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

TL;DR

This study experimentally investigates the wall-induced forces on a slightly denser sphere in a rotating liquid-filled cylinder, revealing orbital motion due to wall effects and modeling the wall force as inversely proportional to the fourth power of the distance.

Contribution

It demonstrates the wall force's role in orbital motion of a sphere in rotating flow and models this force as proportional to L^{-4}, matching experimental trajectories.

Findings

Wall force causes orbital motion of the sphere.

Model including wall force reproduces experimental trajectories.

The sphere does not spin around its axis during orbit.

Abstract

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 rotation flows. In the confinement of the rotational flow by a cylindrical wall a heavy sphere with density 1.05 g/cm$^3$ 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 ($L$): $F_W \propto L^{-4}$ as proposed by Takemura and Magnaudet (2003). Remarkably, the path from the model including $F_w$ reproduce 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.