Author(s)

E.M. Tory & R.A. Ford

Abstract

The slow sedimentation of small particles in a viscous fluid is a long-standing problem with many important applications. One-dimensional sedimentation of a suspension of rigid spheres in a Newtonian fluid involves three param- eters: the mean, variance, and autocorrelation of the vertical component of particle velocities. The mean corresponds to Kynch's unique (or character- istic) velocity, the variance reflects the spatial and temporal variability of particle velocities, and the autocorrelation preserves the continuity of the velocity of each individual particle. To account for these properties, Tory and Pickard formulated a three-parameter Markov model in which identical particles in the same environment are governed, independently, by the same stochastic process. This model preserves the short-term predictability of deterministic solu

Keywords