Liquidlike sloshing dynamics of monodisperse granulate

Analogies between fluid flows and granular flows are useful because they pave the way for continuum treatments of granular media. However, in practice it is impossible to predict under what experimental conditions the dynamics of fluids and granulates are qualitatively similar. In the case of unsteadily driven systems no such analogy is known. For example, in a partially filled container subject to horizontal oscillations liquids slosh, whereas granular media of complex particles exhibit large-scale convection rolls. We here show that smooth monodisperse steel spheres exhibit liquidlike sloshing dynamics. Our findings highlight the role of particle material and geometry for the dynamics and phase transitions of the system.

Figure 1

Sketch of the experimental setup. A rectangular container is partly filled with monodisperse steel spheres and mounted on a sledge. The sledge is harmonically driven by a step motor with a frequency of 3 Hz, while the amplitude is varied to change the acceleration. The dynamics of the spheres is monitored by a camera from the front. In most of the measurements the diameter of the spheres is 4 mm.

Figure 2

Sequences of snapshots at about $0,\frac{1}{4},\frac{1}{2},\frac{3}{4}$ of the driving period for three layers of monodisperse spheres with $d=4\text{mm}$. The phase of 0 corresponds to the maximum leftward displacement of the box, where the direction reversal takes place (indicated by a double-headed arrow). Single-headed arrows illustrate the instantaneous direction of the movement of the box. The granular sloshing (left panel) occurs at $\mathrm{\Gamma }\approx 0.62$ and a dynamics of projectilelike motion similar to the gaslike state (right panel) of a monolayer [17] dominates at $\mathrm{\Gamma }\approx 1.00$.

Figure 3

Direct comparison of the liquidlike sloshing state (five layers of spheres with $d=2$ mm at $\mathrm{\Gamma }\approx 0.80$) with the sloshing dynamics of a liquid ($A=7$ mm, $f=1.7$ Hz). As in Fig. 2, snapshots are taken at about $0,\frac{1}{4},\frac{1}{2},\frac{3}{4}$ of the driving period, where the phase 0 is defined as the maximum leftward displacement.

Figure 4

Phase diagram of monodisperse spheres of diameter 4 mm summarizing the occurrence of the (I) solidlike state ($▵$), the (II) granular ($▿$) and (III) liquidlike sloshing ($\square$), and the (IV) gaslike state ($\circ$). The diagram was obtained for increasing and decreasing $\mathrm{\Gamma }$, indicated by the full and empty symbols of slightly different color that are on top of each other. A hysteresis arises between the solidlike state and the granular sloshing, which is indicated by the horizontal stripe pattern for better recognition. One layer consists of 337 particles, so that, e.g., 3.5 layers correspond to $3.5\times 337\approx 1180$ spheres.