Stripe Formation in Granular Mixtures due to the Differential Influence of Drag

We describe an investigation of fluid-immersed granular mixtures subjected to horizontal vibration. For sufficiently large amplitudes of vibration, a mixture of equal-sized glass and bronze particles in water is found to separate into a striped pattern. Numerical simulations based on soft-sphere molecular dynamics coupled to the interstitial fluid are able to capture many of the features observed experimentally. We propose a general pattern-formation mechanism based on the differential influence of drag on the components of the mixture. An expression for the number of stripes as a function of the system parameters is derived and shown to be in good agreement with experiments.

Figure 1

Snapshots showing the time evolution of the granular mixture starting from a well-mixed initial configuration. From top to bottom, the times correspond to $t=1.0$, 2.0, 2.3, 3.0 min. The darker spheres represent the bronze component. The arrows indicate the axis of vibration.

Figure 2

Snapshots from simulations showing the time evolution of the granular mixture starting from a well-mixed initial configuration. From top to bottom, the times correspond to $t=0$.0, 0.5, 2.0, 5.0 min. The darker spheres represent the bronze component.

Figure 3

The dependence of the steady-state mean bronze cluster size, in units of particle diameters, on amplitude for a mixture vibrated at $50\mathrm{H}\mathrm{z}$ in 2D. Inset: Snapshots from simulations showing the cluster morphology for amplitudes $A=1.0$, 2.0, 2.7, 3.5, and 4.5 grain diameters, with periodic boundary conditions.

Figure 4

The stable number of stripes $N_s$ vs $1/\Gamma$ obtained in the quasi-2D experiments. The crosses represent the experimentally observed number of stripes, while the squares represent the average for each value of $N_s$. The continuous line is a linear fit through the circular points which were derived from the theoretical predictions of Eq. (3). The inset shows a comparison between simulations and this line.