Caging Dynamics in a Granular Fluid

We report an experimental investigation of the caging motion in a uniformly heated granular fluid for a wide range of filling fractions, $\varphi$. At low $\varphi$ the classic diffusive behavior of a fluid is observed. However, as $\varphi$ is increased, temporary cages develop and particles become increasingly trapped by their neighbors. We statistically analyze particle trajectories and observe a number of robust features typically associated with dense molecular liquids and colloids. Even though our monodisperse and quasi-2D system is known to not exhibit a glass transition, we still observe many of the precursors usually associated with glassy dynamics. We speculate that this is due to a process of structural arrest provided, in our case, by the presence of crystallization.

Figure 1

Experimental frames with superposed typical trajectories of a single particle: (a) $\varphi =0.567$, (b) $\varphi =0.701$, and (c) $\varphi =0.749$. Note that even though only a single trajectory is shown for each $\varphi$, particle tracking and statistics were performed over all particles within the imaging window. The scale bar is 2 mm.

Figure 2

Time dependence of the MSD for filling fractions shown in the box. The curve marked with $+$ is for a single particle in the cell. The arrow points in the direction of increasing $\varphi$. Along the arrow, the symbols ($*$) and ($+$) are located at ${\varphi }_l$ and ${\varphi }_s$, respectively, to aid locate the curves in the fluid’s phase diagram. The horizontal line at $9.954{\mathrm{mm}}^2$ corresponds to the square of $1/4\mathrm{th}$ of the linear dimension of the imaging window, above which finite system size effects become important.

Figure 3

Time dependence of the intermediate scattering function, with $qD=2.14$, for various filling fractions (numerical values of $\varphi$ given in the box). The arrow points in the direction of increasing $\varphi$. Along the arrow, the symbols ($*$) and ($+$) are located at ${\varphi }_l$ and ${\varphi }_s$, respectively, to aid locate the curves in the fluid’s phase diagram. The solid lines are fits to Eq. (2).

Figure 4

(a) Wave vector dependence of the relaxation time, $\tau$, and (b) local stretching exponent, $\beta$, for various values of filling fraction. The arrows point in the direction of increasing $\varphi$, and the numerical values of $\varphi$ are given in the boxes. Along the arrow, the symbols ($*$) and ($+$) are located at ${\varphi }_l$ and ${\varphi }_s$, respectively.

Figure 5

Relaxation time, $\tau$, extracted from the intermediate scattering function as a function of filling fraction. The solid line is a fit to the Vogel-Fulcher law of Eq. (3). Dashed and solid lines represent the location of the liquidus and solidus points, respectively.