Hindered Settling and Hydrodynamic Dispersion of Sedimenting Spheres

Abstract

The motion of an individual sphere settling in the midst of a random suspension of identical spheres has been examined experimentally for suspensions with volume concentrations, ⌽ of 2.5% - 10.0%, under creeping flow conditions and in the absence of Brownian motion. In the experiments, silvered glass spheres were tracked in optically transparent suspensions of glass beads. Arrival times measured at a series of horizontal planes were converted into average settling speeds, . These values of , normalized by the Stokes settling speed, V0, yield the hindered settling function, f(⌽), shown in Figure 1 to have a 1–3.7⌽dependence for the entire range of ⌽ investigated. The experimentally determined O(⌽) coefficient is significantly less than the 6.55 found analytically by Batchelor (1972) for a “well-stirred” suspension of spheres. The discrepancy between the two coefficients can be attributed to the existence of structure even in suspensions sedimenting from a random initial state. The nature of such structure may be accessible through simulations such as those described by Durlofsky et al. (1987).