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

Abstract

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.

Experimental Study and Numerical Simulation of Viscosity Measurement of Solid Propellant Slurry by Press Bar‐Fall Ball Viscometer

“…Therefore, the expression of the viscous resistance should be revised. It should be indicated that the most widely used expression is the Faxon correction formula as the following [16]: …”

Wall effects for spherical particle in confined shear-thickening fluids

“…Results presented in the work of Rajasekhar and Kishore [33] with  = 5 are also cited in Table 3, showing differences of ~ 96% at Re = 1 and up to ~ 124% at Re = 100 from present work. For a power law fluid of n = 0.4, predicted results were compared with literature [32] in term of normalised drag coefficient, which was normalised by the corresponding values in Newtonian fluids at same  and Re. Good consistency is shown at Re = 1, 10 and 100, respectively, as indicated in Table 4.…”

Prediction of the Wall Factor of Arbitrary Particle Settling through Various Fluid Media in a Cylindrical Tube Using Artificial Intelligence

“…Machač and Lecjaks [ 11 ] and Malhotra and Sharma [ 12 ] established wall factor correlations for spheres settling through power law fluids and surfactant-based shear thinning viscoelastic fluids in rectangular ducts and parallel plates. Kawase and Ulbrecht [ 13 ], Missirlis et al [ 14 ], and Song et al [ 15 ] theoretically studied and numerically simulated the settling velocity of a sphere in bound non-Newtonian fluid. It is now widely accepted that the elasticity and shear thinning behavior of non-Newtonian fluids reduce the retardation effect of the confining walls.…”