The influence of rheological properties on the slow flow past spheres

Abstract The present communication is intended as part of a systematic investigation of the influence of rheological properties of various fluids upon the translational motion of a sphere. Drag measurements are presented for spheres of various diameters moving longitudinally with constant translational velocity, along the central axis of cylindrical containers of different radii. Four different types of fluids (based upon measurements of shear viscosity and first normal stress difference) are considered, namely Newtonian, viscoelastic, inelastic and constant viscosity-elastic liquids. The influence of each rheological property of these fluids upon the drag force is evaluated and analyzed. In the case of negligible wall effects, it is concluded that small perturbation theories provide an adequate description of the flow field for the creeping flow regime. The drag departure for viscoelastic liquids from the purely viscous Newtonian value has a quadratic dependence on the We number. Elastic effects are of primary importance at extremely low shear rates. For higher shear rates, shear thinning effects become predominant and an accurate drag prediction based on simple shear dependent viscosity values is presented. For non-Newtonian fluids, wall proximity effects are considerably reduced from the purely viscous Newtonian value. Both elasticity and shear thinning properties of the fluid contribute to that reduction. Elastic effects on the drag may be accounted for using Caswell's wall correction term derived from small perturbation theories for creeping flow and its validity exceeds the limit of small We numbers; this is substantiated by numerical techniques. Fluid elasticity diminishes wall effects but is a rapidly decreasing function, valid only for small We numbers and large sphere/container ratios. Beyond this region, shear thinning effects are predominant both upon the drag force and upon the wall correction term. These inelastic effects may be evaluated quite accurately using a modified version of Caswell's correction formula, which requires only a simple knowledge of the shear thinning viscosity function.

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