We study the combined effects of electrostatic and hydrodynamic interactions (HI) on the short-time dynamics of charge-stabilized colloidal spheres. For this purpose, we calculate the translational and the rotational self-diffusion coefficients, $D^t_s$ and $D^r_s$, as function of volume fraction $phi$ for various values of the effective particle charge $Z$ and various concentrations $n_s$ of added 1--1 electrolyte. Our results show that the self-diffusion coefficients in deionized suspensions are less affected by HI than in suspensions with added electrolyte. For very large $n_s$, we recover the well-known results for hard spheres, i.e. a linear $phi$-dependence of $D^t_s$ and $D^r_s$ at small $phi$. In contrast, for deionized charged suspensions at small $phi$, we observe the interesting non-linear scaling properties $D^t_spropto1-a_tphi^{4/3}$ and $D^r_spropto 1-a_rphi^2$. The coefficients $a_t$ and $a_r$ are found to be nearly independent of $Z$. The qualitative differences between the dynamics of charged and uncharged particles can be well explained in terms of an effective hard sphere (EHS) model.
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