Settling velocity of ellipsoidal grains as related to shape entropy

Many different shape indices have been used in the past in attempts to predict the settling velocity of non-spherical particles. In this paper, the relative axial uniformity or shape entropy is employed, which is defined as: H-r = - (p(1) . In p(1)) + (p(i) . In p(i)) + (p(s) . ln p(s))/1.0986 where p(1), p(i) and p(s) are the proportions of the major, intermediate and minor axes of the grain, respectively. The entropy value of the particle plotted against the ratio of its observed settling velocity and the predicted settling velocity of a sphere with the same volume, defines a straight line. Linear regression yields the equation: W = W-s H-r - 0.5833/0.4167 where W is the settling velocity of the particle and W, is the settling velocity of the equivalent sphere. The settling velocities predicted from this equation are more accurate than those based on the Corey or Janke shape factors, with the main advantage being that it can be employed at Reynold numbers of up to 50,000 or more. The method is applicable to ellipsoidal particles of any density settling in various fluids.