Estimating the density of individual particles from the settling of a particle cloud

The density of individual particles is commonly assessed experimentally by quantifying the settling velocity of a collection of particles transferred into a settling column and allowed to settle under the action of gravity. The individual settling velocities of the particles are recorded close to the bottom of the settling column, in a region where it is assumed that the particles have reached their Stokes terminal velocity after the particle cloud has broken up. In the present study we use numerical particle-based simulations in the Stokes regime to demonstrate that this fundamental assumption might not be fulfilled in practice. Even at low volume fraction of monodisperse spheres, a large deviation from the Stokes settling velocity was found. In the case of a collection of polydisperse spheres, a distinction could be made between particles belonging to a cloud, and particles trailing the cloud. It was found that the velocity of the largest trail particles is reasonably close to their Stokes settling velocity. However, the particles close to the core of the cloud can have velocities more than ten times their Stokes velocities, making the use of the single-particle Stokes velocity based on the core particle not suitable to extract the particle density without corrections. An expression based on the local volume fraction, the cloud radius and the particle settling velocity in the cloud is proposed to estimate the single-particle Stokes settling velocity, and therefrom the particle density.