Gravitational settling of small spherical particles in unsteady cellular flow fields

We study the average settling velocity of small spherical particles under gravity through an infinite, periodic, non-divergent unsteady cellular flow held subject to the effects of a Stoke's drag force and the inertia of the particles. In particular, the role of the spatial and temporal variations of the flow held on the settling rate is investigated It is shown that the particles merge into isolated trajectories which are independent of their initial positions and velocities, and the cellular dow causes a net increase in settling velocity in the case V-T/sigma(u) less than or equal to 0.7 (where V-T is the terminal velocity in still fluid normalized by the characteristic velocity of the flow) and the maximum decrease in settling rate occurs for V-T/sigma(u) approximate to 1 when the dow is steady and with one length scale. As the cellular flow field is slightly perturbed with-some unsteadiness or with the introduction of more length scales, the difference between the computed settling rate < V-T > in the cellular flow and that in still fluid decreases. In particular when the degree of unsteadiness is greater than some critical value or when the number of length scales is more than four, the computed < V-T > is always less than V-T. This is consistent with the results of Fung (1993, J. geophys Res. 98, 20,287-20,297), who studied the settling of particles in a random velocity field. However, for all the parameters studied, particle accumulation is still a recurring feature except for a large unsteady parameter - then the particle motion can be chaotic. The fluid velocity u(x(p), t) sampled by the particles along these isolated trajectories is used to explain the difference in settling rate between cellular flow and still fluid. (C) 1997 Elsevier Science Ltd.