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 proportional to R-G(df), providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction f. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., phi -> phi(c). Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S-4(q,t) and the dynamical susceptibility chi(4)(t). S-4(q, t) is shown to obey scaling in the full range of packing fractions, 0.6 <= phi <= 0.805, and to become increasingly long-ranged as phi -> phi(c). Finite size scaling of chi(4)(t) provides a consistency check for the previously analyzed divergences of chi(4)(t) proportional to (phi - phi(c))-(gamma chi) and the correlation length xi proportional to (phi - phi(c))-(gamma xi). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for phi -> phi(c) suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.