The simulation parameters are comparable to the experimental setup, except that the tube is very thin so that axial density variations are suppressed. At low rotation speeds the particles are confined to a small volume on the lift side of the tube. Particles next to the wall are lifted by the rotation of the tube, but in adjacent layers the gravitational forces exceed the viscous drag from the fluid and they slip down to the bottom, so that there is a constant circulatio of particles. At a slightly higher rotational velocities (a), particles are ejected into the bulk fluid and fall in a more or less semicirculararc rather than straight down, so that the fluid flow in the upper half of the tube is predominantly counter-clockwise. In the lower half of the tube we see a counter-clockwise flow, lifting particles off the base of the tube and returning them to the wall higher up. At higher rotation speeds these counter-rotating regions grow and become more symmetrical, filling the tube cross section at the same time (b), as shown in the upper right picture in Figure 1. At still higher speeds the lower counter-rotating region shrinks (c) and eventually disappears altogether (d), leaving the particles undergoing a more or less rigid-body motion, produced by a delicate balance of rotational, gravitational and hydrodynamic forces. It should be noted that particle dispersion and pattern formation is due to hydrodynamic interactions. A single particle simply rotates about an off-center position, while slowly spiraling to the outside wall,where it eventually reaches a limiting trajectory.
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Particle distributions at different dimensionless rotational frequencies, |
A video clip showing the evolution of the particle distribution with increasing rotation rate can be found here (7.4 MByte AVI-DivX). Particles have been colored according to whether they are moving up (blue) or down (yellow).