Fluidization of a horizontally driven granular monolayer

We consider the transition of a horizontally vibrated monodisperse granular monolayer between its condensed state and its three-dimensional gaseous state as a function of the vibration parameters, amplitude, and frequency as well as particle number density. The transition is characterized by an abrupt change of the dynamical state which leaves its fingerprints in several measurable quantities including dissipation rate, sound emission, and a gap size which characterizes the sloshing motion of the material. The transition and its pronounced hysteresis is explained through the energy due to the collective motion of the particles relative to the container.

Figure 1

Experimental setup shown for the system in solid state (a) and 3D-gaseous state (b), at the time of reversal of the stroke, when the gap size, $l_{\text{g}}$, is maximal. A top view of the system in condensed state is shown in (c) (in false colors for better visibility).

Figure 2

Characterization of the solid-fluid transition, $b\leftrightarrow c$, by means of the dissipation rate, $\eta$ [see Eq. (1)]. (a) Dissipation rate as a function of amplitude, $\eta \left(A\right)$, for fixed frequency, $\omega =18.85{\text{s}}^{-1}$. (b) Dissipation rate as a function of frequency, $\eta \left(\omega \right)$, for fixed amplitude, $A=15\text{mm}$. Error bars show the standard deviation of independent measurements. Red triangle up symbols indicate increasing amplitude $\left(b\to c\right)$; green triangle down symbols stand for decreasing amplitude $\left(c\to b\right)$. Vertical dashed lines labeled A–D correspond to the labels shown in Fig. 3.

Figure 3

The transition $b\to c$ (red, triangle up) and $c\to b$ (green, triangle down) in parameter space $(A,\omega )$. The dashed lines are the solution of our model and indicate that both transitions take place at critical values of the kinetic energy. The range of hysteretic behavior appears gray shaded. The vertical dotted line marks $\omega =2\pi \times 3\text{Hz}$ corresponding to Fig. 2. For this frequency, the insets show snapshots at the end of the left stroke close to the transition amplitudes marked A–D here and in Fig. 2: A, condensed metastable state; B, stable fluidized state; C, metastable fluidized state; D, stable condensed state. The horizontal dotted line marks the particular value, $A=15\text{mm}$, used in Fig. 2. For $A$ and $1/\omega$ both small (marked region), where $A\sim l_{\text{g}}$, the transitions $a\leftrightarrow b$ and $b\leftrightarrow c$ interfere.

Figure 4

Energy dissipation rate of a $\frac{2}{3}$ submonolayer. All other parameters as for Fig. 2. In agreement with the energy argument for the explanation of the hysteresis, here the transition $b\leftrightarrow c$ occurs gradually (no bursts). Consequently, no hysteresis is found.