Effect of particle shape on hindered settling in creeping flow

Abstract

Solid particles of uniform size and shape were used to study the effect of particle shape on hindered settling in creeping flow ( Re o š 0.2), where fluid flow patterns are independent of Reynolds number and the effect of shape is most prominent. The particles of different shape studied were spherical glass beads, cubical sodium chloride crystals and ABS plastic pellets, brick-like sugar crystals, and angular (imperfect octahedral) mineral silicate crystals. The liquids used were aqueous polyethylene glycol solutions and various blends of hydrocarbon oils. Two particle sizes on the average were investigated for each particle shape, and five settling column diameters were employed, so that the overall range of column-to-particle diameter ratio covered was 22 – 226. A Richardson—Zaki type equation of the form u = u iϵ n was found to correlate the constant settling rate data for each particle size and shape over the voidage range ϵ = 0.65 – 0.9. However, the wall effect on hindered settling rate was found in most cases to be considerably smaller than that predicted by Richardson and Zaki. The term u i, obtained by linearly extrapolating the settling velocity u (below ϵ = 0.9) to ϵ = 1 on a log—log plot of u versus ϵ, was found to be measurably lower than the corresponding free settling velocity. The index n varied from an average value of 4.8 for the smooth spheres to 5.4 for the cubes to 5.8 for both the brick-like and the angular particles. These values graphically display a definite trend with settled bed voidage, ϵ b, which is shape-dependent and easily measured, and may therefore be a convenient parameter for taking account of shape variation generally. The method proposed by Beranek and Klumpar for correlating fluidization data on different shaped particles, which depends on ϵ b, was found to be moderately successful in correlating the present settling data for different shapes.