Temporal and spatial heterogeneity in aging colloids: a mesoscopic model

A coarse-grained model of dense hard sphere colloids building on simple notions of particle mobility and spatial coherence is presented and shown to reproduce results of experiments and simulations for key quantities such as the intermediate scattering function, the particle mean-square displacement and the $\chi_{4}$ mobility correlation function. All results are explained by two emerging and interrelated dynamical properties: i) a rate of intermittent events, quakes, which decreases as the inverse of the system age t; ii) a length scale characterizing correlated domains, which increases linearly in log t. This leads to simple and accurate scaling forms expressed in terms of a single scaling variable Finally, we propose a method to experimentally extract the growing length scale of an aging colloid and suggest that a suitable scaling of the probability density function of particle displacement can experimentally reveal the rate of quakes.