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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 ($\varepsilon=1$) as well as inelastic ($\varepsilon < 1$) collisions, are studied. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 \le ϕ\le 0.805$, scaling is shown to hold: $S_4(q,t)/χ_4(t)=s(qξ(t))$. Both the dynamic susceptibility, $χ_4(τ_α)$, as well as the dynamic correlation length, $ξ(τ_α)$, evaluated at the $α$ relaxation time, $τ_α$, can be fitted to a power law divergence at a critical packing fraction. The measured $ξ(τ_α)$ 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, $χ_4(τ_α) \approxξ^{d-p}(τ_α)$, with an exponent $d-p\approx 1.6$. This scaling is remarkably independent of $\varepsilon$, even though the strength of the dynamical heterogeneity increases dramatically as $\varepsilon$ grows.