Spontaneous orbiting of two spheres levitated in a vibrated liquid

In the absence of gravity, particles can form a suspension in a liquid irrespective of the difference in density between the solid and the liquid. If such a suspension is subjected to vibration, there is relative motion between the particles and the fluid which can lead to self-organization and pattern formation. Here, we describe experiments carried out to investigate the behavior of two identical spheres suspended magnetically in a fluid, mimicking weightless conditions. Under vibration, the spheres mutually attract and, for sufficiently large vibration amplitudes, the spheres are observed to spontaneously orbit each other. The collapse of the experimental data onto a single curve indicates that the instability occurs at a critical value of the streaming Reynolds number. Simulations reproduce the observed behavior qualitatively and quantitatively, and are used to identify the features of the flow that are responsible for this instability.