Drag on a Sphere in Poiseuille Flow of Shear-Thinning Power-Law Fluids

Abstract

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.

Effect of Shear-Thinning Behavior on Heat Transfer from a Heated Sphere in Yield-Stress Fluids

“…Table shows such a comparison between the present results for Bn = 10 –3 and that in power-law fluids. Clearly, the close correspondence between the present results and that of Song et al , indicates little or no effect of such a low value of the Bingham number. The reasons for the deviations on the order of 10% in drag values with that of Dhole et al have been advanced by Song et al and thus are not repeated here.…”

“…Clearly, the close correspondence between the present results and that of Song et al , indicates little or no effect of such a low value of the Bingham number. The reasons for the deviations on the order of 10% in drag values with that of Dhole et al have been advanced by Song et al and thus are not repeated here. Intuitively, it appears that for given values of the power-law index and Reynolds number, there will be a critical Bingham number above which the effects of the yield stress begin to influence the results.…”

A New Model of Polymers in Flow

“…Interpretation of the data presented by Stratton indicates that for monodisperse polystyrene, n = -0.82 32 . The value of n=1/2 predicted by the model is well within the range of accepted values for shear thinning polymers 34 .…”

“…The measured dependence of the decrease in the radius with increasing shear rate (power law of -0.08) is in reasonable agreement with the model prediction of -0.16 derived in Equation 8. Furthermore, the model predicts a power law for the viscosity of -0.5 close to the range observed for polymer solutions which vary from -1.0 to -0.2 [32][33][34] . Given that the model uses a first order approximation for the Einstein equation, and the theta condition the model appears a reasonable fit to the dependence of the radius and viscosity with shear rate.…”

“…Values reported for polymeric systems range between n ~ -0.2 to -1 [32][33][34] . Interpretation of the data presented by Stratton indicates that for monodisperse polystyrene, n = -0.82 32 .…”