Dynamical Heterogeneity Close to the Jamming Transition in a Sheared Granular Material

The dynamics of a bidimensional dense granular packing under cyclic shear is experimentally investigated close to the jamming transition. Measurement of multipoint correlation functions are produced. The self-intermediate scattering function, displaying slower than exponential relaxation, suggests dynamic heterogeneity. Further analysis of four point correlation functions reveal that the grain relaxations are strongly correlated and spatially heterogeneous, especially at the time scale of the collective rearrangements. Finally, a dynamical correlation length is extracted from a spatiotemporal pattern of mobility. Our experimental results open the way to a systematic study of dynamic correlation functions in granular materials.

Figure 1

On the left: $F_s(k,t)$ as a function of time for different odd values of the wave vector $k=1,3,\dots ,29$ from top to bottom (as indicated by the arrow and the increasing $k\nearrow$). The black lines are fits of the form $\exp [-\mathbf{(}t/\tau (k){\mathbf{)}}^{\beta (k)}]$. On the right: $\tau (k)$ (top) and $\beta (k)$ (bottom) as a function of $k$.

Figure 2

$Q_a(t)$ as a function of time for $a=0.05,0.1,\dots ,0.5$.

Figure 3

(a) ${\chi }_4^{F_s}(t)$ as a function of time for odd values of $k=1,3,\dots ,29$. Inset: Log-Log plot for $k=7,9,11,13$. (b) ${\chi }_4^Q(t)$ as a function of time for values of $a=0.05,0.1,\dots ,0.5$. Inset: Log-Log plot for $a=0.1,0.15,0.2,0.25$.

Figure 4

Grey-scale plot of ${\widehat{q}}_s^a(r,t)$, at $t=42,435,1113,2526$ from top to bottom ($a=0.15$). Black regions correspond to lower values of ${\widehat{q}}_s^a$. The displacements of the particles during the interval of time $t$ are plotted in white (yellow online). The white (yellow online) dots are particles that have been lost during tracking.

Figure 5

(a) self part of the Van Hove correlation function after angular integration at $t=438$; the solid line is the probability distribution function (pdf) for a Gaussian distribution. (b) $\ln \mathbf{(}{G}_4(r,438)\mathbf{)}$ as a function of $r$ (for $a=0.15$); the straight line is a linear fit.