The Six-Sphere "Inverting Star"

The images below show various configurations of six spheres as they sediment through either a Newtonian or a Boger fluid. The initial configurations are identical, and consist of the sphere centers being placed at the vertices of two, horizontal equilateral triangles. In both cases, the particle Reynolds number is small, so that inertial effects are negligible. In the Newtonian fluid, one sees the "Porter-Bobroff Inverting Star," or the periodic formation of a horizontal star with all six spheres lying in the same plane, followed by re-formation of the original configuration. This periodicity is consistent with the reversibility of Stokes equations. In the Boger fluid, the periodicity (and reversibility) is lost as a result of non-linearities arising from elasticity in the suspending fluid.