Particle clusters settling under gravity in a viscous fluid

Clusters made of a small number of close solid spherical particles at a random configuration, sedimenting through a viscous fluid at small Reynolds number, were experimentally investigated at a short-time scale. The cluster settling velocities were measured and shown to be well approximated by the ensemble-averaged formula derived earlier for the uniform distribution of the point particles inside a spherical volume. It was emphasized that the “effective radius” of this volume in general should be smaller than the actual radius of a cluster made of the spheres, and the relation between both radii was determined. The formula was also shown to account well for the gravitational settling of rigid conglomerates, measured and computed elsewhere.