Anomalous Diffusion of Symmetric and Asymmetric Active Colloids

TL;DR

This paper analytically investigates the complex stochastic dynamics of active colloids, revealing multiple regimes including super-diffusive behavior and non-monotonic diffusion dependence on particle size.

Contribution

It provides a comprehensive analytical framework identifying distinct time scales and regimes for symmetric and asymmetric active colloids, including novel super-diffusive behavior.

Findings

Super-diffusive $t^{3/2}$ regime for symmetric active colloids

Non-monotonic dependence of effective diffusion coefficient on colloid size

Identification of three key time scales affecting colloid dynamics

Abstract

The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is 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 super-diffusive $t^{3/2}$ behavior. At the longest time scales, an effective diffusion coefficient is found which has a non-monotonic dependence on the size of the colloid.