Anomalous Diffusion of Symmetric and Asymmetric Active Colloids

The stochastic dynamics of colloidal particles with surface activity—in the form of catalytic reaction or particle release—and self-phoretic effects are studied analytically. Three different time scales corresponding to inertial effects, solute redistribution, and rotational diffusion are identified and shown to lead to a plethora of different regimes involving inertial, propulsive, anomalous, and diffusive behaviors. For symmetric active colloids, a regime is found where the mean-squared displacement has a superdiffusive t 3 / 2 behavior. At the longest time scales, an effective diffusion coefficient is found which has a nonmonotonic dependence on the size of the colloid.