Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions

Abstract

The motion of an individual sphere settling in the midst of a suspension of like spheres has been examined experimentally for suspensions with volume concentrations, φ, of 2.5–10%, 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 average speeds yield the hindered settling speed as a function of concentration. The hindered settling speed, normalized by the isolated sphere settling speed, exhibits a 1 − 4φ + 8φ 2 dependence for the range of concentrations investigated. The settling speed fluctuations are quite large, ranging up to 46% of the average, and have long-time (large settling distance) behavior characteristic of a Fickian diffusion process. Dispersion coefficients have therefore been determined from the asymptotic dependence upon settling distance of the variance in settling speed. These coefficients scale with the product of the hindered settling speed and the sphere radius. The dimensionless dispersion coefficients, all O(1), increase with concentration for φ < 5%, then slightly decrease at higher concentrations. Verification of the scaling through the use of two particle sizes, care taken to mix the suspensions to random, uniform initial conditions, and the robustness of the statistics over many realizations preclude the possibility of this phenomenon being an experimental artifact and support the hypothesis that hydrodynamic dispersion of suspended particles will result from viscous interactions between the particles.