Chaotic motion of fluid and solid particles in plane wakes

Adaptive algorithms are used to simulate mixing of point and solid particles in the time-dependent wake behind a cylinder for Re = 100. Mixing phenomena qualitatively similar to those observed in externally-forced time-dependent flows take place in this simulated flow. Chaotic regions evolve as a result of tangles of manifolds arising from a downstream hyperbolic periodic point. The unstable manifold of this point creates high stretching regions in the flow. Statistical analysis of the stretching experienced by populations of point particles reveals log-normal distributions that are characteristic of chaotic mixing processes observed in other flows. Viscous wakes generate efficient mixing of fluid particles, but they also generate efficient separation of solid particles. An initially homogeneous mixture of particles with a distribution of Stokes numbers becomes considerably segregated as it is carried downstream the flow. This separation process is governed by the structure of the flow. Small particles with low Stokes numbers accumulate in the center of eddies in the wake; particles with Stokes numbers near unity approach the unstable manifold of the fluid point particles; and large particles with high Stokes number migrate to the center of the wake and move backwards, colliding with the downstream surface of the cylinder.