THE DYNAMICS AND MIXING OF SMALL SPHERICAL-PARTICLES IN A PLANE, FREE SHEAR-LAYER

The equation of motion of small rigid spheres settling under gravity in a two-dimensional inviscid flow given by the Stuart solution of the Euler equations is analyzed as a four-dimensional dynamical system. It is shown that depending on the values of the Stokes, Grashof, and a scaled Reynolds number, particles may either sediment or remain permanently suspended in the flow. When suspension occurs, the particle trajectories are shown to be attracted by a single period, quasiperiodic, or chaotic orbits. A consequence of the existence of a strange attractor (chaotic orbit) is that heavy particles can reach a stage of fluidization by which they remain indefinitely suspended in a layer of finite height located above the center of the Stuart vortices.