Grain Shape Effects on Settling Rates

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Abstract

The departure of a grain from a spherical shape causes a decrease in its settling velocity within a fluid. The more non-spherical the particle the greater the departure from the settling velocity of a spherical grain of the same weight. This study reexamines the various measures of sphericity and their ability to predict the drag coefficient and settling velocity of a non-spherical grain. Experiments were conducted using ellipsoidal pebbles settling in glycerine which has a viscosity some 1,000 times greater than water. The Reynolds numbers range from 0.07-1.5 which is the same range as quartz-density coarse silt through very fine sand settling in water. Therefore the results of the experiments are applicable to common sedimentary materials. The use of pebbles allows for the better determinations of the shape parameters, and eliminates the effects of grain surface roughness and roundness and grain asymmetries that complicate the settling of silt and sand. Analysis of the pebble-settling data indicates that the Corey shape factor provides a much better prediction of the drag coefficient for non-spherical grains than does the sphericity definition of Wadell which is based on the ratio of the surface area of a sphere with the same weight as the pebble to the actual surface area of the pebble. Regression of the data provides an equation which predicts the drag coefficient of the settling particle from its Corey shape factor and the Reynolds number. This drag coefficient relationship is used to obtain a modification of the familiar Stokes settling velocity equation which accounts for non-spherical grain shape effects on the settling rate. The results based on the pebble data are extended to Reynolds numbers up to $$5 x 10^{4}$$ by utilizing the data of Alger (1964) on the settling of larger pebbles in several glycerine-water dilutions. The resulting empirical curves allow the calculation of curves for the settling velocity of quartz-density silts and sands as a function of their size (nominal diameter) and Corey shape factor.

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