53 Effect of particle shape on terminal falling velocity and drag force

A spherical particle is unique in that it presents the same projected area to the oncoming fluid irrespective of its orientation. For non-spherical particles, on the other hand, the orientation must be specified before the drag force can be calculated. The drag force on spheroidal (oblates and prolates) particles moving in shear-thinning and shear-thickening power-law fluids (0.4 < n < 1.8) have been evaluated for Reynolds numbers up to 100 [6, 7]. The values of drag coefficient are given in the original papers [Tripathi et al., 1994; Tripathi and Chhabra, 1995] and the main trends are summarised here. For pseudoplastic fluids (n < 1), creeping flow occurs for Re up to about 1 (based on m equal volume sphere diameter) and for dilatant fluids (n > 1) up to about 0.2-0.5. For a given Reynolds number and aspect ratio (minor/major axis), the drag on oblates is less than that on a sphere of equal volume whereas for prolate particles, it is higher. The drag force in the creeping flow region is higher for shear-thinning fluids than for Newtonian fluids; this is consistent with the behaviour observed for a sphere. The influence of power-law index, however, diminishes with increasing particle Reynolds number. The opposite effect is observed with shear-thickening fluids, i.e. the drag is lower than that in a Newtonian fluid.

Many workers have measured drag coefficients for particles, including cylinders, rectangular prisms, discs, cones settling at their terminal velocities in power-law fluids. Work in this area has recently been reviewed [Chhabra, 1996], but no generalised correlation has yet been proposed. A simple equation which reconciles the bulk of the results for drag on cones, cubes, paral-lelpipeds, and cylinders (falling axially) settling at terminal condition in power-law fluids (Re < 150; 0.77 < n < 1; 0.35 < f < 0.7) is [Venu Madhav and Chhabra, 1994]: 32.5

(oV2~ndn where both CD and Re I ——m- are based on the diameter of the sphere of the same volume; corrections were made for wall effects. The predictions deteriorate progressively as the particle departs from spherical shape, i.e. as sphericity, f, decreases.

The scant experimental and theoretical results available for viscoplastic and visco-elastic fluids have been reviewed elsewhere [Chhabra, 1996].

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