Anisotropic dynamics in a shaken granular dimer gas experiment

The dynamics, velocity fluctuations, and particle-plate interactions for a two-dimensional granular gas of shaken, nonspherical particles are studied experimentally. The experiment consists of a horizontal plate that is vertically oscillated to drive the dynamics of macroscopic dimers, spherical pairs that are loosely connected by a rod that couple the interaction each of the spheres has with the shaking plate. The extended nature of the particles results in more than one energy-momentum transfer between the plate and each dimer per shaking cycle. This complex interaction results in anisotropic behavior for the dimer that is a function of the shaking parameters.

Figure 1

When viewed from above, the horizontal dynamics of the nonspherical particles are described by two angles. The angular displacement of the center of mass for the particle moving $\Delta \mathbf{r}$ relative to the natural director of the particle made by the connecting rod is $\theta$. The motion about the center of mass of the particle $\varphi$ denotes how the orientation of the director moves relative to a fixed frame.

Figure 2

(Color online) Histograms (dark boxes) for $\cos \left(\theta \right)$, the direction of center of mass motion of a single dimer on a plate with a peak acceleration of $2g$ for (a) 50 Hz, (b) 70 Hz, and (c) 90 Hz. The distribution for $\cos \left(\theta \right)$ for a uniform distribution of $\theta$ is shown by the open boxes in each figure. The distribution demonstrates a bias for the dimer to move in a direction along the director rod joining the two spheres of the dimer at low frequency. The bias is shifted to motion perpendicular to the connecting rod as the shaking amplitude is decreased (shaking frequency is increased).

Figure 3

Accelerometer signal for a single dimer chattering on the plate. The vertical scale is 100 mv $\left(1g\right)$ per major division. The horizontal scale is 2.5 ms per major division. The driving frequency was 50 Hz, and the acceleration amplitude was $2g$.

Figure 4

Viewed from the side, the dimer’s motion is biased by the relative motion of the shaking plate during each collision. In (a), the one sphere of the dimer collides while the plate is accelerating downward. In this collision, the plate absorbs some of the momentum of the ball that recoils with a slower velocity as the second sphere begins to fall toward the plate (b). In (c), the second sphere of the dimer collides while the plate is accelerating upward, this collision imparting a momentum gain to the dimer.

Figure 5

Velocity fluctuations for different shaking parameters. Triangles: Frequency is 40 Hz, $\Gamma =1.65g$, $\text{density}=0.27$, $v_{\mathrm{rms}}=1.74\mathrm{cm}∕\mathrm{s}$. Circles: Frequency is 65 Hz, $\Gamma =2.0g$, $\text{density}=0.87$, $v_{\mathrm{rms}}=1.04\mathrm{cm}∕\mathrm{s}$. Diamonds: Frequency is 65 Hz, $\Gamma =1.5g$, $\text{density}=0.55$, $v_{\mathrm{rms}}=0.94\mathrm{cm}∕\mathrm{s}$.