Dispersion in the Residence Time of Size-Dispersed Particles in Sedimentation

Theoretical expressions have previously obtained for the statistics of the residence time distribution of particles falling individually in a stationary, Newtonian liquid. The dispersion in the residence or sedimentation time arises both from the size dispersion that may be present in the particles and also because of fluctuations in the axial velocity of the particles about the time-invariant terminal velocity. Such fluctuations are inevitable, except at extremely low Reynolds numbers. The size dispersion is represented by the Log-Normal distribution, as is customary for many particle populations. The erratic nature of particle velocity is represented by a dispersion coefficient and then incorporated into a corresponding Peclet number. The dispersion coefficient reflects both the level of fluctuation in velocity and the representative time-scale of the velocity fluctuation. In addition to residence time distribution, the level of correlation or dependence between particle size and particle residence time can be determined by this method. The theoretical work was previously validated using glass and plastic particles falling in glycerol and water, characterized by low (Re ≈ 1) and high (Re ≈ 1000) Reynolds numbers, respectively. For this paper, new experiments were conducted examining the fall of expanded polystyrene particles with a range of sizes in air. Experiments were carried out with single particle falls and batch (groups of particles) falls. In addition to using different fluids and particles to the previous work, the tests were conducted over a wider range of Reynolds numbers. Results demonstrated that the theory was still valid for these new experiments. Dispersion in residence time and the relationship between particle size and its residence time were predicted with reasonably good accuracy.