Noninvasive Measurement of Particle-Settling Velocity and Comparison with Stokes’ Law

Abstract

An image-analysis technique was applied for noninvasive measurements of settling rate of polystyrene latex spheres of 6, 10, 20, 50, 100, and 160 μm diameters in a quiescent environment. A CCD (charged couple device) camera and strobe light were used to capture in situ images of the particles, which were analyzed using image-analysis software. To overcome the challenge of noninvasive measurement of very slow-moving particles, variable pixel resolutions were chosen depending on settling speed so that the separation of the particle images in a given camera exposure time was sufficient to determine the temporal displacements of the particles with precision. Particle-settling behavior was not disrupted for any kind of sample handling, and measurements were made without hindering particle settling and allowing particle movement under gravity alone. Measurements were compared with settling rates calculated with Stokes’ law, and the validity of Stokes’ law under low particle Reynolds number (R<0.1) was investigated for solid and spherical particles. While the smaller particles settled at a rate closely predicted by Stokes’ law, the larger particles settled slightly more slowly than was predicted. This effect is likely due to an increase in the drag coefficient with relatively larger-particle Reynolds number, compared to the value used in Stokes’ law.