Length scale dependence of dynamical heterogeneity in a colloidal fractal gel

We use time-resolved dynamic light scattering to investigate the slow dynamics of a colloidal gel. The final decay of the average intensity autocorrelation function is well described by $g_2(q,\tau)-1 \sim \exp[-(\tau/\tau_$\mathrm{f}$)^p]$,with$\tau_$\mathrm{f}$ \sim q^{-1}$and$p$decreasingfrom1.5to1withincreasing$q$. We show that the dynamics is not due to a continuous ballistic process, as proposed in previous works, but rather to rare, intermittent rearrangements. We quantify the dynamical fluctuations resulting from intermittency by means of the variance $\chi (\tau ,q)$ of the instantaneous autocorrelation function, the analogous of the dynamical susceptibility $\chi \mathrm{\_}4$ studied in glass formers. The amplitude of $\chi$ is found to grow linearly with $q$. We propose a simple --yet general-- model of intermittent dynamics that accounts for the $q$ dependence of both the average correlation functions and $\chi$.