Magnitude and Character of Errors Produced by Shape Factors in Stokes' Law Estimates of Particle Radius

Abstract

In order to estimate the possible errors introduced by deviations from the spherical particle shape in Stokes' law estimates of dust particle sizes, a model study was made with objects of various shapes falling in oil of high viscosity. It was found that all shapes fall more slowly than the sphere of the same mass and volume. The true size and mass will, therefore, always be larger than the estimates calculated from their rate of fall by means of Stokes' law. For shapes of extreme dimensions (very thin plates and needles) the error thus introduced exceeded 50 percent. For more common configurations of spheres it was of the order of 20 percent or less. No simple relation between particle surface or any other parameter and the rate of fall could be discovered. All plates and needles turned their planes and longer axes into a horizontal direction when falling freely, unless one side was distinctly weighted. A small asymmetry in weight distribution tilts the planes slightly, causing the model to drift sideways in its fall. In a Hopper and Laby method of particle analysis such a drift makes a particle appear charged, although it may be neutral. It is, therefore, not possible to analyze platelike and needlelike powder and dust particles by such a method.