Particles in steady streaming flows

The way rigid particles interact in oscillatory fluid flows is a challenging problem, especially at intermediate Reynolds numbers where the fluid is both viscous and inertial. Various types of patterns and structures have been observed [1-4] all of which trace the interactions to the phenomenon of steady streaming. Steady streaming is a purely nonlinear effect: it is the non-zero average of a fluctuating fluid flow [5]. For a single isolated oscillating sphere the steady streaming flow is shown in Fig.1.

Fig.1 A schematic diagram showing the streaming flow for a single oscillating sphere, in the plane through the sphere. There is rotational symmetry about the axis of oscillation, indicated by the double arrowed dashed line. There are four vortex rings: two on the left and two on the right of the sphere. The crosses indicate stagnation points.

Here are some chain patterns we have observed for spheres under horizontal vibration in water. Chains form perpendicular to the direction of oscillation (indicated by the double arrowed line).

Fig.2: Chain structures for steel spheres under horizontal vibration, form experiments.

In order to understand the details of the interactions behind these patterns we run experiments and simulations for various systems.

Fig.2 shows the evolution for 64 stainless steel spheres in a cell which is horizontally vibrated from experiments (left) and simulations (right). The spheres are initially dispersed but respond rapidly to the vibration: they form pairs and short chains, they attach to the side walls until there are no free particles. You can also watch the evolution on mpeg files: experiment and simulation.