Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids

Abstract

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $ϕ$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $ϕ\toϕ_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $χ_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6\leqϕ\leq 0.805$, and to become increasingly long-ranged as $ϕ\toϕ_c$. Finite size scaling of $χ_4(t)$ provides a consistency check for the previously analyzed divergences of $χ_4(t)\propto (ϕ-ϕ_c)^{-γ_χ}$ and the correlation length $ξ\propto (ϕ-ϕ_c)^{-γ_ξ}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $ϕ\toϕ_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

14 pages, 25 figures