Drag on a sphere in Poiseuille flow of shear-thinning power-law fluids

The effect of finite boundaries on the drag experienced by a sphere exposed to the Poiseuille flow of power-law fluids in cylindrical vessels has been investigated numerically. In particular, the momentum equations have been solved over the following ranges of conditions: sphere Reynolds number based on the area average velocity in the pipe, Re 1-100; power law index, n: 0.2-1, and sphere-to-tube diameter ratio, λ: 0-0.5. Due to the obstruction in the path of the fluid caused by the sphere fixed at the axis of the tube and the corresponding changes in the velocity field close to the sphere, there is extra viscous dissipation at the walls and this, in turn, leads to an increase in the drag force acting on the sphere. Conversely, there is an extra pressure drop caused by the fixed sphere for the flow of the fluid in the tube. The effect, however, is more significant at low Reynolds numbers than that at high Reynolds numbers. Similarly, the additional drag due to the confining walls increases with the increasing degree of obstruction, i.e., sphere-to-tube diameter ratio. Overall, all else being equal, the wall effect is seen to be less severe in power-law fluids than that 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 scant experimental results available in the literature for Newtonian and power-law fluids