Measurements of the steady streaming flow around oscillating spheres using three dimensional particle tracking velocimetry

Abstract

Granular particles vibrated in a fluid have been found to exhibit self-organization with attractive and repulsive interactions between the particles. These interactions have been attributed to the steady streaming flow around oscillating particles. Here we examine the steady streaming flow surrounding a vertically oscillating sphere using three-dimensional particle tracking velocimetry. We present measurements of the flow with the sphere far from boundaries, close to the bottom wall of the tank, and near another oscillating sphere. For parameters of interest for granular self-organization, the flow around a single sphere far from boundaries differs significantly from an analytical calculation that has been applied to granular organization. Measured positions of the stagnation point support previously observed scaling at small amplitudes, and demonstrate how this scaling changes at large amplitudes. When the sphere is oscillated near the bottom wall, the topology of the flow changes, resulting in a larger repulsive flow region than expected. Previous experiments saw attraction in the region where the flow around a single sphere is repulsive. We conclude that advection in the streaming flow due to a single sphere cannot explain the observed granular attractive and repulsive interactions; rather, nonlinear interactions between the flows around two or more spheres must be responsible.