Role of defects in the onset of wall-induced granular convection

We investigate the onset of wall-induced convection in vertically vibrated granular matter by means of experiments and two-dimensional computer simulations. In both simulations and experiments we find that the wall-induced convection occurs inside the bouncing bed region of the parameter space, in which the granular bed behaves like a bouncing ball. A good agreement between experiments and simulations is found for the peak vibration acceleration at which convection starts. By comparing the results of simulations initialized with and without defects, we find that the onset of convection occurs at lower vibration strengths in the presence of defects. Furthermore, we find that the convection of granular particles initialized in a perfect hexagonal lattice is related to the nucleation of defects and the process is described by an Arrhenius law.

Figure 1

Simulation snapshots of the typical initial configurations for $N_l=60$. The color indicates the local order of the particles according to an analysis with the $q_6$ order parameter [33]. Green (light gray) indicates hexagonal order and red (dark gray) indicates a square local order while other colors indicate a disordered configuration. From left to right: the crystalline and random initializations of the simulation, and the experimental initial configuration.

Figure 2

Sketch of the possible orientations of the hexagonal crystal in contact with the lateral wall of the container box.

Figure 3

Dynamical phases at different accelerations $\Gamma$ and linear density (number of layers) $N_l\sigma$. On the right $y$ axis the energy parameter $K_m$ is also reported. Symbols are for simulation results for either the system initialized randomly (triangles) or in a crystalline configuration (circles). The connected squares are the experimental results.

Figure 4

Granular temperature $T_g$ versus dimensionless energy parameter $K_m$. The dashed lines separate regions with different slopes of the temperature curves. (a) For the system initialized randomly, i.e., with defects. (b) For the system initialized in a perfect hexagonal lattice, i.e., without initial defects.

Figure 5

Slip probability $p_s$ versus the inverse dimensionless energy parameter $1/K_m$. The continuous lines represent exponential fit functions. The dashed lines separate the regions defined in Fig. 4. (a) For the system initialized randomly, i.e., with defects. (b) For the system initialized in a perfect hexagonal lattice, i.e., without initial defects.

Figure 6

Illustration of the contact model of two granular disks at distance ${\mathbf{r}}_{ij}={\mathbf{r}}_i-{\mathbf{r}}_j$ and relative velocity ${\mathbf{v}}_{ij}={\mathbf{v}}_i-{\mathbf{v}}_j$, which overlap by a distance ${\delta }_{n_{ij}}$.