Cluster growth in driven granular gases

We investigate numerically and theoretically the internal structures of a driven granular gas in cuboidal cell geometries. Clustering is reported and particles are classified as gaseous or clustered via a local packing fraction criterion based on a Voronoi tessellation. We observe that small clusters arise in the corners of the box, elucidating early reports of partial clustering. These aggregates have a condensation-like surface growth. When a critical size is reached, a structural transition occurs and all clusters merge together, leaving a hole in the center of the cell. This hole then becomes the new center of particle capture. Taking into account all structural modifications and defining a saturation packing fraction, we propose an empirical model for the cluster growth.

Figure 1

Sketch of the simulated cell in the case of the VIP-Gran (short for vibration-induced phenomena in granular materials) experiment used in the simulations. The length and the width of the cell are denoted by $L$ and $l$, respectively. The length is measured for an average position of the plates. The parameters of the oscillation of both pistons are an amplitude $A=$ 1 mm and a frequency $f$. The clustered grains are colored in blue, while the gaseous particles are in orange. The total number of particles in the cell is $N=7000$.

Figure 2

Probability density function (PDF) of the local packing fraction ${\varphi }_{\text{loc}}$ of the grains in the case of cell number 3 (see Table 1). Different colors correspond to different numbers of particles in the container, and therefore they correspond to different packing fraction $\varphi$ values as noted in the legend at the right. The vertical dashed line ${\varphi }_{\text{loc}}=0.285$ corresponds to the minimal local packing fraction of a caged grain used as a criterion to distinguish gas particles from cluster ones.

Figure 3

Rows 1 and 2: top and front views of the center of cell number 3 for an increasing packing fraction $\varphi$. Only grains belonging to the cluster are shown, i.e., only grains with ${\varphi }_{\text{loc}}>0.285$. Rows 3 and 4: top and front views of the occupancy (defined in Sec. 4b) of the same cell and structure of the interface gas-cluster for an increasing packing fraction. The color scale is the same as the one in Fig. 2. At low packing fraction values, the cluster appears in the corners of the box, and then it grows to form a single dense structure.

Figure 4

Volume fraction of the cluster as a function of the total packing fraction of the cell 3. Before the apparition of the cluster, its volume is equal to zero. The curve is provided by Eq. (5) and is adjusted via the capture rate used in the modeling of the cluster's growth.

Figure 5

Mean packing fraction in the gas phase (${\mathrm{\Phi }}_{\text{g}}$) and the dynamical cluster (${\mathrm{\Phi }}_{\text{cl}}$) as a function of the total packing fraction $\varphi$ in each studied cell. The dashed line corresponds to ${\mathrm{\Phi }}_{\text{g}}=\varphi$. Symbols are chosen according to the conditions listed in Table 1.