Modeling Active Colloids: From Active Brownian Particles to Hydrodynamic and Chemical Fields

Active colloids are self-propelled particles moving in viscous fluids by consuming fuel from their surroundings. Here, we review the numerical and theoretical modeling of active colloids propelled by self-generated near-surface flows. We start with the generic model of an active Brownian particle taking into account potential forces and effective pairwise interaction, which include hydrodynamic and phoretic interactions. Also, the squirmer as a model microswimmer is introduced. We then discuss the explicit modeling of self-generated fluid flow and the full hydrodynamic-chemical coupling. Finally, we discuss recent advances in selected topics in which modeling of active colloids is used to study motion in crowded and complex environments, microrheology in active baths, active colloidal engines, adaptive responses of active colloids with the help of machine learning techniques, as well as effects of colloid and fluid inertia.