Wall forces on a sphere in a rotating liquid-filled cylinder

We experimentally study the behavior of a particle slightly denser than the surrounding liquid in solid body rotating flow. Earlier work revealed that a heavy particle has an unstable equilibrium point in unbounded rotating flows[G. O. Roberts, D. M Kornfeld, and W. W Fowlis, J. Fluid Mech.229, 555–567 (Year: 1991)10.1017/S0022112091003166]. In the confinement of the rotational flow by a cylindrical wall a heavy sphere with density 1.05 g/cm3 describes an orbital motion in our experiments. This is due to the effect of the wall near the sphere, i.e., a repulsive force (F W ). We model F W on the sphere as a function of the distance from the wall (L): F W ∝L −4 as proposed by Takemura et al. [J. Fluid Mech.495, 235–253 (Year: 2003)10.1017/S0022112003006232]. Remarkably, the path evaluated from the model including F W reproduces the experimentally measured trajectory. In addition during an orbital motion the particle does not spin around its axis, and we provide a possible explanation for this phenomenon