflow of the fluid caused by a falling sphere and the corresponding changes in the velocity field close to the sphere, the presence of finite boundaries leads to an increase in the drag force acting on a falling sphere thereby slowing its descent. The effect, however, is more significant at low Reynolds numbers than at high Reynolds numbers. Similarly, the additional drag due to the walls increases with the increasing degree of confinement, i.e., the sphere-to-tube diameter ratio. Overall, all else being equal, the wall effect is less severe in power law fluids than in Newtonian fluids. Furthermore, the confining walls also influence the onset of flow separation and subsequently the size of the recirculation region. The present numerical predictions are consistent with the experimental results available in the literature.