Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($\epsilon =1$) as well as inelastic ($\epsilon <1$) collisions, are studied. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 \le \phi \le 0.805$,scalingisshowntohold:$S_4(q,t)/\chi_4(t)=s(q\xi(t))$. Both the dynamic susceptibility, ${\chi }_4({\tau }_{\alpha })$, as well as the dynamic correlation length, $\xi ({\tau }_{\alpha })$, evaluated at the $\alpha$ relaxation time, ${\tau }_{\alpha }$, can be fitted to a power law divergence at a critical packing fraction. The measured $\xi ({\tau }_{\alpha })$ widely exceeds the largest one previously observed for hard sphere 3d fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, ${\chi }_4({\tau }_{\alpha })\approx {\xi }^{d-p}({\tau }_{\alpha })$, with an exponent $d-p\approx 1.6$. This scaling is remarkably independent of $\epsilon$, even though the strength of the dynamical heterogeneity increases dramatically as $\epsilon$ grows.